Digitized by the Internet Archive in 2009 with funding from University of Toronto http://www.archive.org/details/proceedingsofsecO5akad Koninklijke Akademie van Wetenschappen te Amsterdam. (OL 1 ? } PROCEEDINGS OF THE a Sa © Sel Om Orbis Cl MN es. —_—_—__+-~9> -4-___ wW/ (S) BE} OP MPa WA bt@re AMSTERDAM, JOHANNES MULLER. June 1903, Proceedings of the Meeting » » » » » » C20 Neon SN es. » » 1902 f May 31 - » June 28 > » September 27 » » October 25 » November 29 KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday May 31, 1902. DOCG ae (Translated from: Verslag van de gewone vergadering der Wis- en Natuwkundice Afdeelmg van Zaterdag 31 Mei 1902, Dl. XI). (Gx) ANP Jay aN nese J. D. van pER Waats: ,,Ternary systems,” IV, p. 1. J. D. van per Waats Jr.: ,,Statistical clectro-mechanies,” (Communicated by Prof. J. VAN DER WAALS). p. 22. D, E. Verscnuarrecr: ,,On the prussic acid in the opening buds of Prunus,” (Communicated by Prof. Huco pr Vrirs). p. 31. DP. Zrerman: ,,Observations on the magnetic rotation of the plane of polarisation in the interior of an absorption band.” p. 41. (with one plate ) J. W. vax Wisner: ,,A new method for demonstrating cartilaginous mikroskeletons,” p 47. H. M. Kyrescirer:.,Intramolecular rearrangement of atoms in azoxybenzene and its derivatives”, (Communicated by Prof. C. A. Losry pr Brvyn). p. 51. P. HU. Scnovrr: ,,On the connection of the planes of position of the angles formed by two spaces Sn passing through a point and incident spacial systems,” p. 53. J. W. Layerraan: ,,fhe principle of entropy in physiology”, If. (Communicated by Prof. T. Prace). p. 57. (with one plate). E. F. vay pre Saxpe Baxnuvyzen: ,,On the yearly periodicity of the rates of the standard- clock of the observatory at Leyden, Hohwii Nr. 17,” (First part). p. 68. The following papers were read: (Continued from Vol. TV pag. 694). Physics. — “Ternary systems.“ IV. By Prof. J. D. van per WAAts. B. If we put 7=constant in equation I of our previous com- munication, we find the relation between dp, dv, and dy, at constant temperature in the following form: Ge NG 2) Ore iy, | de, + oy) = (Re = Y.—y ————} adv, - a1 “} | 2 1 Ow? Ys Yi dw, Oy, \ 1 \ 0°76 US) \ (ev, Lv ee S = di sli he ar ay se aaa) Oy,? \ Yy Proceedings Royal Acad. Amsterdam. Vol. V. (11) (2) For a binary system this relation is simplified to: arg U5, dp — (w,—-,) de Ow, 2 , We know from the properties of a binary system, that we have then a curve p= /(r,) and a curve p= /f(r,), and that the branch representing liquid phases is always found higher than the one repre- senting vapour phases, Both curves start at the point representing the vapour-tension of the first component, and finish at the corresponding point for the second component. This however is only true if the temperature is lower than 7), of that component. If 7’> (7,,), then the two curves are joined fluently so that they form a single one. For a ternary system we have to deal with two surfaces p = f (4,.4,) and p= f(r,,7,) instead of the curves p= /(#,) and p= f(x,). We will use as a rule the index 1 for a liquid phasis, the index 2 for a vapour phasis. These surfaces cover the rectangular triangle OY Y, and above the angles of this triangle they have points in common. The common ordinates represent the maximum tensions of the three components. This holds good, if the temperature is lower than 7,, of each of the components. In some cases these sheets may have still another point in common, just as is the case with the two branches for a binary mixture if a maximum pressure occurs. But for the present we will disregard the existence of such a maximum pressure. If T< 7, of one of the components then the two sheets of the p-surface do not cover any longer the whole rectangular triangle, but they have joined fluently to one surface. In the above equation II the properties of these two sheets of the p-surface are expressed in the form of a differential equation; — we will now proceed to deduce the principal properties from this equation. Even for the pressure-curves of a binary mixture the number of these properties is already considerable. For a ternary system they will of course be still much more numerous, and even properties occur which have no analogon for a binary system. But many of the properties of the pressure-curves of a binary mixture may directly be extended to the corresponding ones for the pressure surfaces of a ternary mixture. Such properties need hardly be treated here, as we sup- pose the properties of a binary mixture to be known. Accordingly I will limit myself in the main to treating those properties that are proper to ternary systems but not to binary systems. The study of the ternary systems however has induced me, to give a more detailed discussion of some equations, given in Cont. II for a binary mixture, from a more general point of view. And in some cases this detailed (6) discussion has enabled me to give a more precise and accurate form to some of the equations and to some of the quantities occurring in them. In these cases I shall discuss some properties more extensively, concerning which I had else confined myself to refer to Cont. IL. From a theoretical point of view the relation between p, , and y, at given temperature is not more important than that between v,, x, and y, or between v,, 2, and y,. But even for a simple substance the experimental investigation concerning the maximum pressure has first been executed, and only in these later years it has been followed by an investigation concerning the densities. In the same way we may expect, that also for a ternary system the experiment will occupy itself in the first place with the determination of the pressure, and that the investigation as to the densities of the phases coexisting with other phases, will follow later. The surface representing for all tem- peratures the pressure as function of the composition of a binary mixture has been called by me “surface of saturation’. We might call for a ternary system the surface whose properties we are about to investigate “surface of saturation for a given temperature”. Wherever it is not ambiguous [ shall speak simply of “surface of saturation”. In the following considerations we will take triangle OY Y in a horizontal plane; the direction in which the pressure is laid off is then vertical. We represent the maximum pressures of the three com- ponents by p,, p, and p, where we choose the indices in such a way that Pr < Ps < Ps: If 7 > T., for one of the components, then the surface of satu- ration does not reach the corresponding angle and the corresponding maximum pressure does not exist any longer. a. Curves of equal pressure. For curves of equal pressure, we have dp =O, and equation II is reduced to: | arg ay | Jee) Ow,? ae (Ysa) Ow,0y, | dx, + °c 07g ) SE Gp ri) ——— y.— = eh. ==) I i 2 vy) dw,0y, a5 (¥ 1) dy? \ Yi The projection of these curves is of course the same as the projection of the connodal curve of the S-surface construed for this pressure. We have discussed this projection in our first communi- cation p. 461. If p is chosen such that p, = =log}1 +a,(e ~—1)+y,(¢ “— 1)} t fer, yy — Ct, — Yall, —n ma It appears already from this form of p, that this pressure of this system may be considered as a coincidence pressure, and as this system can be realised, it may be considered as an ordinary maxi- mum tension. If we now consider g’,, and pg’, to be small, so that ’ fa pw we may put ¢ “—1=p’,, and e “—1—~y’,, and ‘log tl + &, Ws, +4, Hy} — in ts, +N Hy, ’ then we find for mixtures, whose composition does not differ much from 2, and yp : Pp log . = Hayy, — Bm - m If we write: (Wl emyn)?, then we should also get ellipses for the curves of equal pressure, but then we should have p>pm, and the ternary system would present a minimum pressure, which would also lead to minimum pressures for the pairs of which the system consists. If maximum critical temperature for a binary System should really occur in nature, and if we then formed a ternary system, of which one par of components presented a maximum and muether pair a minimum value of 7’,., then «’,,. and (Um might have opposite signs, and the point for which wr» and w’,, vanish would be a stationary point as to the pressure, and the curves of equal pressure would intersect in that point. In figure 12 the course of the curves of equal pressure has been represented schematically for the case of maxi- mum pressure for the three pairs of components and for maximum pressure for a point of the system. The sue- : a cession of the values of the pressure rs . eee APs then Fig. 12. Pr ) to the rule of Koxowanow for a binary system, if this latter rule is duly extended. If on the other hand P, lies on the liquid sheet, dp then v,, and therefore also is negative. This signifies that the t vapour branch of the curves of equal pressure moves on towards the heterogeneous region if the pressure decreases, and on the other hand towards the region which at constant pressure belonged to the homogeneous region, if the temperature dcréases. If the pressure is varied the two branches move, in such a way, that one of the branches retreats for the other. If there is not yet question of eri- tical phenomena, a point for which v,, =O does not yet exist, and the given rule holds without exceptions. For the case that no maximum pressure exists, the two branches of the projection of the curves of equal pressure consist of two curves, originating both in the same side of the rightangled triangle, and ending again in the same side. Every point on one of the branches has a conju- gated point on the other branch. We will call the lines joining such a pair of conjugated poimts (coexisting phases) chords. The first of these chords have the direction of one of the sides of the rightangled triangle and the last the direction of the other side. If these two sides are the sides containing the right angle, then the chord turns over an angle of 90°. It occurs however only as an exception that the chord is directed towards the origin in other points than the extremities. Afterwards we will return to this question. If a maximum pressure exists, the branches of the curves of equal pressure form closed curves near the phasis, whose pressure is maxi- mum. The liquid branch contracts if the pressure increases, and according to the rule, deduced above, it moves towards the branch of the vapour phases. This branch therefore must also form a closed curve round the point of maximum pressure and that a smaller one. For the limiting case, the curve for the liquid phases is an ellipse the curve for the vapour phases is also closed, but has other dimen- sions, and its axes have other directions and another ratio, in the limiting ease, however, it must coincide with the ellipse of the liquid phases. At any rate therefore, the position of the liquid branches being given for increasing pressure we may immediately conclude to the relative position of the vapour branches. (To be continued.) ( 22 Physics.. “Statistical Electro-mechanics.“ By Dr. 3. D. VAN DER Waats Jr. (Communicated by Prof. van per WaAatzs). Prof. Gisss has newly published a treatise entitled “Elementary principles in statistical mechanics’, in which he communicates some considerations, belonging to a science, which he calls “Statistical mechanics,” and of which he states that “on account of the elegance and simplicity of its principles’ it is eminently worthy that the laws to which it is subjected, are studied. The laws relate to the behaviour of a great number of systems, whose motions are mutually independent, These systems quite agree with one another as to their nature, and only differ in so far, that the integration constants of the differential equations of motion have different values, or, What comes to the same, that the values of the generalized coér- dinates and of the generalized velocities at an arbitrary moment (e.g. at the moment ¢—0) differ for different systems. The laws, which hold for such ensembles of systems have a very general character, as Gipps shows; yet in their application they are confined to systems, consisting exclusively of ordinary matter. Now the question arises whether such like considerations might be applied io electro-magnetic systems, and whether in doing so we might extend our very limited knowledge of the phenomena of radiation in connection with the laws of thermodynamics. We cannot deny however that we must not expect too much from these considerations. The greater part of the theses deduced by Grpss are exclusively or principally applicable to ensembles of systems which he calls canonical and which have such an important phace in his considerations, because they represent the simplest law possible of the distribution of the systems over the different “phases” *). Mathematical simplicity, however, is not a trustworthy criterion, when we want to investigate, what is actually to be found in nature. For our mathematical representation e.g. the simplest motion, a vibrating string can perform, is an harmonic motion, yet we should be utterly mistaken if we should assume, that every vibrating string would execute such a motion. Perhaps we run the risk of making similar mistakes if we assume, that all systems in nature will follow the laws which we have deduced on the supposition of a canonical distribution of the systems of an ensemble. It is true that Gress shows in his chapters XI—NXIII that the cano- 1) Two systems are considered to be in the same phase when they are to be found in the same element of extension in phase. nical distribution is the most probable one, provided the only condi- tion, to which the ensemble is subjected, be that the mean value of the energy of the systems is a prescribed quantity; but the main difficulty happens to be to answer the question whether this is indeed the only condition. Systems e.g., consisting of spherical, mutually equal molecules, will not be distributed canonically, for they are still subjected to another condition, namely the distance of two centres of molecules ean never be less than the diameter. To assume the cano- nical distribution comes therefore to the same as to neglect the volume of the molecules, but it is not easy to decide whether nothing else is neglected. In faet choosing the distribution of the systems of an ensemble is equivalent to choosing the cases, which we are to consider as “eases of equal probability’ in a more direct application of the calculus of probabilities. Both are subject to the chance, that the proba- bility a posteriori will prove to be another than we had assumed a priori. Yet such like considerations can be useful, in the /nown region of thermodynamics, because they bring its laws very simply and elegantly together under one point of view; in the yet wnknown region, because they may perhaps suggest formulae, for which comparison with the experiments may decide, whether they are in accordance with the phenomena of nature or not. Law of conservation of density-in-phase. In an investigation, whether the considerations of Grpps are also applicable for electro-magnetic systems, we have in the first place to examine, Whether the “law of conservation of density-in-phase” holds also for them. In the beginning we will confine ourselves to systems devoid of material, electrical or magnetical masses. Now we imagine an ensemble of systems. The different systems ave congruent spaces, enclosed by perfectly retlecting walls. We divide each system into 7 equal cubic elements of space dv dy dz. These elements are so small that the electric and magnetic forces in them may be considered to be constant. The state of each system will be perfectly defined, if in each element of space the components f, g and fh of the electrie displacement, and the components @, 8 and y of the magnetic induction are given. So the state is determined by means of 6” data; according to the assumption, that electric energy is potential, magnetic energy kinetic, the 3 2 components of the electric displacement would represent coordinates, the 37 components of mag- netic conduction generalized momenta, or at least they would be proportional to them. ( 24 ) We mark the elements of space with successive nambers and represent the components of the veetors in the rm element by /*, Ors h,, a, B and y,. Let us select from an ensemble those systems whose data lie between the limits 7, and 7, -+ d/\, 7, and f, + d/,.... J, and fy + df, and in the same way for the other components; the number of these systems may be represented by : Dp dy, ee df, dy, sees ding dh, over diy da, seas dat, dp, see dB, dy, eens dyn or YON KES NCCES eR Sl Here the brackets indicate, that also the other components, the parentheses that the same quantities also for the other elements of space are to be taken. We will call \(df,)\ [(da,)| an element of 1 extension-in-phase, 1 the density-in-phase, ? = vy the coefficient of probability-in-phase (.V- representing the total number of systems in the ensemble) and 9, defined by the equation ?= e*%, the index of probability-in-phase. Let us consider the same ensemble after a short lapse of time ¢//, then the number of systems being ina certain phase, will have varied. We may conceive the variation of that number to be composed of 12 » parts, as the systems may enter or leave a certain phase by passing one of 127 different limits, {(7,)], [(7, + d/))|, [(@)| and [(@, + da,)|. The a passing the limit 7, contribute : D= = dt Ofs men, Or dfn da, aretene diy, dh, ewe dh, [ (da, )}. a ee (2) to the total number with which the quantity J {(/7,)| [(/e,)| increases. The systems passing the limit 7, + df, contribute a decrease amounting to: jos hs = 7 li at ch | ah ose hal (Ge My ae 221 (2) Adding these quantities we get an increase with: : hie pa dt ((d7,)] [(da,)] (4) BERT aT I? Nee eel I eS ea Now we have: ON Ga) = 8D Gio y aa ae of,( dt) Of, at Of, dt : 3 _ Wf The second term of the second member is zero, for |, depends only dt on the rotation of the magnetic induction, and is independent of the value of /,. ( 25 ) In the same way we find the increase in consequence of the systems passing the other limits, — taking into account that all ae . : da, — 3 4 quantities of the form — 7g abe zero. — Paking the sum of all these a, dt 1 partial increases and dividing by [(d/7,)| [(d@,)] we find: OD OD df, “(0D da, : —- = — — — — — — Se eR ure eke eh Foe. 1) Ot lee dt ] (5 dt ] OD 0D df, (0D da, dD hs ns —— — —_- = sh | ae is Ot si OF, dt ar 0a, dt dt 4) oD F : Here = represents the fluction of the density for a phasis whose Ld limits are constant, a for a phasis whose limits partake of the motion dt of the systems of the ensemble. So the density proves to be constant for a phasis, partaking of the motion of the systems, and as, of course, the systems can never pass the limits of an extension-in-phase, when these limits move with the systems, the total number of systems within every extension-in- phase, i.e. D |(d7,)| [(de,)| remains constant, and so also | (¢7,)| | (de,)]}. This proof of the laws of conservation of density-in-phase and of extension-in-phase quite agrees with that one given by Gupps. In our case, however, we have still to pay attention to one circumstance. y OB ces In calculating Ae \(d7;)\|(de,)|, we have assumed, that this number is the swum of the numbers of systems passing the different limits. This comes to the same as to say that no system will pass more than one of the limits during the time dé, or at least, that the number of the systems that pass more than one limit is so small, that it may be neglected. In the proof of GisBs we may assume, that this is ; de really the case,-provided we take df so small, that af dt dt is small compared with dq (where g represents one of the generalized coor- dinates, and «/y one of the dimensions of an element of extension-in- % phase). For our case however this proof is incomplete. Be 7 and s two adjacent elements of space, then [/,] and [/;], [a] and [«;] are no independent quantities, but they must be A approximately equal, as [7] and [a] vary only fluently from point to point. In order to investigate the consequences of O x this circumstance we imagine an ensemble of ( 26 ) systems with only two coordinates « and y, which are subjeeted to the condition that « and y must be equal and continue to be so, All systems will then be found on the line (1 and will move in the direction of this line, so all systems leaving the element of space drawn in the figure, or entering into it, will pass the two limits /v and dy at the same moment. If the condition is not that and y must be rigorously equal, but only that their difference must be very small, then all systems will be huddled up very near the line O.1 and a great part of those that pass the limit ec will also pass the limit /y. It is evident, that this circumstance is caused by the fact, that within the element dedy the density is not homogeneous. If we choose therefore the the dimensions v and dy so small, that the whole element lies with- in a region, where the density may be considered as constant, then we may again assume that the number of systems, passing both limits may be neglected, compared with the number of systems passing only one of the two limits. If we choose therefore |(//,)| and |(d/e,)| small compared with the TR KOF. “On, ; we mean value of lé da and & dx }|, so e.g. having a finite Fi 4 wv 5 ratio to de, and dé again small compared with the quantities |(/7,)| and {(/e,)|, so e.g. having a finite ratio to dv*, it appears that in fact the number of systems passing more than one of the limits may be neglected. So the proof of the law of conservation of density-in- phase is complete. The quasi-canonical distribution. If we wish to distribute the systems of an ensemble over the different phases in such a way, that the distribution does not vary with the time, so that the state of the ensemble is stationary, it is evident that we have to choose for P a function of the coordinates, which is constant in time. Gusss chooses for this purpose the function aS U7] e where e€ represents the energy of a system, and yw and @ are constant quantities for a given ensemble. He calls this distribution the canonical distribution. This simple law cannot be applied to systems consisting of ether. If we assumed it, the quantities [7] and [¢] would vary abruptly from element to element instead of varying fluently, and moreover the distribution would depend on the dimensions of the elements of space, which we have arbitrarily chosen. We must therefore assume another distribution which secures a fluent variation of the electric and magnetic displacements. —— ( 27 To this purpose we will assume a distribution closely resembling those, discussed by Grsps in his chapter [Vas “other distributions having the same properties as the canonical.” These distributions have the characteristic property, that the index of probability a is a linear function of one or more functions /’,, /’, ete. of the coordinates; the functions /,, J, ete. are subjected to the condition that their average value, taken over all systems of the ensemble must be a prescribed quantity. We might form different distributions, all satisfying the conditions. Now we seek the average value of 7 for all these different distributions; this average value of y will be a minimum for that ensemble where 7 is a linear function of /’,, /’, ete. This is proved by Gipss in his chapter XI. I shall call such a distribution a quasi-canonical distribution. The canonical distribution is nothing else but such a quasi-canonical distribution where there is only one function /’, and that represents the energy. As the canonical distri- bution is of little application, e.g. not for systems of molecules with finite diameter, if would perhaps have been preferable to give a broader meaning to the word canonical and to use it in the sense, in which I use quasi-canonical. As Gipps has however used the word ‘canonical exclusively for ensembles for which = as I will use the expression quasi-canonical for ensembles for which 7=w— ak, — bF, — ete. In the ether we cannot have canonical ensembles, and so we will discuss only a ae ensembles. We put: a Ne cw te, se (8) where, dt representing an element of space: eee ee (\dz ody OnaeOrs dy ou) \ i a, 1 S((ORmmOyN: ‘Oy 0a “a 0B? om 1622 V2 | IG ee = a (as “D =) % (ay x: =| | dz (10) Oe As ies We a 11 AGE Se oy aS 5) Bie 6) ig ee i iis ee Nie sac scat ars ath (BU era} ne | Ge +34) i aa (118) ih ay aia ewe rae LENS, w= Tf te $e yads, a Ge ath) on een Le LP aL (2) | k, J, and d, are constants, and Jd, and Jd, are infinitely small. The 2,4 2, erik ——) —— rae has been added, that we should have only to ( 28 ) deal with systems, consisting of free ether. Systems, containing electric masses are not absolutely exeluded, but still their number is very small and may be neglected compared with that of the systems which ; : 0a op O2 , are devoid of these masses. As + - is always zero, systems Ow Ow Oy x E for which this expression has another value can never occur; yet we may admit them in such a small number, that they have no influence on the results. Finally we cannot take into consideration systems consisting of infinite space, for a finite quantity of energy would spread in it and we could not have a stationary distribution in the ensemble. Therefore it is necessary to enclose the electro- magnetic energy within absolutely reflecting walls. But then it is necessary to add a term to 4, which expresses, that the walls reflect absolutely, i. e. the quantities | | are always zero at the walls. The wo . term — 7 expresses this; 4 represents a small line in a direction 2 normal to the surface; we make this line decrease indefinitely ; dé represents an element of area. If this distribution is to be for ether systems, what the canonical distribution is for material systems, then in the first place 7 must be a constant in time. For the other terms this is immediately evident, so we have only to show it for the term Bee The relation, we have to prove may be written : dp dy a wee We will make use of the relations da OW oh -=47 f?)-—— = Maree ees, (es! dt = (z =) ( ) If ay 0; ay = _—- us —_ a 4 5 x 4 > * (15) dt 4a \dz oy and of the following relations, that may be deduced from them : Tht i 077 077 077 . SS = PS) - ee ls 16 dt} @ ' Oy? a Oz? na Pa may Aiba Wiers ahs. > ea" (Getoetsa) eee x ee and also of the corresponding relations for the other components. Now we have: dp “T/0q Oh\dfdq Oh” —= —_— — J-| — —— ] Id fs ae LO dt J Ié sage =) - (is) JS Ve at ss » JF Integrating partially we get : _ — a number of surface integrals — a ee Ea 0" fi ork 074 dy Oy 0°74 077 07h oe )t Soot 58-5 as) Oy? Oadz dwdy dt\ 02 Ow Owdy dydz , dh (07h vk or 0? g | li. (19 - ee 4 Ou? AR a dyde \' REL es han) taps fis (19) shes df . ee In the coefficient of — in the cubic-integral we have : at oh 024 0 Og Oh oa? — —— — ine = ee ee (PAN) Ove Oxdy - Oa Oy dz) Ow? -4 Of og — Oh ie : at least if we put, ay fee =(), so if we neglect the systems in ah < ; se af which electric masses occur. So we get for the coefficient of — the de eplOe ft Wit expression —- ~~ and for the cubic integral : V? o¢ 1 df df d 1 - 0p oy d 0p oy F dy ee eee al a) : : ip As at the absolutely reflecting walls [| and therefore also | a ¢ continue to be zero, the surface integrals disappear; so equation (13) is proved. The quantities g and y which are introduced in order that the variation of the electric displacement and the magnetic induction may take place fluently, are defined as the sum of the squares of the components of the rotations of those vectors, if we disregard the : 1 : coefficient 16a? V3 introduced in order that equation (18) may be satisfied. 627 V2 This seems to me the simplest definition for g and x. It might, ay dy Oh however, appear that we are not yet sure that Aeon ant F get v Oy Zz convenient values. In order to show that this is not the case, we will prove the following relations we Ciao we CO \ s aaa) ete oe CS ay =| da\? : (22) Lia 16a? V? | | (se +(5- +(5") | : ie where again the brackets indicate that we have to take also the cor- 30 responding terms in which the other components occur, In order to show this we expand the squares of equation (9) and consider sepa- rately the terms: Og Oh On OF a7 0 ‘12 ised TAL Yate: EESEY clips A “= Oe oy Ou Oz Oy Ow \ , Oa Oh : Og Oh Oy Oh é . For 2 — we write + and integrate the first: term Oz 7] Oz Oy Oe Ov partially according to 2, the second according to y. The surface inte- erals vanish again aml we get: dt + g + +f + ' Onde ‘O02 "Oades * Ode * Ovdy day 4 Vs. 10) (09 oh = 0 ee of ) | a4 s— % it 5, SG + ae +49 By oe + Be fh oF Aas ete) dr. (24) =—f| [+3 aOnTa By integrating once more partially, where once more the surface (| 07h 0%9 or Oh Oa. 1 ras i; MIE MO i eS BR Ae integrals vanish, we get: () EN | sS= () | dt i Oa, fl so equation (21) is proved. Equation (22) is proved in the same way. Three constants occur in the exponent 4 namely »p, @ and &, wis a constant which must be chosen such, that integration of P over all systems of the ensemble yields 1. The two constants 7 and & determine therefore the state of the systems. This is connected with the fact, that the nature of the radiation inside a closed surface, as Lorentz‘) has shown, depends besides on the temperature, also on the charge of the electrons by which the radiation is emitted. The fact that inside all bodies radiation of the same nature is formed, proves that in all bodies the electrons have the same charge. The constant quantity / must depend on that charge; it will therefore have the same value for spaces enclosed within all bodies as they are found in nature at least if the temperature is the same and its value would for a certain temperature only be different, if we imagined walls with electrons whose charge was different from those actually occurring. 1) Lorentz. Proceedings. Vol. I, p. 436. Botany. — “On the prussic acid in the opening buds of Prunus.” | DE VRIES). we y Prof. E. Vurscuarrent, (Communicated by Prof. Huco During last winter and the spring of 1902 I made a series of determinations to ascertain the amount of hydroeyanic acid which can be prepared from different organs in species of Prunus. They were untertaken with the view of investigating the changes that occur during the budding, regarding the prussic acid-compounds. In these analyses the titration-method of Liesié was always used in the following manner. The parts of the plants to be examined — mostly -300 em." of water to 60° C., so as to kill the protoplasm without destroying 5—15 gers. freshly gathered material, — were heated in 200 the emulsin. Though it will direetly be shown that this treatment answers the purpose, the heating to 60° was repeated after some hours or the next day, to be certain that no cells were still living. Between both treatments and also during 24 hours after the second heating, the organs remained, immersed in water, in a well corked flask, that the emulsin might have time to splitcompletely the HCN- elucosides. After that, the distillation was performed, the prussic acid being collected in a little flask containing some drops of KOH- solution, and the titration was made after the method described in the treatises, with +*/,, normal nitrate of silver. The distillate was always collected in a flask of 100 em.’ capacity; by taking with a pipette a known volume, I was able to repeat the titration two or three times in the same experiment. The quantities of plant-material and water being as aboye, it appeared without exception that the whole of the prussic acid had been condensed together with the first 100 em.* of water. The necessity of allowing the objects to macerate for some time after the killing is clearly shown by the following preliminary experiment. From 25 leaves, one year old, of Prunus Laurocerasus (Bot. G. Amsterdam) gathered 9. 12. O1. the halves of the blades were cut on each side of the middle-nerve. The halves a weighed 11,85 grs., the halves 6 11,35 ers. The first portion was immediately submitted to distillation after having been immersed in the proper quantity of water, and gave 0,0160 grs. HCN. The portion 4 was heated to 60° C., and remained under water till the next day ; this time the amount of HCN was 0,0254 er. As soon however as both portions are treated as 6, the concordance of the results is very satisfactory : 32 19, 19. 01. 25.1., a: .0,0223 er., 3.: 0,0226 er: HCN, 18.12. O01. 25.1., a.: 00878 er., 6.:°0,0387 er. HCN, 10,. 2-02; 25.1., a. 30.0289 er., 0,: '0:0942'-or; HON: In the same manner it could be ascertained that it was quite suflicient, after killing at 60°, to macerate during one day only, to obtain a complete splitting of the glucoside; also that the heating in 200—300 cm.” at 60°, at two different times or even once, had left no living portions in the plant-organs. The species studied were Prunus Laurocerasus L. and Prunus Padus L. \t was chiefly my intention to follow the changes undergone by the prussic acid-compounds during the opening of the leaf-buds, As of both above named species the second is the earliest, and also yielded shoots a long time before the cherry-laurel, when cut bran- ches were placed in the hot house, it was with 2? Padus that the most complete experiments were made, those with P. Laurocerasus rather serving to control the former. In the very first place, | asked myself the question whether the amount of HCN in resting buds — whatever might be the form of combination — did exhibit changes, when the buds began to grow. To know this, the estimation of the percentage in buds and young shoots issued therefrom is insufficient; one must compare the absolute quantity of prussic acid contained in a given number of buds with the amount in a same number of shoots. As the dimensions of both the buds and the shoots vary considerably, a satisfactory medium- value could only be obtained by the analysis of a great number of these objects, a precaution already made necessary on account of the buds being small. The amount of HCN contained in resting buds of P. Padus will appear with sufficient exactness by the following three estimations: 10. 2. 02. 195 buds (Bot. G. Amsterdam); weight: 4,80 er.-HCN : 0,0067 gr., i.e. O14 °/,; in 100 buds: 0,0034 gr. 11. 2. O02. 280 buds (B. G. Amsterdam); weight: 6,35 er-HCN: 0,0094 gr., i.e. O15 °/,; in 100 buds: 0,0034 er. 20. 3. 02. 100 buds (B. G. Amsterdam; the buds are about to open, many show a green top); weight: 2,75 gr.-HCN: 0,0040 er., i.e. O15 °/,; in 100 buds: 0,0040 er. ~ 0 In the first two analyses, the buds, as always was the case with the paris examined, in order to avoid losses of hydrocyanic acid, were immersed in water without being cut into fragments, and killed by heat. However, as it might be feared that the bud-seales should hinder the diffusion of glucoside and enzyme, the buds were, in the ( 33 ) third experiment, cut in halves, to see whether they should yield more HCN. As no marked difference was to be noticed, there surely Was no prussi¢ acid that in the first two instances had remained unestimated. It was presently the turn of the opening buds to be studied. On the 2 of February cut branches of P. Padus, dipping in water, were placed on a well lighted spot in the hot house, the temperature being circa 20° C. After some weeks, a great number of buds had opened, and yielded shoots, which, though short, were nevertheless well fur- nished with leaves. 5. 3. 02. 75 shoots taken; weight: 5,20 er.-HCN: 0.0079 er., i.e. O15 °/,; in 100 shoots: 0.0105 er. Cut branches placed in hot house 26. 2. 02. I4. 3. 02. 60 shoots; weight: 8,70 gr.-HCN: 0,0108 er.; i.e. O12 °/,; in 100 shoots: 0,0180 er. When one considers the weight of the shoots examined, it will be seen that in the second experiment they were more fully developed than in the first. It is clear that, as the shoots go on growing, a steadily increasing absolute amount of HCN-compounds gathers therein, so much so that even at a very early stage they contain three to four times the quantity found in the resting buds. As, on the other hand, the percentage of prussic acid depends on a number of circumstances, chiefly on the proportion of water in the shoots, a factor which itself is so very lable to modification, the changes under- gone by this relative amount of HCN are much less interesting. It will however be noticed that, notwithstanding the fact that the weight of the young shoots exceeds many times that of the buds, the per- centage of prussic acid is but feebly or not diminished. I should wish to recall here that Hdm. and Lm. Tima *), estimating the HCN in young leaf-buds of P. Padus, while these were opening in April, found no higher proportion than 0,05 °/,. This undoubtedly is due to the fact that the authors, distilling off after having added some sulfuric acid, did not obtain a ‘complete splitting up of the elucosides. It will now be asked, whether the prussie acid which appears in the growing shoots is formed in the same, or perhaps transferred to them from the branches. As the green unfolding leaves will very probably begin to assimilate, it seems credible enough that the hydro- eyanie acid should be made by a process of “photosynthesis”. Whether 1) Zeitschr. Allgem. Oesterr. Apoth. Ver. 1892, p. 330, 3 Proceedings Royal Acad. Amsterdam. Vol. VY. ( 34 ) this js the case or not will easily be ascertained by analysing shoots developed in the dark. Branches of P. Padus, placed in the hot house 10, 2. 02., covered by a blackened box. After some weeks, numerous etiolated shoots had been developed. 5. 3. 02. 50° short shoots taken; weight: 540 er.-HCN; O,0061 gr., i.e. O11 °/,; in 100 shoots: 0,0122 gr. Branches put in the dark 24. 2. 02. 17. 8. 02. 380 well grown, etiolated shoots, for the most part 4 1 dM. in length; weight: 7,90 gr.-HCN: 0,0054 gr; i.e. 0,07 °/,; in LOO shoots: O.OLS8O er. There can be no doubt, from the results given above, that shoots grown in the dark also contain a much larger quantity of HON-com- pounds than the resting buds, and that these substances cannot have been built up by an assimilatory process, under the action of sunlight. Results of quite the same kind were obtained in studying Prunus Laurocerasus. Resting buds.-28. 12. OL. 115 buds, mostly axillar (from the growers of medicinal plants GroeneveLp and Linpnovut, at Noordwijk); weight: 1,65 gr.-HCN: 0,0040 gr.; i.e. 0,24 °/,; in 100 buds: 0,0035 gr. Shoots developed in the light (also mostly from axillar buds).-24. 4. 02. 50 shoots, still short, cut from the shrubs growing in the Botan. G. Amsterdam; the pale green leaves are not quite unfolded; weight: 9,30 er-HCN: 0,0278 er., i.e. 0,80 °/,; in 100 shoots: 0,0556 er. 27. 4. 02. 50 shoots, vounger than the former, or newly opened buds; weight: 4,90 er-HCN: 0,0188 er.; i. e. 0,28"/,; in 100 shoots: 0.0276 er. *) Etiolated shoots. — Branches of P. Laurocerasus (B. G. Amsterdam) placed in the hot house, under blackened cylinders 23. 4. 02. 10. 5. 02. 5 shoots taken; weight: 2,25 gr.-HCN : 0,0047 er. ; i. e. 0,21°/,; in 100 shoots : 0,0940 er. Branches in the dark 25. 4.02. 4.5.02. 10 very short shoots ; weight: 1.65 gr-HCN: 0.0037 er., i. e. 0,22°/,; in 100 shoots 0,0370 er. Branches in the dark 27. 4. 02. 12. 5. 02. 11 shoots; weight : 4,70 er.-HCN : 0,0083 er. ; i. e. 0,18°/,; in 100 shoots : 0,0755 er. *) 1) A. J. van pe Ven. (Cyaanwaterstofzuur bij) de Prunaceae. Dissertation Amsterdam. 1898; also Archives Néerlandaises, 2e Série, tome II, 1899 (reports (p. 34 resp. p. 391) for young shoots 0,19-0}23/5. 2) Van pe Ven (I. c. p. 37 resp. p. 393) applying the test of GresHorr—Treve, was not «ble to detect prussic acid in etiolated shoots of P. Law ocerasus. This affords a new proof that microchemical reactions, as soon as the substarces are not very abundant, necessarily require analytical confirmation. Mostly so when the test yields negative results. ( 35 ) Referring to what has been said with relation to P. Padus, the above given results require no further discussion. That in both species the percentage of HCN appears to be smaller in the etiolated shoots than in the green ones, has no very great importance. Etio- lated shoots indeed are known to contain much more water, the evaporation being less active under the opaque bell-jar. After it has thus been shown that buds opening in the dark also increase, as they grow, their amount of HCN, there still remain two ways of accounting for this augmentation. Perhaps the prussic acid — in whatever form it may be present — is made in the growing shoots out of other substances ; it could however be drawn from other parts of the plants; that is to say the branches in P. Padus, possibly also the leaves in the evergreen P. Laurocerasus. 1 regret not to have succeeded in establishing with certainty which of the two explanations is the right one. All I can say for the present is that the HCN gathering in the shoots is not derived from the internodes, which bear the buds examined. However, the possibility of the acid being supplied by more distant parts cannot at the present time be said to be excluded completely. In this part of the research, | again chiefly made use of P. Padus, as this species, bearing no leaves in winter, was especially favourable. The point to be ascertained was whether the increase of HCN in the opening buds should be accompanied by changes in the adjacent internodes. . In the first place the amount of HCN was determined in the inter- nodes below resting buds. As the length and thickness of these organs are exceedingly variable, it once more was necessary to analyse a not too small portion of plant-material. 10. 2. 02. 100 internodes (Bot. G. Amsterdam) ; weight : 11,75 er.- HCN : 0,0108 er., i. e. 0,09°/, ; in 100 internodes: O,OLO8 er. 7. 3. 02. 250 internodes (B. G.); weight : 18,95.-HCN : 0,0246 er. ; i. e. 0,13°/,; in 100 internodes : 0.0098 er. With these amounts will be compared those observed in the inter- nodes below etiolated shoots. Branches (B. G. Amsterdam) placed in hot house 24. 2. 02., and covered by opaque bell-jars. 17. 3. 02. 80 internodes are taken from below long etiolated shoots; weight: 3,85 gr-HCN 0,0057 er.; i. e. 0,15°/,; in 100 internodes : 0,0190 er. Already this first experiment does not prove in favour of the view, that the HCN-compounds should be drawn from the adjacent inter- 3* nodes. That this really is not the case will clearly be shown by the further analyses, in which were examined, on the one hand resting buds, on the other etiolated shoots, both with the corresponding internodes, Resting buds 18. 2. OB. 8O buds 72. Padus (Bot. Go, and inter- nodes bearing them; weight: 5,80 gr.-HCN : O,OL21 gr. ; i.e. O14"), ; in LOO; OOLSL gr. 8. 2. O02. 125 buds and internodes; weight: 9,90) gr.-HCON : 0,0159 er. ; i. e. 0,16°/,; in 100: 0,0127 er. 21. 3. 02. 100 buds and internodes (the buds beginning to open at the top for the greater part); weight: 8,35 gr-HCN : 0,0092 er, ; i. e. 0,11°/,; in 100: 0,0092 gr. 29. 3. O02. 127 buds and internodes (cut on other shrubs as the foregoing ; buds about to open); weight: 13,50 gr.-HCN : 0.0125 er. ; i. e. 0,09°/,; in 100: 0,0098 gr. Young shoots. Branches placed in the dark 24. 2. 02. 17. 3. 02. 30 shoots and internodes; weight: 11,75 er. HCN: 0,0111 er., ie. 0,09°/,; in 100: 0,0870 gr. Branches in the dark 24. 2. 02.; 25. 3. 02. 25 shoots and inter- nodes; weight: 5,05 gr-HCN: 0,0051 gr.; i.e. 0,10°/,; in 100: 0,0204 gr. The considerable increase in the quantity of prussic acid: two to three times the original amount, shows clearly that it has not been augmented in the shoots at the cost of the internodes immediately belonging to the buds. I can even go farther, and suggest that neither it can have been supplied by the more distant internodes, one year old. In the analyses of shoots with the adjacent internodes, as well as in the experiment with internodes only, the material was taken from twigs developed the summer before, which in the experi- ment had yielded shoots at different heights. Therefore, if the more basal internodes had furnished the HCN-material for the shoots nearer the top, then the estimations would have shown it, since in that case so great an increase as was noticed would have been impossible. If consequently during the growth of the young shoots prussic acid might be drawn from the branches, it could be only from the older parts. I should have liked very much to establish with certainty whether the shoots form themselves the hydrocyanic acid they contain. For that purpose I several times analysed branches of P. Padus as well as of P. Laurocerasus, so as to determine the amount of HCN pre- sent in the entire branches, before and after the opening of the buds. These estimations however did not yield satisfactory results, because, when the branches used were small, the buds in the dark only gave (i593) short shoots, containing too small a quantity of HON, and the diffe- rence between the two portions compared lay within the range of individual variation. If on the other side one will use larger branches, it is exceedingly difficult to choose two portions which can be compared ; the limits of error of the experiment presently widen, and consequently the desired end is not reached. The experiments on branches longitudi- nally cut in two, which were undertaken with 2. Laiwrocerasus, one moiety being immediately analysed, the other one, bearing the buds, being put in the dark till it had given off etiolated shoots, failed for the same reason. In consequence this question must remain wnan- swered for the present; perhaps experiments to be made next spring with rooted cuttings will meet with more success. I will now endeavour to show that the cherry-laurel behaves in so far quite like P. Padus, that the parts situated immediately below the growing shoots retain their percentage of HCN nearly completely unchanged. Here the experiment becomes in a certain degree com- plicated, but also on the other hand is made more interesting, by the presence-of the leaves. Therefore [ must begin to tell something respecting the amount of HCN in these organs. They have been analysed several times for pharmaceutical purposes. I only will recall here that Friickienr ') gave as the average of esti- mations, protacted during ten years, on cherry-laurels growing on the banks of the lake of Thune, 0,12°/, of the weight of fresh leaves. Folia Laurocerasi, bought in December and Jannary from GROENEVELD and Lixpnovr, yielded 0,14—0,16°/,, while the shrubs grown in the Botanical Garden at Amsterdam were found to contun in their leaves an amount ranging from 0,12 till O0,21° Ae according to the individual analysed. Those were at least the quantities found in the course of the season December May. The last named high figure is regularly yielded by the leaves of a certain shrub, that consequently could if wished be made the starting point of a selection to obtain a race containing much prussic acid. It also may be of importance to acquire an idea of the absolute quantity of hydroeyanie acid contained in one leaf. Of course, owing io the variable dimensions of these organs, this quantity also varies considerably. 1 found 0,0015 — 0.0086 er. HON, the maximum-value in large leaves supplied by GrorxevetpD and Linpuour, with a per- centage of 0,15°/,. Before studying the modifications in the amount of HCN in the !) Pharmakognosie des Pflanzerreichs. 3e Aufl. LS9L p. 766. 38) leaves, brought about by the opening of the buds, also in the dark, one should know the changes caused by the occlusion of the light, independently of the formation of shoots. I properly ought to have done the same with the twigs of P?. Padus, but nobody will, I trust, expect that these organs, with their peridermal coating, should show energetical processes of assimilatory kind. The experiments with 7. Laurocerasus took place not only with cut leaves, but also with branches bearing leaves. To examine whether cut leaves should change in the dark their amount of HCN, the halves of the freshly plucked organs were cut off along the middle- nerve and killed immediately. The other halves, with the middle-nerves still adhering to them, were brought in the hot house, and placed, under blackened bell-jars, in a glass, the petioli dipping in water. At the end of the experiment, the middle nerves were cut off, and the remaining halves of the blades analysed. It appears that by staying even a fairly large number of days in the dark, the leaves undergo no modification whatever as regards the amount of HCN, at least not in winter *). 25 leaves (Noordwyk). 13. 12. O1. Halves @ analysed immediately : HCN: 0,0135. Halves 4, after staying in the dark till 29. 12. OL., HCN: 0,0142 gr. 25 leaves (Noordwyk). Halves a: 13: 12: Of; “O}035%er HON: Halves b: 9. 2.°02., 0:0351 or. HCN: It follows that even after about one month no change whatever is to be noticed. Recently F. F. Bhackman and G. L. C. Marrnant *) have shown that the leaves of the cherry-laurel remain fresh and living in the dark even after fifty days. On the other side, the results given above quite agree with those obtained by A. J. van bE VEN *), using microchemical methods. However, after a longer stay in the dark, or even, in certain cases, at a temperature of 20° C., after a shorter stay, pathological changes become noticeable in the leaves. Yellow spots, originating along the middle-nerve and the more important side-nerves, cover by and by the surface of the leaf till it becomes uniformly yellow. However, these organs don’t die at once; they remain fresh many days, but the analysis shows that they lose rapidly their hydrocyanic acid. 1) J. Corarp- (Journal de Pharmacie de Lié¢ge, 2e année, 1895 p. 1) states that leaves of cherry-laurel, when the entire shrubs remained in the dark from May lill August, yielded a percentage of HCN, somewhat inferior to the percentage in plants exposed to the light. 2) Annals of Botany, XV. 1901, p. 553. 8) Dissertation Amsterdam. 1898, p. 35. Archives Neéerlandaises, |. ¢. p. 392, ( 39 ) wm Or leaves (Noordwyk). Halves a: 23. 12. O1., 0,0165 or. HCN. Halves 6: 7 along the nerves): 0,0142 er. HCN. 20 leaves ( Cee OD ee tee ees eneee OCG) Yor SCN. 5). 1. O2., (beginning to show yellow streaks Bot. G. Amsterdam). (iio SS). 02. (yellow patches) 0,0113 gr. HCN. 25 leaves (Noordwyk). aig Die WS, Oil bs an SOO PASsS fea Nal GIN J b: 20. 1. 02. (yellow) 0,0089 gr. HCN. 25 leaves (Bot. G. Amsterdam), ag NG. AD Oi, 6 os eS WORE) oan, Val Oiny 6: 20. 1. 02. (yellow) 0,0067 gr. HCN. Just the same processes can be observed, when cut branches bearing leaves are placed under opaque cylinders. The leaves can remain fresh and green many weeks, and keep their amount of HCN unal- tered. The halves a of the blades were analysed immediately ; the halves 6 vemained, adherine to the middle-nerve, on the branches till the end of the experiment. 25 leaves, from branches placed in the dark 5. 12. O1. Gao OL O02 (OV orasElONe 6: 22: 12. 01. 0.0283 gr. HCN. 25 leaves, from the same branches (5. 12. OL in the dark). dl. 12. O1.; halves cut off; the other ones remaim on the branches. a: 0,0243 or. HCN. 6: 16. 1. O02.; remaining halves yellow ; it appears that in this stage they fall off, or sit but loosely on the branches ; 0.0196 gr. HON, Branches placed in the dark 17. 12. OL. ; 1 1 (022; 10 yellow leaves, about to: be dropped; weight: 17,65 or.-HON:: 0,0094 er.; i. e. 0,05 °/.. From the same branches I took the same day 25 fresh green leaves, and cut off the halves; weight: 13,15 e@r.-HCN: 0,0229 er., seen) IN gn Halves >; 14. 1. 02 for the greatest part yellow, and falling off — HCN: 0,0155 er. This experiment therefore is also of importance, because it shows how the diminution in the amount of HCN eves clearly together with the discoloration and dropping of the leaves, and does not directly depend upon the length of the stay in the dark. In fact, when | placed separated branches in the hot house, but exposed them to the light, there always were a certain number of leaves that became ( 40 ) yellow; and in those the amount of HON could also be shown to have diminished considerably. Branches in hot house 26. 12. OL, Leaves yellow and falling off 22. 1. O2.: weight: 2010 er-HCN: 0.0089 gr.; i. e. O,04°/,. Moreover, the same is the case with certain leaves directly taken from the shrubs grown in the Botan. G. 27. 4. 02.; 15 yellowish leaves are picked; weight: 24,95 gr.- HCN: 0.0158 er. ; i. e. 0,06°/,; in one leave: 0,0011 gr. The figures for fresh leaves, mentioned formerly, show that but a small part of the HCN normally present had been retained here. As the hydroeyanie acid was also observed to disappear from the cut leaves, when they became yellow, it seems very probable that this substance or its compounds — are not transferred from the leaves to the branches, but must have undergone a chemical trans- formation. The budding however, at least in the first periods that I examined, has no influence whatever on the quantity of prussic acid in the leaves and twigs. For instance, 80. 4. 02 were gathered, on the cherry-laurels of the Bot. G. Amsterdam, 10 leaves, one year old, each being inserted below a well grown young shoot; weight : 11,60 er.-HCN: 0,0251 oer.; i. e. 0,22°/,; in one leaf: 0,0025 er. These figures are of quite the same order as were yielded in December by the same shrub. 30. 4. 02 also were eut, below opening buds, twigs one year old; I chose intentionally twigs which though they bore numerous, and fairiy big shoots, had no more leaves, these being cut or having fallen off at an earlier period, before the budding ; weight: 8,25 er-HCN: 0,0086 er., i. e. O10 °/,. I have found however, in twigs one year old, taken from the different shrubs in the Bot. G., during winter, a percentage of HCN ranging from 0,06 till O11 °/,. It is clear that there was no diminution after the opening of the buds. Neither was this the case after the budding in the dark. Branches having been placed in the hot house, under darkened boxes, 29. 4. 02, leaves were cut 4. 5. 02, below etiolated shoots. The percentage: 0,14" /,, was the same as leaves from the same shrub had yielded before. Finally, it could be shown in P. Padus that, though the young branches issued from the winter buds are already considerably deve- loped, and bear numerous leaves of fair size, the amount of HCN- compounds in the internodes below is still the same as before the budding. This was observed 25. 4. 02, when 130 internodes of P. Padus, from the vear before, were taken below long shoots, well furnished ( 41 ) with leaves; weight: 10,90 gr-HCN: 0,0140 er.; i. e. 018°, ; in LOO internodes: O,OL08 er. Resuming, I am brought to the conclusion that in both species of Prunus examined (P. Padus and P. Lawrocerasus), when the buds open, there appears in the shoots growing from them a steadily increasing absolute quantity of HCN-compounds, whereas the percentage changes little in the period examined. In this same period at least, and at any rate for a great part, these substances appear independently of the light. Neither is this prussic acid drawn from the internodes directly bearing the buds, and developed the year before. Whether it is supphed by more distant organs, or is formed in the growing twigs out of other substances, this remains to be shown. It is also still a point of research in what form the prussic acid is contained in the growing parts. That it is necessary to macerate the killed organs before the total amount of hydrocyanic acid can be distilled off, speaks in favour of the presence of a compound that ean be split up by an enzyme. Moreover, as the liquid distilled from etiolated as well as from green shoots of P. Padus and Laurocerasis, has an intense smell of benzaldehyde, it is very probable that these organs also contain glucosides of the amygdalin-ty pe. Physics. — “Observations on the magnetic rotation of the plane of pola- risation un the interior of an absorption band”. By Prot. P. Zeeman. 1. The difficulties of a complete theory of emission are partly avoided in a treatment beginning with the absorption, and this may have been the reason why Vorcr’) has followed this procedure, though it must be granted that im his method an explanation of the mechanism of the phenomenon as in Lorenrz’s theory cannot be given *). In Vorer’s theory the separation of a spectral line by the action of a magnetic field is found as the separation of an absorp- tion line. Some particulars in this separation were anticipated by this theory *) and confirmed by experiment '). 1) Vorar. Wied. Ann. 67, p. 345, 1899. 2) For a comparison of the advantages of the theories of Lorenrz and of Voter, see Lorentz. Rapports, congrés, Paris T. Ill. p. 16, 33, 1900. en Phys. Zeitschr. 1 p. 39, 1899. ef. also Pranex. Sitz.ber. Ak. Berlin, p. 470, 1902. *) Voter. Drude’s Ann. 1, p. 376, 1900. 4) Zeeman. Vers]. Akad. Amsterdam. Dec. 1899. Archiv. Néerl. (2), 5, p. 237. ( 42 } The long since known phenomenon of the rotation of the plane of polarisation and “the magnetic separation of the spectral lines were closely connected *). One result however of Votat’s*) theory relating to the rotation of the plane of polarisation in the interior of an absorption band seemed to be ino contradiction with the results of Corpo *) or at ) The theory of Voie? requires a negative *) rotation of the plane of polarisation least were not contirmed by the experiments of Semavss * in the interior of an absorption band, Corsiso however only succeeded in observing a very small positive rotation. It would be very remarkable however, if there existed a disagreement between theory and observation in this special field so closely con- nected with other well understood phenomena, | have been experimenting already some time on this subject. In executing these experiments | have been aided in an excellent manner by Mr. Hanwo. I have sueceeded in observing a negative rotation in the interior of an absorption band, the results of my observations being in perfect qualitative agreement with Voter's theory. 2. The method used in the following observations on the rotation in sodium vapour is principally the same as that which has been used by Voir") in his demonstration of the double refraction of sodium vapour placed in a magnetic field. Already Husst*) used it in a determination of the naturel rotation of the plane of polarisation in quartz, and also Corpixo in his first experiments on sodium. By means of a system of quartz prisms (as has been used by FresNeL in his experiment on the division of a plane-polarised ray into two circularly polarised rays) a number of horizontal interference fringes are formed in a spectrum. The light traverses the prism in the direction of the axis and the edges are horizontal and perpendi- cular to the slit of the spectroscope. The prism system (length 50 mm.) was placed in my experiments as near as possible before the slit of spectral apparatus and a small Nicol, used as analysator, behind the slit. The polarising Nicol was placed, of course, before the electro- 1) ef. also Larmor. Aether and Matter, p. 203. 2) Vorar. Ann. der Physik. (4), 6, p. 784, 1901. 3) Corso. Atti R. Acc. dei Lineei. Vol. 10 p. 137, 1901, Nuovo cimento Febbraio 1902. ') Scumauss. Ann. d. Phys. 2 p. 280, 1900. ®) The magnetic rotation in the vicinity of the band is positive in sodium vapour. 6) Vorer. Wied. Ann. 67, p. 360, 1899. 7) Husset, Wied Ann. Bd. 48, p. 498, 1891. (64011) inagnet (of the Runmkorrr type). The spectroscope was a Rownanp’s erating, for which I am indebted to’ the kindness of the Directors of the Dutch Society of Sciences at Harlem; it has a radius of 6.5 M., 10.000 lines to the inch and a divided surface of nearly 414 em. The grating was mounted for parallel light in the manner indicated by Runew and Pascun’). The source of light was in most cases the electri¢ are, in some the sun. Using this arrangement of the experiment we can deduce immediately from the deformation of the interference fringes in the neighbourhood of the absorption bands, when the sodium vapowr is under the action of the magnetic field, the value of the rotation of the plane of polarisation for different wave lengths. Fig. 1 of the Plate gives an idea of the aspect of the fringes in absence of the field in the neighbourhood of the sodium lines, rather much sodium being present in the flame between the poles. The observations were made in the second order. 3. In the experiments first to be described, the distance between the perforated poles was about 4 m.m. and the intensity of the field about 15.000 ¢. g.s. units. In this field was placed a gas flame fed with oxygen and a small quantity of sodium introduced in it by means ofa glass rod. After removal of the polarisator and of the Frusxnn prism the two doublets, in which the sodiumlines are separated, in the inverse magnetic spectral effect were observed. Between the components of the doublet were seen the very narrow reversed sodiumlines due to the are light itself. The polarisator and the prism were now introduced in their proper places. The field of view was then crossed by the above mentioned (2) dark, nearly horizontal interference fringes. I now wished to ascertain the deformation of the fringes by increasing continuously the quantity of sodium vapour, the field remaining constant. This method must be preferred for obvious reasons to the other which might have been followed also, viz: the examination of a flame with constant percentage of sodium under varying magnetic intensities. The following observations refer to D, : If the quantity of sodium in the magnetic field was only extremely small, the interference fringe exhibited at the place of the reversed sodium line a protuberance — let us say downward the lines of the doublet being somewhat stronger just above the interference fringe. In fig. 1 this behaviour is represented schematically. 1) Kayser. Handbuch. Bd. I, p. 482. jt y: HH Fig. 1. Fig. 2. Fig. 3. Increasing now the quantity of sodium (always remaining very small however, absolutely) the interference fringes moved upward along the components of the doublet, whereas the part of the fringe between the components seemed no longer connected to the exterior fringes and accepted the shape figured schematically in fig. 2. Increasing still further the density of the vapour the interior part of the fringe slid downward with increasing velocity and then resembled an arrow with point directed upward, the parts more removed from the medium line fading away and disappearing (ef, the schematic fig. 3). At last the arrow entirely disappeared by the increase of the density of the vapour. It then became impossible to distinguish the fringes or any trace of structure in the field between the components. Rather much light was transmitted. The entire width of the components of the doublet was now about of the same order as the distance of their central lines. A further increase of the quantity of sodium obscured the central part more and more (see further (8)) The exterior fringes moved continuously upward while the density was being increased. In a field of about 20000 units the downward displacement could be followed over a distance of more than the double of the distance between two fringes, corresponding to a negative rotation of above 2 « 180°, say 400°. The distance between the poles was 4 mM. Some more accurate data will be given on another occasion. In the case of DP, the phenomena were in the main of the same character. For D, it was however characteristic that the stage of the nearly or entirely vanishing of the interior fringes was reached with smaller field, whereas also the shape of the interior fringe differed from the one observed in the case of D,. Hence there exists also in this case a difference between D, and D,, a difference already known to exist in the phenomena of reversal, of the separation by a magnetic field and of the rotation of the plane of polarisation in the vicinity of the absorption band. (45 ) 4. It appeared possible to keep stationary each of the stages des- cribed in (8) during a considerable time. Excellent photographs could be secured with plates which were sensitised for yellow light with erythro- sine silver. Instead of the gasflame fed with oxygen if was easier, in the case of greater distances between the poles, to use a Bunsen burner wherein common salt was introduced. 5. If the density of the vapour was maintained as constant as possible and if it and the fieldintensity corresponded to the cireum- o, 3 (8) then an ‘crease of the field gave z @. 3) (3) upwards, corresponding to a decrease stances represented in fi a motion of the arrow (fi of the negative rotation and reciprocally. It was possible to observe by eye observation very clearly this decrease when the field was changed e.g. from 18000 to 25000. If the circumstances were more in accordance with fig. 2 (8) then the same change of field produced a change only just perceptible of the negative rotation but in the same. sense as mentioned in the case of fig. 3. An enlarged reproduction of one of the photographs is shown in fig. 2 of the plate. The distance between the poles in this experi- ment was 6,3 mM., the field intensity about 14000 7°). The negative rotation in the case of D, is somewhat less than 90°. In the ease of D, yet only some traces of the interior fringes can be seen (3). The negative rotation is about 180°. In the photograph are seen also the reversed very narrow J,-line and the broader /,-line, which ave due to the are itselfand have nothing to do with our subject. 6. The observations (3, 4, 5) agree qualitatively in an excellent manner with the conclusions from Vorer’s theory. According to it, the negative rotation must be of the same order of magnitude as the positive one. This last was known from Macatuso’s and Corsixo’s experiments to be very great. The enormous value and the sign of the negative rotation given in (3) may thus be regarded as a beautiful confirmation of the theory. As much is this the case with the direction (5) of the change of the negative rotation with inereasing field. In order to see this we cR a (ft = fieldintensity, ¢ and ® parameters of the absorptionband), for must know the value of the quantity occurring in the theory ? = which the comparison must take place. It was possible to assign a value to P by comparison of the phenomenon with Voicr’s figure 1°). 1) The intensities of the field were measured by means of a bismuth spiral in the centre of the field. Probably the values given are somewhat too high. Measure- ments of the magnetic change of the spectral lines give lower values, *) Annalen der Physik, 6 p. 789, 1901. ( 46 ) This figure gives ny, (yz, angle of rotation, 7 a mean value of the index of refraction) as function of a certain variable 2, whereas our as a function of 4. Reducing ‘, or ‘/,, we obtain diagrams phenomenon is a representation of z, the abseis of the mentioned fig. 1 to resembling in the main features fig. 2 of the Plate. To the greater observed negative rotation (3) correspond values of 7, whieh can be estimated at 5 or 8. The smallest easily observed rotations in the used strong field are probably in the vicinity of the critical value | £1 7. The slope of the exterior interference fringes is greater towards the side of the greater wavelengths than towards the violet, at least so far as the rotation due to one band does not influence visibly the rotation due to the other. At the same distances, if not very small, of each of the two 7 lines the rotation at the side of the violet is greatest. The interior fringes also show a slight asymmetry, so e. g. the point of the arrow in fig. 8 (38) ought to be asymmetrical. The part atthe side of the violet is predominating. It is clear that these phenomena depend upon an asymmetry of the dispersion curve. 8. With very dense sodinm vapour, hence under circumstances which are beyond the last stage of (3), | observed phenomena very probably identical with those observed by Corsino. In my first expe- riments with those dense vapours | thought it absolutely necessary for securing sufficient intensity to widen the slit beyond the width used in the already given experiments. I now see however that this is unnecessary. Using these very dense vapours one sees in the absorption band a horizontal part of an interference fringe, which seems to have under- gone a very small displacement wpivards by the action of the field. These horizontal parts are more ill-defined and broader and the whole phenomenon in the bands is darker than under the cirewm- stances described in (3), (4), (5). Figs. 3 and 4 of the Plate will give a clearer, impression of the change in the phenomenon than a long description. Fig. 38 was obtained with a field of 4500 units and much sodium. | have made some measurements, according to a method not to be given here, concerning the displacement of the central (in horizontal and vertical direction) part of the interference fringe, and I have found a displacement, which would correspond to a positive rotation of about 8° with both D-lines. Fig. 4 was taken with a field of LO700 and much sodium. The exterior interference fringes are very clear and much deformed; the rotation in the parts adjacent to the absorp- e r| A P. ZEEMAN. Magnetic Rotation in the Interior of an Absorption Band oceedings hioyal Acad. Amsterdam. Vol. Y. ed) tion band surpass 180°. The interior interference fringes are very indistinct. Their appearance would suggest that in the case of D, in Fig. 4 the stage has been scarcely surpassed, reached for DY, in fig. 2. This however cannot be the case because there was too much sodium in the flame. A comparison with fig. 2 will show that the lines are much broader in fig. 4. Measurements taken on other uegatives gave me for fields of 11000, displacements of about ‘/,, of the distance between two fringes, corresponding to a positive rotation of 11°. Hence the displacements in these cases are precisely of the same order of magnitude as in Corsino’s experiments. The paleness of the boarders of the band is easily accounted for by the remark that there the intensity one of the circularly polarised rays largely exceeds the other. I do not believe that these facts are in contradiction with theory. It is true that it requires for very high values of P a value zero for (ny,),. If we must take as the locus of the fringe the mean vertical height, then really the rotation would be positive. It seems possible that with those broad fringes the case is different. It is also possible that the circumstances, assumed in the theory are not wholly realised in the experiments with dense vapours. I am making some new expe- riments about this subject and therefore shall not discuss further the different possibilities. HEXO PAV AGN AUTO UN) 5) He sianhs Pate As Ty The Plate gives about sixfold enlargements of the photographs. Fie. “1. Interference fringes and absorption liaes im absence of the field and rather much sodium. (2) ys Vig. 2. Same lines. Field intensity about 14000, little sodium. (5) (5) Fig. 3. Same lines. Field intensity about 4500, much sodium. (5) Fig. 4. Same lines. Field intensity about 10700, much sodium. (8) Anatomy. — 4A new Method sor demonstrating cartilaginous Mikroskeletons." By Prof. J. W. van WisHe. It is a well-known quality of cartilage that it firmly retains certain anilinstains. Taking advantage of this quality, I have for some years endeavoured to find a stain, which will remain permanent in the cartilage, after it will have been entirely extracted out of the other tissues. If the object is made transparent in canada balsam, the cartilaginous skeleton will then be seen as if it were prepared. [I was more or less successful with most of the so-called basal anilin-pigments, best of all however with methylene-blue, and so T was induced to use this latter stain exclusively. ( 48 ) The coloring of the cartilage was attempted with full-grown objects as well as with embryos, but as the coloring-method is chiefly useful when applied to small objects, with which the ordinary preparation- method proves deficient, it will chietly be applied to embryos. Whenever we wanted to examine the cartilaginous skeleton of an embryo, we were, up to the present time, obliged to make series of sections and to construct an enlarged model after these sections, all of which took up a good deal of time. As a rule it would have taken much too long to model a whole skeleton; therefore in most cases only a part was constructed, for instance the head-skeleton or the pelvis. Working on this plan a single object requires many months of labor, and besides at the end you have not the object itself, but an imitation. Following the coloring-method, on the contrary, a great number of entire skeletons are obtained in a short time with little trouble, not clumsy imitations, but the objects themselves with all parts in their natural connection and the contours of the whole embryo and of different organs besides, for notwithstanding the transparency of the organs the outlines of many are still clearly recognizable. Although the cartilage is colored intensely blue, it remains transparent: so for instance the spinal column glimmers through the shoulder-blade. The method is as follows: The embryo is fixed in the usual way in 5°/, sublimate-solution, or 10°/, formol, or in Zenker’s liquid and is preserved in alcohol. No doubt it may be fixed in many other ways; I even obtained useful results with old preparations of aleohol from the collection. /, sublimate-solution, to which is added 0 I mostly fix the embryos in 5 */,) Volumen formol, shortly before using. The object may now be brought immediately from the alcohol into the pigment-solution, but it has seemed advisable to me to extract previously for a day or two with alcohol, which contains some C/,°/o) hydro-chlorie acid. The acid alcohol must be renewed if it has turned yellow the next day, which often happens when iodine has been used in extracting the sublimate. The iodine is fatal for the coloring, as it forms with methylene-blue an almost insoluble preci- pitate and with neutral alcohol the iodine cannot be quite removed. This is proved when seemingly white objects, preserved for a year and more in aleohol which has remained colorless, being brought into acid alcohol, cause this liquid to turn yellow the next day. The yellow color disappears after the addition of a few drops of sublimate- solution. ( 49 ) From the acid alcohol the object is: placed fora day at least, rather for a week, into an alcoholic solution of methylene-blue, to whieh 1°/, hydro-chloric acid has been added. It is sufficient when */, gram of methylene-blue is dissolved in 100 ce. alcohol of about 70°/,. If more coloring-matter is taken, a sediment remains on the bottom of the bottle. After the addition of the hydro-chlorie acid, blue crystal- line needles separate themselves from the liquid. For this reason it is desirable that this addition should be made not at the moment of using, but some time before. The object when taken from the pigment, should not show any sediment. If it does, it has not been extracted long enough with acid alcohol. Although it is not lost yet, it may cost months before the sediment is removed. The intensely blue-colored object is treated in the usual manner in the above mentioned acid alcohol, which is renewed several times on the first day and once daily afterwards. The renewal is continued until the aleohol shows no blue tinge the next day. The time required for this is, of course, dependent on the size of the embryo. This time can be shortened by taking alternately alcohol of about 70°/, and a stronger one and hanging the object one day in the stronger alcohol, whereas the next day it is allowed to settle on the bottom of the bottle; this is not necessary however. In about a week the stain has been removed from all the tissues, except from the fundamental substance of the cartilage. It is not necessary anxiously to observe the day when the alcohol shows no more coloring; objects kept for a year and longer in the colorless acid alcohol, showed the cartilage still distinetly blue. The object is now dehydrated in absolute alcohol, in the usual way, and rendered transparent in xylol. To avoid wrinkles, it is not put immediately from the alcohol into xylol, but first in a mixture of two parts of absolute aleohol with one part of xylol, then in a mixture of one part of absolute alcohol with two parts of xylol and only after that in xylol only. Larger-sized embryos are cut in halves or in different pieces with the razor. After that the objects are put first in a thin, afterwards in a thick solution of canada-balsam in xylol and finally in a solution, which in ordinary temperature is solid, but liquid at 60°. In this solution they remain in the thermostat at 60° during a couple of hours and are then enclosed in glass-cells under a covering-glass. The glass-cells in trade are usually too low, higher ones can easily be obtained by fixing stripes of window-pane with canada-balsam on an object-glass. 4 Proceedings Royal Acad. Amsterdam. Vol. Y. 50 My experience has not been long enough to enable me to assure that the objects will not fade in the long run, I can only say, that even my oldest preparations, which have been enclosed in canada- balsam for a couple of years, have not faded visibly. I have taken care however to dissolve in xylol the solid, neutral canada-balsam of GriipLer’s myself because the commercial solution often contains turpentine. The staining method here described has been suecessful with the cartilaginous skeleton of representatives of all classes of vertebrate animals, as for instance with Amphioxus, with embryos of sharks and rays, of salmons and roaches, of frogs and lizards, of birds, of mice, rabbits and man. With regard to man, it is of importance that the coloring can still be suecessful with embryos in a far proceeded state of dissociation and which otherwise one would be inclined to throw away. Magnified slightly, the preparations are particularly suitable for demonstration. I here demonstrate the skeleton of a human embryo of about five weeks old and draw your attention to the rudiment of the shoulder-blade. It is still exclusively adjacent to the neck, on a level with the 5, 6' and 7 cervical vertebrae, with the point still above the first rib. Eleven ribs show the blue color of the cartilage, the undermost, the twelfth, not yet. In this second embryo, which is somewhat older, the shoulder- blade has left the 5 cervical vertebra and lies on a level with the 6 and 7™ cervical- and the 1s* and 24 thoracic vertebrae; it reaches with its point as far as the third rib. Not only all the twelve ribs are visible on the twelve thoracic vertebrae, the rudiment of a rib on the last cervical vertebra is seen besides, which rudiment fuses with this vertebra later on, as is well-known. In this third embryo, which I received in perfect condition and which after fixation was 25mm. long in its natural curve, it may be seen that the shoulder-blade has again gone down a little. At the neck it does not reach higher than the level of the last cervical vertebra and reaches with the point as far as the 4" rib. Further the rudiment of the pelvis may here be noticed, on the level of the fourth lumbar — and the first sacrum-vertebrae and on the head the cartilage of the occiput, the ear case, the cartilage of Mecker and the rudiment of the incus. Other preparations show the paired rudiment of the rabbit’s and the chicken’s sternum. Also for macroscopic museum-preparations this is a suitable method; I could show you, for instance, the cartilaginous skeleton of shark- (ot) embryos more than 2 dm. long, preserved in xylol. These preparations were exceedingly beautiful at first and the non-cartilaginous tissues transparent, as clear as crystal; later on however they lost the transparency for the greater part and became opalescent. The cause of this change is unknown to me. Such macroscopic preparations ought therefore also to be enclosed in canada-balsam or dammavr-resin. Chemistry. — “Intramolecular rearrangement of atoms in azoxy- benzene and is derivatives.” By Dr. H. M. Knipscuerer. (Com- municated by Prof. Lopry pr Bruyn.) Watiacn and Beni’) noticed a long time ago that azoxybenzene is converted into its isomer p-azoxybenzene by gently heating it with sulphuric acid, or by means of fuming sulphuric acid at the ordinary temperature. Bampyreer found that in this process there is also formed half a percent of o-oxyazobenzene a substance discovered by him some time ago when acting on nitrosobenzene with aqueous caustic soda at 100°. The reaction noticed by Watiacn and Beitr must be represented as follows : N—N SOA Sulphuric acid was up to the present the only reagent capable of C,H C, H, > C, H, N=NC, H, OH (4.2 and 1.4). causing the said intramolecular rearrangement of atoms. WAcKER °*), however, when stating in his paper on @-azoxynaphtalene that this substance turns red by exposure to direct sunlight, also remarks that azoxybenzene is likewise sensitive to sunlight, but he only mentions that it turns deep yellow without having investigated the nature of the change. Various derivatives of azoxybenzene also appeared to be liable to the same intramolecular rearrangement of atoms, but again sulphuric acid is mentioned as the only reagent capable of causing the change. The result of those investigations showed that some of the substitution products, namely the meta-derivatives, are almost quantitatively con- verted into the isomeric phenols, while the ortho- and para-derivatives are only affected to a small extent or not at all. *) Ber. 18. 525 (1880). 2) Ber. 33. 3192 (1900). 8) Ber. 33. 1939 (1900). 4) Ann. 317. 313 (1901). 4* 92 SenviTz scarcely obtained any dichlore-oxyazobenzene when treating p-p-dichloro-azoxy benzene with fuming sulphuric acid, but p-p-dichloro- azobenzene was formed ; m-im-dichloro-azoxybenzene however yielded m-in-dichloro-oxyazobenzene in large quantity. Kiincer and Prrscuke*) sueceeded in almost entirely converting m-m-dinitro-azoxybenzene into m-n-dinitro-oxyazobenzene by heating the same with sulphuric acid at 140°. By heating o-o-azoxytoluene with sulphuric acid at 100°—120° they could only obtain 0-0-azo- toluene accompanied by acids such as 0-tolylazobenzoic acid. Limpricut ') converted azoxytoluidine into oxyazotoluidine in an analogous manner, whilst Ens and Scnwarz *) succeeded in converting p-p-diamino-o-o-azoxytoluene into p-p-diamino-o-o-oxyazotoluene — by heating it with sulphurie acid at 100°—105°. ~ My object now was to ascertain whether the above described intra- molecular rearrangement might be realised by other means than by the use of sulphuric acid. It was ascertained that the intramole- cular rearrangement of atoms in azoxybenzene is also possible by raising the temperature to at least 200° and by the influence of direct sunlight. In the first case a mixture is formed of p- with much o-oxyazobenzene ; in the second case only 0o-oxyazobenzene is obtained, None of these changes is reversible. Also those derivatives of azoxy- benzene which undergo intramolecular rearrangement by the action of H,SO, are converted by the said agencies, but the action is slower and the amount is smaller than that obtained from azoxybenzene. The investigation of these derivatives has not yet been quite concluded. Acetic anhydride is without effect on azoxybenzene at the boiling temperature ; on heating however at 200° the change already takes place in a notable degree, much better than by merely heating the substance itself, while an acetate is either not formed at all, or only in very small quantity. /-oxyazobenzene is not formed at 200° but only the o-isomer. Solutions of azoxybenzene derivatives in acetic anhydride do not however suffer any intramolecular change at 200°, Addition of Zn Cl, or P,O, to acetic anhydride does not enable it to cause the change at the boiling point; heating with the so-called BECKMANN’s mixture is also without avail. By heating a solution of azoxybenzene in this mixture at 150° and 180° it appears that azoxy- benzene which, when prepared in the ordinary way is a yellow substance, is perfectly white when in a pure condition. The ordinary 5) Ber. 17, 464 (1884). 6) Ber. 18, 2552 (1885). 1) Ber. 18, 1405 (1885). 2) Journ. f. pr. chem. 171. 567 (1901). ( 53 ) product therefore contains a yellow impurity, whieh cannot be removed by veerystallisation. The intramolecular change was attempted in vain by means of the following reagents : Acetyl chloride, butyryl chloride, benzoyl chloride, phosphorus pentachloride, phosphorus oxychloride, phosphoric acid, aluminium chloride, aqueous caustic soda, copper oxide, zine oxide and zine carbonate. Of these reagents the following deserve to be specially mentioned on account of their action on azoxybenzene : Acetyl chloride: formation of p-p-dichloro-azobenzene and p-chloro- acetanilide ; benzoyl chloride: formation of azobenzene ; phosphorus pentachloride : formation of azobenzene with evolution of chlorine ; auminium chloride: formation of p-chloro-azobenzene. Mathematics. — 4On the connection of the planes of position of the angles formed by two spaces S, passing through a point and incident spacial systems.” By Prof. P. H. Scnourr. 1. If in a space Sy, with 27 dimensions two spaces \S, are given arbitrarily, these have in general only a single point OU in common and they form in this pomt with each other 7 angles differing in general respectively. These angles are situated in 7 definite planes through Y and the line at infinite distance of such a plane of position has a point in common with the two given spaces S,), S,@ as wellas with the spaces S,’), 0S,’ drawn perpendicular to the just named spaces through any arbitrary point, say QV, not at infinite distance. In this way the two planes of position of two planes «,, ¢, taken arbitrarily in S, are determined by the common transversals of four lines situated in a three-dimensional space, viz. of the lines g,, 9, and the lines of ¢,, «, im the space S, at infinite distance in S, Ys Jo’, normally conjugate in this S, to ¢,,9,. 2. Let us consider the particular case when the » angles formed by SJ0, SS, are alike; as an introduction we take in S, again two planes ¢,, «, forming with each other in their point of intersection O two equal angles. It is known that in that case the four above mentioned lines 9,, Y,4,/s gs’ ave generators of an hyperboloid ; so they admit of not only two but of an infinite number of common trans- versals, to which answer likewise an infinite number of planes of position. If the system of those transversals ¢ is indicated by (4), the 54 ) system of the lines y intersecting all the lines (4) by (y), there exists between the two incident systems of lines (y), (4 at infinite distance this reciprocal connection that the plane passing through an arbitrarily chosen point O at finite distance and an arbitrary line of one of the two systems is a plane of position for the pair of the planes connect- ing the point O with two arbitrary lines of the other system. From the manner in which the quadratic seroll (4 is formed out of g,, Ys y's Ys’ Namely ensues that the surface //* of order two, bearer of the two systems (y), (4), agrees with itself in the polar system = at infinity in S, of which the imaginary sphere 3 common to all hyperspheres is at the same time the locus of the points lying in their polar planes and the envelope of the planes passing through their poles; for to each line ¢ intersecting y,, 4,, 7,’ g’, regarded as locus of points agrees in that correspondence a line /’ lying with dy’ Jas Gr» Yo M a plane regarded as axis of a pencil of planes, ete. If we make the lines y, y’ of (y) normally conjugate to each other to correspond to each other, then between the lines of (v7) a quadratie involution is formed; the double rays yg; g; of this involution must lie on J2%,, being normally conjugate to themselves. Likewise does Bz contain the double rays f, 4 of the involution formed in quite the same way between the lines /, ¢’ normally conjugate to each other. So H2, and £2 intersect each other in the sides of a skew quadrilateral whose pairs of opposite sides are the double rays (yi, g,) and (t,, ti) of the pairs of rays (g, g’) and (¢,t’) of (y) and (A) normally conjugate to each other. If (y,g’) are two normally conjugate rays y and (f, ¢’) likewise two normally conjugate rays ¢ and if we take the planes Oy, Oy’ and Of, Of as coordinate planes (VY, X,, O.N,.X, and OY, N,, ON, N,, then the surface /77 must be characterised with respect to this rectan- gular system of coordinates by the equation .7.7, = vv, between the infinite coordinates. For the quadratic surface vr, + pry, =, brought through thé lines at infinite distance of the four mentioned coordinate planes, corresponds to itself in the polar system with the sphere #,*? + 7,7 + 4,7? +.4,7=0 at infinite distance as surface of incidence only when the absolute value of p is equal to unity. For ihe normally conjugate line of 7, = Ar,, Ar, + pr,=O0 is 27, +7,=0, pe, = 4c, and this new line lies only for p*—=1 with the original one on wv, 0, + pr,av,=O0. So by reversing if need be the sign of one of the coordinates we can always bring the equation of //2 into the form 2, 7; ==252,- 3. Before passing on to the genéral case we shall consider the (55 j ease, when in 5S, two three-dimensional spaces S,, S,@) are given arbitrarily. The line gy, at infinite distance of the plane of position of one of the angles formed by those spaces in their point of inter- section ( is then a common transversal of the planes at infinite distance &),e@) of S,(,S,@) and the planes &, «@) normally con- jugate to these. As the common transversals y, of the three planes a) 62), e() form a “variety”? |7,° of order three of three dimensions and this curved space is intersected in three points by &{), the spaces S,©, 8,2 make in O three angles with each other. This variety V,° is not only (compare i. a. the first part of my ‘“Mehrdimensionale Geometrie’, vol. XX XV of the Sammlung ScuuBErtr’, N°. 102, 103) the locus of a twofold infinite series of transversals g,, but at the same time the locus of a simple infinite series of planes ¢,, each of which determines with &),e2, ef on the lines y, quadruples of points with a definite anharmonic ratio, i. e. JV,* is the bearer of two incident systems which we represent according to the nature and the multiplicity of the elements by (y,), and (¢,),. Beside the general case, where ¢) has in common with J’,* three points not situated on a right line, the particularity may arise that &{?) has a line in common with one of the planes s, of («,), or coincides with one of those planes; to this answer the particularities that two of three generally different angles of position or all three of them become equal to each other. In the last case of the three equal angles of position, to which we restrict ourselves here, there is between the two systems of incidence this connection, that the plane passing through an arbitrarily chosen point © at finite distance and an arbitrary line 7, of (y,,), Is a plane of position for the pair of spaces connecting O with each of two arbitrarily chosen planes ¢, of («,),. If namely we make on each of the lines y, of (y,,), those points to correspond to each other which are conjugate to each other in the involution determined by the pairs of points of intersection of that line with the planes @), «f) and e2), &@), then between the planes «, of (€ formed a quadratic involution, from which ensues that the plane ¢, é ) Is a/i normally conjugate to the plane ¢, of the variety J’, lies likewise mm: 14,2, ete: The two double planes &;, &; 7 of the involution (G25 Ge) form part of the imaginary hypersphere £,? with four dimensions at infinite distance common to all hyperspheres ,* with five dimensions of S,- So the section V,° of V. and a J7,* which must now necessarily be the locus of the trans- , and 4, consists of these two planes versals gy, of (g,,), lying entirely on 4,°?. Whilst as is known the lines y, vesting on any arbitrary right line of ¢, form a surface of order two, the locus of the lines vy, resting on the conic of section of «, and B,’ isa V,'. 4. If finally in 3, two spaces S, are taken arbitrarily, these form with each other, as was mentioned above, in their point of intersection QO in. general nv angles differing from each other and the line at infinite distance of the plane of position of each of those angles in the space at infinite distance \So,—; of Sy, intersects att ' ee : 74 oy’? again four spaces S,—;, the spaces at infinite distance S oa S i— a= . - a(t) a f2) 11) 1(2) of the two given spaces S’’, S° and the spaces S 5, _, normally n n n— 7— 5 conjugate to these. If now the special case presents itself that each : : : a (2 {2 right line cutting three of the four spaces ee Sie gy7 1 —1 v n—1 also cuts the fourth, the 7 angles of position are mutually alike and the locus of the n-fold infinite svstem (y_), of the lines yg. at infinite distance - ain Ja +( 1 i a . . “y* . . ri . . . . of the planes of position is a variety 17" of order x with 7 dimensions, " n appearing likewise as the locus ofa simple infinite number of spaces S,—1, ie. in the form of (S,—1),, namely of the spaces S,—-;, determining with Go) gs a ’ n—1 n— 2) 5 2) : ’ S 5 and now also with JS aie ae the lines g, of (7a )n mutually projective series of points. In that case a plane connecting an arbitrary point © at finite distance with a line y, of (gz), Is always a plane of position of each two of the spaces S, connecting O with spaces S,—, of (S,—) n Be a . : . . P : rn . As is immediately evident, in this special case the section J”, of 4 n—2 rn e - < F : 5 ] , With the hypersphere /S , with 2n—2 dimensions common to all : n 2 > . hyperspheres 1) , Of Son breaks up into the two double spaces ; 1S 10) ~{ ;) . . . . ‘al ve “ ee peat, of the involution of the spaces S,-1, S’n—1 of (S;—1), — a = ay r? ; “ (n—1) . ‘ normally conjugate to each other and into a_ J : , locus of the lines rhe n— 9 Yo Of (Y.)a lying entirely on By. (57 ) Physiology. — “The principle of entropy in physiology.” By Dr. J. W. Laneenaan. 3'¢ part. (Communicated by Prof. T. Piacer). All investigations made with the intention of testing the law of FrcuNnr at the experiment, have proved, that this law is only satisfied within a small interval and within that interval only by approximation. In order to find out the causes of these deviations, I have tried to deduce the law of Frcuner (considered as a physiological law) from a general physical principle. It has appeared from this deduction that this formula rests on very special premises, and that the curcum- stances assumed in these premises, are never realized in nature. In a series of experiments I have tried to fulfil as accurately as possible the conditions required by this law according to its dedue- tion. To this purpose the spinal cord of a frog*) was cut between the cranium and first vertebra; then the whole frog, with exception of the hind leg which was used for the experiment, was wrapped up in wads and fastened to a glass rod. The leg hung down in a wide vessel which could contain about 600 cem. of fluid. In the sole of the foot a hook was put and a horsehair was attached to this hook, which passed outside through a very small opening in the bottom of the vessel. This horsehair was fixed to the arm of a length-recorder. The small opening through which the hair passed was filled up with vaseline; this prevented almost perfectly the fluid to drip out, while the friction experienced by the horsehair was very slight. By suspending a weight to the length-recorder the leg was charged with 15 erams. Then the vessel was filled with 850 cem. of water, and the lee immersed till the knee. To the stand bearing the glass and the frog, a clamp was fixed bearing a burette. This burette contained a solution of oxalic acid in distilled water. By opening the tap this solution flowed into the water in which the leg hung. A bent stirrer always kept in slow motion (but which did not touch the leg), caused the acid to be thoroughly mixed with the fluid. Then so much acid was slowly added to the liquid till the leg began to contract. The vertical motion of the leg, three times magnified, was registered on a slowly rotating cylindre by the length-recorder. In order to prevent too large excursions, the length-recorder struck against a piece of cork, so that the contraction in the beginning took place isotonically, at the end isometrically.: After the leg had returned to rest, we waited about 5 minutes and 1) Small male specimens of Rana esculenta proved to be the most suitable for the experiment. then again so much acid was added, till a new group of reflex-con- tractions appeared. In these experiments the acid in the burette con- tained 40 grams of oxalic acid per liter solution. As a measure of the stimulus in physical units the concentration of the solution, in which the leg was immersed, was chosen. The concentration is defined as the proportion between the quantities of oxalic acid and water, while as the unity of weight the molecular weight was chosen (126 for oxalic acid, 18 for water). The result of the experiments was given in a table in the following way. The first column gives the concentration of the solution in the vessel, just at the moment the leg begins to show a group of retlex-contractions. The second column contains the increment, which the concentration in the vessel must undergo to produce again a set of retlex-contractions. The third column gives the relation between this quantity and the absolute value of the concentration at the moment that the reflex-contractions appear. This column contains therefore the quotient of Weber. Let us now consider in how far this experiment satisfies the con- ditions put by the formula. The researches of EckHarp, KoscHeWwNikorr, C. Meyer and Sa#errincron have proved, that the same spinal segments which innervate the skin of the hind leg, supply also the muscles of the leg with nerves. If we have cut the spinal cord at the upper end and have therefore annulled the influence of the higher centra, we have in the hind leg a segmental primary reflex-apparatus. The receptive organs of this reflex-apparatus lay in the skin, while the muscle forms the transformer. Adopting the simple law of distribution, I record only the mechanical effect. In this respect the experiment fulfils the required conditions. The interpretation of the mechanical effect is very difficult as the new state of equilibrium is not reached at once, but only after oscillating round this new state. It is therefore hard to say what part of the total effect must be considered as the quantity A FP of the formula. Fig. I is the reproduction of a typical tracing. After the reflex-apparatus is in perfect rest, the tap of the burette is opened at the moment indicated in the curve by a couple of vertical small lines on the base line and oxalic acid is slowly added under continuous stirring. At the moment that the first contraction appears, the tap of the burette is closed and no more acid is added. At this moment the increase of concentration amounted to 3.210-—° the initial concen- tration being 15.910—-%. The curve represents the mechanical effect, following upon this increase of the concentration of the acid in the yessel. This effect consists of a group of great contractions, followed ( 59 ) by some smaller ones of decreasing size. If we should be at first inclined to consider this group of large contractions as the mechanical effect corresponding to the quantity A / of the formula, this concep- tion offers many difficulties when the mechanical effect assumes a form as*is represented by the curve which is reproduced by fig. IH. In con- sequence of a small increase of concentration we do not see a definite effect appear, not even partly defined, but the reflex-apparatus comes in rythmieal contraction. Where in the first case the resistances in the chemical system are such that the oscillations rapidly die away, and the new state is reached after a few oscillations, these resistances in the second case are so small, that once the equilibrium disturbed, the system remains oscillating round its new state of equilibrium. This oscillation documents itself as a rythmical mechanical effect. If the rate of decay of these oscillations is very small, these rythmical TABLE I. (Fig. V). TABLE II. (Fig. VI.) Nore (12,95 1011/5) Nop Ga IE nD) Y | & Cone. | Q Cone Cone. | A&A Cone. - - Cone. A Conc. ee | Conc. | Cone. | | 0.0<10~° | : 0.0<10~° | | 10.4><10~° 26.6<10—-° 10.1 | 26 6 2.8 0.218 ee) 0.158 1OE9 31.6 esi’ 0.209 229 0.086 ? 1623 34.5 4.0 0.496 cee 0.085 9.3 | tev 4A OR 1G7 2.3 0.058 24.4 40 0 43 0.150 2.0 0.047 Q8 .7 42.0 4.9 | 0.447 1.6 0 O37 33.6 43.6 48 | 0.123 Wifi 0.059 38.4 | 46.3 10.7 0.28 a) 0.069 AOA | 49.8 20.8 ; 0.2998 | 5.4 0.098 69.9 | a 10.7 | 0.133 10.8 0.164 80.6 66.0 19.3 0.226 SA, SEL Ce 85.3 Section of the medulla 10 A.M. | beginning of the experiment 11.15 A.M. Temp. 13.5 C. Section of the medulla 10.35 A.M. beginning of the experiment 12.40 P.M Temp. 13 C. { 60 ) contractions can last for several hours and often with great regularity ‘), Under these circumstances, however, 4 / is no more a determined quantity and the experiment cannot fulfil the condition of the formula, that 4 / be a constant quantity in the successive determinations. If we only use those experiments, in which the resistances are pretty considerable, and the new state of equilibrium is reached after a few oscillations, 4 /7 fullils the condition, that it represents a small quantity in successive determinations. The experiment does not allow another more definite conception of this quantity. By the addition of acid from the burette to the liquid in whieh the leg is immerged, the level of the liquid rises, and the stimulated surface increases. So the experiment does not fulfil the condition of the formula in this respect either. TABLE III. TABLE IV. (Fig VIL) No 24; (i; 25 (07°) No. 44.- (24 995. a0) A Conc. | A Conc. Cone. A Cone. — Cone. A.Conc a es Cone / | Cone. 0.010" ; Ut U4 UN ; = 3, O10 OER | ie 3.6 15.9. ° 1.7 0.397 = HA O.A68 5.3 19.4 1.4 0.203 4.5 0.192 6.7 93.6 2 0.236 7.3 0.235 S38 30.9 3.6 0.292 8.0 0.207 12.4 38.9 6.3 0.339 4.3 0.098 18.7 43.2 10.5 0.359 38 0.082 99 2 47 .O 12.4 0.297 19:9 0.297 41.6 66.9 8.7 0.173 27.6 0.292 50.3 j 94.5 26.0 0.271 16.8 0.4151 76.3 1 ff OY 15.3 0.4121 126.6 Section of the medulla 19.45 A.M. beginning of the experiment 12.56 P.M. Temp. 15 C. Section of the medulla 10 P.M. 20 9. beginning of the exper. 12.1 P.M. 21.9 Temp. 16.5 C. 1) It seems to me that the heart is in this condition, and it would be worth while to repeat many experiments from the physiology of the heart on this ryth- mically acting reflex-apparatus. ( 61 ) Similar experiments as described by me, were performed by Winkier and Van WayrNBurG some years before. The method followed by them, which slightly deviated from mine, enabled them to extend the experiment only over a small interval of variation of concentration. They concluded for this small interval, that the reflex-apparatus of the frog follows the law of Frcnner*). In the experiments communi- cated by them slight deviations from this law proved to ocewr and it was with the purpose of learning something about these deviations, that I repeated these experiments extended over a greater interval. Table I, U, Ul and IV represent four of these experiments. If we take R as the value of the stimulus in physical measure (i. e. the concentration of the solution of the acid in which the lee is immerged) and if we take AF as the value of the increment of this stimulus which is required to call forth a change in the system, the quotient AR a is not constant, but in general a function of R. v Oar oO gO ator SOL GO a0. §. 80=:. 90 0 *f 2B PNGB HDL SON, S60 70% £0) (5, 90 Fig. VI (table Il, exper. 35). 0 /0 10 OMI Cman 50) 60 jo & 9 0 yo Zo 130 Fig. VIL (table IV, exper. 14). 1) Van Wayensure, Dissertation 1897, pag. 117, Fig. V, VI, and VII are the graphical representation of Table I, Il and IV. In this graphical representation | have considered the amount of water as constant (10° unities of weight) and put as abscissae the number of solved unities of weight of the acid. The relative increases of the concentration, in percents, have been chosen as ordinates. The points, representing successive determinations, are connected by a curve. The graphical representation of the result of the experiment by a continuous curve is only an approximation, remaining in the same course of thoughts as that, which has led us to represent the phenomenon analytically by a continuous funetion. If the law of Fecuxer was satisfied, the line representing graphically AR the quotient n * function of FR, would be a straight one. But u instead the experiment furnishes a curved line. In order to elucidate the form of this curve further, fig. V is given, which is the graphical representation of an experiment, where the first descending branch is determined by as large a number of observations as is possible. Fig. VI shows a reduction in the extent of the first descending branch and this enables us to determine the ascending branch by a greater number of observations. In the experiment represented by fig. VIL this reduction of the first descending branch is so con- siderable, that it no more appears in the experiment; this makes it possible to determine the top of the ascending branch and the de- scending branch following on it. The whole course of the second descending branch cannot be given, as always a discontinuity occurs at a point which seems to be near a second minimum. After this discontinuity a new period sets in, and as far as it is possible to follow this new period, it appears to be considerably greater, whereas AR the oscillation which the value of the quotient shows in this period, seems to be relatively smaller. For a skin-muscle reflex- Kk : -e apparatus the quotient ze must therefore be considered as a periodic function of 7. If we inquire what is the signification of this disconti- nuity, it seems that only those variables, which are the representation of the independently variable components of the chemical system, can be able to show discontinuities. This brings about a change in the nature of the system and this must be attended by a discontinuous variation of the quantity A, which occurs in formula I of the second communication. The experiment communicated by Massart *) seems 1) Bull. Acad. royale de Belgique 3me Série, T. 16, 1888, pag. 590. /SiieiOmen SONNY 630) 50 60 p £0 go Fig. VIIL (table V, exper. 25). TABLE V. (Vig. VIII.) Ne, Bain (Uhl. «1D, 01.) A Cone. Cone. A Cone. — Cone. 0.0XK10-° : 8.8X<10-° 8.8 Dial 0.232 al fay ell 0.187 14.9 2.6 0.156 16.8 2.4 0.129 19.2 2.0 0.093 Al 4 0 0.160 Dyed) 4.0 0.136 99.2 4A 0.123 33.3 4.5 0.120 37.8 43 | 0.423 421 5.8 0.079 45.9 3.0 0.061 48.9 25 0.050 51 4 21.0 | 0.289 72.4 | 11.8 i OLA 84.2 | el 0.097 93.3 | 5.0 0.051 98.3 Section of the medulla 8.30 A.M. beginning of the experiment 12.5 P.M. Temp. 13 C. rE /00 ( 64) fo show the same phenomenon, Another phenomenon, whieh sometimes oceurred in my experiments, was the dividing ofa period into several parts. Fig. VIIL (able V) is the graphical representation of such an experiment. As far as my experiments go, this small discontinuity can appear at every moment in a given period, followed by the outset of a new period. If we compare these results obtained by the primary reflex-apparatus with those of experimental psychology, they appear to concord in many points. As appears from the critical summary of Foucac.t *) also there a variable quantity showing a minimum is found for the get AEE. ra . . quotient pr most cases. The shape of the curve representing the ‘ quotient pr *® function of 2, makes us suppose, that the experimental ‘ psychology has seen only part of a large period. By the dividing of a R period into several parts, the quotient Fz Seems to show multiple minima and this occurs also in some experiments of the experimental psychology. Hence there is agreement in these respects between the results of the psychological and the physiological experiment. With regard to the mechanical effect I have pointed out, that this is greatly dependent on the rate of decay of the oscillations of the system. The rapidity of this decay is determined by the passive resistances in the chemical system. If these passive resistances are slight, a small increase of / will be sufficient to call forth a change = d- o ee in the system. Therefore the value of the quotient Re? which is a measure of the value of these passive resistances, will determine the rapidity of the decay of these oscillations. In correspondence with this the experiment shows that the height and the number of the elevations in every successive determination e : , AR~ =. increases with decrease of the value of the quotient Re: Fig. Il (table II) observation 2, 3, 4, 5 shows this clearly. At the 5% obser- vation the resistances are so slight, that the system continues to oscillate for several seconds. Observation 8 and 10 show this same phenomenon at a higher value of F&, in the same series of observations. If we compare, however, observation 8 with observation 5, in which two LR observations the value of the quotient R almost the same, and L —s 1) M. Foveautt. La psychopbysique, 1901. ( 65 also observation 10 with observations 3 and 4, it appears, that in the second place the rate of decay is dependent on the absolute value of fF. Supported by these and more similar observations we may say that the rapidity of the decay of the oscillations increases with : re A increasing value of # and with increasing value of the quotient 1 In this we have to keep in view, that the first observation always occupies a special place; for this observation AR is always very large, and though the method followed does not enable us to deter- 2 AR mine the quotient a for this observation, this quotient is probably L also very great. Notwithstanding this we always see that the rate of decay is very slight and from this we should have to conclude, that the influence of the absolute value of on the rapidity of this decay is preponderant in the beginning. The same experiments which I have described: for the frog whose spinal cord is cut through, can also be performed with perfectly intact frogs. For this it is necessary to wrap up the whole animal carefully in wads with exception of the hind leg which is used for the experiment. If we take care to avoid tactile and auditory stimuli, the frog remains quiet during the experiment also under these circumstances *). In this case the result of the experiment is the same as that of the preceding one. Fig. IX (table VI) is the graphical representation of an experiment. 64% 40 o 40 4 660 FO f00 20 jo 160 PO 200 120 40 160 So Fig. IX (Table VI, exper. 46). If the first period is small, it is possible to see also here a part of a second period appear (Fig. X, table VII). This second period seems also greater than the first, while the oscillation, which the value ot AR the quotient R shows in this period, seems relatively to be smaller. L 1) In these experiments the solution of acid in the burette contained 80 grams of oxalic acid per liter solution. Proceedings Royal Acad, Amsterdam. Vol. V, ‘iodxo JA a1qey) X “4 (OG oo/ s TABLE VI. (Fig. IX.) & Cone. Cone. /, Cone, Cone, 0.0><10 6. > 10 26.9 44.6 0.562 O1.5 94.1 0 282 R56 32 A 0.273 117.7 55.9 0.322 173.6 | | 52.3 6.231 995.9 ay 0.187 178.41 Medulla intact. Beginning of the experi- ment 11.46 AM Temp. 13.5 C. TABLE VII. (Fig. X.) No 50. (26. 4. 02.) A Cone. Cone. A Cone. : Conc. mw | | 0.0107? | “i | 29.3<10-° | 29.3 | | 44.9 0.605 74.2 | 29 & 0.234 96.8 39.0 0.546 135.8 | 5.2 0 206 171.0 44 | 0.495 195.4 | 53.0 0.213 DAS. 4 71.6 | 0.294 320.0 55.4 0.448 375.4 | ete re 093 413.9 | Medulla intact. Beginning of the experi- ment 3.0 P.M. Temp. 41.5 C. (oF ) The number of my experiments in which a second period appears, is, however, not great. Therefore we may say also in this case, that , if the quotient R probably to be considered as a periodical function ry; AR of F&. The value of the quotient R” however, is in these experi- v ments considerably greater than in the preceding experiments, while in concordance with this the rapidity of the decay of the oscillations of the system is also greater. Figure IV (table VIL) which is the reproduction of four observations from the same series, shows this clearly ; the new state of equilibrium is reached after a few oscillations. If we compare observation 3, 5 and 6, the system proves to be a periodical one, at the third obser- vation; at observation 5 and 6 the rapidity of the decay de- 2 AR creases with decreasing value of the quotient Rr At the tenth obser- V ae: a vation, where the quotient R shows a very low value, the rapidity of the decay is very small notwithstanding the high value of /. If we summa- rize these differences briefly, we conclude that in consequence of the high section of the spinal cord, the passive resistances in the chemical system of the skin-muscle reflex-apparatus considerably decrease. On account of clinical observation chiefly regarding the plantar-reflex, it seems to me, that we have to deal here with a very general pheno- menon occurring always where there is a wasting of systems. In this case the rapidity of the decay of the oscillations of the system is very small in consequence of the decrease of the passive resistances in the chemical system. If is obvious that a good motor function can only exist, when the rapidity of the decay is so great, that the system is almost aperiodic. The motor disturbances, which occur in multiple sclérosis, in locomotor ataxy and many other diseases of the nervous system seems to be partly due to the decreasing resistances in the chemical system of the reflex are. If the system is perfectly aperiodic, then the quantity 4F is a perfectly determined quantity. This condition must also be fulfilled by the systems, to which the experimental psychology extends its experiments; if this condition is not satisfied, then the effect is a not determined quantity as in the physiological experiment. ( 68 3 Astronomy. “On the yearly periodicity af the rates of the Standard-clock of the vbservatory at Leiden, Honwt N® 17.4 First part. By Dr. E. F. van pe Sande Baknoyzen. |. Jntroduction. 1. When the observatory at Leiden was founded in 1561, it was fitted with a clock made by Mr. A. Honwié of Amsterdam, and by him designated as N’ 17. Accurate investigations of Katser') soon showed the great regularity of its rate, in which point it was superior to all clocks about which an investigation had so far been published, Since that time it has continually been used as the standard-clock of the observatory and at the present moment its rate is still eminently satisfactory. The clock was originally mounted in the transit-room of the observatory on a brick pier which rests on the foundations of the meridian-circle. The stability of the mounting thus left nothing to be desired. On the other hand the temperature at this place was rather variable, showing very clearly a daily period; moreover entirely irre- gular changes of temperature were often caused by the opening and closing of the shutters. From 1861 the clock has been going regularly until 1874, with- out being touched during this time except for the purpose of winding once a week. On the 17" of June of the latter year however it stopped spontaneously, after having shown for about a month a particular irregularity. As the intention existed already to make considerable changes as well in the transit-room as in the meridian-circle, it was thought best to defer a thorough cleaning and overhauling of the clock till the time of these alterations. Accordingly the clock was then only provisorily cleaned, and was set going again after a few days. The intended alterations were made in the second half of 1876 and the beginning of 1877, and in June of that year everything was again in working order, and also the clock Honwi 17 was mounted again. Though Prof. H. G. vay pe Sanpe Bakuvyzen did consider the possibility of removing it to a better position, out of the transit-room, 1) F. Katser, Onderzoekingen omtrent den gang van het hoofduurwerk der sterrenwacht te Leiden, de pendule Honwi N°. 17. Versl. en Meded. K. Akad. Amsterdam D. XVII, 1865. F. Kaiser, Untersuchungen iiber den Gang der Hauptuhr der Sternwarte in Leiden, Honwi' N°’. 17. Astr. Nachr. N°. 1502. this gave rise to too many difficulties at the time, and it was only tried to diminish the variations of temperature by making a second wooden case round the clock. *) In the meantime the chronographic method had been generally adopted at the observatory for the meridian observations. Now it had been shown repeatedly that the introduction of an electrical contact in a clock diminishes the regularity of its rate, and on the other hand we had found that the comparison of two clocks could be effected with extreme accuracy by means of signals given by hand *). Accordingly the clock Honwi was not connected with the chronograph, but the clock by Kxosiich was used for this purpose. On the 26th of November 1877 the clock was stopped for a short time in order more completely to adjust its beats; since that date however it has been going uninterruptedly until August 1898. At that time the clock was again dismounted at the occasion offered by alterations in’ the transit-room, and cleaned and overhauled by Mr. Honwi, In December 1898 the clock was remounted, and this time the former plan of removing it from the transit-room was carried out, and. it was fixed to the pier of the 1Oinch refractor. In order better to secure a constant temperature, Prof. H. G. van pr Sanpe BaknuyzEn resolved to have a niche cut out from this pier in the large hall of the observatory, and to place the clock in this niche. The clock Honwi N° 17 has now been in its new place for over three years. It is still enclosed in two wooden cases, and the niche itself is closed by a glass door. We may remark already at this place that by this arrangement the aim of excluding rapid variations of temperature has been attaied in a very perfect manner. 2. In 1887 Mr. Witrrrpink investigated for a special purpose the rate of the clock Honmwé 17 during the period 1886 January to 1887 July. It then appeared that after reduction for temperature and barometer the mean rates for the summer- and the winter- half-years were in very satisfactory agreement, while on the other 1) At the same time a small mirror was attached to the pendulum-bob, to permit more accurate determinations of the amplitude of oscillation. See: H. G. vay pe Sanne Baxuuyzen, Verslag van den staat der sterrenwacht te Leiden 1S76—1877, page 12. 2) From series of signals given by the two observers Witrerpriyk and FE, FP. VAN pe Sanpe Baxknvuyzen immediately after each other, on a great number of days, the Mean Error of the result of a series of about 24 signals, (including the variation of the constant error during an interval of about a month) is found to be © 08.0077. (70) hand a verv marked systematic difference existed between the means for the half-vears January—June and July—Deeember, Mr. Winrerpink found Obs.—-Comp. 1886 January —June + O°.045 July —December 0.08 1887 Jannary—June + 0.085. Consequently, when in 1890 [ undertook the definitive discussion of the time-determinations and clock-rates for the period 1877—1882, it appeared desirable to me to investigate whether a similar phenomenon would again show itself. [| then found that the years 1878—1852 (before May 1878 the rate was not yet sufliciently regular) were im this respect entirely similar to 1886—87, and, investigating the pheno- menon more closely, | moreover found that the rates, after correction for temperature, still showed a yearly periodicity which accordingly had its maxima in the months of equal temperatures April and October and the amplitude of which was about 0°10. I then continued my investigation (the results of which were brietly published in the 4“ Verslay van den staat der sterrenwacht te Leiden 1S89—1890," pages 14—15) in the same direction and included on the one side the years 1882—90, using provisional results of the time-determinations, and on the other side the years 1862—1864, using the results of Katser’s investigation in str. NVachr. 1502. For these two periods I also found the same unexplained inequality. After 1890 this investigation was abandoned for the time being, and it was only taken up again last year. In the mean time the clock had been removed to its new position, and it now appeared that, notwithstanding the fact that the changes of temperature had become much more gradual, still the yearly periodicity of the rate showed itself in the same way as before, and its deviation from the yearly periodicity of the temperature was certainly not less evident’). It became thus evident that there was no question of accidental circumstances, which could be altered by cleaning the clock, nor of such conditions as depend on the special nature of the changes of temperature to which the clock is subjected, but that the cause of the phenomenon must lie deeper. It therefore appeared desirable to subject the way in which it showed itself in the three periods (77z: before and after the cleaning 1) See also ,Verslag van den staat der sterrenwacht te Leiden 18S98—1900 pages 12—13. of 1877, and after the cleaning and removal of 1898) to a new investigation which had to embrace the whole of these periods. The results of this investigation are given in the present paper. I have confined myself to such results as could be derived from the mean daily rates during periods of about a month. Thus it was not necessary that the time-determinations on which the investigation is based were discussed with the utmost accuracy. In this way I inves- tigated successively the three periods, 1877—1898, 1862—1874 and 1899—1902. The results for these three periods will be com- municated in this order. Then the observed amplitudes of the period 1877—1898 will be investigated, so far as their yearly periodicity is concerned, and finally the several results will be compared with each other. As a consequence of the restriction of the investigation to the monthly means, the question is considered from one point of view only. In the mean time however Mr. Werper has definitively discussed all the time-determinations from 1882—1898, and has undertaken investigations about the rates of the clock during shorter periods. It is to be expected that, when these investigations will be completed, the comparison of his results with mine will also throw more light on the phenomenon which is here treated. Very recently, while my investigation was already nearly com- pleted, I had occasion more closely to study the computations which Kaiser made about the clock Honwi 17 during the last years of his life, and which are preserved im manuscript at the observatory. | then found that as early as 1870 his attention had been drawn to this particular yearly inequality as to a remarkable phenome- non. Among the papers I found a summary of monthly means of rates, corrected for barometer and temperature, from which mean results had been formed by combining the corresponding months of the years 1862—1870. These means show clearly a periodicity having its maxima in May and October, and a total amplitude of O°.09. Further I found means for the half-years February—July and August— January for each of the years 1863 to 1870. The differences between the two half-years vary between + 0.026 and + 0.5048 and Katser adds the remark that the only difference between the two half-years is that in one of them the temperature is, in the mean, rising, while in the other it is falling. I. The period 1877—1898. 3. The clock-rates which were taken as the basis of the inves- tigation were, for the period 1877—March 1882, derived from the (ne) definitive discussion of the time-determinations during that period. For the following years they were taken from the provisional results whieh had been computed immediately after the observations, Mr. Wreprr’s results being not yet completed last year. | only applied small corrections in a few cases for the personal differences between the observers, Which have become better known since the provisional computations were made. I always used time-determinations as near as possible to the beginning of each month. The mean temperatures and barometerreadings required for the inves- tigation were derived in the following way. The temperature was read on two thermometers suspended in the clock-case, one at the level of the upper part of the pendulum rod the other at the level of the pendulum bob. These thermometers were read five times a day viz. at 8 a.m., noon, 4 p.m., 8 pam. and midnight. The seales were Reacmur’s and were divided into full degrees. We will first investigate the relation between the results given by the two thermometers. The readings of the years 1878, 1879, 1584 and 1885 were discussed for this purpose. In the following table the monthly means of the differences between the two thermometers are given for each of these four years, after application of the index- corrections. The differences are taken in the sense upper thernometer- lower thermometer. The last column gives the means of the four years. [878 1879 IS84 ASS5 Mean January ...:) + O16 | +042 | +019 |) +046 | + 0.16 February ...| + 0.48 | +046 | +049 |+0 |+ 0.48 March ...... +0.20 | +0. | +0. | 40.90 |+4+0.21 / AST US oxjoneie + 0.33 | + 0.9 | +09 +097 [+ 0.97 May. . ....| + 0:98 |+ 0.99 | 40.97 | +094 | 4+ 0.97 Tit” Ak cnk +0.299 |+0.9 |4+026 |+0.9 | + 0.98 July.... ...] 4.0.96 | 4+ 0.9% |-+0.95 | +098 | + 0.96 August. ...| + 0.22 | + 0.99 |} 40.97 |+0.% [+ 0.%4 September ..) + 0.21 + 0.20 | + 0.22 |+ 0292 [+ 0.21 October..... +048 | +049 | +0.20 +0419 [+ 0.19 November...) ++ 0.16 + 0.48 | + 0.20 + 0.18 + 0.18 December...| + 0.13 | +048 | +048 |+0.17 |+4 0.16 There appears to be a constant difference of about + 0°.2 between ; (73) ) the two temperatures. There also seems to be a small yearly inequality. We will return later on to these small differences between the separate months, and investigate the influence which they can have had on the rate of the clock, ¢f they ave real. For the rest of the investigation the readings of the upper thermo- meter were used exclusively. I first formed daily means *) the day being reckoned from midnight to midnight — and then means for the periods of about one month. The index-correction, which may be taken constant and equal to — 0°.6 for the whole period, was not applied. Until May 1886 the heights of the barometer were read and reduced in exactly the same way as the temperatures. The readings were made on a mercurial barometer which was suspended in the {ransit-room from the same pier which also carried the clock. After that time a barograph of Ricnarpd was used, which was placed on the top of this same pier. Its corrections were determined by comparison with the mercurial barometer *). The daily means were then derived by integration by means of a planimeter of AMSLER. During the period in question three different cistern barometers were used; in consequence of cleaning and refilling we must however distinguish 7 periods. The corrections for these 7 periods were determined by intercomparisons, by comparisons with simultaneous readings of the barometer of the Meteorological Institute at Utrecht, and finally by comparisons with a 4“Cistern-syphon” barometer by Burss, which in 1890 was provided for the observatory, to be used as a Standard barometer. Since however before 1590 no correction had been applied and the neglected corrections amounted to approxi- mately -+- 0.3 mim. during the whole period, the readings after 1890 were reduced to: Normal barometer — 0.3 mi. The barometer-readings were not reduced to 0°. This reduction Was omitted on purpose, though the errors introduced thereby are by no means negligible (at 760™" the effect of 1° Raum. is 0.15 ™). The influence of these errors on the rate of the clock is however nearly completely compensated by the fact that also the influence of the temperature on the vate, which is thus found, differs from the true one. It is here supposed that the temperatures of the barometer has always been equal to that of the pendulum, which condition is 1) The mean was taken of the readings at 12%, 20%, 4», 125) giving half weight to the extreme values. 2) A constant correction was taken for each weekly barograph sheet derived from one or two readings of the mercurial barometer daily. nearly fulfilled in the present case‘). The only thing that is thus neglected is the difference between the influence of the same tempe- rature on high and on low barometer-readings, which is extremely small, 4. The observed rates were first reduced to 7T60™ and + 10° R. by means of previously determined values of the coeflicients 4 and ¢ in the formula: Daily Rate = a + 4 (h—760) + c¢(t—10°) b= + 0.0140 — — (0) .0268 The value of 4 was derived from a rigorous discussion of the c period 1877—1882, in which only rates observed under high and low barometric pressure during the same month were compared. This value must be very near to the truth. In all investigations, not only about Honuwi 17, but also about other clocks with similar, or even with different forms of pendulum, barometer-coefficients have always been found of nearly the same amount, and it is not prob- able that its value would vary with the time for one and the same clock. The value / = + 0°.0140 has therefore been considered definitive, and I have not attempted to improve it. The following table gives, for each month from 1877 December to 1898 July, the mean observed daily rate, the mean height of the barometer and the mean temperature, and, in the column headed »Red@. D. R. 12’, the daily rates reduced to 760™ = and + 10° R by the formula given above. The meaning of the two last columns can only be explained later. 1) See also the particulars given in connection with the investigation of the period 1862—1874. @ i ) SS D. it Bar. | Temp. | pe | pn | O-. {877 Dec. | 40.444 | 760.7 | + 4.4 | — 0.016 1878 Jan. | 0.%1 | 66.8 | 3.9 | — 0.016 Febr. | 0.491 | 677 | 6.1 | — 0.020 March 0.163 | 59.4 4.9 + 0.034 April 0.448 | 59.5 | 8.6. | 0.118 May 0.406 | 589 | 441.92 | 0.489 June |= 03135 62.0 | Sv 0.206 July 0.100 63.4 | WAS tion | 0.179 Aug. 0.0388 | 58.3 | 44.6 0.184 Sept. | O03 | 625 | 413.0 | 0.149 Oct. 0.043 56.9 oy 0.077 Nov. | 0.062 | 53.9 5.4 0.025 + 0.119 | ae De: | O45 | 544] 2.5 0.030 097 | —43 1879 Jan. O3M@ | 61.6 | 1.6 | 0.097 | 144 | + 98 Febr. 0.145 | 50.9 | 2.8 0 079 106 = AG March 0.326 62.2 he. OST 149 91 | at April O51 | 53.6 6.3 0144 WAgy |) IESG) > oe May 0.241 | 62.6 8.3 0 161 161 20 June } 0.084 | 59.5 12.8 0.165 163 16 July 0.00% | 58:4 | 413.4 0.433 stata aes es Aug. 0.039 | 61.3 14.0 0.497 | 58.) — 4 Sept. 0.061 62.6 12.3 0 O88 153 — 1) Oct. 0.139 65.2 94 | 0.042 141 — 30 Nov. 0.301 | 64.7 |+ 4.6 0.092 isl | + 4 Dec. 0.598 | 69.3 |— 0.3 | [0.191 } 1880 Jan, os | ms |4 4.7 | — [0.145] | 179 | — 40 Febr. 0.203 | 56.6 4.5 | 0.102 | 126) | a — 70 March 0.321 65.6 6.2 | 0.144 148 | — 54 April 0.214 | 60.8 8.4 0.458 | 456 | — 52 May!} 0.245 64.4 9.8 | 0.183 180 l= 34 June | 0.078 | G02 | 42.8 | 0.449 | 147 | — 73 July | 0.070 | 61.0 141 0.467 lig, | — 48 ( 76 ) a Bar. Temp. ae I 8 5 ISSO Aug, + O11 763.3 + 15.4 + 0.208 Sept. 0.080 62.0 13.8 0,152 Oct. O.4171 60.0 94 OAT Nov. ODA G12 5.7 0.183 Dee. 0.279 58.7 ao O.189 ISS1 Jan. 0.471 58.7 0.4 [0.283] Febr. O.383 as .2 O40 O.AN74 Mareh 0.375 59.2 5:4 0.255 April 0.361 GLA 6.8 | 0.258 May | 0.306 65.5 10,4 0.239 June | 0.296 62.6 12.3 0.250 July 0.480 | 63.7 15.0 0.264 Aug. | 0.073 | 58.0 13.4 0.191 Sept. 0.198 | 62.2 12.0. |} 7 00:42 Oct. 0217 | 61.8 7.4 | OAR Nov. | 0.972 63.0 feo. 0.158 Dee. 0.399 62.7 4.6 0.140 1882 Jan. 0.479 | 7410 4.2 | 0.170 Febr. | 0.499 | 71.0 3.5 | 0.474 March | 0.352 64.5 20 | 0.208 April 0.189 Saveur 8.4 | O.A71 May | 0 250 64.6 ‘le hersig 0.2294 June 0.135 60.7 12.5 | 0.192 July O413 60.9 13.9 | 0.905 Aug. 0.086 59.7 13.6 O.AS7 Sept. O4105 59.8 42.0 0.4162 Oct. 0.087 59.4 9.3 0.081 Nov. ) O.413 54-4 6.1 0.091 Dec. | 0.156 | 54.0 4.3 | 0.087 1883 Jan. | 0.309 60.9 3.5 | 0.422 Febr. | 0.361 | 66.4 59 | 0.440 Mareh 0.349 59.8 3.3 0.172 Reda b. R. I + 0.256 24 246 209 29 24 0.—C, + + er — 13 —2 — 20 0 — 3 ( fC >) DR. Bar Temp. | 4°R. 1 | Dk nm | O--¢. 1883 April | + 0.301 | 761.1 |+ 7.7 | 40.993 | +0.95 | 458 May 0.203 | 62.4 | 411.0 0.196 | 183 | + 45 June 0.134 | 626 13.0 OATS | 163 | — 2 July 0.053 | 592 13 9 0.169 | (34 (EE 4 Aug. 0.107 | 63.8 13.9 0.159 | 174 | +46 Sept. 0 020 SORE 7) QO O99 | iy | — 4 Oct. 1 0.050 60.0 9.8 0.045 139 | — 13 | Nov. | 0.078 | 59.0 18 0.020 | 1Ozas eee Dee. 0.254 64.2 4.9 O_OD58 | 132 — 15 1S8% Jan. 0.212 63.4 5.9 0.058 105 = EY) Febr, 0.242 | G24 5.0 0.078 112 | — 98 March 0,221 61.0 6.6 0.116 fie) || sf) April | 0.482 | 57.3 7.5 0.153. | 156 | 48 May | 0.905 | 64.0 1g ost | 172 | + 32 June 0.150 63.9 12.4 0.151 147 |} + 3 a ce 15.6 0.164 164 | -b 45 Aug. 0.087 | 64.3 15.7 0.179 199 | + 44 Sept. 0.078 | 63.6 13.8 0.130 AST ea Oct. 0.104 | 69.4 10.4 0.073 19 | 4 4 Nov. | 0.393 | 65.9 5.7 0.195 4 | + Dec. 0.2972 59.0 44 0.1386 203 + bia} saew | 0,203 |\ sae 1.4 [0.190] 2 | 4 30 Febr. | 0,962 | 57.2 5.6 0.183 208 | + 93 March 0.399 | 63.6 4.8 0.210 99% | + 34 April 0.201 | 56.5 8.7 0.215 a9 | 447 May | 0.448 | 58.4 9.2 0.154 138 | — 47 June O51 63.6 (le)? 0.187 194 | == hil July 0.191 | 67.7 14.5 0.204 995 | + 45 Aug. 0.447 | 61.9 12.9 0-168 HO 4 Sept 0.097 60.3 Ae 0.138 PAG — 8 Oct. | 0.031 54.2 8.8 0.080 180 — 4B Nove | 1 (0:305 |}, G0.s 48 0.159 39 | +44 | nm, a Redd Reda Db. R Bar. | Temp, | p Ri pb ROU 185 Dec. | 40-42 | 7654 |4 4.3 + 0.197 | + 0.251 IS86 Jan, | 0.83 | 54.6 | 23 0.225 257 Febr, | 0.505 | 63.4 | LS 0.299 24 Marsh "| Moet ons iste, 0.267 | 209 April 0.353 | 61.7 | 74 0.259 25 May 0.250 | 61.3 11.4 0.269 | 268 June 0207 | 61.6 | 42.2 | 0.9% Day July 0493 | o.4 | 444 | 0.221 a2 Aug. 0.123 63.0 14.4 0.199 241 Sept. | 0.126 64.1 14.1 0.178 2514 Oct. 0.417 | 59.4 9.9 0.127 297 Nov. 0.197 59:05} 7.3 0.139 219 Dec. | 0.936 | 52.4 3.7 [0 178] 215 1887 Jan. | 0.492 63.3 1.4 [0 215] Q47 Febr. 0.595 | 70.4 | 2.9 0.259 287 March | 0.437 | G24 | 3.8 0.241 257 April | 0.304 | 62.9 6.6 0.272 281 May 0.257 | 64.3 9.7 0.230 239 June 0.296 69.0 Biel 0.253 269 July 0.200 64.4 | 15.0 0.972 300 Aug. 0.495 | 62.4 | 14.0 0.268 310 Sept. 0.481 | 61.7 12.3 0.219 273 Oct. 0.307 | 61.4 8.0 0.233 204 Nov. | 0.304 | 56.4 5.5 0.233 294 Dec. ~ | 0.38% | 55.9 4 3.5 0.268 | 322 IS88 Jan. 0.58 | 67.6 | 2.3 [0.271] 305 Febr. 0.530 | 59.3 | 1.3 [0.307] 299 March 0.32 | 50.9 | 3.3 0.273 289 April 0.3% | 59.2 | 6.6 0.311 320 May 0.384 | 64.9 | 10.2 0.320 329 June 0.188 60.0 13.4 0.279 295 July 0.4145 | 57.8 13.0 0.226 254 Reda Dt. Bar. | Temp | per | peru | o-° 1888 Aug. + 0.198 | 763.6 |4+ 431 | + 0.90 | +0.263 | — 27 \ Sept. 0.257 | 662 11.9 0.221 975 | — 45 Oct. 0.304 62.6 8.2 0,220 QS — 9 Nov. 0.333 | 59.4 5.9 0.231 992 | + 2 Dee. 0.415 63.0 4.7 0.231 285 — 5 1889 Jan. 0.544 | 66.5 2.6 0.255 Oram eee Febr. 0.420 | 57.3 3.1 [0.273] 296 | + 6 March 0.437 | 60.6 hh 0.279 995 | + 5 April 0.270 | 56.0 7.6 0.262 om | — 19 May 0.204 | 59.7 13.0 0.289 boste ears June 0.216 64.4 15.0 0.292 308 | + 18 July 0.150 | 60.3 14.0 0.252 980 | — 10 Aug. 0.133 | 593 13.6 0.239 Bo | a) Sept. 0.932 | 634 12.9 0.947 301 | +. 44 Oct. 0.181 | 55.7 8.8 0.20 | on | — 49 Nov. 0.408 | 66.9 6.4 0.215 | 276 | — 44 Dec. 0.518 | 66.4 2.9 0.242 996 | + 6 1890 Jan. 0.420 | 60.9 4.3 0.254 996 | + 6 Yebr. 0.589 67.4 2.6 0.287 315 + 25 March 0.324 57.4 (Seal 0.260 276 — 14 April 0.982 | 55.5 7.2 0.270 979) | -—= 40 May 0.296 | 58.4 41.4 0.285 994 |} + 5 June 0.282 | 63.6 12.4 0.295 311 | + 23 July 0.199 | 60.0 43.7 0.299 307 | + 40 Aug. 0.180 | 61.3 13.5 0.256 agg | + 13 Sept. 0.264 | 66.8 13.4 0.251 Fi || see Oct. 0.283 | 63.4 | 9.6 0.295 pe || aE Nov. 0.24 | 578 | ES fea 0.198 259 | — 19 Dee 0.677 63.3 | — 0:8 {0.340] | A8O1 Jan. Ott | 628 | — 0.2 [0.368] Febr. 0.620 |! 73:2 |--° 3.3 0.956 984 | + 45 March 0.320 | 568 7 0.293 939 | — 28 ( 80 ) Obs Bar. Temp Bedi Reds Db. RK. " DRI D. RK. ISO1 April + 0.360 TW0.8 + 5.8 -}- 0.2536 fo 0.2 May 0.183 57.0 9.6 | 0 2h June O.184 O34 | ee | 0.223 July 0.458 | 62.2 | 14.3 0.242 Aug. O14 | a8 .0 | isu 0 297 | Sept. 0.125 | 63.7 | 13.4 0. 104 Oct. 0.136 | D7 4 10.9 0.198 | Nov. OfSae 4) 7 61),.3 6 | 0220 | } | Dee, 04% | 629 ee | [0.238] | 1x02 Jan, 0.382 | 57.3 | 2.6 | [o.29] | | | Febr. 0.326 56.6 3.6 0,202 | Mareh 0.466 | 63.0 3.3 | (0.244) | April Ou3i5 61.3 is" 0.285 May : 0.296 62.4 9.9 0.261 June | 0.220 62.8 S| 0.953 July 0.172 63.6 43.7 0.274 Aug. | 0.4153 | 62.6 14.6 0.239 |! Sept. | 0.469 | 62.7 | 43.0 0.212 | Oct. 0.448 | 55.3 9.2 0.192 Nov. 0.963 | 62.3 | 7.7 0.169 . 1893 Jan. 0 568 63.1 0.6 [0.272] Febr. 0.313 56.2 4.3 0.214 March 0.391 64.7 6.4 0.224 April 0.498 | 674 9.2 0.307 May | 0.975 | 64.2 11.7 0.263 June, | 0.950 | 68.7 13.5 0.292 July 0.153 60.7 14.9 0.274 Aug | 0.468 | 64.9 15.5 0.248 Sept. 0 184 59.5 12.6 0.260 0.227 Oct. | 0.213 60.1 10.6 Noy. 0.333 60.9 5.7 0.204 | Dec. 0 382 | 61.5 [0.206] ( 81 ) Dk. ioe | Ca | DRI 1893 Dee. + 0.300 | 762.2 |+ 5.0 | 4.0.99 1894 Jan. | 0.459 | 61.3 2.5 | [0.239} Febr. 0.431 62.4 4.2 [0.247] March 0.348 | 61.7 6.2 | 0.998 April 0.263 | 60.5 9.9 | 0.253 May 0.293 | 60.2 40.5 | 0.302 June 0.%2 | 62.6 12.0 0.269 July 0.139 | 60.9 15.0 0.260 Aug. 0.136 61.2 13.8 0 220 Sept. 0.246 | 64.7 11.9 0.232 Oct. 0.221 | 60.9 9.3 0.190 Nov 0.2997 | 63.4 7.5 0.182 Dec 0.310 | 60.0 4.7 0.168 1895 Jan. 0.320 | 54.3 1.8 (0.181) Febr. 0.562 | 61.3 0.0 [0.275] Mareh 0.7 | 56.2 46 0.156 April 0.950 | 60.8 8.6 0.201 May 0.296 | 64.0 14.4 0.270 June 0.273 64.6 13.6 0.306 July 0.441 | 60.2 14.6 0,261 Aug 0.1433 | 61.4 14.6 0,241 Sept. 0.938 | 67.4 44.2 0.248 Oct 0190 | 58.4 9.7 0.203 Nov 0.201 | 641.4 6.9 0.191 Dec 0.973 | 55.3 a) 0.183 1896 Jan. 0.458 68.9 3.3 0.155 Febr. 0.481 | 72.4 4, 0.152 March 0.279 | 58.5 5.9 0.190 April 0.35 64.3 7.6 0.934 May 0.356 66 2 10.0 0.269 June O.A71 62.7 14.9 0.248 July 0.166 | 64.4 14.9 0,239 Proceedings Royal Acad. Amsterdam. Vol. V. 291 260 246, 282 241 $2 ) DR Bar, Temp. DR. I pt It O.=8, i806 Aug, oe 0.156 762 7 | + 44.0 + 0.296 -f- 0.225 + 12 Sept. 0.089 57.8 13.2 0,206 24 | +144 Oct. 0.448 | 57.2 9.5 0.173 998 | + 94 Nov. 0 289 62.1 5.7 O.145 230 + 2 Dec. 0.248 dR_& 3.4 0.081 180) — ae 1807 Jan. 0,300 DR 4 24 0414 a Febr. 0.312 63.3 4.5 O.419 1S8 — 44 March 0.161 55.2 6.4 0.130 184 — 17 April (0).294 60.7 S74 0.163 | 03 | + 2 May 0.191 G14 10.9 | 0.195 | 212 + 41 June | 0.170 | 63.8 13.8 0 218 a2 | +4 July 0.129 63.6 14.8 | 0.206 | 192 | =o Aug. | 0.034 | 59.4 14.7 | 0.472 158 | — 4 Sept. 0.174 | O44 12.0 0.170 178 | — 28 Oct. 0.3299 | 67.5 9.9 0.203 934 | + 33 Nov 0.388 | 66.6 | 64 0.191 247 | + 46 Dee 0.340 | 62.3 4A | 0.448 220 | +19 49989an. | 0367 | 70.0 | 5.5 | 0.408 167. | =—- Febr. | 0.216 | 58.4 | AD | 0.106 172 | — w4 March | 0.48 | 586 | 5.0 | 0.133 58: | 3 April | 0.94 | 60.5 | 8.8 0 182 216 | +45 May | 0.48 | 583 | 40.4 | 0.214 235 | + 3h June O.A74 63.5 | 13.4 | 0.207 206 + 5 July | 0.481 Was | 13.4 0.205 22 |} +1 ' I The table shows clearly that during the first months following the starting of the clock the rate has been varying rather considerably, as probably will be the case with all clocks. It will be seen at the same time that oniy after about 10 years the greatest regularity was attained. In the last years however the rate again began to get slightly less regular, which is shown especially in the mean rates during short periods, and when the clock was taken to pieces in 1898 it appeared that this ought not to have been deferred so long. It was ( 83 ) found that the pivots were more or less affected, and on the suspen- sion-spring there was a small stain of rust, which had fortunately not eaten into the metal. Further rather large deviations are shown by the reduced rates, whenever the temperature was below 0°. This is clearly shown by the monthly means for 1890 December and 1891 January, during which months the temperature was almost constantly below zero. It might be thought that this points to the existence ofa term depend- ing on the square of the deviation of the temperature from its mean value. Such a term might be explained by an influence of the temperature on the elasticity of the suspension-spring. *) It appeared however, as will more amply be shown below, that the monthly means show little evidence of the influence of a qua- dratic term, so long as the temperature remains above zero. It would seem that the temperature-coefficient changes more or less abruptly near 0°, its value for lower temperatures being much larger. I have therefore excluded all periods during which the tempera- ture was below O° (or rather below —0.°6 R.) Four months, viz: 1879 Dee., 90 Dee., 91 Jan. and 93 Jan. must consequently be exclud- ed entirely. In 16 other months the temperature was below zero on 104 days. For these months new .means were formed, excluding those days.*) The following table gives the altered reduced mean daily rates, together with the corresponding mean temperatures. Redd || = Redd Temp. DRI Temp. Deke I W880 January. + 2.4 + 0. 133 | 1891 December) -+ 5.4 + 0.208 1881 January.) + 2.3 199 || 1892 January .,; + 3.4 nl95 1885 January .. + 2.5 164 » March + 3.9 239 1886 December + 4.2 A161 |) » December, + 4.6 190 || 1887 January .| + 1.5 205 1894 January.) + 3.2 216 1888 January .| + 2.9 263 || » February| -+ 4.9 9392, » February) -+ 2.7 264 |) 1895 January + 2.3 74 1889 February) -+ 3.4 .268 » February, -+ 2.2 146 1) Investigations by Dr. P. J. Kaiser about the clock Honwit 27, belonging to the Bureau of Verification of the Nautical instruments belonging to the Dutch navy, have shown that the nature of the suspension-spring has a considerable influence on the value of the temperature-coefficient. *) Since there were not always time-delerminations exactly at the beginning and the end of each cold period, some more days had to be excluded. 6° ( 84 ) These means have further been used instead of the original valnes. 5. The reduced daily rates I, as given in the tables above, formed the basis of the further investigation. The first 5 months have been excluded from the beginning. To begin with, it is possible without much computation, simply by combining the reduced rates into groups, to show that they must still contain a term of yearly period which cannot be explained by a direct influence of the temperature. This is done as follows. The monthly means of the rates and of the temperatures were arranged in groups of one year each, the year beginning with May and ending with the following April. Then the means were taken of the rates for each year, and the differences between the monthly means and their yearly mean were formed. Thus I derived for each year a series of 12 differences: monthly means of rate — yearly mean, and also a series of 12 corresponding temperatures. In each of these series the mean was then taken of the first and the last value, of the second and the last but one, and so on. Finally also similar results were derived substituting for the temperatures the differences between the actual temperature of the month and that of the preceding month (4 Temp). Then the same process was repeated with the only difference that the yearly groups commenced with February and ended with January. The aim of this process will become clear when the results are considered. For brevity’s sake I confine myself here to the five years 1884 to 1888. The differences: monthly means of rate — yearly mean are given separately for each year, and also for the mean of the five years. For the temperatures and the 4 Temp. only the means are given. The differences of the rates are expressed in thousandth parts of a second as unit. It is evident at first sight that in the first arrangement all the series of rates show a very marked progression, while the temperatures are nearly the same. In the second arrangement the reverse is true. On the other hand the variation of the rate is roughly parallel to that of the 4 Temp. Hence the rates contain a term which does not depend on the actual temperature, but of which the maxima coincide with those of the yearly change of temperature, or, in other words, the yearly periodicity in the rate of the clock does not coincide with that of the temperature, and from the values just quoted we easily derive that the first lags about half a month behind the latter. 6. Before a closer investigation of the phenomenon is possible, it @ Sor) | 1884 | 4885 | 1886 | 1887 | 1888 | 84—ss | Zemp. | 4 Temp 1884 | 4885 | 4886 | 1887 | 4 Go)) salad eee : | May,. April.........| +89 | 48 | +60 444 | 449 Se ee ee ee June, March ....... +99 | 198 | 139) -+ 61407] +95 [+85] + 2.0 | | July, February..... 4414 | +98 | +30) +44 )—5]7 +46 [+88] +138 August, January ...; +11 | +8)}—8&|/+ 8); -16] +141 /4+ 82] —1.8 September, December, —26 | —22 —40 | —14|) —26] —26 J|+ 85] — 1.5 October, November. .| —60 | —70 | —77 | —24 | —24 ==15) + 7.4 3 February, January .| —18 | +97 | +9) -+10|/+4+3] +6 [+3.0] —08 March, December...) - 44 | +97) -+6|]+4/—2] +5 |+4.5] — 0.2 April, November... | + 2 | +10|-—9 | +2] -=+20] +5 ]+66] — 0.2 May, October...... —410 | —60 |} —10 | —20 | +146] —17 | +96] —0.4 | | June, September ...| + 4} —14/ +3] —15|—4] —5 |+12.8] + 0.6 July, August....... +5' +9)|)+2 | H9} —30] +7 | 41442] + 0.6 | sare must first be ascertained whether the adopted temperature-coefficient represents the observations for the whole period.*) For this purpose each year was treated separately. The years beginning with February were used, since in that case the temperature- coefficient is found nearly independent of the changes in the rate which are proportional to the time. Gradual variations with the time are namely clearly marked, and over lone periods they are not even proportional to the time. This is seen from the following summary of the yearly means in which I have taken the years beginning with May in order to be able to include 1878. 4878 + 0.199 1883 + 0-411 4888 + 0.252 1803 + 0.243 1879 120 188% 159 1889 4 1894 .208 1880 189 1885 189 1890 DAT 1895 220 1881 A186 1886 210 1891 218 1896 AT6 1882 457 1887 57 1892 299 1897 169 1) In the investigation of this section and also in that of § 7, it was in- advertently omitted to apply corrections amounting to 0*.005 to six rates of the years “88 and ’89. The influence of this omission is negligible. For the four months, in which the rates were rejected on account of the low temperatures, interpolated values were used. Two methods have been applied to derive the temperature-coefli- cients. In the first method I used the deviations of the monthly means from the yearly means, while in the second the deviations of these same monthly means from approximate values of the term a, i.e. the non-periodic part of the rate, were used. These values were derived from a curve which represents as nearly as possible the yearly means for years beginning with May, with August, with November and with February *). These two methods gave the following series of corrections, headed 1 and II respectively, which must be applied to the value — 0.*0268 of the temperature-coeflicient. They are expressed in units of one fenthousandth. part of a second, 1879 aes fe 1889 ra 9 cae iso ol ++ 8+ 19 1890 + 32 +91 i981 +47 + 41 (SOT oR A re i882 +70 +68 1892 + % +498 Ss es Oe 803. 5a gs I88i 6 199 4 34 1894 + 65 + 64 ee Se 189 + 98 +96 1e86.) ==." 9 Vaeed 1896 +102 4 96 (ser)? fo ee i807 6k SBF 4888 —12 — 4 The two methods thus give practically the same results. Although this agreement is of course not a measure of the real accuracy of the corrections found, it is nevertheless evident that the temperature- coefficient has not been constant during the whole period, but that the adopted value requires a positive correction as well in the first as in the last years, the latter being the most marked. If the whole period is divided into three parts, we get the following mean results, according to the second computation (those of the first method are nearly the same): 18791884 Ac=-+ 38 1885—1892 Ee 1893—1897 4+ 74 1) In first approximation it was assumed that e.g. the mean for the year from ‘78 May to ’79 April gave the value of @ for ‘78 Nov. 1. Afterwards these vaiues were in some cases slightly altered. ( 87 ) Throughout the preceding investigation if was assumed that the influence of the temperature is proportional to its first power. It is important to investigate the results which will be found, if we repre- sent the influence of the temperature by the formula: c, (€—%,) -+4- (OS (UR) Jar For this purpose I used the deviations of the monthly means from the values of @ derived from the curve. These deviations were represented by the formula Aa + Le, (t—t,) + ¢, ((—t,)?. I did not investigate the separate years, but I derived mean results for the three periods mentioned above; ¢, is then in each case the mean temperature of the period, and differs but little from + $8.7 (= + 8.1 Réaumur). In this way I found the following values of 4c, and ¢,, both expressed in tenthousandth paris of a second : Le 1 Cs 1879-1884 30 39 18851890, 15) 653.9 18931897 +75 —7S The values of Ac, nearly agree with those previously found for Ac. Those of c, are small and of different sign, and their reality is doubtful. The rates for temperatures below zero would require positive and much larger values of c,. In order to represent e. @. the two results for the months 1890 Dee. and 1891 Jan. it would be necessary to assume c, = + 15. I think therefore to have acted correctly by excluding the rates corresponding to temperatures below O°. For the other temperatures we may certainly provisionally adopt a linear formula for the influence of the temperature. As to the coefficient ¢ of this formula, I do not think that it could be represented as a function of the time which would have any real meaning. Probably, however, it will be better to assume it constant during shorter periods only, e.g. thus: Loe c S79 = SNe eet 247 1eg63) == 59) = 916 feeder Pais 957 eS5= oie nd 269 (39293) 237) |= 934 igo =9q 8h = 4.87 Finally I will show how these coefficients would be altered (see SS before) if the barometer-veadings had been reduced to one tempe- rature, in other words, what are the values of the fre lemperature- coefficiads, Por 760 mm. the reduction for 1° Réauwer amounts to O.152 mo, of which the effect on the rate is 0*.0021, Consequently the ve temperature-coeflicient is found by applying a correction of + 0.0021 to the apparent value. 7. We shall now apply to the reduced mean rates the reductions due tothe corrections found for the temperature-coeflicient. The adopted corrections are of this coefficient : 1878 May—1884 April 4¢= + 39 1884. May—1893 April 0 1893 May—1898 July + 75 Though probably the values mentioned at the end of § 6 are preferable, it did not seem necessary to repeat the computations with these altered values. After this the deviations of the corrected monthly means from the values of @*) derived from the curve were formed and_ these means were arranged in yearly groups, each year beginning with May.*) For brevity’s sake I do not give the results for the separate years, but only the means for four groups of years, viz: 1879—1882, 1583—1886, 1887 —1891 and 1892—1896. If the deviations of the monthly means from the yearly means are used, the mean results for those four groups are not appreciably altered. All values are given in units of one thousandth part of a second. It will be seen that the results of the first and the second groups agree very well inter se, and also those of the third and the fourth groups, I have therefore finally formed the means for the periods 1879—1886 and 1887—1896. The principal difference between these two periods seems to be that the low minimum in October which is shown in the first, has disappeared in the last. In the years, 1892—1896, however, the whole periodicity begins to be less marked, and in 1897 it is no longer shown by the monthly means. The monthly means of 1878 (i. e. °*78 May—79 April) are in good agreement with the results for the period 1879—1886. 1) Since this curve is relative to the temperature + 10°, while the mean yearly temperature is + 8°.7 its first and last part had to be slightly altered, to account for the altered values of the temperature-coefficient. *) The curve for @ can only be drawn from *78 Noy. to “98 Jan., therefore ihe present investigation can only include the period “79 May—'97 April. 1879 1887 | 79—82 | 88—86 | 87—91 | 92—96 — | — | 1886 1896 May ac... | sella, Mette) ar CP ea see) a dane’ ace: | SET ay ees Ou NCO) wth O74 1.49 |) 95 | Tite. 24s| aC) | Se Op te gh | a, 5 August | eta 3 | — 7) => 4 er == 16) + 2! —10 September. — 38 — 32 | — 27 — 9 — 3d | — 18 Oeteber tee eee l= aah ale —=.98) |) Senos 74. => os November.) — 22 — 54 — 26 | 91 38 | D4 | | December.| — 22) — 26 13 16 24 | 14 | | January | +412} — 5) — 7| — 6] + 4 | = & | | February / == to nee | — 9 )) =. 9 | tes! | NEEM Boeal| SEMIN) SS Se ea) ey Serie April..... | ee Se) || SE AG SLB) |) spore) |) See oi During the period 1887—1896 the periodicity can be very satis- factorily represented by a simple sinusoide. We find: T— May 5 365 where the amplitude has been expressed in tenthousandth paris of a second 7). Mp == + 254 cos 2a For the first period such a representation is impossible, and even when a term containing the double angle is introduced, the repre- sentation is not entirely sufficient. In that case we find: 4 T—Apr. 24 4 T—Apr. 23 Ar = + 455 cos 2% ———— — 95 cos 4a —_____.. 365 305 An entirely satisfactory representation can only be obtained by an empirical curve. This curve, together with the points which indicate the observations to be represented, is here reproduced in fig. 1. The sinusoide of the second period is given in fig. 2 *). Moreover the following table gives for the first period the differences 1) From the period 1887—1891 alone we find T— May 1 365 2) These figures will be published together with the second part of this paper. Ar = + 274 cos 2x ( 90.) Obs.—Comp IT and Obs.—Comp. II, where Computation | means the representation by the formula, while Comp. II refers to the curve. For the second period the differences Obs.—Comp. are also given, Everything is expressed in thousandths of a second. Rice we 8716 W— 3 | Foe G—eijo.-o1| 7° 0.—6.1| 0.—Cin| Pes MSs Sacre: | + 2 + 2 + 6 November . + 12 + 7 +414 June......., —412]/ — 9/ + 5 December... + 3) — 5) + 6 July ! will be Gy, = aks te dag te = = an In order to determine this sum we have to find an arbitrary substitution for which the exponent assumes the form Yy° and then We must substitute the new variables y into the second factor. A substitution fulfilling this condition may easily be found. The exponent namely may be written as follows: oS UB Saag or sae Piet: = ise + = = (foti—fr)” —— (@fr—B fon)? v k i > T 2 2 where : GP Se ir ee St aint = 207 |) e oe ker hr So we find for @ and ~: Yi) ny ee gee azs—i — } — SS - — -- a) a . are : o o ke Now we choose as new variables : ij 9 Ol This substitution does not yield the accurate coefficients for 7? and j,° for, in order to get 7 quantities %, we have to take as one of the new variables x,=e/, —®87,; so we introduce moreover a term 2aB/, 7, which does not occur in the exponent. As however the exponent consists of an infinite number of infinitely small terms, ( 118 ) these three terms which have not the proper coefficients will be of little importance. These new variables are now to be introduced into equation (27). Yet it is not necessary to execute the substitution completely, for, as we have only to determine the sum of the coefficients of the squares ze", we may leave the coefficients of the products %» y% out of account. In the first place we have to express the old variables 7 in the new variables 7%. We have: h=as,— Bs, 1 ig as, — BS, 7 af,—Bf, From this follows: [| a =p 0 0. Oe Dy is 0 0.9 90"...came 07? Sai— PF OP 0h Ont 4, a4—8* 0 ©... ee 7, | 0 0 a8 0... O] =. |x 0 af 0... 0 | ——fP 10) 910) m0 aU teyars ee Yn 0- "0! On er or f,(e— PF) = 4 "+ ek ae Ba Be In the same way we find for /;, Fo (a®9—B") = yo a! + Yop a? B+ Yoo a B?.... ven rl Bev Ay, a2 BrP yy BIT. www (88) In determining the produets 7.7 we shall always suppose that v’>r, and so we shall integrate + between the limits O and 7’; re between the limits O and x. In fhis way we get only one half of the quantity we have to determine. In order to find the amount contributed by the product /)f.cos(v’—r)rp to the coeflicient of = we have to distinguish three different cases: Ist. O Integrating partially we find: Wy Th Ta \# . 1] fave “14 P a Net | G cos p(u —u)du—=— res p(id—u) | —— {| ig p(w —u) du= Jb ie BNE to nee ob 0 i hb 0 a 4 u malt Jrosrt! — ie fal (; ds p(n) ie AG Jeos p(u'— u)du Bay Se b Ee which follows: cos p(w —u)du= —-- f po 4 pp db In the same way we have : a \ Gi\aa all ; : wy 1—) —| — | +-eos pu | — psinpu (MGNae b | J( cos p(u' —u)du= b 0 a re c ne is cos pu {=p sin pu ic a P+ pt ( 120 ) If we introduce these values into expression (33), it assumes the following form: t 1 : P I i3 \ ‘ j u " a 4 ee b — ln) (5) { j! - cos pu — Face (OV 5, (es —— Jan b — ON b \P aan pu adi Integrating this Pare. we get: oes a a — (ah — bf ye . ~t, — (ai—bn) 1 5 p— (ah + 1) ; +. , , +P + (ah + bh) P ; (sin pt, ++ cos pt,) + (ai—b") ple (sin pt, —cos nt) ) , The fact that the terms with si pf, and cos pt, occur, shows that the distribution depends on ¢,. We might have expected this, specially as we have chosen @ /,—/, as one of new variables for the substitution and therefore introduced the condition that 7, and 7, have about the same value. If however we take a considerable value for ¢, then a ihe term (a—b') 1 t, will have decisive influence. If we now con- J sider a region of the spectrum of some, though it be an extremely small extension and not a rigorously simple wave, then we have to admit slight variations in the value of p. The terms sim pf, and cos pt, Will then have alternately the positive and the negative sign and yield zero on an average. If 7, has a sufficiently great value then the course of the function of Aa ; 1 : : is principally determined by the factor =———. This expression does t = b+ Pe not present a well defined maximum value, but it has its greatest value for p = o (i.e. for infinite wave-lengths), it decreases gradually with increasing p and is zero for p= (i.e. for infinitely small wave-lengths). So this equation does not at all represent the distribution of black radiation. I only communicate these calculations in order to show that equations analogous to (8) or (Sq) determine in fact a distribution of the energy over the different periods and to indicate a method for analysing such like equations. C120) Physics. — “Ternary systems.” V. By Prof. J. D. van per Waats. (Continued from pag. 21). If the temperature is so low that there is no question of critical phenomena, and if therefore both liquid sheet and vapour sheet cover the whole triangle, v,, is for all points either positive or negative, and the given rules for the displacement of the curves of equal pressure will therefore be followed by all points of these curves. If on the other hand the temperature is chosen so high, that the surface of saturation does not cover any longer the whole triangle, and if therefore the liquid sheet and the vapour sheet pass into each other above a certain locus in the triangle, v,, vanishes for the phases represented by this locus. We may form an idea of the shape of the surface of saturation with the aid of fig. 11 (Cont. II, p. 135). Let us imagine that this figure represents a section by the vertical plane which contains the X-axis of the triangle and let us take a similar section by the vertical plane which contains the Y-axis. The value of 7 is then chosen such that 7’>(7,,),, and also 7’'>(T7,,),. In the figure men- tioned P is the point, where a vertical tangent may be drawn, so this point represents a phasis which is in critical point-of-contact circumstance, and for which v,,=0. The point C represents the plaitpoint. If we now imagine different planes which contain the axis erected in the point O normal to the plane of the triangle, these planes will cut the surface of saturation, and the sections will be analogous figures, which however change their shape fluently from that which they have in the POX-plane to that which they have in the POY-plane. If the pressure is lower than the lowest pressure of the points P, the two branches of the curves of equal pressure are perfectly separated lines which, if the pressure is increased, will be displaced. according to the rules given above. If however the pressure has risen till the pressure of a point P has been reached, then the two branches are still separated, but on the vapour branch occurs a point for which v,,—0O. Such a point is not displaced when the pressure increases. The locus of these points forms the limit of the mixtures which may be splitted up into two phases at the given temperature. From a geometrical point of view it is the envelope of the projections of the horizontal sections of the surface of saturation, or the envelope of the projections of the curves of equal pressure. If the pressure has been increased till it has attained the value of the lowest of the pressures of the point C, then the two branches of the curves of equal pressure pass continuously into one ( 122 ) another. But if we continue to call those phases represented by the lower sheet, vapour phases, and those phases represented by the higher sheet, liquid phases, then the vapour phases do not reach the point, where the connection of the two branches has taken place (the plaitpoint), but only the point where the value of »,, is zero, i.e. the point, where two successive curves of equal pressure intersect. For all points lying on one of the sides of that point of intersection, — e.g. on the side where the plaitpoint occurs, — v,, is positive. These points will be displaced towards the conjugated point, when the pressure is increased; all points on the other side of the point of intersection will move away from the points, representing coexisting phases. If we, therefore, continue to use the expressions “liquid phasis” and “vapour phasis” with the same meaning as we have done till now, we must say that for points between the plaitpoint and the point for which v,,=0 two liquid phases coexist. If for the two pairs of the ternary system we had a course of the presstre as is represented in Cont. Il, p. 135, fig. 12, the above rules would continue to hold; but in this case we find a series of vapour phases coexisting with vapour phases between the plaitpoint and the point, for which v,,—0. For these points we have then retrograde con- densation of the second kind. We may expect that it will be easier to observe this phenomenon for a ternary system, than for a binary one. In order that retrogade condensation may be easily observed a rather great distance between the two sheets of the surface of satur- ation is required; and the distance between the sheets will be more considerable in the middle than at the ends, where we have to deal with a binary mixture, because the requirements for sta- bility and coexistence for a ternary mixture are stricter than those for a binary mixture (See Vol. IV, p. 577). But then we have to avoid the case that a real maximum pressure occurs, for in that case we have also in the middle of the figure a point in which the two sheets touch each other, c. Curves of slope and nodal envelopes. If for a binary mixture we have construed the curves p= f(7,) and p= f(w,), we have at the same time answered the question, what phases may coexist with each other. Every line parallel to the X-axis joins a pair of coexisting phases. If on the other hand we have construed the two sheets of the surface of saturation for a ternary system, this is not sufficient in order to answer the question which ( 123 ) phasis coexists with a given phasis. It is true that we know that the pressure must be the same, and that therefore the second phasis will be found on the other sheet at the same height as the first phasis, but as the section of the second sheet by a plane ata height equal to p is a curve and not a point, the question is not yet per- fectly determined. Therefore, besides the series of curves of equal pres- sure, which are already given as the points which have the same height, still another series of curves must be traced on the surface of saturation which pass from lower to higher pressure and whose properties enable us to answer the question, which phasis of one of the sheets corresponds with a given phasis of the other sheet. We will again begin with treating the simplest case, in which maximum-pressures are excluded, as well for the pairs of components of which the ternary system consists, as for the ternary system itself, so the ease for which the lowest pressure is equal to p, and the highest to p,. The question is then, what systems of curves, starting at the point where the pressure has the lowest value and ending in the point where the pressure has the highest value, may be traced on one of the sheets or on both sheets of the surface of saturation which enable us to find, what phases coexist with each other. Such a system of curves will be found in the course of a person who would climb the inclined sheet, e.g. the liquid sheet, always moving in such a direction that he has the phasis, coexisting with the point, where he is at the moment, just in front of him. If we now project the tangent to the way which he has followed ona horizontal plane, the point in which this projection cuts the vapour sheet will indicate the coexisting phasis. The projection of such curves on the plane of triangle OXY has therefore the property that the tangent passes through the conjugate point, and is therefore the chord, joining the points 1 and 2; from this follows again that these projections are the envelopes of these chords. If therefore in the plane of the triangle we have drawn the two branches of the curves of equal pressure, and if we have joined a pair of nodes by a chord, an element of the curve in question will be represented by an infinitely small part of this chord. Let the point from which we start represent a liquid phasis and be its coordinates v, and y,. The projections of the element of the way followed are then the quantities dv, and dy,. At the end of the elementary way the second phasis is also changed, of course, and the consequence of this will be that we have to follow a curve. But the direction of the infinitely small way will always be the same as that of the chord joining the nodes; and the differential equation will therefore be given by: ( 124 ) de dy, Use, Ya" For these curves on the surface of saturation | have chosen the name of “curves of slope’. This series of curves begins and ends with the following curves; I the curve p= /f(y,) for the pair (1, 3), and 2"¢ the curve consisting of a p= /'(«,) part for the pair 1, 2) and of a corresponding part for the pair (2, 3). [If we draw these curves on the vapour sheet, we must imagine that we descend instead of ascending. For the projection of these curves on the plane of the triangle I have chosen the name of “nodal envelope’. The outmost curves of this series are: 18* one of the sides of the triangle, adjacent to the right angle, namely that one corresponding to the third component, and 2"4 a line consisting of the other side adjacent to the right angle and the hypothenuse of the triangle. For the solution of the differential equation of these curves it is required that we may express «, and y, in «, and y,. This is possible (p. 7) when the second phasis is a rare gas phasis, if we namely assume the functions gw’, and p’,, to be known. For that case the equation we have to integrate may be written: de, dy, x, {(1—z,) (e*% —1) —y, (e*°"—1)} y, (1—»,) (en —1)—2,(e"" —1)} or di, 1; js. Oe VOD ENP yan Ayan 1. a! ul ut (1— BY 1 es or aoe nai) MG 3) ehh gay ee th 1—a,—y, Pe es, my \ de, d(1—w,—y;) - (e* 11) dy, i d1i—«,—y,) [w a 1—2z,—y, n 1—a«,—y, The last er may also be written as follows: cd = (e"% —1)dlog 5 ae a 1—w,—y, —«;—Y, (e” 4 —1) dlog e : ‘ wt ? For the case that the liquid sheet is a plane, e°“—1ande“"—1 ._— _.— )P. are constant, and equal to Ea ig and eoitie equation of Pr Pr the nodal envelope will be given by: rah" Po Pi cy Wh =e( ny ) Pi ——7 1—2,—y, ( 125 ) ( PsP (= Ps—Ps ) PM Pr | or av, a) yy (l—w«,—y,) ; an equation in which all exponents are positive as appears from the values of p,, p, and ,. For C=O this equation is satisfied by ,—=O0 and therefore the nodal envelope coincides with the Y-axis. For C=» either y, or 1—vr,—y, is zero, and for this value of C' the nodal envelope coincides with the X-axis and the hypothenuse. For the special case, for which pP,=2p, and p,=3p, the equation assumes the following shape: vw? = Cy, (l—a,—y,). This is the equation of a conic section which touches the X-axis and the hypothenuse in the points in which they cut the Y-axis. Whatever the values of p,, p, and p, may be, the curve will touch the X-axis and the hypothenuse in the points mentioned, if only the condition p,< p, p, > p, be fulfilled. The nodal envelope for which C=O will of course be an exception to this rule. In the adjoined figure 13 the Bs general course of the nodal envelope is represented in the above de- scribed circumstances. Though the calculated formula only holds for w’,, and w',,= constant the shape of the curve will agree in main features with the one, drawn here, always if neither on the sides, nor anywhere in the middle of the surface of saturation a maxi- f 1-% hy, 4 mum pressure occurs. Fig. 13. Only the details are different. For the locus of the points where the tangent of the nodal envelope is parallel to the J-axis for instance, we find in the case that uy, and w',, are constant a right line passing through the intersection of : dy, the X-axis and the hypothenuse. For os rode so dz, = 0. But then also z,—2, = 0. =o for such points and As follows from the equations (p. 11). w—#, (1—2,) ¢ *—1) —y, ¢* * —1) a, eee, (Gh = 1) ey (eo 21) yr Proceedings Royal Acad. Amsterdam. Vol. V 126 ) and 9.—y, _. (l—y,)'(e*%—1) —2, (6 —1) ho Dh ay C1) +y, C1) we have: t,—2, = 0 é a 1 if 1—x, —a A Ser ane 2 e %—] This equation represents a right line, if the factor of y, is constant, and it yields 2,=1 if y,=0. If the surface of saturation is a : ws, continues to be satisfied, will start from the same angle of the triangle. In this case the line for which «2,—7,—=0O does no longer coincide with the line for which the pressure is equal to p,. If we put in equation (7) of p. 12. er rarity if 1—a, a oars i= a then we find: ~ == My, (1—w,) ws, —Y, Ky, —l. If we denote the value of u for c=1 and y=0 by «,,, then we have: R ! ' a Bay + —2,) ts, I, Hy, Hoe a The second member of this equation represents the distance between the point of intersection of the tangential plane to the p-surface and the vertical axis of the second component, and between the ordinate f,,- If the whole surface lies below the tangential plane, as is probable, then the second member is positive and p > p,, and the difference between p and p, increases, if the point of intersection ( 127 ) lies at a greater distance from the second component, and if the deviation of the surface « from a plane surface is more considerable. The succession of the values of the pressures p,, p, and p, involves that the condition y, — y,=90, which would lead to: ‘ Ae ee 1 ek Sn 7 e Capa 1 cannot be fulfilled, for in that case the factor of «, would be less than unity, and the equation: ' a te ie Ons ——il! with constant value of w,, and w’,, would then in fact represent a line through the summit of the triangle; but a line outside the triangle. But we will return to this condition presently. These nodal envelopes have an analogous significance as that of the lines of force in the magnetic field. In the same way as the tangents of the lines of force determine the direction of the force, but not its intensity, so the tangents of the envelopes determine the direction in which the second phasis is to be found; but they do not indicate the distance between the points 1 and 2. This distance, however, is perfectly determined if also both branches of the curves of equal pressure and triangle OXY are drawn. Then we find the second phasis which coexisis with a given liquid phasis, by drawing in the point representing the liquid phasis the tangent to the nodal envelope of that point; the point of intersection of this tangent and the vapour branch for the pressure of the liquid phasis represents the second phasis. If we do this for all points of the same nodal envelope then we get a new locus, which we may call conjugated curve of the nodal envelope. In order to give the equation of this conjugated curve we must be able to express ., and y, as functions of x, and y, and we must substitute these functions in the equation of the envelope. In general, however, we are not able to do this, not even in the case that the second phasis is a rare gas phasis. Only in the case that y’,, and w,, may be considered as constants it can easily be executed. If we write the equation of the envelope as follows : a, i ‘”— 1) ( fr :: ea aes 1) = =p) (eee ; si Wi ah which only may be admitted for constant value of w’,, and w’,, , and if we take into account that: ge 128 ' —Mx a“, __ @,e 1 —t,— 1 — ones » Hy, and _ 41 Neal 1—«,- uv, 1- “0,—¥ then the substitution into the equation of the envelope yields the following formula: lat liam Ae Re obs: 1—wz,—y, “ 1—«,—y, : Jn, =e | yh wes 1) or as : = (i eee oe ( ‘ 1—#,—y, l—w,—y, From this follows that the conjugated curve of a nodal envelope of liquid phases, is, in the chosen circumstances again a nodal enve- lope, with another value of the constant, namely: oe a o=o(?) ” @ Pl Hh Ps If p, << ps wy,, if both are positive. The condition that the tangent is parallel to the hypothenuse may be derived from: Ys 91 Ty, — re From this we deduce: pris {neste 2 Vy @ aa] , 1 fy ell Therefore a tangent of the nodal envelope parallel to the hypo- thenuse can only occur in the case that w,, and w’,, have different sign. All these relations apply only to the case that q’,, and aie may be equated to zero; and the given rules will require corrections when the temperature is increased and approaches one of the critical temperatures. If 7 has reached a value higher than (7’,,.), for instance, and consequently the surface of saturation does not cover the whole triangle any more, the envelopes can no longer pass through the angle of the third component. Even without knowledge of the equation of the envelopes we can understand in the following way what peculiarity will then come into the shape of those curves. The surface of saturation has in the vertical plane containing the )’-axis, and also in that containing the hypothenuse still the shape of fig. 11, Cont. II. The first curve of slope lies in the first mentioned ver- tical plane and consists of that part of the p curve of the figure mentioned which extends to the maximum, i.e. to the point C. All other points of this pressure-curve, as well those between C and LP as those forming the lower branch, represent coexisting phases and belong to the conjugated curve of this curve of slope. The last of these curves of slope lies above the X-axis and above the hypothenuse, but above the hypothenuse it also extends only to the projection of the point of maximum pressure. Every intermediate nodal envelope has initially the shape of fig. 13, has also still a vertical tangent, but ends in a point (the projection of a plaitpoint) before it has reached the locus which represents the limit of the points above which the surface of saturation extends. Above such a limiting point of the nodal envelope the curve of slope of which it is the projection has reached its highest point. Before the limiting point however the course has been modified. In order to discuss this modification we will derive the second d*y derivative function, namely = ~. From: Dy dy, Y.—1 ae a follows dz, L,—2, By, ie _@, a, )(dy, —dy,)—(y,—y)(dv,—ade,) de? es («,—2,)? ; ly, ; (dy, — (yi) wficaoth yo a If the gas phases are very rarified the latter equation may be sim- plified to: 1 dp Sesh p dy, y.(l—y,)’ which form is identical with that which applies if a second component is added to a simple substance, and from which accordingly the quantity v', has disappeared. This identity of the form of the equation does, however, not justify the conclusion that also the shape of the curve p= f(y.) will be identical. The same form of the equation applies also to a binary system, and yet it includes the great variety of curves which the pressure as a function of the composition of the vapour can present. All those differences in shape are to be ascribed to the different ways in which y, and y, depend ypon each other. In the same way every plane section of the vapour sheet for a ternary system by a plane, normal to the plane of the triangle and passing through the summit, will be represented by this equation, though these sections may present an infinite variety of forms, which again may differ from those of a binary system. Yet we may make use of this equation and deduce some general properties from it. f dp ; Ap : - So e.g. ae will be zero if on the chosen section a point #,, 7, oceurs for which ee If the suecession of the values of the pressures is p, << py < Dy this can never occur. In this discussion, however, we will think the succession to be changed according to the circumstances in order that we are not obliged to draw the section every time through another angle of the triangle. If the succession is p,< p,< p, a locus occurs indeed, for which y, = y, and this locus coincides with that for which the pressure of the vapour phases which occur on the chosen section is maximum or minimum. We might have expected a priori that in general a maximum or minimum would be found on the section which passes through the angle for the component whose pressure lies between those of the other components, and which cuts the opposite side in a point with the same pressure. This maximum or minimum will, however, not have the same significance as that of a binary system. For in the case of a binary system the composition of the vapour is the same as that of the liquid phasis; for a ternary system only y, and y, are equal, but.7, and «, differ. In such a point the pressure of the liquid phasis is not equal to that of the vapour phasis as is the case with the maximum pressure of a binary system, — but the pressure of 136 the liquid is higher than that of the vapour. The two sheets do not touch one another in’ such points. It is true that the pressure for a point conjugated to such a point is the same, but dp. dp is different from zero, as appears from the equation for ip dy, dy, If we substitute in this equation y, = y,, we find: 1 dp re, Bae a Ae (vw —a ) Le any, —* EL any pdy, The factor «,—v7,, which also may be written ~ depends on the 1 curvature of the p-surface, and in all cases in which the surface is only slightly bent it will have only a small value; but only in very special cases if will be rigorously zero. In general therefore we may assume, that this locus of the maximum liquid pressures does not deviate much from the locus for which y,—y, = 0. If the pro- jections of the curves of equal pressure are drawn, the points of maximum pressure and the sections discussed by us are of course immediately to be determined, by tracing the tangents, passing through the angles of the triangle. = - UC, dp : The value of —*— assumes exactly the same shape it has for MRI dy, * ; Pare Atty, binary system if either (7,—,7,) or - are zero. The value of 7,—, € Yy vanishes in the first place if the quantity we have denoted by «, is zero, and in the second place if it is equal to unity. But in these cases we are really dealing with binary systems; in the first case with the pair 1,3 and in the second with the pair 2,3. In the first case we have: 1 " SS SE AS SS = ul , MRT dy, (¥. Y;) Gia +] A and in the second case, if 1—2z,—y, = 1—2,—y,, OY #,—2, SS IF) 1 MRT dy, y¥,d—) The quantity «’,, — 2e".,,, + u',, has for the pair 2,3 the same signification as «”,,, for the pair 1,3, as is easily understood. v dp 21 == (¥s—Y1) | + Ca =e Bl ny SF e's, ' v dp 21 MRT dy, peculiar points, where «,—z,=O either inside the triangle or on The quantity assumes also this simple shape in the very : du',, ‘ one of its sides, and also in the points where —— vanishes. a& 1 (LS) But in general the quantity (#7,—2,) (w's,,—7,«w's,) will cause a modification in the course of the value of the pressure which is very slight. The value of the pressure depending principally on the term yd—y,)_ ; We will consider more closely this last quantity, which represents SUPAE : ae the limiting value of — OL — OM Ory u— le tor a, binary p dy, mixture and which for a ternary system is to be augmented with Ul . » Mex (t,—2,)o Gite 0 ayy . 3 ; c ; Yoel We have found before the following value for *——: Yr , uw. Pi te ae 1) ae are ce Sa Pon See in) Ohi (l=a,—y,) ff a,e° 74+ y, From this value we deduce, if we set y, =O and w,=w« 0 ot af = ' yy, 2 (eB —I)—a2(e""—1) se 1 1 ’ — <5 Pox, i yid—y,) fee" 1) 1—2,+e, e"* where «,, and w,, have the values they have in the point whose coordinates are 7, =x, and y,=0. This value, which for 2, —=0 ay oe 1 5) ; and now the way in which ] HS 4 iJ > Poa, — is equal to e “'—1, has for «, —1 the final value e’ ” and varies fluently with increasing « 1 dp . 3 ! , C “ . TAD ! r : — —— varies depends upon the relation between w,, and w,. This p dy, value may have reversed its sign, either from negative to positive 0 or from positive to negative. The quantity f’,,—w, represents the variation of me for the motion along the hypothenuse towards the summit of the triangle in the same way as wy, represents the varia- tion for the motion alone the J}-axis towards the summit. If there- fore 7. for the summit is lower than (7%,.),, then w,, is positive, and if 7, for the summit is higher than (7-,), then «’,,—('2, 1s negative. It is not superfluous to point out in how high a degree the value yo dp Ne Om — —— depends on the value of u’,, p dy, : direction of a curve of equal pressure for a binary system. According , if it represents the initial to our former observations this value is equal to Cit ee lit eve 1 dp Yo—Y hss also draw the vapour curve, then — Pf —”—“* and soit is equal to: P dy, Ye 138 ) \ “oo 1 Nia | ay 5 a =1l—e ". If we draw moreover the curve of the double eo th dp rl Oo ; points then we have a Ua For the case that uy, 0 we always peu . . l dp l dp ‘| dp find zero as well for the value of — . as for — : and f P dy, P dy, P dy If wy, is positive, the three lines ascend, and they descend if my, is negative. If the value of wy, is very small, there is only a small difference in the slope of the three curves. But if w',, has not so very small a value, then there is a very great difference in the slope of the three curves, and the liquid branch ascends exceedingly fast. ip FM bee d log Per LT dy; dy, , “. dT é 5 we shall have a great value «’,,, if 7%, has a considerable negative dy, value, so if the 7% of the second component is much lower, e.g. if we press a permanent gas into a liquid. As in general 7), does As {Uy, — el : d log Per : . not depend linearly on v, and ; has a value differing from ay, : zero, we shall not find the accurate value for ’y,, putting: ly Ay , r Uy, = ipl cr), —( cr )a} but only amore or less approximated value. If we choose for the second component a substance whose 7’,, is much lower than 7’ and for the first component a substance, whose 7’. is much higher than 7’, we do not take I 2 : an impossible value for «’,,, if we give it the value 14 or 15 for ordinary temperature. In that case e* may in rough approxima- tion be represented by 10°. If we might apply the results we have obtained, also in the case of water, though its behaviour is specially at low temperatures very abnormal, then we might form an idea of the degree of approximation by means of the absorption coefficients of gases solved in water. According to our results we find for small values of y,, if we neglect the vapour pressure of the first component compared with the total pressure: PSP (e"% a): Here p, represents the vapour pressure of the first component. Further we have, denoting the absorption coefficient by @, and the molecular weight and the density of that component by m, and d, : NT ~ - pe m 7 - If we neglect unity toe 2 ; We may derive from these two equations : ah Cassy AL 1 . APOE é Tae ~m, 0,0013 ap,” If we put in this equation d,=1, m,=—18 and one (as) Atmospheres, and @ = 0,02 as is the case for .V,, then we find for w,, a value between 16 and 17. This result shows that the equation 7 = 273 (La dw nan (Ler) N,} does indeed hold as an approximation. If we had chosen as second component a substance of small volatility and whose 77, is much higher than (7,),, then we might form an idea of the value of w’,, by making use of the approximation: Poa i Ly, — oT (Les) — (le) ae but then we should find a very great negative value for ww, and 41 When we add a third component to a binary system whose com- ut 9 cpr . . =e "a value which differs only slightly from zero. for position is determined by «,, then we have found for the value of a 2. ¢ : ——., if y, is infinitely small: p dy, I dp en " " a dy i 1+-(@y—#)o {Hy yn Vol x3 PR Seks eo eee The two branches of the pressure-curve of this section do not start in the same point and so they differ already from the beginning from those of a binary system. Only if (7,—7,), = O they start at the same point. But as the factor of 2,—a, depends on the curvature of the uw surface the influence of this term may be neglected specially when w,, is great or when the curvature is considerable. So we find for : : 1 dp : F the value of 2, for which — “P vanishes approximately : 1D ath pe Gees al Xo SS SSS 2 px e~—] Only when w'y,< pz, this yields a possible value for x, at least if as well wy, as wz, are positive. ( 140 ) , Geology. — “Cumbrian Erratic-blocks at Hemelum in the South-west of Frisia” By J. HH. Bornema. (Communicated by Prof. J. W. Motz): To the East of Molkwerum, a railway-station between Leeuwarden and Stavoren, stretches a region that from a geological point of view is very remarkable; as was especially shown by the interesting researches of Dr. VAN CAPPELLE. ‘) The road first leads in a North-eastern direction to the village of Koudum, which is situated on elevated ground. As far as here the surface showed alluvial clay only; now we see for the first time diluvial formations. The outer part of this elevation consists of boulder-clay, whereas in two sand-pits it may be easily observed that preglacial layers form the inner part. A little farther on, when the alluvial grounds are reached again, one comes to the Galama-dams. They are found on the Morra, according to the above-named author a bottommoraine-lake. About a mile farther upward we again find diluvial soil, and on continuing our journey in the direction of Rijs we see, just before leaving Hemelumer-Oldephaert and Noordwolde, and entering the domain belonging to Gaasterland, in a meadow to the right of the road a large pit 8 metres deep. From this pit for some years boulder-clay has been dug in behalf of the brick-works of the Comp. WGaasterland’, at a short distance, on the other side of the road. As far as I know, these are the only brick-works in the Northern part of the Netherlands, where bricks are made of boulder-clay. The boulder-clay, which forms a bottom-moraine here and which must be found very deep in the earth, is coloured blue-grey. Only quite near the humus-layer it has become red-brown, under the influence 1) Van Cappette, Les Escarpements du ,Gaasterland” sur la céte meridionale de la Frise. Extrait du Bulletin de la Société Belge de géologie, de paléontologie et @hydrologie 1889. Vay Capprette, Bijdrage tot de kennis van Frieslands bodem. Il. Eenige mede- deelirgen betreffende de Gaasterlandsche kliffen. Tijdschrift v. h. Koninkl. Neder. Aardryksk. Genootschap. 1890. Van Cappette, Bijdrage tot de kennis van Frieslands bodem. IV. Eenige mede- deelingen over de diluviale heuvels in de gemeente Hemelumer-Oldephaert en Noord- wolde. Tijdschr. vy. h. Kon. Nederl. Aardrijksk. Genootschap. 1892. Van Cappete, Biydrage tot de kennis van Frieslands bodem. V. Karteering van *t diluvium van Gaasterland en Hemelumer-Oldephaert er: Noordwolde. Tijdschr. v. h. Kon. Neder]. Aardrijksk. Genootschap. 1895. : Van Cappette, Diluvialstudien im Siidwesten von Friesland. Verhandelingen der Koninkl. Akad. v. Wetensch. te Amsterdam. 1895. ( 141 ) of the weather. It contains comparatively few erratic-blocks. They often show very fine glacier-scratches and are mostly of average size. During the time when this opportunity of gathering erratic-blocks has presented itself, [ have several times visited, from Leeuwarden, this loam-pit. The result of these visits is that | brought home rather a large number of erratic-blocks (probably between 800 and 400). The sedimentary ones are still here at present; after studying them I intend to present them to the Geological Institute at Groningen. The others, whose number is small compared with that of the sedi- mentary stones, have already been given to this Institute. Though my collection is still small, it is large enough to confirm my opinion that our knowledge of our sedimentary erratic-blocks leaves much to be desired. I formed this opinion already after examining the erratic-blocks of Kloosterholt. *) In gathering erratic-blocks in the Gron. Hondsrug I had gradually come to the conclusion that our sedimentary ones almost exclusively originated from Silurian layers, and that the latter must have shown much resemblance to those of the Russian Baltic-sea provinces, perhaps ave still to be found there. On getting acquainted with the erratic- blocks in the boulder-clay of Kloosterholt, however, I could not but see very soon that at any rate this rule does not hold good in all cases. In this place I often found pieces of older and younger forma- tions, while corresponding stones occur as firm rocks in Sweden and Denmark. The very same phenomena, as I hope I shall indicate, are seen in the erratic-blocks of Hemelum. Besides Silurian formations, others, both older and younger, are numerously represented. At the same time all of them show almost exclusively a West-baltic character. We should then see the remarkable phenomenon that at Groningen, which is situated between Kloosterholt and Rijs, erratic-blocks greatly differ from those of the two places mentioned. Gradually, however, I am beginning to doubt whether my opinion about the character of the erratic-blocks in the Groningen Hondsrug should be the right one. In the years when I used to gather there, digging was atmost entirely confined to the upper layers, so the chances are, that deeper parts contain other kinds of erratic-blocks. A few facts seem to indicate this. First of all : while a deep cave was being dug under the brewery called Barbarossa, at Helpman, big blocks of Saltholmlime with Terebratula lens Nilss made their 1) Vay Carxer. Ueber eine Sammlung von Geschieben von Kloosterholt. Zeitschr. d. Deutsch. Geol. Gesellsch. Jahrgang 1898 p. 234. Bonnema, De sedimentaire zwerfblokken van Kloosterholt. Versl. v. d. Koninkl. Akad. van Wetensch. te Amsterdam 1898 pag. 448. 10 Proceedings Royal Acad. Amsterdam. Vol. V. ( 142 ) appearance, Some pieces of this material are still to be seen in the Geological Institute at Groningen, Secondly: van Cannen '), When the ramparts near one of the gules (Boteringepoort), which ramparts had certainly been made of the boulder-clay from the very deep ditches in that neighbourhood, were dug off, — found some erratic-blocks consisting of kinds of stone such as T never found afterward, and which do not oeeur in the Russian Baltie-Sea provinces, ia. slate with graptolites, Faxe-lime and sandy glauconite lime-stone with Terebratula lens Nilss. Deeper cuts made into the Hondsrug may afterwards give us an opportunity of learning whether my original opinion was entirely right, or is the true one only as far as the outer layers are concerned. I should now like to tell something about the chief Cambrian pieces that are found in my collection. | am going to treat only of those stones whose age may be more or less precisely determined. IT. Lower-Cambrian Stones. lL. Scolithus-sandstone. Eleven stones consisting of this material are found in my collection. Nine of them are typical grey, quartz- iferous Scolithus-sandstone, showing a peculiar, fatty lustre on the side where they were broken off. No layers are visible as long as the stone is not changed by the influence of the weather. Only if this takes place, the layers become more or less visible. In one stone they are rather distinct and turn upward (perhaps downward) near the “scolithus.”. Two other stones, one of which is blue-grey, whilst the other moreover contains red parts, are clearly divided into layers and contain much finer tubes than are found in the typical stone. In the regions from which our erratic-blocks come, Scolithus-sand- stone was first seen as firm rock in the isle of Runé near Oscars- hamm, where according to Torr. *) it was discovered by Dr. Houm- strOM. Afterwards it was also met with as such by Narnorst *), in the isle of Furén, not far from Runé. I was wrong when, in treating of the Kloosterholt erratie-blocks, I told that Scolithus-sandstone as firm rock is found in Sweden, in the neighbourhood of Lund and Kalmar. The same mistake was 1) Van Catker, Beitriige zur Kenntniss des Groninger Diluviums. Zeitsch. d. deutsch geo]. Gesellsch. Jahrg. 1884 pag. 718 and 727. *) Torett, Petrificata Suecana formationis cambricae. Lunds Univ. Arsskrift. Tom. VI 1869 pag. 12. *) Natnorst, Geol. Féreningens i Stockholm Férhandlingar 1879. Bd IV, pag. 293.. 1 made by ScHRoEDER VAN DER Kok *) and by Srevsiorr *). The latter and | probably came to make it unter the influence of what was told by Ropmer*) with regard to the origin of this kind of erratic- blocks. With Scnrorper v. bp. Kok this is certainly the case, as appears from the note at the bottom of the page. As to their being: found at Hardeberga in the neighbourhood of Lund, Rormpr seems to have forgotten the fact that Torenn *), though he at first communicated that the Hardeberga sandstone contained worm-shaped bodies probably belonging to Scolithuslinearis Hail, afterwards makes mention of a new kind, viz. Scolithuserrans Torrent *). The latter are distinguished for being mostly curbed and running through the stone in various directions. Rormmer’s information that Torin describes Scolithuslinearis from an erratie-block found near Lund, and that according to Nitsson Scolithus-sandstone occurs near Calmar (as firm roel), must be attri- buted to an error. If my imperfect acquaintance with the Swedish language does not deceive me, ToreLi") writes that the place where the pictured stone (an erratic-block) was found, cannot be indicated for sure, but that Ninsson thinks he remembers that it was found near Calmar. In the Northern part of the Netherlands erratic-blocks of Scolithus- sandstone are rather common. In Frisia were found, besides the stone treated of above, one in the Roode klif (Red Cliff)7), one in the Mirnsercliff*) and one at Warns (see number 3). Among the erratic-blocks of the Gron. Hondsrug *) only one piece was found up to this time, whereas I formerly described already two pieces from Kloosterholt '*) and afterwards gathered more of them there. In the 1) Scuroever van peR Kork, Biydrage tot de kennis der verspreiding onzer kris- talline zwervelingen. Dissertatie pag. 50. *) Sreustorr, Sedimentiirgeschiebe von Neubrandenburg. Archiv des Vereins der Freunde der Naturgeschichte in Mecklenburg. Jahrg. 45 pag. 162. 5) Roemer, Lethaea erratica pag. 23. ‘) Torett, Bidrag till Sparagmitetagens geognosi och paleontologi. Lunds Univ. Arsskrift. Tom. IV. pag. 35. 5) Torett, Petrif. Suec. format. cambric. pag. 12. 5) Torett, Bidsag till Sparagmitetagens geogn. och paleontol. pag. 29. 1) Van Cappette, Bijdrage tot de kennis van Frieslands bodem. Il pag. 12. 5) Van Cappente, Les Escarpements du ,Gaasterland”, pag. 236. ‘) Van Catker, Ueber das Vorkommen cambrischer und untersilurischer Geschiebe bei Groningen. Zeilschr. d, deutsch. geol. Gesellsch. Bd XLII pag. 793. 1) Van Catxer, Ueber eine Sammlung yon Geschieben yon Kloosterholt, pag. 235. Boynema, De sedim. zwerfblokken van Kloosterholt, pag. 449. 1O* ( 144 ) province of Drente van CaLker') mentions Buinen, Steenbergen and Zeegse as places where he came across these stones, whereas | myself found some at Odoorn. 2. Grey sandstone with interlaced coloured layers. A small piece of quartziferous sandstone, 7 centimetres long, is almost entirely grey-coloured. Two systems of coloured layers, varying from red to violet, interlacing under angles of about 30 degrees, are also found. The layers of each system separately ran parallel to ach other. Surfaces of deposit do not ocenr and the size of the grains of sand is everywhere the same, so that it is impossible to examine which layer-system runs parallel to them. This sandstone was made mention of for the first time by Nar- Horst *), who found erratic-blocks consisting of it in Jungfrun in the Kalmarsund. With Dames*) he found the same kind of stone in Oeland, a few vears after. Later on the latter writer ‘) could tell about this kind of erratic-block occurring in diluvial layers in the neighbourhood of Berlin. As one of the pieces found there contains Scolithus-tubes, he could also draw the conclusion that their age is the same as that of the above mentioned Scolithus-sandstone. This conclusion is confirmed by means of a piece of Scolithus-sandstone that I found at Warns a short time ago. Through the grey piece of sandstone run on one side a few violet-coloured layers, which are intersecting the Scolithus- tubes under an angle of 60 degrees, while the latter always stand perpendicularly on the surfaces of deposit, which are not seen here. That this stone also occurs in the Dutch diluvium, was already shown by van Canker *); he proves that it is found in the erratie- blocks of the Gron. Hondsrug. IT. Mid-Cambrian Stones. 3. Limesandstone with Paradoxides-remains. In my collection I have also a piece of grey, fine-grained sand- stone with a large quantity of calcium-carbonate as binding-material. 1) Van Catker, Ueber ein Vorkommen yon Kantengeschieben und von Hyolithus- und Scolithus-Sandstein in Holland. Zeitschr. d. deutsch. geol. Gese!lsch. Jahrg. 1890 pag. 583. *) Naruorst, Geol. Féreningens i Stockholm Férhandlingar 1879. Bd IV pag. 293. 5) Dames, Geol. Reisenotizen aus Schweden. Zeitschrift der deutsch. geol. Gesell- schaft. Jahrg. 1881 pag. 417. 4) Dames, Zeitschr. d. deutsch. geol. Gesellsch. Jahrg. 1890. Bd XLIIL pag. 777. °) Van Catker, Zeitschr. der deutsch. geoi. Gesellsch. Jahrg. 1891. Bd XLII pag. 793, ( 145 } Through the stone run intersecting passages of the same mineral. Here and there are small grains of glauconite and pyrites-crystals. Besides many Paradoxides-fragments arranged in layers, my stone contains remains of horn-shelled Brachiopoda. The former are cream- coloured and do not allow of being further defined. Among the latter ave easily found valves of Acrotele granulata Linn. About this stone I have up to this time nowhere found any infor- mation. It is probably of the same age with the layers of Paradox- ides Tessini Brongn., or it is a little older than these are. 4. Gravel-stone with Paradoxides Tessini Brongn. a. It is a piece of fine-grained, hard sand-stone, yellow-grey inside and light grey nearer the surface, whilst the surface itself is brown in some places. With a magnifying-glass some grains of glauconite and a few mica-scales may be distinguished in it. With muriatic acid applied to it, there is no effervescence; conse- quently it does not contain calcium-carbonate. There are no layers. The chief remnant occurring in this erratie-block is a mid-shell, a little more than 1 centimetre long, of a Paradoxides, which mid-shell is visible for the greater part. The cream-coloured shell is still almost entirely present. That this remnant originates from Paradoxides Tessini 3ronen., could be easily determined by means of the description and the pictures which Liynarsson ') gave us of this kind. Prof. Moprre, to whom I had the honour of showing this erratic-block, when visit- ing Lund, thought my determination right. The eglabella increases in breadth towards the front; quite near the front it is broadest. The front-edge is rounded off. On each side the elabella has two side-furrows, which in the middle run into those of the other side, which is also the case with Paradoxides Oelandicus. Of smaller furrows, which according to LINNarsson are sometimes found in the latter, nothing is to be seen here. The edge before the elabella is very narrow in the middle and broadens towards the ends. This is characteristic of Paradoxides Tessini, whilst with Paradoxides Oelandicus the breadth of the edge before the glabella is rather con- siderable, and remains about the same towards the sides. We also find here a piece of a thorax-ring of a kind of Paradoxides, in which it may be seen that the pleurae first run straightway towards the outside and then turn to the back, forming an almost right angle. This also oceurs with Paradoxides Tessini, whereas with Paradoxides Oelandicus this turning to the back takes place gradually. 1) Liyyarsson, Om Faunan i Kalken med Conocoryphe exsulans (,Coronatus kalken”). Sveriges geologiska undersdkning. Series C. NY 35 pag. 6. Scene l fig 1—4, ( 146 ) Finally are found in this erratic-block a few small valves of horn- shelled Brachiopoda, among which is one of Lingula or Lingulella. b. Besides the piece treated of just now [| found a piece of sand- stone with Paradoxides-remains, which shows no effervescence when hydrochloric acid is applied to it, and which consequently is gravel-stone. It is a flat piece, consisting of two parts of a different nature. One of them is formed by sandstone and does not present many layers. This sandstone greatly resembles the material of which consists the erratic-block treated of under @, but is a little bluish. Some small mica-scales and glauconite-grains are also present here. The other part shows many more layers and has a dark bluish-grey colour. Some- times the layers are as thin as paper, so that the material becomes slate-like. Just as in the other piece of stone, the Paradoxides-remains are cream-coloured here. They are, however, too fragmentary to enable us to draw the conclusion that they originate from Paradoxides Tessini. As up to this time, however, only sandstone with this kind of Para- doxides has been found in diluvial grounds, and the petrographical nature of one part of them bears a great resemblance to that of the previous piece, I think I may suppose this much, and I venture to range this erratic-block under this head. I think that both pieces originate from a layer-complex of gravel- stone with Paradoxides Tessini-remains, which complex consisted both of slate-like blue-grey parts and of thicker light-coloured layers. The last-mentioned erratic-block may originate from the former, whereas the one treated of under @ would be a piece of a thicker layer. If my supposition is not false, it may be easily explained from the difference in firmness and the difference in fitness for being trans- ported issuing from this, why in literature nothing is found about erratic-blocks that should bear resemblance to the last-mentioned piece, whilst two or three communications have been received about the finding of erratic-blocks that most probably are more like the piece treated of in the first place. The first communication we got from Rormer.*) It deals with a piece of gravel-stone that was found in a sand-pit of Nieder-Kunzendort near Freiberg in Silesia. It seems to have been more exposed to the influence of the weather than the erratic-block found by me, the writer mentioned speaking of a ferrugious outer crust, while round my piece such a erust begins to form itself. Probably I must also range among this kind a piece of sandstone 1) Roemer, Zeitschr. der deutsch. geol. Gesellschaft. Bd 9. Jahrg. 1857 pag. 511. ag (147 ) with Paradoxides Tessini-remains that was found in the collection of Groningen erratic-bloeks, given to the geological Institute at Lund by Mr. pe Sirrer, L. L. D., then burgomaster of Groningen. It was described by Luxperen*). I am sorry that we do not learn whether it is gravel-stone or lime-sandstone. I wrote to Prof. Mopmre, director of the Institute mentioned above, in order to ask after this, but he could not give me any information concerning the piece just then. I think, however, that it is gravel-stone, Lunpcren telling us that the colour is yerahvit”, while according to Rormer*) lime-sandstone with Paradoxides Tessini is dark grey. While in the previous case it has not yet been with certainty determined which kind of sandstone one has to deal with, Rawers’*) has announced another gravel-stone with Paradoxides-remains having been found. This erratic-block differs from the piece I described under a in the fossils being coloured brown by manganite-superoxide. However, I think this of littke importance, as it may be just as well a consequence of infiltration that oceurred in diluvial grounds or even before that time. Gravel-stone with Paradoxides Tessini has up to this time not been met with as firm rock. Probably it occurs as such, or did so in former times, in the neighbourhood of Oeland; for on the Western coast of this isle is found, in several places, lime-sandstone with the same kind of trilobites. IIT. Upper-Cambrian Stones. 5. Alum-slate with Agnostus pisiformis L. var. socialis Tullb. One time I was so fortunate as to find a piece of black slate, in Which are scattered the grey head- and tailshields, preserved in relief, of a kind of Agnostus. They have a length and a breadth of 3 millimetres at most. The head-shields are moderately vaulted. The dorsal furrows meet in front, and a tongue-shaped glabella is bounded by them. At the front-part of the glabella is on each side a lateral furrow. The two lateral furrows run into each other and in this way cut off a small part in front. At the foot of the elabella two small lobes are separated from the rest by means of two lateral furrows slanting backward. The central, largest part of the e¢labella shows 1) Lunparen, Geologiska Féreningens i Stockholm Férhandlingar. 1874. If N° 2 y Th pag. 44. *) Roemer, Lethaea erratica, pag. 29. 5) Rement, Zeitschr. der deutsch. geol. Gesellschaft. Bd 35, Jahrg, 1883 pag. 871. ( 148 ) in the midst a wedge-shaped elevation. The cheeks are in front separated by a furrow running from the front of the glabella to the edge-furrow. The tail-shields are much more vaulted. This is especially the case with the rhachis, which broadens towards the back and stretches nearly as far as the edge. Consequently, the lateral parts of the pygidium, which are already narrow, become even more so towards the back part. They are not separated by a furrow, as it is the case with those of the head-shields. The pygidia have at the back-edge on either side a litthe cog pointing backward. The rhachis of the pygidia is clearly divided into three parts. The back-part is the largest by far and is particularly swollen. The lateral furrows of one side do not meet those of the other, as they are separated by a wedge-shaped elevation passing on from the second part to the first and ending towards the back in a blunt point slanting upward. From the properties mentioned it may be easily seen why this kind of Agnostus was described by TULLBERG ') as Agnostus pisifor- mis LL. var. socialis. Pictures of it have been given by BréGGer *) and PompEckt *). Up to this time this erratic-block is the only piece of alum-slate with Agnostus pisiformis L. var. socialis that was found in our diluvial grounds. In Germany they also seem to be very rare. Only GorTscHE *) mentions such a piece from ScuvLav. This one also contains, however, remains of Olenus truncatus Briinn. As firm rock such alumeslate with this variety of trilobites occurs in Sweden (Oeland and Bornholm included), in different places, as I learned from Prof. Mosere, to whom I showed a piece of the erratic-block. Microbiology. — “Accumulation experiments with denitrifying bacteria’. By G. VAN Iverson Jr. (Communicated by Prof. M. W.. Bewerincr). The great signification of the denitrifving bacteria for the circulation of nitrogen in organic life and the important biochemisms to which they give rise, male the study of these organisms very attractive. 1) Tuttperc, Om Agnostus-arterna i de Kambriska aflagringarne vid Andrarum. Ds oo. Sveriges geologiska Undersékning. Ser. CG. N’ 42 pag. 2) Broéccer, Die Silurischen Etagen 2 und 3 im Kristianiagebiet und auf Eker. Pag. 56. Taf. 1. fig. 10 abe. 3) Pompeckt, Die Trilobiten-Fauna der Ost-und Westpreussischen Diluvialgeschiebe. Beitriige zur Naturkunde Preussens herausgegeben von der Physikalisch-Oekono- mischen Gesellschaft zu Kénigsberg. Pag. 15, Taf. IV, fig. 24a b. 4) Gorrscne, Die Sedimentiir-Geschiebe der Proyinz Schleswig-Holstein, pag. 11, ( 149 ) In the first place it was necessary to subject their distribution in nature and their isolation to an investigation, because the literature thereon offers but very deficient data. The best way to attain this object seemed to try whether the method of “accumulation” gave in this case, as in so many others, any definite result, and that for the following reasons. The character of this way of experimenting is the cause, that many biological properties of the species there by accumulated may be predicted ; it renders it possible, in a simple way, directly and with certainty to isolate from nature a determined species; this is of special interest inasmuch the cultures of most bacteria, by being kept in the laboratoria, change their character to such a degree as to become irrecognisable, so, that the descriptions, found in bacteriological literature, according as they are made after newly isolated or long kept material, may be wholly different ; it teaches us to recognise the sought- for species in the different varieties occurring in the material used for infection, as these varieties are bound to corresponding culture conditions; the identification and synonymy of the bacteria, which are always extremely difficult, even in case we possess good descriptions, made of freshly isolated cultures, are much facilitated by good “accumu- lation experiments”; these may, moreover, be controlled by anyone, and render the investigator independent from. material isolated by others. For the arrangement of my experiments [ have followed the examplé given by Dr. H. H. Gran’) of Bergen in his researches in the Bacteriological Laboratory at Delft on denitrifying sea bacteria. By exclusively using nitrate as source of nitrogen in the culture liquid, which was contained in a cotton-plugged flask, so that the air could freely enter, he succeeded to restrict considerably the number of developing species of bacteria, when taking fresh sea-water for infection, bringing the denitrifying species to vigorous growth. He furthermore selected, as source of carbon the caleiumsalts of organic acids, by which the prejudicial alkaline reaction, which appears in bouillon in consequence of the decomposition of the alkalinitrate, was avoided. Mostly calciummalate was used, which is avery good bacterial food, and has moreover the advantage of solving only to 0,8 °/, at 25° C., so that it can be added to an excess, whence, as the salt is oxidised, a new quantity is solved. ') Studien iiber Meereshacterién 1, Bergens Museums Aarbog 1901 N°, 10, ( 150 ) After 2 or 3 suecessive inoculations in the same liquid a constant bacterial mixture was obtained. I tried to apply these principles to the isolation of denitrifying land-baeteria, and so-doing | succeeded indeed, when using caleium- tartrate as source of carbon, to accumulate Bacillus vulpinus, hereafter to be discussed. It proved however to be a fundamental improvement wholly or partly to exelude the access of air as thereby the growth of the denitrifying bacteria is not in the least impeded, whilst a number of other aerobic bacteria are very much hindered in their development. Of the numerous methods of culture under exclusion of air Ihave followed the simplest, namely the “bottle method”, long since in use in the Bacteriological Laboratory at Delft for the examination of the sulphate reduction by microbes and the lactic-acid fermen- tation. For my experiments this method proved perfectly adapted, as the quantity of air which finds access, can thereby easily be regulated. An ordinary, narrow-mouthed stoppered bottle, with an exactly fitting stop, is quite or partly filled with the culture liquid, and after sterilising or not, according to circumstances, the bottle is placed in the thermostat for culture. 1. Historical. The reduction of nitrates by bacteria constantly begins with the formation of nitrite. This may be further converted in five different ways, Viz. : 1st. It may be reduced to ammonia. 24. Tt may be converted into unknown, nonvolatile nitrogen compounds, 3°¢. If in the liquid acid is formed simultaneously, it may give rise to the development of nitrogen-oxygen compounds. 4%. Tt may be decomposed in alkaline solution under formation of nitrogen-oxygen compounds. 5%, The nitrite may, in alkaline solutions, give rise to the devel- opment of nitrogen without the production of nitrogen-oxygen com- pounds. This is denitrification proper, of which here is only question. Already in 1814 Davy’) states that during putrefaction of animal matter nitrogen as such is freed. “Here it is again seen,” says in 1860 G. J. Mcnper?), from whom I borrow this particular, “if one wishes 4) Elemente der Agriculturchemie, Berlin 1814, S. 309. 2) De Scheikunde der Bouwbare Aarde, 1860, dl. 3, blz. 58. ( 454 ) truly to give the cuique suum in this part of science, one often musi retrograde half a century.” Not before 1856 the problem was again taken into research. In that year Reiser’) pointed out, that at the putrefaction of dung and flesh free nitrogen is produced. Later investigators have not been able to observe free nitrogen under these circumstances, i asmuch as no nitrate or nitrite are present, but the putrefaction of albuminous matter as such has still remained an open question from this point of view. It was Priovzn*), who in 1857, for the first time, with certainty stated the disappearance of nitrate during the putrefaction of animal matter. BOUSSINGAULT *) observed in 1858 the disappearance of salt-peter in the soil. He ascribed it “& une cause purement accidentelle, a une action réductrice, exercée par de la matiere végetale morte”. From the year 1875 date very interesting observations of SCHLOESING *) on nitrification. By studying the influence of oxygen on this process, he was led to the examination of denitrification. He found that nitri- fication in the soil was still very active, when it was held in a current of gas, which contained but 1,5 °/, oxygen. If he worked in a current of pure nitrogen, there not only occurred no nitrification, but even the nitrate, originally in the soil, disappeared entirely. He furthermore proved that at this decomposition nitrogen is formed. Experiments of Pasrpur and the well known investigation of Scutorsine and Ménz on nitrification, induced Garon and Dupwrir *) to ascribe denitrification to the action of micro-organisms. In 1882 they communicated their first results and these put the baeterial nature of the process out of all doubt. Their elaborate and excellent researches on this subject were published in 1886 °). Our compatriots Gintay and Aperrson *) isolated, for the first time, in 1892 a denitrifying ferment, and the prescription given by them for the artificial culture liquid has been followed by various later investigators. The attention of bacteriologists was again fixed on these ferments 1) Expéviences sur la putréfaction et sur la formation des fumiers. G. R. 1856, T. 42, p. 53. *) Remarques de M. Penouze. G. R. 1857, T. 44, p. 119. 5) Nouvelles observations sur le développement des hélianthus soumis al action du salpétre donné comme engrais G.R. 1858, T. 47, p. SO7. +) Etude sur Ja nitrification dans les sols, G.R. 1873, T. 77, p. 203. *) Sur la fermentation des nitrates, G.R. 1882, T. 95, p. 644. ®) Recherches sur la réduction des nitrates par les infiniments petits. Nancy. 1S86. 7) Recherches sur un mode de dénitrification et sur le schizomycéte qui la produit. Arch. Neerl. T. 25, 1892, p. 341. ( 152 ) by interesting agricultural experiments of P. Waayer ') in 1895, whieh seemed to point outa danger produced by these bacteria for agriculture. His experiments gave direct cause to the research of Burnt and Srerzer®), who, in the same year, elaborately described two denitri- fying bacteria, From that time this group has been laboriously studied and at present a number of twenty denitrifying species have been deseribed *). To these 1 for my own part might add some ten species more, but of these T will only diseuss those, for which T can point out an accumulation experiment, which gives a constant result. 2. General considerations. The hitherto isolated denitrifying bacteria are all aerobic. In liquids containing nitrate or nitrite, they can, however, grow vigor- ously with a very slight or without access of air, so that in this case they behave like anaerobic bacteria. They then transfer the oxygen of the nitrate or the nitrite to the organie compounds present in the culture liquid. Thence nitrogen is freed and the metals of the salts pass into carbonates or bi-carbonates, which process may be represented by the formulae: 5C..+4KNO, + 2 H,O = 4 KHCO, + 2N, + CO, 3C..+4KNO, + H,O = 2 KHCO, + K,CO, + 2N, The correctness of this representation has been proved by the observations of Gayon and Deprerir, Givray and ApErson, PFEIFFER and Lewuermaxx, Ampona and Unpiant, and also by my own researches. We see from this, that in a liquid, simultaneously with the nitrate, the rate of organie substances decreases, and accordingly also the permaganate number. From a practical point of view this must necessarily be of signification for the explanation of the processes on, which is based the biological purification of sewage and water *). My experiments have furthermore convinced me that denitrification is inseparably connected with the growth, for which traces of free oxygen are always necessary. 1) Die geringe Ausniitzung des Stallmiststickstofls und ihre Ursachen, Landw. Presse, 1895, S. 92. 2) Ueber denitrifizierende Bakterien. Centrbl. f. Bakt. Abt. Il, Bd. 1, 1895, S$. 257. 3) O. Levwermany. Kritische Stadién iiber Denitrifikationsvorgiinge. Jena. 1900, C. Horucu. Vergleichende Untersuchungen jiber die Denitrifikationsbakt. ete. Centrbl. f. Bakt., Abt. Il, Bd. 7, 1902, S. 245. 4) Dr. Jenny Weverman. Biologische stelsels tot reiniging van rioolvocht, enz. Vragen des Tijds. Febr. 1901, Sep., blz. 38, In 1897 Wertssenperc ') pronounced the hypothesis, that, at the redue- tion of nitrate to free nitrogen, nitrite constantly appears as inter- phase. I ean perfectly well share this view, and that for the following reasons: Ist. All denitrifying species which I have studied in the course of this research could, in as much as they produced free nitrogen from nitrate, do the same from nitrite. 2nd. Like Burre and Srurzmr (l.c.) I have been able to isolate a species, which does convert nitrite into free nitrogen, but leaves nitrate intact, so that from a mixture of nitrite with a little nitrate, all the nitrite is removed by this bacterium, whilst the nitrate remains unchanged. Here I must however observe, that at the conversion of nitrate into free nitrogen, not always nitrite can be detected in the culture. This fact has already been stated by Sewerin*) and KtNNeMANN *). It is however by no means in contradiction with WuisseNBERG’s hypothesis, for if the course of the second process: decomposition of nitrite, is quicker, or as quick as the first: reduction of nitrate, the nitrite-phase is no more to be demonstrated. K@NNEMANN observed this fact in a variety of 2. stutzer’, which observation I have been able to confirm ; however, in my opinion, the cultural conditions played in this experiment a much more important part than the character of the variety. In bouillon with 0,1 °/, KNO,, I could often point out no nitrite, whilst here a strong development of gas took place. On the other hand, I obtained with 4 and 5 °/, KNO, only a slight gas development, but a strong reaction of nitrite. For the investigation of a colony on its denitrifying power, sterile test-tubes were filled with 10 €@ 15 Cem. of bouillon, as well with 0,1 °/, KNO, as with 0,1 °/, KNO, and then inoculated. Denitrifying bacteria grow therein sufficiently, after 24 hours to produce a distinct turbidity, whilst, at the surface they form a scum-layer. Sometimes the seum is wanting, but is produced at shaking the test-tube. Besides were used solutions of calcium -salts of organic acids, decocts of pease-leaves with 2°/, cane-sugar, and decocts of potatoes, likewise with O71 °/, KNO, or KNO,. In this case a control experiment was made to decide, whether without addition of nitrate or nitrite, these solutions might cause 1) Studien tiber Denitrification. Arch. f. Hygiene. 1897, Bd. 30, S. 274. *) Zur Frage tiber die Zersetzung von Salpetersauren Salzen durch Bakterien. Centrbl. f. Bakt. Abt. Il, 1897, Bd. 3, S. 504. 5) Ueber denitrifizierende Mikro-organismen. Landw. Versuchs-Stat. 1898, Bd, 50, S. 65. ( 154 ) development of gas, which proved never to be the case with denitri- fying bacteria. In order to obtain perfectly convincing results, to the said culture liquids 10° tion, at about 80° C., some of the culture had been suspended, it , gelatin often was added and, when in the boiled solu- was poured into a test-tube and solidified. The developing gas then remains as bubbles, nearly at the place of its origin, in the gelatin. This method (“tube-culture’) produces a sharp reaction on denitri- fication, especially when controlled by a parallel experiment, using the same culture gelatin, without nitrate or nitrite. This principle may also be used for a rongh computation of the number of denitrifving germs in any material. So it was proved that cirea 2000 of these organisms occur in 1 gr. of garden soil, and cirea LOO in 1 gr. of canal water. In these experiments the potassium-salts may be replaced by natrium- or magnesium-salts; calcium-nitrate, on the other hand, prevents even in dilute solution the growth of many bacteria. Before passing to the deseription of the different accumulation experiments, I have to make a general remark about their arrangement. Which species finally becomes most common in the used eulture liquid depends on many circumstances, difficult to control, in parti- cular on the mutual numerical proportion of the individuals and the nature of the different species in the material originally used for the infection, and likewise on the condition of the microbes themselves in consequence of previous circumstances. This explains why, when using different materials of infection for the accumulation of one and the same species, it is sometimes necessary to modify the cultural conditions in accordance with the nature of that material. I insist on this circumstance in particular to explain the different accumulation experiments described under JZ. stutzeri, on the one hand from water by using tartrate, on the other hand from soil by using malate. 3. Accumulation of Bacterium stutzeri, LEHMANN and NEUMANN °). . ? This interesting bacterium was isolated in 1895 from straw by Beret and Srvrzer (l.c.), whilst in 1892 Brat’) had already shown the presence of denitrifying bacteria thereon. 1) Lenwann u. Neumann. Bakteriologie. Miinchen 1896, S. 237. 2) De la présence dans la paille d’un ferment aérobie, réducteur des nitrates. C.R. 1892, T. 114, p. 681. ( 155 ) In 1898 Kiinnemann (Le.) isolated the same species from soil and a variety from horse-dung and straw. By accumulation experiments, logically carried out, | have succeeded in obtaining this bacillus from soil, canalwater, sewage-water and horse-dung. The following experiment always led practically to a pure culture from canalwater : A bottle of about 200 Cem. is partly filled with fresh canalwater with addition of 2"/, calcium-tartrate, 2°/, KNO, and 0,05°/, KAPO, *), computed after the whole capacity. Then the bottle is filled up to the neck with canalwater and the stop is loosely put in, so that a litthke water is pressed from the bottle. In this way it is filled Without a single bubble of air and, after shaking, put ina thermostat of 25° of 28°. The calcium-tartrate solves at this temperature for only 1°/,, so that this salt remains for a great part at the bottom. Commonly already after one day a feeble production of gas is to be observed, issuing from the non-solved calcium-tartrate at this bottom. The process gets into full course after three or four, sometimes only after five days. So much gas thereby is produced that a coarse, slimy scum originates at the surface and a great quantity of the liquid is pressed out of the bottle. The gas containing only nitrogen and carbondioxyd, the culture remains anaerobic. The liquid grows turbid by the growth of the bacteria and the fine, cristalline calcium-tartrate changes into coarsely granular ealeium-carbonate. After a week, in consequence of the scum formation, the bottle is nearly half void, and after about 12 days the reaction is at an end, in as much, corresponding with the chosen quantity of tartrate, all nitrate has disappeared. If a vigorously growing culture is sown on broth gelatin, a mixture is obtained of colonies of various different species, from which B. stutzeri ean easily be isolated, if we are once acquainted with it. From such a bottle some drops are inoculated into a bottle of about 50 cem. capacity *), which, after sterilisation, is filled for */ with the following sterile culture liquid: Tap-water, 2°/, calcium-tartrate, 2°/, KNO, and 0,05 °/, K,HPO,. After inoculation the bottle is quite filled up with the same liquid in the above described way, and after the lapse of two or three days, the same phenomena appear as in the first bottle. If now, once more, of this transport a plate culture on broth 4 gelatin is made, the great diminution in the number of species is 1) The capacity of the bottle is not indifferent, surprising. All liquefying colonies, and most fluorescents have disap- peared, whereas, among two common and some less frequently occurring species, B. stutzeri developes in great numbers and is easily recognised by the characteristic properties of its colonies. By repeating the said transport this bacterium may still be more multiplied, so that, after three or four successive inoculations, practic- ally a pure culture of this species is obtained, From soil of the garden of the Bacteriological Laboratory | regularly obtained the same bacterium, in the course of the winter of 1901-—2 by applying the “bottle method” with this liquid: calcium-malate, 1 °/, KNO, and 0,05 °/, KLHPO,. In the spring, however, though there were constantly some colonies Tap-water, 2 ° 0 of the species, the number of its germs proved so small that they were replaced by other denitrifving bacteria, particularly 2B. denitro- Juorescens, of which more presently. A detailed description of 4. stutzer? is given by Berri and Srerzer (lhe), as well as Kixnemann (1. ¢.). It will therefore be sufficient here to give the chief characteristics by which this species is direetly, recognised. The bacterium is a short, thick rodlet with a peculiar vibrio-like motion. The colonies on gelatin are extremely characteristic (see Plate). After three or four days they have a diameter of about 0.5 mm. and after a week they attain 1 to 1.5 mm. When magnified they then resemble a rosette, or have an irregularly folded or crispate, greyish surface. The peculiar structure appears only distinctly, when the glass-dish which contains the plate culture, is reversed and the colony is seen through the bottom with about a 30-fold magnification. The most frequent shapes are represented in figures 1—4. But it may happen that the crispate character becomes still more conspicuous and then the image is as in fig. 5. Commonly it seems as if regularly arranged smaller colonies are situated in the larger ones, which may often be observed till in the outer border, and points to a peculiar periodicity of the mucus secretion in the interior of the colony. In the colonies moreover a fine deposit is observed, and sometimes very distinct erystals, which may also be found in the gelatin around. All these characteristics are particularly marked when the cultures have been recently isolated, but they may in the course of time get lost or become indistinct. Another property however remains always quite distinct, i.e. the adhering to the gelatin. Young colonies can only be removed in one piece, and of the older always part remains behind. (uliay7/ 4) Very characteristic also is the growth of this bacterium on a sterilised slice of potato, where the curled and folded structure of the colonies is quite distinct, in consequence of the large dimensions they attain. The colour changes thereby into flesh-red. Old cultures grow soft in consequence of a dissolving process the slimy substance. The compounds whieh can provide the carbon and nitrogen nutrition of this species were determined by means of the auxano- graphic method +), this giving in a simple way a measure for the difference in assimilability of the nutritive substances. “With KNO, as source of nitrogen, a feeble growth was observed with glucose and maltose. Kalium-succinate, malate, malonate, citrate and calcium-tartrate, gave rise to a vigorous growth. No growth was obtained with cane sugur, milk sugar, mannite, galactose and oxalic acid. ~The auxanograms prove that tartrate belongs to the best assimil- able substances, which explains why its use in the accumulation experiment with canal water produces such good. results. With kalium-citrate as source of carbon, NH, Cl, KNO,, KNO,, asparagin, kalium-asparaginate and pepton, could serve as source of nitrogen. — B. stutzeri produces no invertin, does not split indican and ureum but it secretes diastase, although in very slight quantity. This latter fact explains the possibility of denitrifying by this species in solutions containing, besides the salts, only amylum and KNO,. In broth no indol and no sulphureted hydrogen are produced. es stutzert, produces much alkali; even the presence of glucose does not prevent the production of it in a plate of broth gelatin, Very remarkable is the behaviour of B. stutzerd towards free oxygen. “If the arrangement of the moving individuals under the influence of the oxygen of the air*) is examined in the glassroom, we find an accumulation in a. line at rather great distance from the meniscus. On the other hand,, growth is only observed *) in_ the meniscus itself. Hence, in this respect the bacterium behaves quite in accordance with the aerobic spirilla. : B. stutzeri is a very active denitrifying species; to broth could be added up to 4°/, KNO,, and up to 1°/, KNO,, without thereby preven- tine the development of gas. If in the before described way a “tube 1)| Bevertyex. L’anxdnographie ou la méthode de Vhydrodiffusion dans la géla- tine appliquée aux recherches microbiologiques, Arch. Neerl. 1889, T. 23) p. 367. *) Encetmayn, Zur Biologie der Schizomyceten, Botanische Zeitung 1882, Bd. 40,8. 320. ®) Bewercx, Ueber _,Atmungsfiguren beweglicher Bakterién. Ceuty.b!. f. Bakt. 1893, Bd. 14, S. 827. 1 Proceedings Royal Acad. Amsterdam. Vol. V. 158 ) culture’ in broth gelatin is made, with O,1°/, KNQO,, after two or three days the gas bubbles will appear over the whole length of the tube, and herein this species differs from 2. ru/pinus, where the gas bubbles originate at some distance from the meniscus only, I will finally make mention of an instructive experiment I performed with 2B. stutzer?. Some garden soil was mixed with tapwater with 0,05 °), KJHPO,, and a thin layer of this mixture in an ERLENMBYER- flask exposed to a temperature of 25°C. Under these circumstances the production of nitrate becomes very marked after two weeks. If now the whole content of the Ertenmeyer flask is poured into a stoppered bottle, which thereby is quite filled, whilst 2. stutzeri, is used for infection, soon a development of gas sets in and the nitrate disappears completely. Hence it follows that according as the air enters our culture liquid well or not, nitrification or denitrification may occur. This is quite in accordance with older experiences described by Scuiorsine (1. ¢.) in regard to the soil in general. 4. Accumulation of Bacillus denitrofluorescens n. sp. é ; / Sewerrn (1. ¢.) found in 1897 that B. pyocyaneus belongs to the denitrifying ferments. But the group of fluorescents proper was long fruitlessly examined as to their denitrifving power, first by LeHMANN and Neumann and afterwards by Weissensere (1. ¢.). In 1898 KENNEMANN isolated for the first time a denitrifying bacterium, which liquefied gelatin and fluoresced. Though in my experiments I often obtained fine cultures of a similar species, I did not succeed in finding a satisfactory accumulation experiment for it. On the other hand I found such an experiment for a non-liquefying fluorescent Bacillus, which I named &. denitro- Jluorescens. The culture liquid for the accumulation of this species is: Tap-water, 2 °/, calcium-citrate, 1°/, KNO, and 0,05 °/, K,HPO,. In a_ bottle of 50 Cem. capacity, 1 to 2 gr. fresh garden soil is put; it is then quite filled up with the culture liquid, in the way described under B. stutzeri. The culture is made at 25° C. When sowing on broth gelatin the 2»¢ or 3" transport, successively kept in the same culture medium, I always obtained cultures containing almost exclusively colonies of that species. In horse-dung, canal water and sewage water, I also observed this bacterium, but it is with more certainty to be isolated from soil. In exterior appearance of the colony this species differs in no respect from one of the most common fluorescents, characterised by — (HSE) lacking, on the culture gelatin, the smoothly spreading border. In young broth gelatin cultures, the pigment fluoresces blue, and after some time a white precipitate forms in the gelatin. Examined auxanographically, KNO, as source of nitrogen proved to cause a feeble growth with mannite, a vigorous one with kalium- malate, citrate, malonate, succinate and tarivate, as well as with glucose and levulose. On the other hand no growth is seen with cane-sugar maltose, milk-sugar, and raffinose. In broth, with 2°/, glucose, this bacterium, like all fluorescents, produces acid. Broth with 2°/, cane-sugar, becomes however strongly alkaline, which is observed also in all other fluorescent secreting no invertin. This bacterium neither produces diastase, nor can it hydrolise indican or ureum. In broth it forms no sulphureted hydrogen and no indol. In its behaviour towards free oxygen it likewise corresponds with the fluorescents, i.e. with the cover-glass culture in the humid room, both motion and growth cause accumulation in the meniscus. This makes the bacterium strongly contrast with . stutzert and B. vulpinus, whose motion figures show the spirillum type. As to the energy of its denitrifying power B. denitrofluorescens corresponds with 4. stutzeri. At the “tube experiment” with broth gelatin with O,1°/, KNO,, the bubbles form over the whole length of the tube, quite in the same way as with B. stutzer?. 5. Accumulation of Bacillus vulpinus n. sp. Already in my introductory observations I remarked, that an accumulation experiment with full access of air, when using tartrate and nitrate, produced this species, but the accumulation obtained in this way was still very imperfect. By cultivating under partly exclusion of air, I succeeded in improving the experiment very much. I obtained this result by enclosing in the culture bottle with the liquid a determined volume of air, and reinoculating from bottle to bottle under the same conditions three or more times. It is true that thereby not all other species are totally removed, but this is no obstacle to the recognition of L. vulpinizs, whose colonies are extremely charac- teristic, possessing a quite unique brown-red pigment. The experiment is as follows: Into a bottle of 50 Cem. 1 to 2 grams of fresh garden soil is put, and further it is filled up with the following culture liquid, whilst leaving on air bubble of 2 Cem: Tap-water, 2°’, Calcium-tartrate, Oster / NO. and 0:0b:/, K, HRO,. i Here likewise the culture is effected at 25°. With observation of the said proportion and operating as deseribed under 2. stutzeri, the different varieties of B. vulpinus can also be obtained from canal water. The denitrification sets in very slowly and the development of gas gets not by far the intensity perceived in the preceding species. Here, too, by the complete disappearance of all liquefying bacteria already at the first transport, the isolation of the wished, for species is much facilitated. Although at sowing the crude cultures on broth gelatin. some 2. vulpinus colonies may already be pereeived, they, multiply so much in the transports, that plates therewith, prepared, appear, so to say, quite covered with the large, flatly spread, brane parent, fox-coloured colonies of this species. isl If for the accumulation other organic salts, than tartrate are used, or a higher rate of nitrate Bhan 0.2°/,, not a single colony of D. vulpinus is detected, though it was certainly present in, the infe¢tion material as if is universally, pai in the soil. dio By men growth the colonies strongly remind, of the flatly spread variety of 2. jluorescens non liquefaciens, but, of fluorescence nothing is seen. In shape and motility, the bacterium corresponds with B. stutzert. one An interesting property of B.vulpinus is, that the: brown,pigment. only develops under the influence of light. . If simultaneously. two cultures of this species are made on broth gelatin, and one, wrapped in black paper, is put in the dark, and the otherin the light, for the rest in equal conditions, a great difference is perceptible. This becomes more obvious still, when making, reinoculations,or transports of either culture, likewise keeping these respectively in the dark and the light. So-doing a perfectly colourless culture can. be. obtained, but if this is again inoculated in the light, the brown colour returns; The pigment formation only takes place at growth, so, that colonies, full-grown in the dark do not colour when exposed to light... . B. vulpinus belongs to the group of real chromophores *), i.e. the. pigment is bound to the bacterial body, and, the behaviour towards, light is, in my opinion, another indication that. in, this. group. the pigment has a biological function. (BOK The auxanographic examination proved, that with nitrate for, nines nutrition, a feeble growth is obtained. with kalium-malonate,| a vigorous one with levulose, glucose, maltose, kalinm-citrate, succinate ') See Beverwex, La, biologie d'une _bactérie. pigmentaire. Arch. Néerl, 1892,) T, 35..p. 22s. 4 OWS 10 acetate and tartrate, whereas cane-sugar, milk-sugar, mannite and raffinose produce no growth at all. Ammonium-chloride may also serve as source of nitrogen, when using tartrate for carbon nutrition. Pepton, asparagin, and kalium-asparaginate may simultaneously serve as © and N nutriment. The bacterium seeretes neither invertin nor diastase and does not split indican or ureum. In broth it produces no sulphureted hydrogen but a little indol. In the “tube experiment” in broth gelatin with O,1 °/, KNO,, bubbles of nitrogen are exclusively seen to form at a little distance from the meniscus, and moreover, the culture of this species not succeeding in a bottle wholly filled with a culture liquid containing nitrate, we must needs conclude, that 2. vu/pinus wants considerable quantities of oxygen for the denitrification. As regards the other species, which form gas bubbles also in the depth of the tube, I have come to the conviction that they too, want traces of free oxygen to this end. Notwithstanding this different behaviour towards free oxygen, the motion figure, like that of b. stutzeri, shows the spirillum type. By modifying the nutrient liquids and temperatures I have succeeded, as observed above, in accumulating various other denitrifying bacteria, beside those described. Thus I obtained, at 37° C. with calcium-citrate and 0,2°/, KNO,, under exclusion of air, and using garden soil for material of infection, the spirillum-like 5. mdigoferus Voaus*), which denitrifies only feebly, but is interesting by its indigo-like pigment. When using sewage water, | obtained a strongly denitrifying, liquefying, blue pigment bacterium, not yet described. Of all these experiments however, the result is not constant enough to be inserted here. 6. Summary and conclusions. 1st. The fundamental principle of my accumulation experiments was partly or completely to prevent the access of air. By this means I have succeeded, by cultivating in solutions of organie salts and nitrate, only by repeated transports in the same liquid, in bringing many denitrifying bacteria to a more or less perfectly pure culture. 1) Cuagssen. Ueber einen indigoblauen Farbstof erzeugenden Bacillus aus Wasser. Centrbl. f. Bakt. 1890, Bd. 7, S. 13. Voces. Ueber einige im Wasser vorkommende Pigmentbacterién, Centrbl. f. Bakt, 1893, Bd. 14, S. 301. Of these experiments three always gave constant results, and pro- duced respectively 2. studzeré Neumann and Leamany, 3B. denitro- fluorescens Nn. Sp). and 2. vulpinus Nn. sp. zed, 2. stutzeri deserves attention on account of the unique strueture of its colonies, as seen in Fig. 1—5 on our Plate. 3°. B. denitrojluorescens is the first example of a denitrifying, non liquefying fluorescent. 40 BD. vulpinus is a chromophorous pigment bacterium, whose pigment only forms at growth in the light. 5th. B. stutzeri and B. rulpinus behave towards free oxygen like aerobie spirilla, 2. denitrejluorescens behaves like an ordinary aerobic bacterium, 6. Like in soil and dung, in which it had also been found by other experimentators, I have established the general distribution of denitrifying bacteria in canal and sewage water. 7. The denitrifying bacteria can, even with the slightest quantities of various organic substances, cause the disappearance of determined quantities of nitrate under development of free nitrogen. 8". In one and the same culture medium, where nitrification is produced during aeration, denitrification may be caused by exclusion of air, this holds good also in regard to the soil. At the end of this paper I want to express my sincere thanks to Professor Dr. M. W. Benerisck for his kind, invaluable guidance and efficacious assistance, afforded me in these researches. Delft, July 1902. Physics. — “An Hypothesis on the Nature of Solar Prominences.” By Prof. W. H. Juxius. The introduction of the principle of anomalous dispersion into solar physics makes it possible to form an idea of the Sun’s consti- tution from which necessarily follow ia. a great many peculiarities of prominences. which, until now, it has been impossible to deduet in a satisfactory manner from other physical laws. This I will show in the following pages. In my paper on “Solar Phenomena, etc.” read Febr. 24, 1900. I put forth the following hypothesis with respect to that part of the solar atmosphere, situated outside what is called the photosphere *): 1) W. H. Juuvs, Solar Phenomena, considered in connection with Anomalous Dispersion of Light, Proc. Roy. Acad. Amsterdam, II, p. 585. G. VAN ITERSON Jr. ,,Accumulation experiments with denitrifying bacteria.” Fig. Proceedings Royal Acad. Amsterdam. Vol. V. ae luk LU (165; ) “The various elements, whose presence in that atmosphere has been inferred from spectral observations, are much more largely diffused in it than has generally been assumed from the shape of the light phenomena; they may be present everywhere, up to great distances outside the photosphere, and yet be visible in few places only; their proper radiation contributes relatively little to their visibility (with perhaps a few exceptions); the distances, at which the characterisic light of those substances is thought to be seen beyond the Sun’s lamb, are mainly determined by their local differ- ences of density and their power to call forth anomalous dispersion.” How we were to imagine the condition of the matter inside the pho- iosphere, was not considered there. Our hypothesis on the origin of the light of the chromosphere was kept free from any special conceptions as to the nature of the photosphere. Only where the principle of anomalous dispersion was made use of also to explain spectral phenomena observed in sunspots '), we had to fall back upon A. Scumipt’s theory *), according to which the Sun is an unlimited gasball, so that the apparent surface of the photosphere should not be considered to be the real boundary of a body, but to correspond to a “eritical sphere”, defined by the property that its radius equals the radius of curvature of horizontal rays, passing through a point of its surface. At present, however, in working out the problem of the nature of the chromosphere and the prominences, we likewise will take asa starting poimt the first of the three Theses, in which Scammr sums up the main points of his theory. Accordingly, we suppose the Sun to be an unlimited mass of gas, in which the density and luminosity (not considering local irregularities) gradually diminish from the centre outward. But our conception of the properties and composition of this gaseous body can in a certain respect be much simpler than would be the case, if we accepted the whole of Scumupr’s theory. Indeed, Scumupr explains both the edge of the Sun’s disk by the laws of regular refraction (or ray-curving) in a stratified medium, and the prominences by refraction in “Schlieren” *); but in order to account for the fact that the light from the prominences as well as that from the chromosphere, instead of being white, shows a bright ime spectrum of varying appearance, he supposes the strongly radiat- iy elS casper SDs *) A, Scumpr, Die Strahlenbrechung auf der Sonne. Ein geometrischer Beitrag zur Sonnenphysik. Stuttgart 1891. 5) A. Scamipr, Erklarung der Sonnenprotuberanzen als Wirkungen der Re raction in einer hochverdiinnten Atmosphire der Sonne. Smrus XXII S. 97—109, Mai 1895, ( 164 ing mass of gases in its outer parts to be composed so as to emit almost exclusively hydrogen-, caleium-, helinmlight, whilst the radiations of sodium, magnesium, titanium, iron are supposed to originate in deeper layers, a.s.o.'). We, on the contrary, by the introduction of anomalous dispersion are permitted to suggest, that throughout the vaseous body, as well inside as outside the critical sphere, the various elements are altogether intrinsically mixed (granting that in the mixture the quantity of materials with greater specific gravity must grow with the depth). For wherever there are local differences of density in the mixture, caused by currents, whirls ete., the conditions for irregular ray-curving are present, and it is evident that specially those elements of the mixture, which possess an exceptionnally high dispersing power for certain waves of the transmitted light, will be able to reveal their presence even at great distances from the disk, while other substances, though also present at the same places, remain invisible there. Thus a purely optical explanation may be given of the fact, that the different gases of the sun are see separated, even though we suppose them to de thoroughly mixed. And surely this last supposition is the simpler by far; it even neces- sarily follows from the fundamental idea, that the Sun may be considered as a rotating, heat-radiating mass of gas, for in such a body the constituent parts must continually mix. A few months ago the main character of the motion that must go on in a sun, supposed to be gaseous, has been discussed by R. EMpEN *). He applies to the Sun the same mathematical deductions, which had been devised by von HktMno.tz for investigating the kind of motion which in our terrestrial atmosphere must result from the united influence of heating by the Sun and of the daily rotation *). Though EmpEN supposes the gaseous Sun to be limited by a well-defined surface, and so far accepts the prevailing views on the constitution of this celestial body, still his mathematical formulae are absolutely independent of the existence of a boundary surface, and so are fully applicable to a sun, such as we are considering here. Radiation causes the outer layers to cool down soonest; they sink inwards and are replaced by ascending hotter gases, so that, 1) As appears from a paper in the Physik. Zeitschr. 3. S. 259—261: entitled »Ueber die Doppellinien im Spectrum der Chromophire” Scumpr adheres to this conception, even after having taken into consideration the possibility of explaining the light of the chromosphere by anomalous dispersion. *) R. Empen, Beitraige zur Sonnentheorie. Ann. d. Phys. [4] 7, p. 176—197. 3) H. von Hetmnottz, Gesammelte Abhandlungen I, p. 146, Il p. 287—355. — oe i ¢ if the Sun did not rotate, we could only expect radial convection currents. But the rotation of the sun completely changes this form of motion; the angular velocity of descending masses increases, of ascending masses diminishes; there will be found side by side gas- layers of different densities, and rotating at different speeds. It has been shown by von Hunmuonrz, that during a certain time such gaslayers can flow side by side, sharply separated by a so-called surface of discontinuity G.e. by a surface, on passing which the values of the velocity and the density change with a leap); but gradually the friction causes this surface to undulate; the waves advance with the more swiftly moving layer, they grow steeper, overhang and break, forming whirls; and thus, by the mingling of the adjacent parts of the two layers a new layer is formed between them, the properties of which will be intermediate between the cor- responding properties of the original layers. From the conditions of the problem we may deduce the position of the surfaces of discontinuity. This has been performed by yon HetmMnoitz with regard to the air-currents in ow atmosphere, and by Empen for the rotating layers of the Sun. He arrives at the con- clusion, that in the Sun the surfaces of discontinuity must in the main have the shape, figured in the accompanying sketch and reminding us of hyperboloids of revolution '). N Pada | ass Zs 7 N ‘ M \ ! 1 | Aequator / ‘ Z 4 ~ Pa Fig. 1. 1) Empen draws the intersections of the surfaces with the plane of the paper only inside the circle, representing the sun’s boundary. [ have dotted this circle, with a view to indicate, that the border is only a seeming one; accordingly | prolonged the intersections outward. 166.) In every annular layer, bounded by two consecutive surfaces of discontinuity, the moment of rotation of unit mass (2 — w 7?) as well as the so-called potential temperature 4 are constant; but in a following layer, farther from the Sun’s axis, 2 has a greater and Ga smaller value. Within every layer there exists a velocity potential, but at the separating surfaces the linear velocity changes discontinuously, the difference between the velocities on each side of one and the same separating surface increasing as that surface approaches the axis. The waves, that are formed in the separating surfaces, will proceed in the direction of the rotation, and when, after growing steeper and steeper, they break, the resulting vortices will have their core-lines perpendicular to the direction of motion of the waves, i.e. coinciding with the generatrices of the surfaces of discontinuity. So, the curves in our figure also give an idea of the position of the vortex-cores. From the theory follows, as we already mentioned, that at each definite surface of discontinuity the leap of the velocity is greater at a short than at a long distance from the Sun’s axis; therefore, the transition from a wave into a whirl must, as a rule, begin in those parts of that wave, which are nearer to the axis, and appear afterwards in the outer parts. Further it is clear that, because every whirling leads to mingling of the adjacent parts of two layers and to the formation of two new surfaces of discontinuity, there will never exist a complete surface, such as indicated by our sketch. Everywhere we shall meet with pieces of surfaces of discontinuity; only their main character and the average direction of the vortex-cores will correspond to the sketch. And in spite of the continual mixing of layers, which leads to equalization of differing rotational velocities, the motion still remains nearly stationary; for within each layer, temporarily enclosed between two surfaces of discontinuity, the convection currents carry cooled matter inwards and hot matter outwards, by which process the differences in rotational velocity are renewed. Forced as we are to admit, that such an uninterrupted mixing process is going on in the Sun, the advantage of explaining the chromosphere and the prominences by anomalous dispersion of white light, must appear to us very obvious. All other explanations, that I know of, must start from the hardly tenable supposition, that the different gases of the chromosphere are separately present in large quantities. Empen has succeeded in deducing many properties of sun-spots from the supposition, that the spots show us the places, where huge whirls attain the Sun’s surface. It seems to me that EmpEn’s views ( 167 ) on sun-spots would become even much more acceptable, if the notion of a real surface of the Sun were given up and if the consequences of normal and anomalous refraction (better ray-curving) in those whirls were allowed for. But to this subject I desire to come back on another occasion. For the present we will confine owr attention to those parts of the whirls, optically projecting beyond the edge of the Sun’s disk, and we propose the hypothesis, that the whole chromosphere with all its prominences is nothing but this system of waves and whirls, made visible within shorter or Joneer distances from the Sun’s edge by anomalous dispersion of light, coming from deeper layers. (Perhaps the structure of the corona, with its polar streamers, arches, ete., might tell us something about the course of the surfaces of discontinuity at very great distances outside the critical sphere ; this point too, however, I will only hint at here). So we ascribe the chromosphere to the smaller vortices, to the continual rolling up of the surfaces of discontinuity ; in the prominences we see the whirling, in which the rarer, very large waves of the solar ocean dissipate. The particular siructure of the chromosphere, suggesting the com- parison with a grass-field in vertical section, follows immediately from this hypothesis. Prominences likewise nearly always show a tissue of stripes, bands and filaments *). These, according to our view, indicate the position of the whirl-cores. In the whole region, where whirling is going on, the density will, of course, vary in a very irregular way ; we therefore may expect to find in the spectrum of that region as well the light on the red as that on the violet side of the absorption lines, 1. e. the chromospheric and flash lines must be double lines 2). Along the core of a vortex g the density is a minimum. If, now, a vortex intersect the ap- parent limb of the sun obliquely, vt Rare y | ' as in Fig. 2, where py represents if the core-line, the light coming Fig. 2 from a point @ must differ from the light, coming from 4. Indeed, following in @ the Sun’s radius 1) J. Fénvr 8. J., Protuberanzen, beobachtet in den Jahren 1888, 1889 und 1890 am Haynald—Observatorium, p. 5. (Kalocsa, 1902). 2) W. H. Jutivs. On the Origin of Double Lines in the Spectrum of the Chromo- sphere, Due to Anomalous Dispersion of the Light from the Photosphere. Proce. Roy. Acad. Amst. Vol. Ill, p. 193. 168 ) outward, we at first get into layers of increasing density, whereas, ascending from 4, we meet with layers of decreasing density. Conse- quently, in the spectrum of @ the “violet-facing’’ components of the double lines must be prominent and in the spectrum of / the red- facing ones. If the slit be placed tangentially, through the points a and “4, the two cases will be seen at a short distance on the same spectral lines. And when during a total eclipse of the Sun the chromosheri¢ are itself functions as a slit (the prismatic camera being used), the same phenomenon may be met with on numerous places of the crescents. Many instances thereof are visible on the plates, obtained in Sumatra by the Dutch expedition for observing the total eclipse of May 18" L901. With large prominences the phenomenon sometimes appears very intensely. In the important work by Ffxvi1, mentioned before, we read for instance on p. 121, in the description of a carefully observed prominence, the following passage: .ylm unteren Teile zeigte die Protuberanz am Anfange ihrer Entwickelung eine grosse Stérung in der H, Linie. Bei engem (tan- gentiell gestelltem) Spalte reichten zwei Spitzkegel iiber denselben hinaus, der eine, gréssere erstreckte sich gegen rot, der andere kleine gegen blau und stand etwas siidlicher. Die Grosse des ersteren betrug 9" im Gesichtsfelde ; auf Grund einer neuen Bestimmung der thatsachlichen Dispersion des Spektroskops ergibt sich daraus fiir diese Stelle der Protuberanz eine Bewegung von uns mit der Geschwindigkeit von 240.4 Kim. in der Secunde. Die Verschiebung gegen blan betrug nach dem Augenmaasse etwa die Halfte der ersteren gegen rot. Die entgegengesetzten Bewegungen neben einander und die Kegel- formige Form des veranderten Lichtes wiirden unschwer die Deutung auf eine Wirbelbewegung am Grunde der Protuberanz gestatten. Aus der Ungleichheit der Kegel wiirde ein Vorschreiten des Wirbels von uns mit der Geschwindigkeit von 180 Klm. sich ergeben. Die Beobach- tung steht auch nicht allein da; eine alnliche Erscheinung wurde von Youneé am 3. Aug. 1872 (The Sun, p. 210) eine andere von Tuouton in Nizza (C. R. XC p. 87, XCI p. 487) beobachtet ; ahnliches wurde auch von mir bei anderen Gelegenheiten beobachtet.” Thus, interpreting the light on both sides of the hydrogen-line after Doppier’s principle, Féxyi arrives at the very astonishing con- clusion, that the whirling mass of hydrogen moves at a speed of 180 kilometers per second. Moreover, there is a much greater diffi- culty, not even mentioned by Féxvyi, viz. that the coherent outbuds of the line impose upon him the necessity of supposing that velocity to be very different for the various parts of the whirl, adjacent (i692) pieces of the prominence not even taking any part in the enormous motion along the line of sight. The above-given explanation of the phenomenon by anomalous dispersion solves all these mysteries. It ocews very seldom that prominences show a rapid sideward motion, i.e. a motion in the meridian of the Sun. FENyr mentions as an exceptional case a sideward velocity of 25 kilometers per sec’). As, on the other hand, velocities of 250 lilometers and more in the direction of the. parallel (caleulated after: Dorpiyr) are by no as is admitted means a g@reat exception, we meet with contradictions also by Fényr — from which it appears impossible to escape, unless we doubt the reality of the velocities. It is surprising and. satisfactory to see how nearly all the peeu- liarities in the behaviour of prominences, as described by Youne, F¥nyt and many others, appear quite intelligible as soon as’ we look at these phenomena from ow point of view. Let us choose only a few more examples out: of the vast material. Fényt, says (loc. po 215):0 Schon: seit) Jahren habe ‘ich bemerkt, dass helle hervortretende, Punkte:in der Chromosphare, welche eine kleine. Verschiebung gegen blau zeigen, der Ort sind, wo alsogleich der Aufstie@ einer Flamme oder einer kleinen: Protuberanz erfolgt.” Now the process of whirl-formation in a surface of discontinuity proceeds,.as,a rule, from the inner parts of the Sun outwards. In the axis, of a whirl the density is a minimum. Consequently, at: the moment the whirling reaches the apparent edge af the Sun, a mini- mum,of density will be found just projecting beyond the edge. Here we have a place, where the density increases from the photo- sphere outward and where, therefore, the violet-facing component of the chromospheric double-line temporarily prevails: it seems as ifva shifting towards the violet occurs. Shortly afterwards the more distant paris set a whirling and the prominence appears. An the description of a great prominence, observed by FENyr on the 18 of Aug. 1890, we read i.a. the following particulars *): Hin. ganz, besonderes Interesse verleihen dieser an und fiir sich schon grossartigen Erscheinung die Kigenbewegungen in der Gesichts=' linie, die an derselben beobachtet wurden. Hine ungefahr zwischen 40", und. 50" Hohe liegende Schicht, (deren Lage in der beigeeebenen Vigur,.genau bezeichnet ist), zeigte eine heftigze Bewegung geeen' die Erde, zu. Das rote Licht des;Hydrogeniums ergoss sich daselbst in verworrenen Formen iiber den Spaltrand gegen blaw hinaus ohne 1) Fenvi, lc. p. 114. 3) Finx) ls Gop./129) C176) indessen den Spalt ganz zu verlassen. Die Bewegung war durechaus local, die Umgebung zeigte keine Spur ciner Bewegung. Die Geschwin- digkeit derselben war keine ungewohnlich grosse; ich erhielt aus 4 mit dem Fadenmikrometer gemachten Messungen zwischen 11 h. 45 m. und 12 h. 15 m. verschiedene, zwischen 94 und 201 kim. sehwan- kende Werthe. Was aber die Erscheinung zu einer besonders merk- wiirdigen gestaltet ist der Umstand dass, wiihrend diese in der Hohe vor sich gehende ganz locale Bewegung nicht einer Ausstr6mung zugeschrieben werden kann, dieselbe trotzdem doch eine halbe Stunde lang beobachtet wurde! Nehmen wir als Mittelwerth der Geschwin- digkeit 150 kim. per Secunde an, so hatte dieser bewegte Teil der Protuberanz wiahrend der zwischenzeit von 30 Minuten gegen 270.000 kim. durchlaufen, also wohl auch den scheinbaren Ort andern miissen.” Of course this contradiction immediately vanishes if we only suppose, that in the part of the prominence, showing the persistent shift of the hydrogen light towards the blue, the density of the solar matter was increasing in the direction from the photosphere outwards. This supposition is quite in harmony, too, with the fact, that the picture of this prominence shows very important whirling 4e/ow the part in question and no disturbance worth mentioning above it. Observers have often been puzzled at the rapid disappearing of enormous prominences and at the perfect calm in the whole region, including the Sun’s surface, a short time after such a violent “erup- tion” had taken place. It was hardly conceivable that the ejected incandescent gases could loose their huge quantities of heat so rapidly, nor that the eruption had no further visible consequences. In our theory a large prominence is nothing but the visible token, that whirling is going on almost simultaneously over vast regions. The very important varieties of density in the whirling mass may, however, be annulled by displacements of much matter over relatively small distances, which process, of course, may go on without violent movements and yet be accomplished in a short time. So there is no reason whatever to expect, that a great prominence will leave the medium in a highly disturbed condition. Whosoever wishes to consider prominences as eruptions, must grant, that it is one of the most difficult problems to account both for the tremendous values of the ascending velocities sometimes observed and for the most capricious way, in which the speed often suddenly changes without any conceivable cause. The 20% of Sept. 1893 Fényi witnessed a prominence ascending 500000 kilometers in a quarter of an hour, that is at an average velocity of more than Garis) 550 kilom. per sec. In another case, also observed by F¥xy1 (July 15th 1889), in the course of 10 minutes the ascending velocity passed through the values 72, 6, 65, 24, 154 kilometers per second; and with the prominence of Oct. 6'®, 1890, in 30 minutes’ time through the values 33,8, 79,8, 67,6, 72,7, 127,7 275,5, 242,3, 121, 57,3 kilom. per sec. Considering the problem from the new point of view we see the difficulties disappear in consequence of the observation, that, properly speaking, we have not to do with velocities at all. We may speak of the velocity with which matter moves or with which a disturbance is transmitted by a medium; but neither of these cases is met with here. Wherever the whirling sets in, it results from local conditions and cannot be considered as directly transmitted from places, where whirling was going on a little earlier. Though it is true that, as a rule, the breaking of a wave begins in those parts of a surface of discontinuity, that are nearer to the Sun’s axis, and from there proceeds outwards, yet this does not involve that we should have a right to call this process a transmission of matter or of motion in the direction of the vortex-cores. And where there is no transmission, there is no velocity. When at the sea-shore a wide wave approaches and breaks, now here, then farther and farther, nobody will speak of the ,velocity” with which the foam or the whirling is moving alone the coast. Every body knows, that the foam, the visible token of the whirling, is successively formed at different places. Such about is the case with the prominences, the visible spots in the breakers of the solar ocean. Chemistry. — Professor Losey pre Bruyy communicates a paper by himself and Mr. J. W. Dito. “The boiling point-curve of the system: hydrazine ++ water”. In a previous report’) Mr. Drro has communicated the results of determinations of the densities of mixtures of hydrazine and water; the figures showed that a maximum density corresponds exactly (or nearly so) with the composition N, H,-H,O. At the end of that note it was stated that we would endeavour to determine the boiling- point-curve of the system: hydrazine + water. Vee have lately been engaged with that determination; the result is given in the following table and annexed curve. 1) Proc. of April 19, 1902, p. 838. 172 —— Amount of mixture Number mols. of NH, on 100 mols. Temp. and barometer, liquid, vapour. SS = 102 2 9.4 OAS 300 grm. 755.5 | 104.6 14,2 ” 105.0 1.6 j 107.45 19 5 2.7 eM Ye ; rit A {00 415 3.9 ‘ ” 114.0 6.2 » 114.95 } 34.0 13.8 " 2) 117.95 "1.7 25.0 f ed & er. 768.0 18.6 | 42.9 30.3 P 119 2 45.2 34.9 . 119.8 4 50.3 SAAT, 38 gr.) ~~ 770.8 120.9 Dt.8 44.6 ul | ’ 7 1 hi 1 ; 120.35 53.3 48.75 : } } iy] v 120.45 54.8 52 8 7 | * 420.5 56.0 53 5 tow | [120% 58.5 wopgi5ybod yevd 771-4 i 790145") 62.5 | = } t ’ , 120.95 65.8 72 » 119.9 68.3 (Eyal q i 19.5 p.pcytd gp -wHeaiaredO y 119.95 T3'Gt Peal eRe | 50 er. ” i} 148.8 | 76 It) should be observed beforehand that the figures obtained, parti- cularly those relating to the mixtures rich in hydrazine, cannot pos’ sess that accuracy attainable with other mixtures. In the: first place! free hydrazine isa costly substance; working with a large quantity’ such as is required for the accurate determination of a boilingpoint: curve, therefore, ‘leads to not inconsiderable expenses. Moreover, free hydrazine and its mixtures with little water (also the hvdrate'N, H,- H,O) are very hygroscopic and also easily oxidisable by the oxygen of the air. During the volumetric determination of the amount of 120 119 its a7, 116 115 114 113 112 1 110 109 108 107 106 105 104 103 102 101 100 A vapour B liquid 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 hydrazine in the liquid and condensed vapour, it was impossible to avoid contact with the atmosphere. The operation was carried out in such a manner that each time after distilling off a certain quan- tity (LO—20 ¢.c. in the case of the greater concentrations), two por- tions (3 taneously collected in tared weighing bottles contaming about 5 c¢.e. 4 drops) of the condensed vapow and residue were simul- of water. On account of the many weighings a certain time neces- sarily elapsed between the taking of the samples and the titration and, considering that the bottles also contained a little vapour of hydrazine mixed with air, this must have excercised some influence. This explains why the agreement between the various duplicate determinations often left much to be desired; in one case a discre- pancy occurred amounting to 2 mols. per 100. Finally, another source of error is found in the fact that on account of the many weighines and titrations, the determinations had to be done on dif- ferent days, so that the distillations were conducted under different barometric conditions. Notwithstanding this, the results allow of the construction of a curve, the regular course of which is a guarantee that the figures observed 12 Proceedings Royal Acad. Amsterdam, Vol. V. ( 174 ) express the entire phenomenon with a certain amount of accuracy. As already stated, more correct results can only be obtained by repeating the experiments with larger quantities of hydrazine '), Our experiments have led to the interesting result that hydrazine- hydrate does not at all represent a chemical compound N,H,. 1,0 with a constant boilingpoint of about 120°, as hitherto believed. This however is not surprising, particularly after Kxrerscn’s experiments on the system sulphurtrioxide -- water’). The tendency of SO, and H,O to enter into combination is greater than that of N, H, and H,O. As the boilingpoint curve of the system sulphurtrioxide + water shows a maximum not belonging to the compound H,50, but to a mixture of 95,5°/, of H,S5O, and 1,5°/, of H,O, it is not at all surprising that in the system hydrazine -+- water the maximum does not correspond with the composition N, H,.H,O. It is seen from these figures that a liquid boiling at 119°.5 and having the composition 50 mols. N,H, -- 50 mols. of H,O yields a vapour containing about 42 mols. of N, H, and 58 mols. of water, while a vapour of about the composition N, H,.H,O is given off at 120°.4 by a liquid containing about 54 mols. of N,H, and 46 mols. of water. From the course of the curve it appears that a maximum boiling- point of about 120°.5 corresponds with a liquid with about 58 mols. of N,H,. The experiment has shown that a mixture of about 58.5 mols. of N, H, and 41.5 mols. of H, O has a constant boilingpoint of 120°.1 at 760 mm. In the table 120°.5 therefore corresponds with 771 m.m. The course of the first half of the curve plainly shows the pheno- menon observed by Curtivs namely, that on boiling dilute solutions of hydrazine the distillate consists at first almost exclusively of water, although the boilingpoint has very sensibly increased. It may be assumed that the same thing happens in the reverse case of much hydrazine and little water; for reasons stated we have not been able to ascertain this. One of us (Divo) is already engaged with the determination of the viscosity of the system: hydrazine +- water; while with the co-operation of Professor Ernst Coun experiments have already been startedy several months ago, on the electrolytic conductivity of the same system and of solutions of salts in hydrazine *). 1) Ber. 34. 4088 (1901). *) Curtivs states that concentrated solutions of hydrazine attack glass when boiling at ordinary pressure. We did not notice any such action of even highly concentrated solutions on our glass fractional distilling apparatus and condensing tube. 3) Recueil 15, 179. Chemistry. — Professor Losry bE Bruyn presents, also in the name of Mr. W. AxperpaA vAN EKENSTEIN, a Communication on “ Formaldehyd (methylene) derivatives of sugars and glucosides.” In a previous communication’) we have already stated that an aqueous solution of formaldehyde when evaporated with some of the sugars reacts on the same. This was shown by the great changes in the rotation. We then also remarked that attempts to isolate the crystalline compounds from the syrupy mass had not proved successful. These, moreover, are readily dissociated by evaporation in the pre- sence of much water, the pure sugars being left behind. *) About the same time *) ToLiens had prepared a crystallised methy- leneglucose by mixing a solution of glucose in formaldehyde with hydrochloric and acetic acids and setting the liquid aside for some months. He obtained a monoformal-derivative which still powerfully reduced Frniine’s liquid. Other sugars gave a negative result. On continuing our researches it appeared that substances, of an apparently different nature and more stable than those occurring in the said syrups, are formed when the dry sugars are melted with polymerised formaldehyde (trioxymethylene). The rotatory power then appears strongly modified and the reducing power decreased : this, however, reaches ifs normal figure on boiling with dilute acid. From this follows that during the reaction of the sugar with the formaldehyde, the aldehyde groups disappear. We now succeeded in isolating in the case of several sugars (and glucosides) crystallised compounds or such having a constant boiling point, by introducing the fused mass into sulphuric acid of various concentrations or phosphoric acid and then agitating the liquid with an organic solvent such as chloroform, which dissolves the diformal compounds. In some cases there are formed, simulta- neously, monoformal derivatives which are readily soluble in alcohol and water, but sparingly soluble in chloroform and so behave in this respect quite the reverse from the diformal derivatives. Both the di- and the mono-methylenesugars no longer react with Frunine’s solution and behave indifferently toward phenylhydrazine ; the carbonyl groups have therefore disappeared during the action of the formaldehyde. After boiling with dilute acids, the reducing power returns. These substances must therefore in the first place 1) Proc. 1900. 9. ®) Rurr and Ottenporrr, Ber. 32. 3236 (1899), have regenerated some sugars from different hydrazmes by evaporation with solution of formaldehyde. 8) Ber 32. 2585 (1900); his experiments had commenced some years previously. 12* ( 176 ) be regarded as glucosides, derived from methylenglycol CH, (OH), *), Which is unknown in the free state. Two of the alcoholic hydroxy! groups of the sugar-molecule have also taken part in the formation of the diformal-derivatives. A hydroxyl group is no longer present in formalmethylenexyloside and -arabinoside, for acetic anhydride and benzoyl chloride do not act on these substances. As, according to the analysis, two mols. of water have been eliminated, the following constitutional formulae, for instance, may be drawn up for the said pentose derivatives. HC—O~. vis ea CH, HC CH, <— HOO 7 [SO ae CH \. HC—O or re a ~ 4“ HC—O\, GH: fOH, ®) | YH eee? \. HC—0/7 H,C—O | CH, Diformalxylose (C, H,, O,) erystallises very neatly from benzene or light petroleum; melting point 56°—57°,{@|p(2"/, solution in methylalcohol) = -++ 25°,7; may be readily sublimed. Diformalarabinose is a somewhat oily, colorless liquid which may be distilled in vacuum without decomposition. Boiling point 155° at about 32 m.m. pressure; [@]p (2°/, solution in methylalcohol) ——— 16". With glucose a syrupy diformalderivative may be separated from a solid mono-compound by taking advantage of the said difference in solubility. Neither of these substances have any reducing power or react with phenylhydrazine. They are probably mixtures; the white substance, although crystalline, does not possess a definite 10 melting point (140—150°) and on analysis gives no satisfactory figures, but it could not up to the present be resolved by recrystallisation into components. The diformal-derivative, left in contact with solvents for many months, remained syrupy. Both compounds still contain one or more free hydroxyl groups ; 1) The methyleneglucose obtained by Tottens (l.c.) has still a strong reducing action; it appears to us that it should not be regarded as a glucoside (which Tottexs does); apparently two alcoholic groups of the glucose have taken part m its formation, Py the products of the reaction with acetic anhydride and benzoy] chloride could not as yet be obtained in a erystalline form. They are not liable to fermentation but do not prevent the fermen- tation of any free glucose, although they retard the same. The simultaneous formation of various isomeric mono- and diformal- elucosides may, as will be easily seen, explain the unsatisfactory result. Galactose yielded products comparable with those obtained from glucose. The indistinetly crystalline methylenegalactoside (monoformal derivative) seems, however, to be a pure substance as the melting point (203) remained unaltered; [@]p (in 2°/ -++ 124°.8. It is still being investigated. Fructose yields a well-crystallised formalmethylenefructoside ; when preparing the same a 50°/, sulphuric acid should be used. Melting point 92°; [@]p (2°/, aqueous solution) = — 34°.9. d-Sorbose yields a derivative melting at 54° and [é] p (2°/, aqueous solution) = — 25°. Rhammose yields a product melting at 76° and [@]p [0.4°/, aqueous solution) = — 18°; mannose also yields a erys- aqueous solution) = 0 talline derivative. The (mono)methyleneglucosides also derive a certain importance from the analogy which they show, as regards their properties, with ordinary canesugar. In the same way as the latter has been formed from glucose and fructose, they are also formed, with the loss of two carbonyl groups, from two aldehydes from which one mol. of water has been eliminated. The reducing power is lost; towards phenylhydrazine they have become indifferent. On boiling with dilute acids, however, the components are regenerated. It cannot be a matter of astonishment that the methylglueosides are quite as capable as the hexites, the oxy-acids and the sugars to give condensation products with formaldehyde. They are formed in abundance by simply melting the powdered elucosides with dry trioxymethylene. In a properly crystallised state were obtained the formalderivatives of methylmannoside |m.p. 127°, («|p = + 107.5], of 3-methyl-d-gluco- side m. p. 136°, inactive} and of « and 3-methyl-d-galactoside. The derivatives of e-methyl-d-glucoside and of amyl- and aethy]-d- glucoside are viscious liquids. It is worthy of notice that saccharose melted with trioxymethylene is decomposed with the formation of a mixture of formalderivatives of glucose and fructose, from which the latter was separated in a crystalline condition. (178 y Chemistry. — / The intramolecular rearrangement in halogen-aceta- nilides and its velocity’. By Dr. J. J. Buanksma. (Communicated by Prof. Losry pr Brey). In a former paper’) attention was called to the fact that the ready bromination, nitration, sulphonation ete. of phenol and aniline deri- vatives may be explained by assuming that the halogen atom or the groups NO, or SO, 1H first enter the side-chain and then pass into the nucleus by intramolecular migration. Although a great many compounds are now already known containing groups linked to N or O which, under the influence of certain agencies, shift towards the nucleus, it was in these cases up to the present not proved with absolute certainty that we are really dealing here with a rearrangement of atoms or groups in a molecule and not with a reaction in which several molecules take part, which according to some authors is not improbable *). In order to investigate this it became necessary to know the velocity of reaction. If the reaction took place mono- molecularly, we should be really dealing with an intramolecular displacement; a bimolecular reaction would point to a double decom- position between two molecules. As a suitable example for this research, Prof. Losry pr Brey pointed out to me the conversion of acetylchloroanilide into para- chloroacetanilide under the influence of hydrochlorie acid, first discovered by Brnper *) Ch ae. CH, CONC DH => CH, CO NC /Cl. It is known that the chlorine in acetylchloroanilide may be determ- ined by adding potassiumiodide to its acetie acid solution and titra- ting the liberated iodine; p-chloroacetanilide does not react with K I: C, H, NCI CO CH, + 2 HI=C, H, NHCOCH, + HCI+T.- The acetylehloroanilide was prepared according to the directions of Cuartaway and Orton‘) by shaking acetanilide with a solution of bleaching powder containing potassium bicarbonate. Within half a minute to a minute it will be noticed that the acetanilide has nearly entirely dissolved; after a few minutes the acetylehloroanilide sepa- rates in a crystalline state. Cuarraway and Orron siate that this 1) Proc. 25 Jan. and 29 March 1902. 2) Armstrone, Journ. Chem. Soc. 77. 1053. 3) Ber. 19. 2273. Stossex, Ber. 28. 3265. +) Journ. Chem. Soc. 79, 278. (179 ) compound is unstable and is spontaneously converted into p-chloro- acetanilide. A closer investigation showed me that the cause of this must be attributed to the action of sunlight. After 14 days exposure to the light (May 14-28), the atmosphere being cloudy, this substance was entirely converted into p-chloroaceianilide while on a bright day in June the conversion was complete in a day. In the same manner it was shown that the analogous bromo-compound ©, fH, N Br CO CH, had been entirely converted after 3—4 hours exposure to direct sunlight on an afternoon in June and in 70 hours by exposure to incandescent gaslight; in diffuse daylight the conversion was complete after a few days, while both the cblorine and the bromine compound, could be preserved unaltered in the dark. We therefore see that Br and Cl linked to N, shift to the nueleus under the influence of light. On consulting the literature it was found that Bamerrenr’) had already shown that phenylnitramine is converted by sunlight into o- and p-nitraniline, while he had also found that nitrosophenylhydroxylamine is very rapidly decomposed by direct sunlight and sometimes even explodes. The reaction takes here a more complicated course, the first stage of the reaction is probably the migration of the NO group to the nucleus. Recently Kxipscurrer *) has shown that azoxybenzene is converted by direct sunlight into 0-oxyazobenzene. We therefore see that under the influence of sunlight Br, Cl, NO,, NO and O attached to N migrate from the side-chain to the nucleus and change place with an atom of hydrogen *). In the previous communication (l.c.) attention was called to the analogy of the CH,-group with NH, and OH. Now however, we notice a difference. Whereas sunlight promotes the entering of atoms or groups into the nucleus of the NH,-derivatives, it causes the for- mation of Br and Cl compounds in the side-chain of the CH,-derivatives, for instance in the bromination or chlorination of toluene *). We may briefly refer to the experiments of Srprk *) and Errara °) who have proved that on chlorinating parabromotoluene p-bromo- 1) Berichte 27, 364, 1554, 34, 66. 2) Proc. 31 May 1902. 3) No experiments showing the effect of light have, as yet, been made with phenol derivatives containing atoms or groups attached to the oxygen. It is probable that sunlight will in this case also excercise an influence on the migration of atoms or groups of the side-chain to the nucleus, This should be borne in mind when preparing these compounds. 4) Scuramm, Ber. 18, 608. *y Monatsch. f. Chem. 11, 431. 6) Gazz. Chim. Ital, 17, 202. ( 180 ) henzylbromide is formed in’ addition to p-bromobenzylehloride ; in this case the bromine leaves the nucleus and is introduced into the side-chain‘). This question merits further investigation, After several preliminary experiments which showed that the interchange of Cl and H is much promoted by the catalytical action of acids, I determined the velocity of reaction in the following manner. 3—4 grams of the acetylehloroanilide were dissolved in 100° grams of glacial acetic acid (100°/,), 10 ec. of hydrochloric acid containing 2.9127 grams of HCl were added and finally the liquid was diluted with water to 500 cc. This solution was put into a black bottle and kept in a thermostat at 25°. As soon as the temperature had reached 25° 50 ce. were removed with a pipette and delivered into 100 ce. of water to stop the reaction. Excess of solution of potassium- iodide was added and the liberated iodine titrated with sodium thiosulphate (0,150 N). The following results were obtained. t in hours. ec. Na, §,0,. k. 0 49.3 NE 42 0.160 1 35.6 0.162 iba 30.25 0.163 2 25.75 0.162 2"), 21.8 0.163 3 18.5 0.160 4 13.8 0.160 6 7.3 0.160 8 4.8 0.162 i Ae By applying the formula for the monomolecular reaction /—=— se values are found for / which may be regarded as constants. This proves that the reaction is really monomolecular and that we ave dealing with an actual intramolecular rearrangement of atoms. If instead of 10 ce., 20 ce. of hydrochloric acid were added the value for & was found to be 0.610; (the average result of eight obser- vations); by using double the quantity of acid the velocity has there- fore increased nearly four times. If instead of hydrochloric acid sulphuric acid of the same concentration was used, the conversion was very slow and a good constant was not obtained (52.8 ce. of Na, 8,0, at first, 29 ce. after 24 hours). In glacial acetic acid (99—100 °/,) the reaction takes place much 1) Cf. Hanzscu, Ber. 30, 2334. Tuét and Ecker, Ber. 26, 1104. ( 181 ) more rapidly so that addition of very little hydrochloric acid suffices for the complete conversion. The substance was again dissolved in glacial acetic acid and 3 ce. of a solution of dry hydrogenchloride in glacial acetic acid were added. The quantity of HCl thus introduced into 500 ce. of the solution amounted to only 0.0135 gram or not quite '/,,, part of the quantity present in the experiment with aqueous acetic acid. The progressive change of the reaction was as follows: ¢ in hours ces Nays. 0: 0 30.3 Wp 29.7 1 : 28 Sip 24 2 22.6 2/, 19.8 3 17.2 Eu 14.2 4 12.4 4"), 10.5 : : : 1 HALES Dy. On calculating £ according to the formula /: = a eae it will be seen that it keeps on increasing; this shows that the amount of the catalyser increases. On repeating the experiment it was found that, after the reaction, more hydrochloric acid existed (weighed as Ag Cl) than corresponded with the quantity added. A graphie representation of the above figures plainly shows. that we are dealing here with a reaction the velocity of which has been accelerated by an increase of the catalyser '). In the experiment with 20 per cent acetic acid the small inerease of the relatively large amount of HCl is not perceptible. Even when we do not add hydrochloric acid but set the acetic acid solution aside in the dark we meet with the same type of progressive change of the reaction. 10 ¢.c. of a solution in glacial acetic acid were titrated from day to day and took : Lode, 906, (oo, 20040 and 1seie: Nas. (0, which figures again reveal the character of a reaction accelerated by a catalyser. It moreover shows that it is not the glacial acetic acid which starts and continues the reaction, but that the conversion is due to the catalyser formed from the product itself; in the first 1) Osrwatp, Lehirb. d. allgem. Chem. Bd. UH, T. Il, 266. ( 182 ) ease it ought to be possible to caleulate a constant by means of the formula employed for monomolecular reactions, We are, therefore, dealing here with a case quite analogous to that of the spontaneous decomposition of alkyl sulphurie acid and nitrocellulose mentioned by OstrwaLp; it is known that this may be prevented by adding a little K,CO, or Ca CO,, The reaction in the presence of alcohol takes place in a similar manner; On warming on the waterbath it may according to CHATTAWAY and Orrox become so violent that the alcohol begins to boil. This may be prevented by adding a trace of Na,CO, which fact has been noticed by ARrMsTRONG (l. ¢.). We therefore, see : , 1. That the conversion of acetylehloroacetanilide into p-chloro- acetanilide proceeds like a monomolecular reaction and that it repre- sents a true intramolecular rearrangement of atoms. It may therefore be compared to the case of the transformation of the bromo-amides under the influence of alkalis studied by van Dam and Aperson *). 2. That Br, Cl, NO,, NO, and O attached to N change place, under the influence of sunlight, with an H-atom present in the nucleus. 3. That the conversion of acetylehloroacetanilide in aleoholie or acetic acid solution is caused by the formation of a catalyser which ‘auses the reaction to proceed at an increasing rate (particularly in sunlight); this may be prevented by adding a trace of sodium carbonate or acetate as this removes the catalyser. The investigation will be continued in various directions. Chemistry. — “Galvanic cells and the phase rule.” By Dr. W. teinDERS of Breda. (Communicated by Prof. H. W. Baknets RoozEBoom). Nernst *?) and, more recently, Bancrorr*) have tried to establish a relation between galvanic cells, consisting of a combination of two metals surrounded by electrolytes in communication with each other, and the phase rule. Neither of them, however has paid sufficient attention to the fact that: When the phase A is in equilibrium with B and also with C, then B must be also in equilibrium with C. They regard the liquid electrolyte. in contact with the metals, as one homogeneous phase, whilst in reality two phases exist which are 1) Recueil 19. 318 (1900). 2) Theor. Chem. le Aufl. p. 560, 3e Aufl. p. 660. 8) J. of phys. Ch. I 427 (1898), ( 183 ) not in equilibriam with each other; in fact various means are employed to prevent them from forming a homogeneous mixture. The following contains a new effort to study the galvanic cell from the point of view of phase rule. Those cells have been considered, which consist of a combination of 2 metallic electrodes, each surrounded by an electrolyte, containing the cation of the metal and connected with each other either directly or by means of an electrolyte. Equilibrium may exist between both the eleetrodes and the sur- rounding electrolyte and when that equilibrium is reached, there exists at the plane of separation a certain potential difference, which is the measure of the energy required to transfer an equivalent of the metal from the one phase into the other. 3ANcROFT is therefore in error in regarding the E.F. as an in- dependent variable, as a further condition of equilibrium. He says: “In addition to the ordinary conditions of equilibrium there is also the electromotive force.” The variables would then be the 7 components, temperature, pressure and the potential difference and from this it would follow that for an invariant system 7+ 3 phases were required. This is not the ease, for a is completely defined when 7 phases are present in a system of 7 components at a given temperature and pressure (for instance by the formula of Nernst when 2 — 2 or 8). There exists, however, no equilibrium between the two electrolytes in the cell. They will tend to form a homogeneous mixture in which case the composition is changed and the equilibrium with the electrode disturbed. Therefore, there can be no question of a real equilibrium in the whole of the cell so long as both electrodes cannot be in equilibrium with the same electrolyte and the EMF becomes zero. An apparent equilibrium may, however, be got by preventing as much as possible the diffusion of the two electrolytes. Considering the cell as a combination of two systems consisting of metal and electrolyte, the equilibrium of the separate systems should be discussed before alluding to that existing in the cell. The equilibrium between the metalle electrode and the surrounding electrolyte and the potential difference at their plane of separation. A. The electrode consists of a single metal and the surrounding electrolyte also contains cations of that metal alone. When the electrolyte is a fused salt of the metal, we have a system of 2 components in 2 phases which at a given temperature and press- ( 184 ) ure is completely defined. If the electrolyte is a solution of a salt of the metal, there will be 3 components and, therefore, the concentration must also be given. The potential difference is determined by the for- eo: ie vas. : . . ; mula of Nernst: a= / in which “”= the solution tension of n P the metal, p—=the osmotic pressure of the cation and = the valency of the metal. B. The electrolyte consists of two different metallic salts M,Z and M,Z and in the electrode both metals of these salts may be present. Assuming that the electrolyte forms one homogeneous phase, the following distinction may be made in the equilibria of the electrode and electrolyte. I. At the given temperature there is no reaction between the tivo metals; they form therefore neither a compound nov a liquid or solid solution. Starting from the electrolyte, containing only the salt 17,7 (fused or in solution), there is a series of electrolytes with an increasing amount of J/,Z, which can only be in equilibrium with J/,, and another series, starting from 1/,7 with increasing quantities of M,Z, which are only in equilibrium with J/,. Where these two series meet, we have an electrolyte, which is in equilibrium with both J/, and J/,. When there is no solvent and we are consequently dealing with a fused salt mixture, there is only one electrolyte which satisfies this equilibrium. We then have 3 phases: electrolyte, 1/7, and J/, and 3 components VW, MM, and the acid group 7 The equilibrium at a given ¢ and p is, there- fore, completely defined. If, however, a solvent, and consequentiy a fourth component is also present, then, according to the quantity of this solvent, there will be a series of electrolytes which satisfy the conditions of equilibrium. To follow the change in the potential difference, we may imagine, that a part of the ions J/, in the electrolyte containing 17,7, has been replaced by J/,, but in such a way, that the total concentra- tion of the ions /, + J/, remains constant. The potential difference between ./, and the electrolyte will increase, because in the equation _ RTP, x —1—, p, becomes smaller and consequently 2, becomes greater. 1 ny P 1 The same applies to z,, the potential difference between the metal M, and an electrolyte containing only .J/, cations, when part of these ions is replaced by ions J/,. (185 ) In fig, 1 AD and BD ave the lines giving a graphic representation of the change of a as function of the ratio of the ions J/, and B JM, at a constant total concentration of the cations. A pomt on AD, therefore, gives the concentration of the JW, and J/, ions in an electrolyte, which is in equilibrium with A, and the potential difference at the plane 4 //. of separation between this electrolyte and the electrode. LD does the same for J/,. Both ~ °pf,-ions. lines are logarithmic curves. AD, therefore, asymptotically approaches the ordinate .J/,5, until it is interseeted in D by the line BD. In D the electrolyte is in equilibrium with the two metals J/, and JMf,. To the left of it, I, is precipitated by J/,, to its right, J/, by JM,. The condition of equilibrium in D is 2,= a2, By 1 Pry therefore log = log n 1 Pi Ny Ps ny Pi Ny Py or ———— sa By P2 and, for metals of the same valency P;: Piz = p, : p.- In words: in this equilibrium the ratio of the concentrations of the cations is equal to the ratio of the solution tensions of the metals. Owing to the great difference in the solution tensions, p, must in most cases be very small and consequently the possibility of the second metal existing in contact with the mixed electrolyte, is limited to very minute concentrations of the first metallic salt; whereas the first metal may be in equilibrium with almost all the electrolytes, whatever the proportions of the two salts may be. The point D is, therefore, situated nearest to the less noble metal and almost coincides with B. DanneeL *) has investigated an instance of this equilibrium, namely 2HI-+4+ 2 Ag 2 AegI+H,. The solution, which is in equilibrium with both Ag and H, under 1 atm. pressure, is saturated with Agel (¢ = 0,567X10-8) and 0,043 normal in HI. I. The two metals form a homogencous liquid or solid solution. This is the case with the liquid amalgams and other fused metals, with Zn—Ag *), Sb—Sn *) and other alloys. 1) Z. f. Phys. Ch. 83, 415. ®) Heycock en Nevinte. J. Chem. Soc. 1897, 415. 5) Heycock en Nevitie. J. Chem. Soc. 330, 387; van Buterr, Z. f. phys. Ch, 8, 357 en Retoers Z. f. anorg. Ch. 25, 113. ( 186 ) Starting with the one pure metal and a solution, containing only the first metallie salt, it is found that on addition of the second metallic salt a small portion of the second metal will be separated and dissolved in the first one until the metallic phase is again in equilibrium with the electrolyte. This equilibrium requires that 2, = <2, or for dilute solutions ; AO ALR ee log — fr od 4 Pr ns Pa ny P Ny P or also i = Py Bs in which 7, and P, are the partial solution tensions of the two metals in the homogeneous metal phase. ?, and 7, are not constant here, but vary with the composition of the electrode. This formula was obtained by Nernxst') and verified by Oae *) by means of the example Hg + AgNO, 2 HgNO, + Ag. The electrode now contains both metals, as may also happen in the case of non-homogeneous mixtures (2) in fig. 1). The difference, however, is that there the metals form 2 phases and here only one. If the electrolyte is a mixture of fused salts or a solution in whieh the total concentration of the two eations is constant, then, at a constant temperature and pressure, the system will still be monovariant ny Ng ny Ng and the relation V~P,:VP, or Vp,:Vp, may still be variable. Once ny Nig however, the relation Wp,:Vp,, that is the composition of the electro- PitV Ps n Ne lyte, having been given, VP, :-V P, or the composition of the metal phase, is also determined and consequently also 2. At each temperature a series of two such coexisting phases are possible. The potential difference continuously changes with their composition. In order to trace the general course of this a-line it must first be ascertained how P, and P, depend on the composition of the electrode. If, in the metal phase, there are « atoms of JM, and 1—v atoms of Jf, and & is small, the lowering of the solution tension may be taken as proportional to the number of dissolved molecules of the second metal, which is analogous to the lowering of the vapour pressure in liquid mixtures. If we call the solution tension of the pure metal M, P,, then P, = P;(1—2). For small concentrations P, is proportional to the concentration 1) Z. fiir phys. Ch. 22, 539. 2) Z. fiir phys. Ch. 27, 285. ( 187 ) of the second metal, as has alre: ady been proved by the investigations of Meyer‘), Ricnarp and Lewis’) and Oae*). Therefore P, = Kv. The factor A is unknown. For «1 it becomes however = /[7,. For small values of 2 however this is not necessarily the case, for it is to be expected that its value will be influenced by the nature of the first metal. The condition of equilibrium then becomes : es, by De V Ka or OO ak ny “ ny ies Vp, V Pii—z) 3 Kare: and for 1,=n, Laie esiy Pp Py; 1—a In words: The ratio of the ions in the electrolyte is to that of the atoms in the metal as A’: Py. When the ratio A: P; is very great, p,:/, will also be great, even when « has but a small value, that is to say that the electrolyte will contain almost exclusively cations of the baser metal even when the concentration of that metal in the electrode is small. In calculating the potential difference, the concentration of these IRIE Ge ions (p,) may, therefore, be taken as constant. et = a logarithmic function of « and, for small values of 2, will increase , ; u Gass RT 1 rapidly with it. | — 5 du ar & is then The graphic representation of this function is a curve rising rapidly from the potential of the nobler metal at a small distance from the a-axis. As « increases, A approaches to the value /;, becoming equal to P; when «= after a small further rise reaches to the value of the potential of 7, in a solution of pure J/,7. 1. The curve, therefore, bends sharply and The ratio of the ions in the coexisting electrolyte _" __ increases Pr from 0 to nearly 1 for quite small values of v. The curve, which represents a as a function of this ratio, runs, therefore, at a slight incline towards the ordinate representing these baser metal, finally approaching it almost asymptotically. eA tephys. Chev, 277. Ynn » » 28, 1. SB) eGs ( 188 ) The same results are obtained by considering the equation RT. Py A—w) =e l a Py a. When the two metals form homogeneous mixtures in all pro- 7 Fig. 2. portions, the curves will therefore possess the general form shown in figure 2. r B The points on these curves, which are situated on the same horizontal line, are co- existing phases. The ordinate of the points gives the potential difference at the plane of separation. Although it is not impossible, a maximum A aie io App > Oh eR will rarely occur, unless the 4 * solution tensions of the two components ), j 7 r ba ta 1 aT Bere P os s differ very little. PitP; 4. If the metals are not homogeneously miscible in every proportion, and the series of mixtures is therefore discontinuous, the two metallic phases, which are in equilibrium with each other (the end points of the break), will also be in equilibrium with the same electrolyte. The potential in this electrolyte must be the same for both metallic phases, for if such were not the case, a current might be generated and the equilibrium would be disturbed. According to whether the potential difference in this non-variant equilibrium is greater than those of the pure metals in solutions of their salts or intermediate between them, the figures 3 or 4 are obtained. Fig. 4. T A mM, —_—> uw or Be te ” — ——— Pi +P: sin’ PitP: ( and D are the two metallic phases in equilibrium with each other. £ is the coexisting electrolyte. The case of fig. 3 becomes identical with that of fig. 1 if Cand D ( 189 coincide to the right and the left with the a-axis, that is when the metals do not mix. An example of the case of fig. 4 is found in my investigation ’ of the equilibrium between fused lead, zine and their chiorides. At Sor isn = Oo) a Olek, 4107/5 (ob Zn>, 97 °/, of Zn, 3 °/, of Ph ; E=99,9 °/, of ZnCl,, 0,1°/, of PbCl, and if 2,4 is taken as 0 then CED — 0,277 Volt and 7g = 0,283 Volt. A second example is found in the cadmium amalgams, investigated by JagcER *) and Bi. *). Further researches are those of Mryer and Ricwarps and Lewis on the dilute amalgams, those of LixpEck *) and those of HurscukowitscH*), who met with the case represented by fig. 4 in his investigation of Cd—Sn, Cd—Pb, Zn—Sn, Zn—bi, Cu—Ag. In all these cases the concentration of the nobler metal in the electrolyte is very small; to a large extent the curve ALB almost coincides with J, 2. HI. The tivo metals form a compound. If the compound is present in a pure condition there will only be 2 phases and at least 8 components. Even without solvent the system is still monovariant at constant temperature and pressure. As in case I, if one of the pure metals forms the electrode, a series of solutions exists with varying proportions of the salts 7,7 and M,Z, which may be in equilibrium with this compound. The limit of this series is reached when the solutions are also in equili- brium with a second metallic phase (one of the pure components, a liquid or solid solution or a second compound). In order to make use of Nernst’s formula to calculate the potential difference, if is necessary to assume that the electrode forms ions of the same composition as the compound, for instance of AuAl,, Zn, Ag, ete., and to substitute the concentration of these ions in the formula. The solution pressure is then a definite constant for this compound, as it is for every pure metal: therefore v= 1) Z. f. anorg. Ch. 25 126. 2) Wied. Ann. 65 106. 5) Inang. Dissert., Amsterdam 1901. *) Wied. Ann. 35 311. 5) Z. f. phys. Ch. 27 193. Proceedings Royal Acad. Amsterdam. Vol. V. ( 190 ) If the formula of the compound is .W,¢ 4," , then owing to disso- ciation, ions J, and JW, will occur along with ions WW, J/,% and between these an equilibrium will exist expressed by the equation: Dp, — Kp... When the total concentration of the ions remains constant, /—p, may be substituted for p, and the equation becomes P:* (k—p,)? — KP,.s° The maximum value of p,, is reached when the first differential quotient with respect to p, = 0, that is, when ap,* s (k—p,)° i bp,* (k—p,)' —- or a (k oy =) 7 or Diss es Py, therefore reaches a maximum and a a minimum where the ratio of the ions J/, and J/, in the electrolyte is equal to that of the metals in the compound. a. If the compound can be in equilibrium with an electrolyte in which the ratio of the cathions is the same as that of the metals in the compound and if in addition to the com- pound only the metals in a pure condition are capable of existence, then the a-curve will have the form indicated in fig. 5. The points on the line AG give the compositions of electrolytes in equilibrium with pure J/, and the corresponding potential differences. With the electrolyte G both J/, and the compound are in equilibrium. So long as both metal phases are present, the potential difference remains constant. Should /, have entirely disappeared, so that the electrode consists of the pure compound (composition = /), the electrolyte may vary from @ to A while the potential difference first falls to Hand then again rises to A. In A there is again a non-variant equilibrium between the compound, pure .J/, and the electrolyte A’ and so long as these phases exist the potential difference remains constant. But when the compound has disappeared, it falls to 6, while the electrolyte changes from A’ to pure J/,7Z. From an electrolyte having a composition situated between G and A the compound JV, is precipitated by JW, and also by J,. (aight) Owing to the small rise of the line AG, the first case is sure to occur but rarely, as the line GHA’ then stands a chance of not being again intersected by AG and this ease will pass into that of 4 (see below). H may be situated higher or lower than A. Fig. 6. If, in addition to the compound, two solid solutions are possible (J/, in which a little M, and M, in which a little J/, is dissolved), the a-curve takes the course indicated in fig. 6, which differs from fig. 5 in this, that in presence of the electrolytes A to G pure J, is replaced by an electrode of varying composition, repre- sented by the line AC, and in presence of the electrolytes B to AK metallic phases 2 to occur. The line BF may either rise or fall’). An example of this case is probably the system Hg, Ag, NO,, examined by Oge (Le.) for dilute solutions of Ag in He. b. If the compound cannot exist in presence of an electrolyte in which the ratio of the cations is the same as that of the atoms in the compound and if we consider the case in which in addition to ihe compound two solid solutions are possible, we get fig. 7. Metallic phases from A to C are in equili- brium with electrolytes from A to G. From (to D the electrode consists of a mixture of the two phases C (a solution of J/, in AW,) and PD (the compound). The potential difference is constant. As therefore, the compound is not in equilibrium with an electrolyte having the same ionic ratio, it will, in contact with such an electrolyte, dissolve with separation of J/,, and tend towards the equilibrium G, D, C. If, before attaining this, D has totally dissolved, a metaliic phase on the line AC’ and an electrolyte on the line AG will remain. From D to # the pure compound is in equilibrium with an elee- trolyte of varying composition, situated on the line GA. The potential difference rises. The metallic phase / and the compound £ are in equilibrium with the electrolyte A. As long as these three are present, the potential difference is constant. If, however, the electrode reaches a composition to the right of /’, the compound will have disappeared 1) In fig. 6 to read K instead of F’ and F instead of P. ( 192 ) and there will be equilibrium of the metallic phases / to B with the electrolytes A’ to BL. a rises or falls (as in fig. 3). It may be expected here as in II, that the line AGAS will toa large extent run close to the a-axis of 1/7, and that in consequence the concentration in .W,-ions in G and A’ will be very small. When no solid mixtures of the two metals are possible AC and BF coincide with the z-axis. / then lies above DB. If there is more than one compound, the sudden change of potential DE is repeated for such compound. Herscnkowrrscn (1.c.) has noticed these sudden rises with Zn ,Cu, Zn,Ag, Zn Sb,, Cu,sn, Ag,Sn and has regarded them as evidence of the existence of these compounds. We should, however, be careful when drawing such conclusions as to the composition of alloys from measurements of potential dif- ference, for an alloy, obtained by melting together the two components and rapidly cooling the mass, is a badly defined substance and often contains more than two phases which are not at all in equilibrium. When they are brought into contact with an electrolyte consisting of a salt of the less noble metal, the unstable compounds in the alloy may be converted into the more stable ones and this reaction, which ~ is caused by a short circuited element (unstable compound, electrolyte, stable compound), continues until only the two phases, which are really in equilibrium, remain. During this period the £./F observed is not necessarily constant. The constant cells. As already stated, there is no equilibrium between the two elee- trolytes of a cell; they tend to form a homogeneous mixture by diffusion. The potential difference between two electrolytes is, howe- ver, generally very small and when the diffusion is small, it will change very little. As, moreover, the 2 MF of a cell consists of the sum of the potential differences between the two electrolytes and between electrolytes and the electrodes, an apparent equilibrium and consequently a constant # I/F may be secured by making the dif- fusion as small as possible. To attain this it is necessary that there should be equilibrium between the electrodes and their electrolytes. But, in a constant cell, that equilibrium must not be modified when the current is allowed to flow and an interchange between the phases takes place in con- sequence. At constant ¢ and p the system must be invariant. If the electrode consists of a single metal, the concentration of the ions of the metal in the electrolyte must be kept constant. In case (Sallam) the electrolyte consists of a solution of the metallic salt, the presence of this salt in a third phase of constant composition, such as a solid hydrate, is required. ‘These conditions are satisfied in the original form of the Clark cell, which contains on one side Zn and a saturated solution of ZnSO,, 7TH,O and on the other side mercury and a saturated solution of He, SO,. If the electrode consists of two metals forming only one phase (liquid solution, solid solution or compound), the current will neces- sarily cause a change in the equilibrium, because the ratio of the metals in the electrolyte is generally different from that in the elec- trode. The equilibrium will only then become invariant when a second metallic phase appears. If there is no solvent, and the electrolyte therefore consists of a mixture of the two fused metallic salts, its Composition is completely defined by the presence of 3 phases of the 8 components (1/,, J/, and the common acid radicle). If, however, there is also a fourth component in the form of a solvent, a fourth phase must be present to make the equilibrium invariant such as the crystals of one of the two salts. The choice between the two salts is not an arbitrary one, but is regulated by the required relation of the concentration of the cations and the solubility of the two salts. From this it follows, that on passing the current, only that metal, the salt of which is present in a second constant phase, can dissolve or deposit on the electrode (which consists of a mixture of the two metal phases). The ratio of the quantities of the two metallic phases must be regulated accordingly. An example, from among the commonly used normal elements is the Weston cell in which the Cd-electrode consists of a mixture of a liquid phase (Hg with 5°/, Cd) and a solid one (Hg with 14 °/, Cd)*) while the surrounding electrolyte consists of a solution of E 8 Cd SO, and traces of Hg, 5O,, saturated with Cd SO, = HO: The Clark cell in which a zine amalgam with 10—15°/, of zine is used, is clearly a similar combination. 1) Byl. Le. 194 ) Astronomy. WOn the yearly periodicity of the rates of the Standardclock of the observatory at Leyden, Houwt No, 17.” Second part. By Dr. E. F. van pr Sanpk BakHUyZEN, Ill. The period 1862—1874. 9. As was mentioned, several investigations about the rate of the clock Honwi 17 during this period have been made by Katser. They have been partly published. These published investigations are relative to the period 1862 May—1864 August '). Afterwards, in the autumn of 1870, Katskr undertook a new investigation founded on the period 1862—1870?%). In 1872 this investigation was continued and extended over the last year and a half *). Kaiser was engaged in this investigation, the results of which were intended for the 3° Volume of the Annals of the observatory, till the last months of his life. It was unfinished, however, at his death. The results which Kaiser had obtained did not wholly satisfy him. Several singular irregularities had shown themselves; moreover he was aware of the fact that the barometer-readings, one of the foun- dations of the investigation, might still be affected by rather consider- able systematic errors, even after they had been corrected as well as possible. These barometer-readings had been derived by him from observations repeated three times every day on an old defective mer- cury barometer oi Burt hanging in his study (during a year and a half on an Aneroid-barometer). The correction of this barometer was derived from simultaneous readings of the barometer in the transit-room. It appeared to be variable with the height of the barometer and increased considerably in the course of the years ; moreover the temperature of the barometer was quite uncertain. For these reasons H. G. VAN pr SANDE BaknuyzeNn, when in 1873 he planned the continuation of the investigation of the clock, deemed it necessary, first of all to procure better data about the atmospheric pressure to which the clock had been exposed *). He intended to derive these by the help of the regular barometer-readings made at the meteorological Institute at Utrecht. In the first place the constant differences between the barometer- readings at Utrecht and those at Leyden (the barometer in the transit- room) had to be derived. From extensive calculations, which have 1) F. Kaiser |. ec. 2) Vide: Virslag van den staat der sterrenwacht le Leiden. 1870—71 pp. 15 and 16. 8) Vide: Verslag van den staat der sterrenwacht te Leiden. 1871—72 pp. 14 and 15. 4) Vide: Verslag van den staat der sterrenwacht te Leiden 1872—73 p. 4. (195 ) been continued afterwards, it finally appeared that, when the neces- sary corrections’) and the reduction for difference in altitude had been applied, the mean barometer-readings at both places are in perfect agreement *). After the completion of this preparatory work H. G. VAN DE SANDE Bakuvyzen has been prevented by want of time from further inves- tigations of the rates of the clock Honwt 17. 10. When last year the investigation of the clock in the period 1862—74, was resumed by me, I have soon given up the attempt to derive trustworthy corrections for the barometer of Burrr and 1 too have used the readings at Utrecht. It appeared that in this way we can get a precision sufficient for our purpose, at least for the mean monthly barometer-readings. I had at my disposal readings of the barometer at Utrecht for 20", 2" and 10". From these I derived mean barometerreadings reduced to 0° for the whole of our period *}. In addition to these, however, we have readings of the barometer at Leyden for the last months. For, to begin with July 1873, the barometer in the transit- room has been regularly read five times a day. From these I could derive, in the same way as I had done for the time after 1877 mean barometerreadings, which afterwards I reduced to 0°. The comparison of the monthly means obtained in the two ways stands as follows : L. — U. L. — U. 1873 July + 0.38 Mm. 1873 Dee. + 0.8 Mim. Aug. 0.0 1874 Jan. — 0.2 Sept. — 0.2 Febr. + 0.2 Oci. —— 0:2 March + 0.8 Nov. — 0.1 April + 014 The differences thus appear to be very small. They would have turned out still smaller perhaps, if we had not neglected the hundredth parts of the millimeters in all the computations. The mean value amounts only to + 0,05 Mm. 1) About the errors of the barometer at Utrecht see: J. D. van per Praars, ,Over den barometer van het K. Nederl. Meteor. Inst.’ (Meteor. Jaarboek voor 1888). At Leyden the barometer-readings were reduced to those of the standard-barometer of Furss. 2) See also: Annalen der Sternwarte in Leiden. Vol. VI pp. CXIV—CXVI. 3) Ky taking the means of the readings at 10°, 20", 2°, 10" and giving half weight to both the extreme values I obtained the daily means from midnight to midnight. 196.) 11. For the derivation of the temperature of the clock 1 had the following data at my disposal. From 1862 to 1866 May a thermometer hanging at the pier of the clock was read at 8°30" in the morning. Beginning from that time two thermometers suspended in the clock case were regularly read, but from 1866 June to 1873 June these readings were only made at 8" 30° in the morning. Since 1873 July both thermometers were read five times a day. From July 1873 it was possible therefore to take daily means of the temperature according to the upper thermometer in the clock case in the same way as was done for the time after 1877. For former periods | bad to find corrections in order to reduce to daily means of the latter thermometer. For the purpose of finding these corrections | compared : Ist. For the years 1871, 1872 and 1873 the readings at 8" 30" in the morning of the upper thermometer in the clock case with those of the thermometer at the clockpier ; 2¢. for the years 18783 —75 the readings at 8» in the morning of the upper thermometer in the clock case with their daily means. From the two comparisons I found the following monthly means of the differences 4, = clock case — pier and 4, = daily means — readings at 8", everything being expressed in degrees Ré£avmer. The index-corrections have been taken into account. ray A, 4, A, Jan. + 0.21 + 0.22 July + 0.01 + 0.36 Febr. sila 19 Aug. AS Al March 14 44 Sept. 16 46 April 5 48 Oct. .20 .26 May 06 38 Noy. 16 29 June 03 AT Dec. 16 O04 For all the months I adopted for 4, the general mean + 0,13. For A, I adopted October—February + 0.20 March—September -+ 0.43 With the aid of these values and of the index-errors determined at regular intervals the necessary’ reductions were applied. Lastly I compared the temperatures according to the upper and lower thermometer, as has been done for the subsequent period, the difference in the two eases being that, for the period now under discussion, the clock was only enclosed in a single case. I will set down only the results which I found for the means of the 5 daily readings in the years 1873—76. u.—l. u—l. Jan. + 0.32 July + 0.44 Febr. —+ 0.54 Aug. + 0.40 March + 0.38 Sept. -+ 0.54 April -++ 0.42 Oct.” 2.70130 May + 0.44 Nov. + 0.31 June + 0.44 Dee. + 0.31 These differences are corrected for index-errors. 12. With a few exceptions I used for the time before 1872 the same time-determinations from which Kaispr had formed his monthly means of the rates. Some corrections however could be applied. The clock had been set going in June 1861 but I left out the first year and placed the beginning of my investigation at 1862 May, as Kaiser had done. It ends April 1874, a short time before the oceur- rence of the perturbation. The observed rates were first reduced to 760 Mm. at O° and to +10° R. For the coefficient 6 I again took + 0:.0140 (Kaiser in his last investigation found + 0+.0134) and for ¢ I adopted the value —0:.0174 which is the mean result of Katsur’s last investigation, allowance being made for the fact that [now reduced the barometer- readings to 0”. In the following table all the columns have the same meaning as the corresponding ones in the table for the period 1877—1898. 198 ) DR. as Tecap. DRI pit } 8 | ’ ‘ * 1862 May =| — 0.322 | 759.5 | +12.7 | —0.268 | — 0.209 June =| 0.300 | 58.2 | 43.0 0.213 | 3333 July 0.408 60.3 | 13.8 0.346 | 350 Aug. 0 424 60.6 45 0.354 B41 Sept. | 0.998 | 62.9 | 13.0 0.317 | 200) Oct. 0 346 59.4 10.6 | 0.328 204 Nov. 0.245 | 60.0 6.2 0.311 280 Dec, | 0.192 | 61.6 5.0 | 0,301 | 281 1863 Jan. | 0 301 56.9 4.8 | 0.348 | 344 Febr. OAM 69.4 5,2 0.352. | 305 March | 0 246 | 584 6.4 0.287 | 314 April | 0.237 Gio | 8.8 | 0.272 306 May 023 | Gt.7 | 10.8 | 0.223 | 24 June 0.388 | 59.9 36 | 0.324 | 344 July 0.247 | 64.3 1442 | 0/934 | 238 Ane | 0415 | 604) 454°) ~ O.go77] 314 Sept. 0.406 | 58.2 | 44.8 | 0.348 321 Oct. 0.442 | 58.8 10.3 0.420 386 No. | 0.9397 | 63.9 | 6.4 0.355 304 Dec. | — 0.277 | 63.4 6.0 | 0.390 370 1864 Jan. | +.0.032 | 68.8 08 0.251 27 Febr. — 0.165 | 598 99 0.298 | 3H March 0 305 54.0 aye 0.306 333 April 0.121 63.9 6.9 0.230 264 May 0208 | 61.4 4o1 | 0.996 257 June 0.34 60.2 1907 0.298 318 July 0.375 | 62.0 39 0 335 339 Aug. 0347 | 632 132 0.338 323 Sept. 0.401 | 61.2 12.5 0.374 347 Oct. 0.369 | 59.0 8.7 | 0.378 344 Nov. 0.268 | 58.8 4.6 0.345 314 Dec. 0463 | 63.8 | 4.2 | [0.3693 | 370 } ' | eS Bar. Temp. er D. aa 0.—C 4865 Jan. HG 530 750.0), P24 | = 0.495, |= 0.401, — 60 Febr. 0.10 | 50.5 | 4-4 0.358 su | — 5 March 0.964 | 57.9 | 2.7 0.362 389 | — 47 April 0.278 65.2 8.6 0.375 409 — 3 May 0.390 | 61.4 12.3 0.365 396 | — 42 June 0.352 65.3 12 6 0.381 AO | — 1 July | 0.464 61.2 15.4 0.387 391 + 45 Aug. 0.487 59.0 14.0 | 0.403 390 a M1 Sept. 0.389 68.2 14.4 | 0.433 406 + 1 Oct 0.485 | 53.3 9.5 | 0.400 66 | + 46 Nov. 0.376 | 604 6.5 | 0.438 407 | + 4 Dec. 0.237 68.6 41 | 0.460 440 | —17 1866 Jan 0.366 | 58.7 5.1 | 0.433 joo | — 2 Febr 0.473 | 544 47 0.487 00 | — 69 March 0.4295 54 3 4.8 0.435 462 — 7 April 0.394 | 602 8.4 0.495 459 | — 24 May 0.347 | 61.7 9.2 0.385 M6 | + 95 June 0419 | 60.2 | 44.9 | 0.397 “a7 | + 96 July 0.477 | 599 | 144 0.405 409 | + 35 Auge. | 0.536 | 56.6 | 43.3 0.434 4g | + 97 Sept 0.599 | 56.7 | 12.5 0.509 LAS) |) a BIS) Oct | 0 392 | 64.9 | 94 0.477 ZW IES 3 Nowe Obao1'=!| 58.6 |) a4 0.451 400 | +96 Dec. 0.351 60.6 5.2 | 0.443 493 | + 23 4867 Jan. | 0.376 | 52.9 2.2 | 0.413 409 | + 36_ Febr. 0.985 | 64.4 5.5 | 0.495 Pes | es March 0.407 | 56.2 3.8 | 0.462 489 | — April 0.457 | 559 7.8 0.438 Aig | — 29 May 0.396 | 59.8 10.4 | 0.386 AT | + 9% June 0.413 63.4 4(6) 409 499 | + 14 July 0.497 | 59.4 3.3 | 0.497 rn Aug. 0.505 | 62.2 14,4 | 0.459 446 | — 40 | ( 199 ) { 200 ) Reda ei Bar, | Temp. | pie y | pen | O-% 1867 Sept. — 0.484 | 763.7 | 4+ 13.2 | —0.480 | — 0.453 | — 49 Oct. 0.455, | 59.4 | 8.9 0.466 | 432 0 Nov. 0.312 65.9 | 6.4 ) 0.458 427 -f 2 Dec. 0.26 | 62.2 | 34 0.417 307 + 30 1868 Jan. 0.088 | 38.9 | 24 0.M0 | 406 19 Febr. 0.298 | 64.6 4.9 0.451 | 464 | — Mf March 0.302 60.6 5.8 0.383 M0 + 11 April 0.344 | 60.4 7.4 0.395 | 499 | —40 May 0.359 62.6 12 5 0.351 382 oa 35 June 0.396 65.6 14.0 0.404 424 — 9 July 0.493 | 62.4 16.5 0.414 M8 | - 5 Aug. 0.592 60.0 | 16.4 0.486 AT3 — 2 Sept. | osto | 93 | 43.2 0 444 7 | - 8 Oct. 0.381 60 3 8.4 0.413 379 + 28 Nov. 0.263 61.7 5.6 0.364 333 | + 7A Dec, 0.421 | 52.4 59 0.386 | 356 | + 36 1869 Jan. 0.237 | 63.7 2.9 0.413 409 | — 9 Febr. 0.269 | 60.9 5.7 0.357 370 | + 28 March 0.318 | 56.4 3.7 0 378 40s: |= April 0.336 | 62.4 8.8 0.391 45 | — 34 May 0.383 | 57.2 9.9 0.346 377 | -- 44 June 0.358 63.0 He0 0.383 - | 403 = 44 July 0.415 | 64.2 14.4 0 397 A | —44 Aug. 0.420 | 64.2 13.6 0.416 | 403 | —48 Sept. 0.456 | 58.0 12.8 0.379 352 | + 31 Oct. 0.409 | 61.3 9.2 0.44 407 | — %6 Nov. 0.40 | 58.6 | 6.0 0.390 | 359 | +20 Dee 0.349 | 56.5 | 2.9 0.424 | 404 | —97 1870 Jan. 0.202 | 62.7 3.4 0.360 | 356 | +49 Febr. 0.132 } 60.0 0.9 [0.290] | 344 | + 99 March 0.280 61.6 3.9 0.408 435 —= G5 April | 0.26 | 64 | 7.7 0.337 371 0 ( 201 ) i R. | Bar. | Temp. | pk I DE | Oe: s | ) | s s 1870 May — 0.299 | 763.4 |+ 9.9 | — 0.349 — 0.380 — 10 fans 0.352 | 63.9 12.5 | 0.363 383, | — 44 July 0.457 | 61.4 14.9 | 0.387 Salemi 23 Aug. 0.5386 | 58.5 14.4 | 0.488 AOR = 158 Sept. 0.34 | 644 1.4 | 0.379 3508 | 44 Oct. 0.475 | 54.7 8.9 | 0.420 386 | — 24 Naor hiya. dOraee 56.3 5.9 0.407 376 | — 12 ee 0.217 59.5 HE SP [0.353] soa | eB} ARTA Jan. 0.467 | 58.9 0.1 0.324 320 | + 42 Febr 0.414 | 63.5 2.5 0.293 306 55 March 0.198 | 62.7 6.0 0.306 eee |) dL os April 0.348 | 57.6 7.2 | 0.363 397 | — 36 May 0.250 | 63.2 Gate | wi covsit | 342 | +418 June 0.391 | 58.9 4.6 | 0.348) | 368 | — 8 July 0.458 | 58.7 14.0 | 0.370 | B74 | — 44 Aug. 0.497 | 62.9 15.0 0.381 3680 || —18 Sept. 0.475 | 59.3 12.8 | 0.416 389 | — 99 Oct. 07357 ¢|) 1607 7.6 0.423 389 | — 99 Now 0.309 | 60.9 3.7 | 0.432 Aoi | — A Dec. 0.178 | 64.5 Oye 0.378 | ae |) Se 4872 Jan. 0.285 | 54.6 3.6 0.320 316 | + 44 Febr. 0.973 | 59.8 45 0.366 319 119 March 0.294 57.4 5.9 0.329 | 336 | + 4 ei 0.317 | 58.7 8.9 0.330 BRAN eal. May 0.344 | 59.5 9.6 0.344 ; S15 el eee ane 0.385 | 60.4 43.4 0.337 Sey) | pct) July 0.400 | 60.7 15.5 0.314 | cree eo ey hee 0.430 | 60.4 14.6 0.356 | 38) e|| 047 Sept. 0.464 | 57.6 13.1 0.376 19 | shih Oct. 0.430 | 55.8 8.8 0.392 Bey |e INOW 0.417 55.3 6.9 | 0.405 g74) || — Ae Dae O:377 | 52.3 5A 0.354 334 | + 96 | 202 ) D. R. Be, of EP OR | CORE al eae {873 Jan. ~ 0.30 | 7576 Lt 45 — 0.363 ~ 0.359 + 1 Febr. 0.208 63.6 2.3 0.392 MOD — 45 March | 0.249 5 4.8 0.304 331 +- 29 April 0 263 59.8 vie] 0.504 338 +- 22 May 0.310 6041 8.7 0.334 365° | — 5 June 0.337 60.9 12.7 0 303 3230 | - 37 July 0 405 61.2 14.8 0.338 342 + 18 Aug. 0,429 60.7 14.6 0.359 346) + 14 Sept. 0.406 60 5 1.5 0.387 360 | 0 Oct. 0.426 58.0 9.7 0.403 369 | — 9 Nov. 0.352 59.2 5.9 0 412 381 — 21 Dec. 0.193 69.2 5.0 0 409 389 — 29 1874 Jan 0.253 63.0 4.3 0 394 390 | — 30 Febr. | 0.180 63.8 3.6 0.344 357 | + 3 March | 0.168 | 658 5.5 0.327 | 3k | OG April 0.275 59.0 8.5 | 0.287 321 | + 39 Before | undertook the further investigation of the reduced rates I *) I tried to find out the relation of the rates below O° to those above that temperature. It appeared that a systematic deviation of the former is far less evident than it was in the period 1877—98. In fact such a deviation shows itself clearly only in the two months 1870 February and December. Finally 1 excluded the days with tem- peratures below 0° only for these months and for 1864 December *). The modified reduced rates I, together with the corresponding tem- peratures, are as follows: Temp. Red. D. R._I. 1864 December + 2.4 — 05.390 1870 February + 1.9 — 0.331 December = + 3.6 —— 0.386 D) Sens comparing my values of the reduced rates I for the two first years with those occurring in Katser’s papers, allowance must be mae for the fact that my values apply for a pressure of 760 Mm. at 0°, whereas those of Kaiser may be assumed to apply for a barometer-height of 760 Mm. at + 10°. 2) During 8 other months the deviations were small and variable in sign. ( 203 13. In the first place I have investigated in how far the non-pe- riodic part of the rate, the constant a, has varied during the period under consideration. For this purpose I have combined the monthly means to yearly means. They are as follows, the years beginning with May. 1862 — 03.316 1868 — 03.400 1863 O09 1869 384 1864 oO) 1870 368 1865 A211 1871 07 1866 436 1872 O00 1867 428 187: 008 It is seen that the negative rate has somewhat increased in the beginning and somewhat decreased afterwards and that it remained nearly constant during the last four years. With these values and the corresponding ones for years beginning with August, November and February, I drew, in the same way as was done for the period formerly considered, a curve representing in a first approximation the change of @ with the time. 14. In the second place the influence of the temperature was investigated. I tried to find out: Ist. In how far, if we assume a linear influence of the temper- ature, the adopted temperature-coefficient applies for the whole of the period ; 2nd. whether there is any term varying as the square of the temperature. For the first investigation the several years were kept separate. They were assumed to begin with February. I used 1st. the deviations of the monthly means from their yearly mean, 27. the deviations of these same monthly means from the values of @ taken from the curve. In the third and fourth place the computations were repeated using, not the monthly means them- selves, but the mean value for the first month combined with the last, that for the second combined with the last but one, ete. By this device the influence of the “supplementary term” must be nearly completely eliminated at the outset. In this way I found for the correction of the adopted coefficient —0:.0174, the following four series of values; they are expressed in tenthousandth parts of a second, I II Il I\ [S63 + 5 + 4 a) + 9 [S64 + 28 + 10 + 13 0 1865 + 1 + 4 + 6 + 7 [S866 + 414 + 47 + 40 + 14 LS67 11 6 11 10 [S68 26 23 3l 32 [S69 11 11 15 17 1870 35 28 38 39 [S71 26 27 41 ~ 41 12 1872 2.20 aT 45 at 167a;- 4: 88). BB+ Pe aon eee The results of the four computations are nearly accordant. The value of the temperature coefficient appears to have varied far less than it did subsequently. A small fluctuation however, of the same nature as that which existed afterwards, appears to have occurred. It might be allowable to assume, in accordance with the second com- putation, which in my opinion is to be preferred : 1863—66 Ac=+ 9 c=— 05.0165 1867—71 19 — 0.0193 1872—73 + 26 — 0.0148 From all the years together we should find (8t63—/3. Ac=—1 c = — 08.0175 The investigation about the existence of a quadratic term I only executed for the mean of the 11 years. For this purpose I used the deviations according to the second and fourth computation. If Ac, and ec, represent the correction of the coefficient of #—f, and the coefficient of (#—t,)", ¢, being the mean temperature (= + 8".6 R.), we have, expressing both in tenthousandth parts of the second as unit, Ac, é, 204 Comp. + 0.5 Ge HERS ee — 6.2 — 0.48 At least for the mean of the 11 years, therefore, a quadratic term must be quite insensible. 15. It seemed unnecessary to apply corrections to the reduced rates I on account of the temperature coefficient, before proceeding to the investigation of the supplementary term. For the mean value of ( 205 } this coefficient agrees all but absolutely with the value originally adopted and its fluctuations are certainly inconsiderable. I made use of the deviations of the monthly means from the values of a taken from the curve and I made the years begin with May. For the sake of brevity I will only give the mean results for 4 groups, each of three years. In the last column the general means are set down. 62—64 | 65—67 | 68—70 | 71—73 1862 —1873 | Mayaeccce Se See PS Se) + 48 UO 526c + 4); +29) + 9) +30 + 18 July. ..<.. +12) +290; — 9| +19 + 10 August .... —20/ — 3] —58! — 5 — wv September.) — 96} — 4 | —14| — 32 — 29 October...| — 52 | —17| —40|} — 4 — 38 November.| — 10} —18| — 4| —55 — 2 December.| — 30} — 8| —17; — 20 — 19 January...| — 9| +44| +44] + 1 + 5 February .| — 2) —22) +514} — 8 + 5 March....) +18) + 6] +13] + 39 + 19 April. iin - 46) -- 43] -— 43.) = -59 seat In each of the 4 partial results the supplementary inequality is quite evident. Its amplitude is of the same order of magnitude as in the period 1877—98. There appears to be no reason for assuming any change in this amplitude during the 12 years 1862—74. I therefore tried to represent the general means by a formula and it appeared that a pretty satisfactory representation may be obtained by a simple sine: Ag = + 08.0341 cos 2 x eer aliees fa) The sinusoid corresponding to this formula, together with the points given by the observation is represented in Fig. 4. The differences between the observation and the curve, in thou- sandth parts of the second, are as follows : 14 Proceedings Royal Acad. Amsterdam. Vol. V. ( 206 ) May + 17 Sept. 2 Jan. + 9 Jine 2 Oct. 4 Kebr. 8 July + 6 Nov. + 9 March — 8 Aug. — 9 Dec. + 1 April — 3 The fact that the supplementary term can be represented by a simple sinusoid and that a half-yearly inequality is not shown, agrees with the result found a moment ago, that no term varying as the square of the temperature is indicated *). Properly speaking the two results are equivalent. 16. Finally I have again tried to clear the monthly means of the rates, as well as possible, of all periodic terms. In doing this I have applied no further corrections for the influence of the temperature because the variation of its coefficient — the results of the years 1871 and 1873 are just those differing most considerably — did not seem as yet sufficiently demonstrated. No other reductions were applied, therefore, but those for the supplementary term according to the formula found above. The rates corrected in this way (= term) have been inserted, in the table already given, in the column Red. D. R. II. These values of the term a have been represented as well as possible by a sumple curve reproduced in Fig. 5. ; In this figure the results of the observation are also shown, not for every month separately, but for the mean of any three consecu- tive months *). I have tried to draw this curve about as simply as that for the period 1878—98. The outstanding differences O—C (C = curve) are contained in the last column of the table. These differences lead to the following mean amounts, which we might consider as the mean errors of a monthly mean : . 1862—1867 M. E. = + 05.0309 1868—1874 0273 = 1) The remark made at the end of § 7, p. 23 (90) does not make sufficient - allowance for the fact that, as long as no physical explanation has been given for the ‘supplementary term”, a variability of this term might be deemed no more probable than the variability in the course of time of a term varying as the square of the temperature. 2) On page 24 (91) I forgot to remark that the same was done in Fig. 3, which represents the period 1878—1898. whereas, if we had neglected the consideration of the supplementary term, we should have found : 1862—1867 M. BE. = =+ 03.0382 1868—1874 Oats which values are considerably greater. 1902. IV. The period 1899 17. Since the time, 1898 December, that the clock Honwt 17 has been mounted in the niche of the pier of the 10-inch-refractor, its rates are kept under constant control by computations which are made, immediately after the time-determinations, by Mr. Hamursma, computer at the observatory. He computes moreover mean values of the rate at the end of every month, which are at once imserted in graphical representations. The following investigation was founded on these results only slightly modified. The modification is the consequence of a small correction of the barometer-readings caused by the fact that the temperature of the clock is no longer the same as that of the barometer in the transit- room. The barometer-readings were reduced therefore to what they would have been at the former temperature '). As my investigation, which ineludes no more than three years, must be considered as a preliminary one, it seemed useless to replace the original mean rea- dings by the mean values according to the barograph-diagrams. More- over the constant correction of the barometer used was. neelected. As before the temperatures were determined from the readings of the upper one of the two thermometers suspended in the clock case. The former thermometers had been replaced however by two other ones having centigrade scales. Besides the temperature in the niche below the clockease has been determined for the period of a year by means of a thermo- graph of Ricnarp. It appeared that, even there, no trace of a daily period in the temperature is noticeable. In general the changes in the temperature have now become much slower and much more regular. At the same time the temperature in winter time does not nearly sink to so low a point as formerly ; this is shown even in the monthly means. In the years now under con- sideration the temperature in the clock case never sunk below + 2° C. As was done for the other periods, | have computed the differences 1) The reduction amounted to 0.4 Mm. in maximo. 14% ( 208 ) between the upper and lower thermometer for this period after the clock had been mounted in the niche. The monthly means of these differences, resulting from the five hours of observation and from the three years 1899—1901, are as follows: January + 0.02 July + 021 February + 0.01 August + 0.17 March + 0.01 September +--+ 0.06 : April + 0.02 October + 0.02 May + 0.05 November + 0.01 June + 0.15 December + 0.02 The differences are now expressed in degrees Celsius. The index- errors of these thermometers are insensible. 18. The observed daily rates were originally reduced to 760 Mm. and + 10°C. by means of the coefficients: b = + 08.0140 c= —0 .0170 In the following table, however, the Red. D. R. I. have been computed, not with this value of the temperature coefficient, which had originally been derived from only the first months, but with the value c = — 08.0220 which accords better with the observations. The meaning of the two last columns of the table will be explained hereafter. The four months immediately following the mounting and the regulation of the clock, during which the rate proved to be still some- what variable, have been left out of consideration and have not been inserted in the table. | Obst Bar. | Temp | Rea | © Rega | Reda |. De Ran | DRI | DRM PD. RU | | } Ss 8 | | | | are — 0.457 | —0460 1899 May — 0.416 | 763.2 |4 44.8 | —04 | — 41456 June | 0.432 | 65.7 |~ 45.0 | oso | p47 Eee: Taly 0.192 | 65.4 13.4 |° 0.00 | 4+ 2 |+ 4 Aug. | 0.228 | 66.0 | 48.7 | 0190 | + 36 he 31 Sept. | 0.353 | 5944 160 Pee eee ie be Obsd D. R. Bar. Temp. 1899 Oct. — 0.160 767.0 | + 41.7 Nov. 0.456 67.4 11.6 Dee. 0.048 61.7 Sofi 1900 Jan. 0.097 59.6 Bez Febr. 0.458 52.8 5.4 March 0.058 6L.4 65 April 0.065 62.2 8.4 May 0.153 62.2 Aidan June 0.247 61.7 16.4 July 0.258 63.8 18.3 Aug. 0.328 62.8 18.2 Sept. 0.952, 67.4 16.5 Oct. 0.978 61.9 13.6 Nov. 0.255 58.4 10.2 Dec. — 0.129 61.2 8.8 1901 Jan. + 0.052 63.2 5.2 Febr. + 0.023 61.4 5rd March — 0.098 Bile 6.7 April 0.105 59). 7, 9.6 May 0.104 | 65.4 12.6 June 0.216 64.3 16.0 July 0.266 64.5 19.3 Aug. 0.286 65.5 192 Sept 0.315 | 641.7 16.2 Oct. 0.266 61.7 13.5 Novy. 0.4120 64.0 Badt Dee. 0.4185 56.5 7.3 1902 Jan. 0.070 62.8 es Febr. 0.034 59.6 4.6 March 0.107 57.9 7.8 April 0,085 61.6 10.0 Redd D. RK. I =); Ss 0 On (0), 0. Reda 1D its WL DR Rte eh = 0.457 —0-169 224 ot 4 = 4 225 — 13 — 6 Lota Mele AS ART 40 186 —_— 30 — 29 158 — 18 — 29 151 — 22 — 33 131 — 1008) — eee 147 — 30 — 20 130 — Ali —_ 5 {OSes |aetaeh see ey oD 187 _— 3l — 3 214 = 17 — 8 226 — 4 — 10 DOG leet herria lie tS 172 + 8 + 27 099 + 57 + 52 0908, |) ae ote SS on 134 — 5 — 16 110 + 11 + 14 FSG. ae |ete, Sia 144 — 25 — 16 Poel preis aaecToalh tse 3 161 — 5 = 15 203 ae Gielee==. 24a) See aelOni ect 53 ISSN eI) Vag. ihe), “30 196 — 16 — 6 Gey = Spee ame 147 — 7 — 2% (Yon beget ee a 107 +. 14, + 148 ( 210 ) 19. The reduced daily rates I of this table show at once and with evidence the presence of the supplementary term; for the rest the rate of the clock in the present period appears to be a very regular one. If, first of all, we combine the monthly means into 3 yearly means, from May to April, we find: 1899 — 0.*158 1900 . 156 1901 ae There is no trace of a progressive change in the rate and for the further investigation of the influence of the temperature we may simply use the deviations from the general mean = — 0.157. If in the first place we assume that the influence of the temperature is a linear one, we find 1st from the monthly means, 2d from the means for two months combined in such a way that the supplementary term is nearly completely eliminated, respectively : c = — 0.0224 and = — 0.0220 which values are practically identical with that used for the deter- mination of the reduced daily rates I. In the second place let us assume the existence of a term varying as the square of the temperature. In this assumption we find, proceeding in the same way as before, for the total influence of the temperature: * — 0.50253 (t—10°) + 0.00074 (#—10°)? and — 0. 0247 (#-10°) + 0. 00069 (10°)? respectively. We thus find for this period a quadratic term of appre- ciable value. The difference between the two formulae is small; I will definitively adopt the former. 20. It thus becomes necessary to use a quadratic formula in order to clear the rates completely from the direct influence of the tem- perature, as is required for the determination of the supplementary inequality. We may, however, as well fake the influence of the tem- perature fo be proportional to its first power and then consider the remaining periodic part of the rate as “supplementary inequality”. I have followed both ways. In the following table I have inserted, first, the values found for the supplementary term in the first way, giving the results of the three years separately, as well as in the mean. These mean values are pretty well represented by the following simple sine-formula: 1) The mean temperature of the 3 years was + 11°.6 C. ( 214 ) T—May 3 3 Ag at 0.30465 cos 2x. ———— 365 The last column of the table contains the differences between the observation and the computation. Everything has been expressed in thousandth parts of the second. ] 1899 1900 | 1901 | Mean | 0—C. May........| -- 52 ++ 26 + 55 + 4% — 2 WHS s5honcs + 65 + 30 +19 + 38 + 3 TI Beas | cir + 58 + 17 + 12 + 29 + 14 August ..... + 22 — 40 — 24 — 14 — 5 September ..| — 45 — 54 — 42 — Ai — 16 October..... — 48 — 54 — Al — 48 — 4 November...| — 52 — 59 — 14 — + 4 December...| —25 | — 8 — Al — 2 + 10 January ....| — 44 + 37 — 7 — 5 + 10 February ...| — 20 + 36 —17 0 — 9 March...... — 2 = 415 +32 | +45 | — 16 Mas Seoone | + 31 | ++ 58 + 62 +50 | + 6 The mean monthly results of the observations, together with the sinusoid by which they are represented, have been reproduced in fig. 6. In the second place we give, in the column @Q of the following table, the values of the supplementary inequality which we find in the mean, if we assume — 0°*.0220 (#—10°) for the influence of the temperature. These values are represented by a curve reproduced in fig. 7. The column O.—C. of the table contains the deviations from this curve. 0. 0.—C. 0. 0.—C. May +28 —12 Nov. — 55 0 June +3 — 6 Dee. — 21 +2 July + 45 +18 Jan. + 8 +7 Aug. + 1 0 Febr. Se, +5 Sept. —51 — 11 March -+ 20 —8 Oct. —63 + 2 April + 41 +5 As might have been expected, the curve shows clearly a half- yearly inequality. 21. Finally T have reduced the monthly means of the rates both, by the linear temperatureformula with the curve of fig. 7, and by the quadratic formula with the sinusoid of fig. 6. The rates, thus reduced, have been inserted in the columns Red. D. R. IL and Red. D. R. IL of the general table. These columns do not contain the reduced rates themselves, but their mean values, together with the deviations from the latter. These deviations lead to a mean error of a monthly mean M. E. = + 0°0211 if we adopt the linear formula (Red. D. R. 1D, and M. E. = + 0.°0218. if we adopt the quadratic formula (Red. D. R. IIT). The two methods of reduction thus lead to nearly the same degree of agreement and a decision about the preference to be given to one of the two cannot, therefore, be derived from the monthly rates. If no reduction for the supplementary inequality had been applied, we should have found in the two eases : M. BE. = + 0°.0422 + 0 .0398. | " The increase of the J/. Z. is still considerably greater than it is for the other periods. The quadratic formula now leads to slightly better results than the linear one; the difference is small, however. V. Amplitude of the oscillations of the pendulum in the period 1878—1888. 22. As has been mentioned before, H. G. vAN DE SANDE BaknvyzEN caused a small mirror to be attached to the pendulum in 1877 °), for the purpose of determining accurately the amplitude of the oseil- lation by the aid ot the reflected image of a metallic wire placed before a flame of petroleum. The image was projected on a divided scale by means of a lens. 1 Mm. in the seale nearly corresponds to 0.5 in the total amplitude; the reading could be made accurate to tenths of the millimeter. In this way a determination of the amplitude was made, generally 4 times a day, from 1878 April to 1899. The determinations of the years 1878, 79 and 80 were elaborately studied by H. G. vay br Sanpbe Bakuvuyzen. The influence of the temperature, of the atmospheric pressure and also that of the position of the driving weight were thoroughly investigated. Having the inten- 1) See: Verslag van den staat der sterrenwacht te Leiden 1876—77 pag. 12. ( 218 tion of prosecuting this investigation he did not yet publish his results, 23. It seemed possible that the investigation of these amplitude- observations might contribute to the discovery of an explanation of the supplementary term found in the rates. I intended therefore to inquire whether the corrected amplitudes too would still show a yearly mequality. As H. G. VAN DE Sanpb BaknuyzeN gave leave to take advantage of his results for the present paper, his corrected amplitudes could be compared at once with each other for the period 1878—80. Furthermore I tried to execute a somewhat provisional investigation for the eight following years. For these years the monthly means of the amplitude found in a first approximation ') were corrected for the influence of the atmospheric-pressure, as found by H. G. van DE SANDE Baknvuyzen. A correction for the temperature was not so easily applied, because it appeared that its influence has conside- rably increased in the course of the years. Finally I proceeded simply in this way, that I derived the value of the amplitude for + 8° R. for every spring and every autumn by interpolations between monthly means corrected for the barometer-reading. The results have been brought together in the following table : Spring. Sue Autumn. | A.—S. 1878 37.77 38.99 39.74 + 1.49 1879 38.68 38.76 7AGGe ||) = 110 1880 38.84 | 40.06 | 39.50 | — 0.56 1881 44.27 A). AS | 4.47 =—+-(8) (0) 1882 39.70 39.18 | 39.49 | + 0.01 1883 38.66 35.49 35.67 | + 0.95 1884 32.49 30.70 F)0P |) a Ae 1885 29,20) 30.55 98.35 | — 2.90 1886 31.90 32.30 39.33, | + 0,03 1887 32.74 31.86 SI GSae eee OLAS 1888 31.04 1) As many observations are wanting the corresponding values had to be assumed. ( 214 ) These results are expressed in millimeters of the seale and they represent the total amplitude on that seale diminished by 320 Mm. The 2°¢ and the 4 column contain the results obtained for the spring and the autumn; the 3@ contains the means of two consecutive results for the spring; the 5% the differences autumn — spring obtained by substracting the numbers of the 3 column from those in the 4%. The differences prove to be very small; their mean amounts only to — 0,388 Min. or, if we exclude 1878 on aecount of a possible displacement of the lens, — 0.58 Mm., 7. e. —0’2 or 0.’3 respectively, whereas the effect of 1° R. is 0.’6 in the beginning and about 1’ afterwards. Besides, the sign of the mean difference is the reverse of what we should have found, when the amplitude of the pendulum lags behind the temperature. Thus already this superficial investigation seems to show, that there is no term in the amplitude analogous to the supplementary term in the rates. VI. Comparison of the results. 24. If we consider the results obtained in the preceding pages in their mutual relation, we are struck in the first place by the fact that the clock Honwi 17, which at present has been going for more than forty years, far from showing the defects of old age, has increased on the contrary in regularity of rate in the course of the years. We have seen that both in the period 1862—1874 and in that of 4878— 1898 the greatest regularity was only reached after some years. It may be pointed out now that this regularity has also increased from period to period. For we found for the mean deviation of the monthly means from a simple curve (1st and 2°¢ period) or from a constant value (3"4 period) the numbers : 1862—1874 + 0.0291 1879—1896 0237 1899—1902 0215 The diminution of the mean deviation is considerable and where- as in the 3'¢ period the amelioration in the clock’s position may have contributed towards this diminution, the difference between the first and the second is very striking. We have to consider in this connection that, for the two former periods, a whole year at the beginning has been left out of consideration, whereas for the third the 5 month. has already been taken into aecount. The only poimt in which the second period is at a disadvantage as compared to the first is that the influence of the temperature has been more variable. This however is mainly the case only for the last years, when, evi- dently, the cleaning of the clock had been already too long deferred. If we reduce the temperature-coefticient found for the third period to what it becomes for 1° R. instead of for 1° C., if further we reduce the mean coefficient of the first period to the value which would have been found, had not the barometer-reading been reduced to 0°, and if, lastly, we add the value found for the middle part of the second period +), leaving the quadratic terms out of consideration throughout, we find: 1862—1874 ¢ = — 0.0196 1885—1891 — 0 .0269 1899—1902 — 0 .0275 Between the 2"¢ and the 3"¢ period the pendulum has not been taken to pieces and only a small stain of rust has been removed from the suspension-spring. 25. Let us now consider the results obtained for the supplemen- tary inequality. Setting aside a half-yearly inequality, sometimes shown, which is connected with the precise form of the influence of the temperature, we find in all the periods a supplementary yearly inequality in the rates which ean be nearly represented by a simple sinusoid having its maxima about May 1 and November I, the semi- amplitude of which amounts to: 1862—1874 + 0*.0541 1878—1886 0455 1887—1896 0254 1899—1902 0465 In the latter part of the period 1878—1898 the amplitude of the supplementary inequality seems to have appreciably diminished so that in the years 1897—1898 it is hardly sensible. For the rest the amplitude of the inequality appears to have had nearly the same amount under any circumstances. The question now arises: What explanation can be offered of this inequality ? If we consider only the monthly rates, we may mathematically represent it as a lagging behind of about half a month of the influence of the tem- perature. This cannot be the true physical explanation, however, 1) See also the va'ues of ¢ for the 2nd period on p. 20 (87). ( D463) because it appears from the rates during short periods, that abrupt changes in the temperature are reflected almost immediately. Not- withstanding this, I deemed it possible, at first, that the true expla- nation might be found in such a cause, by assuming that part of the effect of the temperature on the rate perhaps by the intervention of the elasticity of the suspension-spring, — is only felt after along time. In this case however, we ought to find another and smaller temperature-coeflicient from swift changes in temperature than from the comparison of summer- and winterrates. In reality, however, it seems, that the coefficients obtained in the two ways agree in the main, at least as far as can be judged now, before the completion of a more elaborate investigation by Mr. Wreper. Besides a change in the elasticity of the suspension-spring, lagging behind the yearly change of temperature, has become improbable since we found no trace of it in the amplitudes of the oscillations. Another possible explanation might be found in the hypothesis that the temperature of the different parts of the pendulum is permanently unequal and that the distribution of temperature varies systematically with the season, in such a way that it is not identical in the spring and the autumn. The influence of a small inequality of the tempera- ture is considerable. For if the temperature of the pendulum-rod changes only by so much as 0°.1 R., whereas that of the mereury remains constant, the daily rate changes by 0%.065. The differences between the readings of the upper and lower thermometer in the clock-case must throw light on this distribution of the temperature. The information however must be defective 1st. on account of the small accuracy of the thermometers, 2"¢ because we do not know the relation existing between the temperature of the steel and the mercury of the pendulum and that of the surrounding air. If we consult the mean values of these differences of tem- perature for the three periods, we see that in the two former the difference: Upper temperature Lower temperature has been really found + 0°14 R. greater in April and May than in October and November. This would produce a difference in the rate agreeing in sign with that which is really found. In the 34 period, however, spring and autumn agree nearly perfectly. It seems to me still very uncertain, therefore, whether the cause of the phenomenon in question may be found in this distribution of the temperature. The fact that, whereas the clock was in very diffe- rent circumstances, the inequality of the rate was very nearly constant and also the fact that it seems to have diminished in the second period, seem, even a@ priori, contrary to such a hypothesis. (947) And so as yet I feel unable to give a sufficient explanation of the inequality which has been found. EXPLANATION OF THE FIGURES. Fig. 1. Supplementary inequality 1878—1886. 1887—1896. bo be b) » 3. Non-periodic part of the daily rate for + 8°.7 R. 1878—1898. ,» 4. Supplementary mequality 1862—1874. » 9. Non-periodic part of the daily rate for + 10° R. 1862—1874. , 6. Supplementary inequality 1899—1902. » 7. The same inequality if the influence of the temperature is assumed to be linear. In the Fig. 1, 2, 4, 6,7 the letters D., J. etc. stand for: December 1, January 1, ete. In the Fig. 3 and 5 the numbers: 78, 62 etc: stand for: 1878 June 15, 1862 June 15 ete. In Fig. 5 for 79 read 69. ERRATUM: p. 47. Behind the title of the communication of Prof. J. W. van WisHE is omitted : (Communicated in the meeting of April 19, 1902). (August 8, 1902). KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, PROCEEDINGS OF THE MEETING of Saturday September 27, 1902. —$—_—3 sce = (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 27 September 1902, Dl. XI). i QOerNh Ee sais se Ss : — = A. II. Sirks: “On the advantage of metal-etching by means of the electric current’. (Com- municated by Prof. J. L. C. Scurokper yan per Kok), p. 219, (with one plate). J. D. vax per Waars: “On the conditions for the occurrence of 2 minimum critical cemperature for a ternary system”, p. 225, W. HU. Kersom: “Reduction of observation equations contaiaing more than one measured quantity”. (Communicated by Prof. If. KamertimcH Onyes), p. 236. KE. H. M. Beekman: “On the behaviour of disthene and of sillimanite at high temperature”. (Communicated by Prof. J. L. C. Scmrorper van per Korn), p. 240, (with one plate). L. Hf. Srertseaa: “Measurements on the magnetic rotation of the plane of polarisation in liqnefi:d gases under atmospheric pressure. IT. Measurements with methylehloride”. (Communi- eated by Prof. I. Kamertixcm Oxnes), p. 243. (with one plate). H. Waca and C. H. Wixp: “Diffraction of Roéntgen-Rays”, (2nd Communication), p. 247, (with one plate). H. A. Lorentz: “The fundamental equations for electromagnetic phenomena in pondcrable bodies, deduced from the theory of electrons”, p. 254. BE. F. van pe Sanpre Bakuuyzen: “Preliminary investigation of the rate ef the standard- clock of the observatory at Leyden, Hohwii Nr. 17 after :t was mounted in the niche of the great pier’, p. 267. The following papers were read : Physics. — “On the advantage of metal-etching by means of the electric current”. By Mr. A. H. Smks. (Communicated by Prof. J. L. C. ScHropper vAN DER Kork). (Communicated in the meeting of June 28, 1902). Side by side with the tension- and bending-tests to which metals and their alloys are submitted, with the object to find out, whether the material answers to the requirements, Prof. Brearens gives, as a new method: a miscroscopic examination, which is deservedly made 15 Proceedings Royal Acad. Amsterdam. Vol. \ ( 220 ) use of on a large scale. In a special work on the subject; “Das mikroskopische Gefiige der Metalle und Legierungen,” this method and the practical use made of it, is treated exhaustively. The main substance of it is this: A piece of the material, which is to be submitted to microscopic examination is filed, till it is perfectly smooth, different numbers of carborundum-powder being used for the grinding, after which it is polished with tin-oxide or chrome-oxide, if a perfectly smooth slide is required; then, by means of the annealing colours, the ground plane will show a design, sharp-outlined. Since most metals and alloys have crystal-formations at their fractures, the annealing colours will produce a very strongly marked outline between the crystals and the ground-mass, because if is a known fact, that two substances, submitted to the same temperature, but of different formation (the erystals- and the surrounding mother-water) will not take the same tempering-colours. Next by making seratehes on the surface, with needles of known hardness (analogous with the known hardness-seale of Mons) the hardness of the material may be fixed. A similar design, not so minutely detailed however, may be called forth by the corroding influence of acids, bases or salt-solutions, which the crystals and the encompassing matter are not equally proof against. For this purpose the rubbing and polishing need not be done so carefully. This method however has also its difficulties, which may often be very troublesome. As is always the case, when an acid operates upon a metal, also in this etching-process gas will be developed. The microscopically small gas-bubbles which are formed on the slide will locally prevent the corroding process of the acid and be the cause of little holes and dots that have nothing to do with the design and may easily lead to faulty conclusions. The very long time the grinding and polishing sometimes takes (I state here the grinding of different species of iron and babbits) will keep many from applying this method. No satisfactory results, in some cases, being obtained oy this method, althongh the material showed distinct crystals at its fracture. Prof. SCHROEDER VAN DER Kok was struck by the idea, whether it would not be possible to etch metal-planes in another way than by corroding through acids. It is a known fact that a metal in a galvanic cell will corrode at its negative pole. I need only state the equally known fact, that the zine of a bichromate cell, after the electric current is set working, shows a magnificent structure. To forestall the objec- tion, that the chromic-acid of the cell has been predominating here in the etching-process, IT will just remark that a slight experiment, i.e., by putting the zine into the fluid, without letting the cell give a current, was sufficient to prove that the etch-design obtained in the first case, stood out in much stronger relief than had been the case, when exclusively applying acids. As in any electrolytical process anions are formed which together with the metal of the electrode may produce dissoluble salts, it was important to find out what disturbing influence this would have, and combine with it an examination into the practicability of this etching method and see whether it could replace the one of Prof. Brnrens, in case the results might be unsatisfactory. The corroding influence of acids having to be avoided as much as possible, preference has been given to use the electric current of a battery instead of producing it within the apparatus itself, as happens in any cell. The apparatus was constructed as simply as possible and is exactly the same as that used for ordinary electrolytical experiments. The object that was to be etched was used as anode (the place where the electric current enters), whereas a piece of copper-plate serves as cathode. The electric current was furnished by an aceu- mulator-battery, having a terminal voltage of 4 volts. In etching alloys of copper, it proved recommendable, every time to connect two appa- ratuses in series or in some other way to diminish the potential difference, on account of the highly fleeey deposit on the cathode. As electrolyte, water was used to which for every 100 em* + 6 drops of diluted sulphuric-acid had been added, in the first place better to conduct the electric current; in the second place, as much as possible, to prevent the formation of base metal-deposits *). Of course a controll- ing experiment was taken by hanging a second piece of the alloy, per- fectly alike, in a fluid of which the percentage of acid was the same, in order to be able to eliminate etching by the acid. I have prefer- red to begin experimenting with copper-tin- and copper-zinc-alloys on account of the sometimes beautiful results obtained by the rubbing and polishing method. In most cases I melted myself the alloys to be sure of the absence of foreign substances, which may cause very great changes in structure. The metal-slides were hung to a piece of copper-wire, but precan- tions were taken that there was no contact between the wire and the electrolyte, to be sure that the metal-plate, which had to be etched, did its work as electrode. For half an hour the electrolysis went 1) In alloys containing lead (babbits, type-metal, ete.) the sulphuric-acid on account of the indissolubleness of the sulphate of lead was replaced by nitric-acid, 15% on so as to produce a sharply outlined design on the brass- and bronze-slides. That to no other cause any difference might be attributed, all slides were finished off in exactly the same way as had been done for the acid-etchings of Prof Brurens; the etching standing out much stronger, this soon proved to be entirely superfluous and so the slides were filed only with a smooth-file.° The first experiment was taken with a small piece of cast-brass, which proved to be composed of 58.5 °/, of copper, 40.5 "/, of zine, also traces of lead and of tin being found. For half an hour it was submitted to electrolysis, the density of the current being + 2 amp. p. dM?*. The result of this experiment is reproduced in fig. 1. The indented structure is very distinctly visible, there being in the slide besides a marked difference in colour between the erystal- formation and the encompassing ground-mass. Bright yellow, the crystals stand out from the enclosing mother-water. When asecond experiment was taken the same alloy was submitted to electrolysis for 12 hours. Under the anode a glass-cup filled with glycerine and with oxide of magnesium was placed to catch up the erystals that might be hollowed out by electrolysis and which will be caused to sink by their weight, for as was to be expected (a thing which was proved by the experiment) the crystals having a higher percentage of copper than the mother-water (in which zine prevails) will be better proof against electrochemical influence and so in the end get isolated and detached. The residue left in the glass-cup was washed out with alcohol it being found that without this precaution the crystals, that had got detached, easily corroded, leaving nothing behind but a green powder; they were then dried in ether; the residue proved to contain 1.78 mG. metal-erystals. Although these crystals had not got loose entirely intact, they were distinctly angular in form and showed facets. Being submitted to electrolysis (I wish to thank Mr. Vermaxs for his assistance in this) these crystals were found to contain 1.19 mG. of copper, equal to a copper-percentage of 66.8°/,. Traces of lead were found on the anode and proved to be PbO, but the quantity was too small to permit weighing. The second design is of a piece of plate-brass, of which the ground slide is in my possession. Etching and colouring after perfect grinding and polishing, had yielded no result. The result of half an hour’s electrolysis with a current of the same density as with the first expe- riment, and the same fluid as electrolyte, is shown in the adjoined photo- gram. Also the effect of the mechanic treatment can be distinctly noticed. Everywhere in the slide twin-erystals are to be found, which as Prof. Berens explains in his work, are apt to be formed in conse- On the advantage of metal-etching by means of the electric current.” SIRKS. PAWEL Plate-brass. ») Fig coining. for Bronze >, Cast-brass. Fig. 3 V. Vol. Amsterdam. Proceedings Royal Acad. (2255) quence of the mechanic treatment to which the material has been submitted. This slide was the first which was no longer ground with carborundum-powder, but only filed. The ordinary bronze for coining (see fig. 3) equally shows a struc- ture in which the mechanic operation is visible, both in its ecrystal- formation and in the position and direction of the crystals, where the more or less flattened parts meet. From a piece of cast-bronze of a connecting rod a thinnest possible sheet was filed and polished; after heating, stuck on a slide-glass and submitted to etching by electrolysis. A beautifully executed, right-angled lace-work remained, very typical for bronze structures. The encompassing matter of .high tin-percentage had been etched away; the crystals, rich in copper, had remained. From a piece of heavily wrought phosphor-bronze, which had remained unaffected by colouring, I have obtaimed a slide with such a strong relief, that I have not sueceeded in taking a photography of it. Also here even the bare eye could see the right-angled structure. The arrangement of the crystals was like that of tiles on a roof. On account of the great practical use made of white-metal in the tech- nical branches, I have experimented also with that. After half an hour also here, intact cubes of alloy of tin and antimony outlined themselves; also here it was possible to go on etching very deep and without much difficulty to detach the cubes, entirely intact from the alloy. The little time left to me for the moment, necessitates my putting off the analysis of those cubes fill later. Whereas at the beginning only copper-tin and copper-zine alloys were etched, now also iron has been experimented with. The fact, that it is fine-grained, that the etched facets easily oxidize, that base- metal-deposits *) are apt to be formed, all that naturally causes difficulties. The use made of salt-solutions, as electrolyte, to diminish the internal resistance, has yielded no result worth mentioning I have submitted to etching a piece of an iron-bar rolled square. After a few hours the fibrous structure was distinctly visible with the bare eye, both lengthways along the fibres and crosswise, vertically on them. With some difficulty I succeeded in isolating ivon-slivers, which, if only collected in sufficient quantity, might be analysed quantitatively. A socle. of a gaspipe sawed through, showed eubes in the profile: all the crystals having grouped themselves in the rolling-direction. A piece of a steel angle-iron having been submitted to the bending-test, yielded no other result as 1) For on account of the corroding influence of acids on iron and sleel a very small quantity of sulphuric-acid can be experimented with. 224 ) yet, but the one that also here, just as with the piece of bar-iron, the direction of the fibres could be seen with the bare eye, as well as avery distinct difference between the drawn and the compressed fibre. As to the structure and formation of the carbide crystals nothing could be fixed at this first experiment, 1 do not doubt however, but also here the results will be satisfactory. Worth mentioning still is the etching of a cylinder-shaped piece of cast-steel, which was submitted to electrolysis for 36 hours. Although outwardly no etched design could be seen, a porous coat of + */, ineh of some iron-carbide appeared to be have been formed, which, coming in contact with the air, was apt to oxidize, could be cut with a knife, and in the incision glittered like metal. When analysed the iron-per- centage proved to be 91'/, °/,. The great results, obtained also here, are a stimulus to me, to investigate this matter later more thoroughly. Those experiments suggested to Prof. ScHRoEDER VAN DER KOLK the idea, Whether crystals of minerals treated in this way, would show a design. Considering the results, obtained with copper-alloys, a piece of a copper-ore was used for the first experiment. After an hour, also this material showed a distinct etch-design, which is probably connected with a crystal formation. Not to be led away from my subject, 1 will only just mention the phenomenon. Before concluding, I will resume the advantages, gained by the way indiceted. 1-!y. Results having been obtained, where the ordinary grinding- polishing- and etch-methods had failed. 2ndy_ The obtained preparations show a far more detailed design, Which stands out in much stronger relief than the ordinary eteh-slide. 3elly, Tt is not necessary to finish off the slides half so carefully, as the tempering-method requires. duly. From different alloys crystals or fragmentary crystals have been detached which permit of analysis and show remarkable differences with the average percentage of the alloys. The good results are a sufficient recommendation for practical purposes, time may still be saved by connecting many apparatuses ( 225 ) in series, so as to be able to etch different slides at the same time. To my opinion it will be possible with careful treatment (regulating the power of the current and using different acids) in this way, from all east-metals and alloys, to detach the crystals, thus making it possible to find out the quality and formation of the materials. After I had concluded these preliminary experiments, it came to my knowledge that the electric current had already been used as an etching medium in the work called “Contribution & Vétude des Alliages” edited by the Société d’ Encouragement de I Industrie Nationale, Mr. Carry describes a method, successfully made use of by him and which according to the added photograms, shows great resemblance with our method. He namely used an ordinary Danrett-cell to furnish the electric current and in it replaced zine by the alloy, that has to be etched, made a short circuit of the cell and obtained an etched design after having submitted the previously polished plane for half an hour to electrolysis. To my opinion however there are great objections here. For to obtain a somewhat powerful current it is necessary to reduce the inward resistance to a minimum, either by using larger electrodes or by considerably increasing the acid-percentage of the electrolyte. Especially with the etching of iron and steel the high percentage of acid will be an unsurmountable obstacle. A second objection is the impossibility, on account of that acid, to go on etching deep enough to detach crystals, for the angles and ribs which will be laid open by the etching-process will very soon dissolve again. Before I conclude, I will here openly thank Prof. ScHrogpER van pER Kok for his readiness in furnishing me all I wanted, to render this investigation possible. The Hague, June 1902. Physics. — “On the conditions for the occurrence of a minimum critical temperature for a ternary system.’ By Prof. J. D. VAN DER WAALS. Already in my “Molecular theory” I have derived the condition on which a binary system presents a minimum critical temperature (Cont. II, p. 20). Starting from the form of the equation of state I have assumed there, we namely find: ( 226 ) where 7 represents the temperature, for which the maximum and the minimum of the isothermal coincide. Discussing the conditions of coexistence we have pointed out that the critical phenomena for a binary system, though they are different from those which occur for a simple substance, yet in the case that the value of 7, defined by the above equation is a minimum, differ so slightly from those for a simple substance that this equation has a sufficient degree of approximation for the determination of the critical phenomena as we may realize them experimentally. Also for a ternary system the critical phenomena will differ from those for a simple substance, and we may expect that the difference will even be more consider- able than in the case of a binary system. Yet also for a ternary system this difference will not be so great, that the conditions for : . ae ry : : ° the existence of a minimum value of — will differ sensibly from ry the conditions for the existence of the minimum critical temperature as it may be realized experimentally. In order to find this condition for a binary system I have investig- E r dy 7 ated in what circumstances —_ taken as a function of wz, Can assume zx a minimum value, and so I have discussed the equation: iy d— Analogous to this we should have to discuss the following equa- (ions in order to find this condition for a ternary system: and =e At present however I will follow another way, whieh leads us more easily to our aim and which yields the results in such a manner that they may he better surveyed. If we write for a binary system: a, (1—#)* + 2a,, ¢(1—z) +a, 2° _ b, (l—«)? + 2 6,, « (1—x) + b, ey then the solution of the equation: (a,—ab,) (1—a)? 4+ 2 (a,,—25,,) # I—a) + (a,—2 ,) a® = 0 tO Nw “2 Ww q . r hy 3 Z - vields that value of «, for which assumes the eiven value 4. So we find: wt Eas 4 Alte A = (421) (2D) 2 a, —2b, (a,—) b,)? \ iit (a,,—A b,,)? (a,—2 b,) (a,—2 b,) <0, wv . oro the quantity is complex. This cannot be the case if the value ap . : ay a, a5 : ; : of 4 lies between = and —. It ean only occur if 2 is chosen either “il 9 a a, smaller than — and = or greater than both these values. a 9 If 2 is chosen such that (a,—+ b,) (a,—b,) — (a,,—46,,? = 90. . : . . (A) then this equation will yield the minimum value of 2. If we put in this equation either: a, a, 0 D b, then the first member will be negative. If we put: ,= O12 Ove then the sign of the first member will be the same as that of a ; eS = A ° Oe SY) ee (a, 4b.) (a,—ab,). The second member is positive, if —~ is smaller ) 12 a ay ye than — and also smaller than ie Consequently a value of 4 must ) nt 2 4 5 : . : : ay oe exist for which (1) =O and for which therefore 5, assumes a mini- ) x a a a a . . 1 “¢ 2 mum value. This value lies between —2 and —: or if — = lt b b, b 1 2 1 aa, a, between — and —. ) ) 12 2 a a a 12 . 2 + In the case that — is both greater than — and than a the first ) ) ) 123 } 2 member of equation (1) changes its sign in the same way, and the value of 2 for which the first member vanishes, lies also between a a 1 12 san Oe a, a a 7 and — or if Ge between 7 and - ) 1 14 b, det D5 ya 2 So for a minimum a a . 1 . . value of 2 we have An >) * and for a maximum value an : , , 13 i3 If 4 has the value of a, also the following two equations hold: et @,,—Anb,, 1- av = a,—A,b, . and 1—a = (ys —Awb,, ~ a,—Ayb, ve *,* . As ——— must be positive because « must lie between 0 and 1, —Z# the sign of a,,—A,,, is opposite to that of a,—Anb, and a,—Aywh,. This agrees with what we have deduced concerning the relative value of x Os am and —. Ne We should have obtained the same results, if we had written the relation @, = 2), in the following form: a, —ab,)\(1 —*) + (4,,.—4b, ,) ey? a,—Ab, In the case that a,—2, is positive namely this equation cannot be satisfied if the coefficient of «* is positive; so if (a,—Ab,) (a,—Ab,) — (a,,—~b,.)° = 0. If the coefficient of a? is zero, then this equation can only be satisfied if we put: (a, —4b,) (1—2a) + (a,,—4b,,) «= 0. On the other hand in the case that a,—2d, is negative this equation cannot be satisfied if the coefficient of «* is negative. This however uso yields: (a,—4b,) (a,—Ab,) — (a,,—26,,)? > 0. If therefore we have the equation: (a,—b,) (a,—Ab,) = (a,,—Ab,,)? > 0 then the value of 2 must be either less than the minimum value of dy * — or more than the maximum value. dx We must however distinguish between a minimum value of 2 Ud and a minimum value of 2 which oceurs at positive value of ale x corresponding to a negative value of . The former, which really apa, a a a exists, requires that — is both smaller than = and than = . The 13 1 2 (@ 229%) latter cannot of course be realized. Solving the equation (a,—Ab,) (a, —Ab,) — (a,,—4b,,)? = 0 we find: 2 P 2a - : a 2(b,b,—6,,”) " This equation can be satisfied by a real value of 4 if: a(e—2) +(¢ alls fi) 0. 4b,,°\b, 6, b, by) \b, by, " . . . nf 5 Ais . ay This equation is certainly satisfied if —— is both smaller than - ia yy a ‘ es i and than a , but it may also be satisfied in other cases. Let us ) 2 a, Qe Aye a, assume. that =e = and a . If we then have: ) ds 19 bys 2 Gye ONT Be eas CO \c b., 5,/\b, 65 4b NO, a minimum value of 2 occurs indeed, but in this ease it corresponds, . . . * & according tO our previous observations, to a negative value of —— . SS We arrive at the same result starting from the equation of Cont. IT p. 20. Ay, For a ternary system we have, putting —~” ey (a, —2b,)(1—«—y)? + (a, —2b,)a* + (a, —Ab,)y? + 2(a,,—2b,,)e(1-a-y) i + 2(a,,—Ab,,)v(1 — «—y) + 2(a,,—Ab,,)vy = 0. We may represent this by the sum of three squares: [(4, 4b, )1—«—y) + (4,,—Ab, e+ (4,340, 5)y)° =): (a,—Ab,) is a Gee) a Abe — Mi a2 E la, —2b,) = Seren ty | (@,, —4b,,)— (4,5 i)ltas: a an =| . a,—Ab, a,—db, is AR = ‘ Ted ao = 2 7 z (a an) z ae a,—d/b, ahs (@,.—AD, .)(4,;—4,;) |]? (a,,—46,,)° ne a a,—AaAb ae. 2),) 2 ee ee 4, a,—2db, nae yee eoeme) > Z a, —Ab, In the case that a,—’b,>0 and (a,—2b,) (4,—2b,) > (a,,—26,,)', this equation cannot be satisfied if the coefficient of y* is positive. If this coefficient decreases to zero, then the equation is satisfied by only one set of values for w and y, namely by those values for —— =. ) _— a ( 230.) which both the other squares are equal to zero, If the coefficient of ® is negative, then a locus exists (a conic section) which indicates é yy ye 4 all mixtures for which 2" has the same value. If this locus is try reduced to one point, as is the case if the coeflicient of y’ vanishes, then 2 is for that point a minimum, respectively a maximum, The minimum value of 4 satisfies therefore the equation: {(a,—Ab, (a, —4b,)—(a,,— Ah, .)*} (a, —4b, (a, —4b,) —(a,;—Ab, 3)7j — — {(a, —Ab,)(a,,—Ab,,) —(a,,—Ab,.)(4,,;—26,;))? = 9, 13? a,,—Ab,, | a, 4B, 1° (Oy5— 8,5. |= 0. a a | @,,—4b,;, a,,—Ab,, , a, —Ab, or a, —Ab, , a,,—Ab | ay,—Ab 13% For the determination of 2 and y we have moreover the equation : (a, —2b, (1—a—y) + (a,,—4b, a + (a,,;—4b,,)y = 0 and the equation, which follows from the other square when it is equated to zero. Another way in which we might have reduced the equation Ary—Abxy, = 9 to the sum of three squares, would have yielded the following two equations for the determination of « and y. (2,,—26, ,)(l—# -y) + (a, —Ab, )a + (@,,—28,5)y =0 and (a,;—4b, ,)(1—#—y)-+ (a,,—%b,,)@ +(a, —4), )y = 0. Eliminating 1—x—y, 2 and y from these three equations in which they occur linearly, we find again equation (2). In order to calculate « and y we may derive the following rela- tions from these three equations. 1—a—y x y \a,,—2b,, a,,—Ab,, a, —Ab, Ke —ab, , a,— | la, —Ab, 5 @.,—Ab, lays - Ab i 3 23 2 d 237 a, —40;, PRC ee p= aig oo ab, or 1l—wr-y 1s x 2 y la, —ab, , ee re » @,—Ab,, |b, » a, —Ab, lon oh, » 4, —Aab, | \a, 2b, Ss a eg la,,—2B,, » 4,,—db,, and 1—«—y =: « aS y a,,—Ab,, » a —db, ee as Se 2 a,,—ab,,| |a,,—Ab,, 2 As its a,,—Ab,,, 4,,—Ab,, a,3;—4b,,, a, —Ab, | ja, —Ab, , a,,—Ab,, In order that 2 have a minimum value for positive values of 2, y and 1—wv—y the following relations must hold: ( 231 ) a,—ab, > 0 a,—ab, > 0 a,—ab, > 0 (a,-—Ab,) (a,—4b,) ae (4,,—40,,)’ = 0 (a, —Ab,) (a, —A4b,) — (4,,—A46,,)? > 0 (a,—Ab,) (a, —4b,) — (4,;—Ab,,)? > 0 (a,,—4b,.) (4; —4b,,) — (4, —Ab,) (4.;—4b.,) > 9 (a,,—Ab,.) (4,3 —4b,,) — (4, —Ab.) (4,,—A,,) > 9 (4,3 —Ab, 5) (4.; —4b,,) — (4, —2b,) (a,,—Ab,.) > 9, and 2, must satisfy equation (2). The first set of three inequalities indicates, that this value of 4 must be lower than that of the components. The second set indicates that it must be lower than the minimum value of 2 for each of the pairs of components of which the ternary system consists. The third set must be fulfilled in order that v2, y and 1—wx—y be positive. Ge G3 —%3 5 ay Let us assume —<—-<— and suppose that the values of —, Die PEA Ds a, a, , dias Es Va : — and — are higher than that of —— without deciding anything s 3 og : 7 aa a, a, a, about the relation between the values of the quantities —,—and—. I, 3 According to our assumption the expression (4,,—4 8,5) (413— 1 b,,) — (a,—28,) (a,,—4 6,5) : 5 Gio 7 5 O15 ar, we ah , is negative for 2=— * and also for 4=—* and it is positive for ) , 12 13 a * a . . . . a —— and. for 2—= 7 This is perhaps best illustrated by a graphical 793 “i 5 representation. - a ay; Here the points 12 and 13 represent the values of —* and— and 12 1a the parabolic curve passing through these points the value of (4,,—4 b,,) (4,;—4 5,3). In the same way the points 23 and 1 represent the value of ay: b 23 )y the value of = a : ? A and of = and the parabolic curve passing through these points ( 232 (a, —A b,) (a,, —4 b,,). These parabolae intersect between the points 13 and 23 and on the right side of the point of intersection the first mentioned parabola lies higher than the second mentioned; the expression under conside- ration is there therefore positive. The graphical representation of the expression (a,,—A b,,) (a,,—6,;) — (4,—2 b,) (a4,,—A 4,,) has the following shape: from which we see in the same way that these parabolae intersect between the points 13 and 23 and that this expression is positive for higher values of A. The third expression : (a,,;—4 b,5) (a,,;—A4 b.5) — (a,—A b,) (a,,—4 b,,) Qe (33 Mes ay is positive for 2 equal to ——,——,— and — and, when equated to i a b, 13 13 33 zero, it will in general not yield a real root; at least not between 12 and 3. The graphical representation of this third expression has the following form: where the parabola passing through the points 13 and 23 lies every- where higher than the other one. The first mentioned parabola would, if there should exist roots, descend below the second one between the points 13 and 23, and so the two roots would lie between those points. But in this case also the third expression is positive above a certain a a a value of 4 below =*. Or both parabolae might also intersect on the 23 ( 233 ) left side of 12 and on the right side of 1. Also in this case this expression is positive and even within broader limits. In the case that a value of 4 for which the left hand member of equation (2) vanishes, is higher than the value discussed for these three expressions, a minimum value of 2 will exist, which represents a really occurring minimum critical temperature. Let us write equation (2) in the following form: (@:—20,) (a, —46,) — (@,,—2b,,)% {(a, -20,) («,—2'b,) = (a,,—20,,)3 — mea 116-4) (c,d .) = (a2. B,) (a, ~2°0,,)}? == 0: The first member is negative if we choose for the value of 2 cither the minimum value of 2 for the pair 1 and 2, or for the pair 1 and 3. We will denote these minimum values by (Aan),, and (An), 5- On the other hand the first member is positive if we choose for 4a value for which the expression, the square of which must be taken, vanishes, — this holds however only in the case that the value or this last root is lower than that of the quantities (An);. and (An)... In this case the equation (2) has a root which satisfies all the requirements for a minimum value of 2 at positive values of 1—v—y, w and y. As an instance we choose the following numeric values: Pees) (Ose) (bel Oe Oo ee Oty eu ya Denil a Coaic Oy is ra 15 a), Stile ys Se — oa alios C—O —— OS b, b, b, ie Le Jo3 a ee —— ALA C—O oe C—O GQ, 0.4924 1 2 3 12 ; 13 ’ 23 From this we find: (am)y2 <= 2.933 (An), —= 2.962 Gres = alld A value for 2< 2.953.... makes therefore the three following expressions positive : (a,—A b,) (a,—A b,) — (a,,—A b,,)? (a, —A b,) (a, —A b,) — (a,,—A b,,)? and (a,—2 b,) (a,—4 b,) — (a,,—2 b,,)? For the value of 2 for which the quantity : (a,,—2 b,.) (4,,—4 6,,) — (4,—A b,) (@,,—2 5.) is positive we find: 42> 2.884.... For the value for which the expression (a,,—26,,) (a,,—4 b,,) — (a,—4b,) (a,,—26,,) is positive we find: 2 > 2.855 and the last of the given expressions . "ye . . . . a L a is positive within the limits Fae Gee 13 S hee he &> ( 234 ) The value of 4 for whieh the equation (2) vanishes, lies therefore between 2.884... and 2.933, and the shape of this equation shows that it must lie nearer to 2.933 than to 2.884. We find in fact Ama= 2.9252. <.%,. With the aid of this value of 2, we may caleulate the values of : and : from the equations of p. 230. But if the degree l—«—y l—-w -y of approximation with which 2, is determined is not high, the coordinates of the point to which 4, relates, are only known inae- curately. These coordinates however may be calculated directly by means of the following equations : a,(1-0-y)+-a,,0+-a,,4 aya 1-w-y) + Ugly My3(1-"-y) |. Ast GY Ly b ,1-w-7) t b,42 + bu < | l-w-y) +- bya +b,,y b,,(1-w-y)4+b,,¢+b,y We obtain these equations when we determine the centre of the ellipse Cry = 4 Dey and when we eliminate the quantity 4 from the equations /”, = 0 and Py = 0. So we find: __(4,—4,,) (lL—-w—y) + (2,,—4, ) y +E (43=443) HS Ban (oF —b,.) l—« —y) oe (6,,—b, ¥ y+ eae) “ra _@ 43) (1—#—y) + (4,,— a.3;)4 + (4,343) ” WB, —b,,) a v eb] =f (b,,—b,3) y a= (b,,—65) y Introducing the condition, that the centre lies on the ellipse itself we get the given equations. awa b-bd AS ee In the case that 6,,=—>—-, b,= sat > and },, aa TS which = equations may be satisfied approximately, then the locus of the centres is greatly simplified and may be written as follows: (4,—4,,)(1—«—y) a (a,,—a@,)«+ (a,,— (3)! a b,—b, ‘ 2G —a,,)(1—#—y)+(a,,—4,, e+ (a, ,—45)y b, - b, ‘ It is therefore a straight line, at least in approximation. With the given numeric values we find: 0,6(1—a —y)— 0,282 +40,2076y — 1,101—#*—y)+ 0,70762+0,328y = s 0,2 “= 0,6 or 0,7 (1--w—y) - 1,5476 & + 0,2948 y = 0. With this simplification the determination of the coordinates comes therefore to the same as the determination of the point of intersection of a conie section, e.g. Je a( —a—y)+a,,0 +a, | ]— &—Y) Ft Hyg b, (l—w# = y) + b, gl + b 1 3 de b 1 AA 1 —«—y )4 byw +b, 34 with a given straight line. In this case we find: ow 4 1 ay ae) y and ee er = 1—w—y 4 In fact the given numeric values for a, and a, were chosen such that we might find simple values for the coordinates. Because of the asymmetry round the mixture with minimum erilical temperature we might of course have expected that the centre of the ellipses which vary with the temperature, would change its place. For the theory of binary systems it was necessary to introduce the quantity «@,,, whose value we are not yet able to deduce from the properties of the components. From the calculation of (An), by means of the equation (a,—Ab,) (a4, —2b,) — (a,,—Ab,.)? = 0 follows, that for substances with a minimum eritical temperature this quantity cannot be equal to Waa, but that it must be less. If it were equal to 4 y(t, the equation would yield a value 2— 0. 4 : : i Gea, Moreover it would follow from a,a, = a,” that —.— would be ; : Git ae Ay. ; : ereater than ——, as 6,6, in any case will be probably less than 6,,?. moe 12 For the application of our theory on a ternary system therefore, aso knowledge of the quantities @,,, @,, and @,,, is required, which however must be assumed to be known from the knowledge of binary systems. The theory of the ternary systems therefore does not require any new data, above those of the theory of binary systems. 16 Proceedings Royal Acad. Amsterdam, Vol. Y. i) ( 236 ) Physics. — W. H. Kersom. 4 Reduction of observation equations containing more than one measured quantity.” (Supplement N°. 4 to the Communications of the Physical Laboratory at Leiden by Prof. H. KAmertian Ones). (Communicated in the meeting of May 31, 1902), § 1. The most widely read text books on the theory of probabi- lities and the method of least squares treat of the reduction of observation- equations each of them containing one variable. In physical measurements, however, we obtain equations between different quantities each of which must be considered as liable to an accidental error. This, for instance, occurs when we have measured the pressure of a gas or a liquid at different volumes and temperatures, and we want to deduce from the observations the equation which represents the most probable relation between these quantities inves- tigated. As in the literature on this subject I have not found a general solution for such a case, it may be useful to give it here. *) 1) Literature on this subject: Cuas. H. Kuwwet. Reduction of observation equations which contain more than one observed quantity. The Analyst. July, 1879 (Vol. VI, N°. 4. I have not been able to find this volume of the periodical in Holland. Merriman. The Determination, by the Method of Least Squares, of the relation between two variables, connected by the equation Y= AX-- B, both variables being liable to errors of observation. U. S. Coast and Geodetic Survey, Report 1890, p. 687. A Textbook on the Method of Least Squares, § 107. Here an elegant solution of the problem is given for the case in which a linear relation exists between the two measured quantities. Jutes Anprape. Sur la Méthode des moindres carrés. C. R. t. 122, p. 1400, 1896. The author gives a solution for the case when: EBM (a, by(6 er 5 0) = Nas in which ¢; and Ni represent measured quantities, and a, b, ¢.... are to be determined. Ravensuear. The use of the Method of Least Squares in Physies. Nature, March 21, 1901, p. 489. The author, apparently not acquainted with the literature mentioned above, points out that in treating equations between several measured quantities, we must make allowance for the fact that each of these quantities has an error of observation, and he gives a graphic solution for the case in which a linear relation exists between two quantities, some supposition regarding the accuracy of the measure- ments of each of those quantities being assumed. K. Pearson. On Lines and Planes of Closest Fit to Systems of Points in Space. Phil. mag. (6) Vol. 2, p. 559, Nov. 1901. The author gives an elaborate essay on the lines and planes (if necessary in a higher-dimensional space) which are such that the sum of the squares of the perpendicular distances between a number of points not situated in a straight line or a plane, and those lines or planes becomes as small as possible. § 2. Suppose, we have measured some series of the quantities L, M,N ...., between which the following relation exists: JE! Tepes VIG ING cae FONG Gree) a) a ee ean where VY, ¥,7....are unknown quantities which we want to calculate. We assume that the number of equations between the observed quantities is larger than the number of unknown quantities, so that we want to calculate the most probable values of Y, Y, Z.... by means of the method of least squares. Let L,, .1/,, V,.... be a set of values belonging together, as yielded by the observations, 1, m,,n,.... the errors made in these observations, Mi, Mn,» Mn,-.-. the mean errors in those measurements L,, M,, N,...., which we assume to be known before hand, XU; Yu Z -->- & set of approximate values for X, Y, Z.... v,y,2.... the corrections to be caleulated, which must be applied to those approximate values. Hach measurement gives then according to (1) an equation: eee om ON, an, 6. — F- X, n= 2 y-Z, .2...-— 4, - (2) where: OF L.=(= WEY p= ia eto EX Ngee ea ace ee a or aXe — = ODO i pe = Oi i=sie i=) irene eNC— PN ae — ON gieraiete He Ha (ere ADs IN Norce teste 33) Nias tn Zonet eas) Yet x,y,z.... must be chosen so that +) = ee m,° ie : = SS SS = oh Sap ecqoo |mSalinmmommns 4 . (@) mi,” Mn, My.” J If now the coefficients VY, ¥,Z...., are known, what errors, /,, m,,7,..-. correspond to the observed quantities 2,,.1/,, N,...? It is evident that various sets of quantities 1, M/,.V.... may have given rise to the same sets of quantities Z,, J/,,.V,...., and that those values of L, M, N and hence of 7,,m,,n, ave the most probable for which i m,? De : a Rea eS age 2 is a minimum, 1) Kontnauscu, Lehrbuch der praktischen Physik, p. 16 considers the equations: 2) fa (WAL ia su Cay Saute, 3) es) “where 7,s...., and often « are instrumental readings” and yet he determines (see p. LL) A, B, C so that the sum of the squares of errors in wis as small as possible. 16% 238 ) while we have the relation: L, l, }- M, m, + N, ny -}- sees YF - constant, We then obtain /,, m,, m,...., from f + K 5 ——— m),? m —_+K.M,=0 mm, “ 4Kk.N, =0 Mn, where : — --- es — T,?m,; 4+-D?mn,27+-N,?m,, ae With this (8) becomes k= Vy = . . . a So ee ——__———— 1s 8 Minima D,?m 2+ mn? + N,?mn, _ te ee If we define the weight of the observation equation by : 1 ad — — Rem eet .\) L,?m, 714M My, + TS Mig 2 (ote then (4) is reduced to 9,7,’ isa minimum, and the equations for the determination of wz, y, z....: become: or: [og XX Je + [op X Vy + [gp XA]z-..-+ [go XF]=—0 Ig ¥X]e + (oY V+ (op YZie---- + (9 YF |= "| . (6) [yZX]x + [9ZV Wy + yZZ)2..-.+ [yZF] =9! where, according to the usual notation: [gX AX] = 9, %,° + 9, X +:--. Fon De [XY] S05 Xx, xe =f Is XxX, Y, fe a5 In Xp, ¥, if n stands for the number of observations. We hence arrive at this very simple result, that from the equations Ao Vy Bee Fy 0 o Sapo, ')). ’ ' 7 In performing the differentiation we must attend to the change of Pin a point that moves with the velocity ww, If relates to a fixed point of space, we have i! oy oy oy —_=fP+ wm, — + w, — We 5s Ow q y oy + 02 and, since —=5.. Div iv, dt EE ees aoe eS ov = P+ n, ae + Ww, a +- Ww. a YP Div w. Combining this with (21), we get for the mean value of the cur- rent corresponding to the motion of the polarization-electrons P + Rot [). w]. c. Magunetization-electrons. If the body contains magnetized particles (§4,¢), we have nothing to add to 9 and gw. There will however be a new part of ev. We can calculate it by applying (18), because the quantities (5) vanish for every particle. Let us first replace, in the formulae of § 5d, q by ov,. We then find C.— 5 q, = — m., q2=t+ My, and, if we denote by MW the maynetic moment for unit volume or the magnetization, a vector that is to be defined in a similar way as }, ye Dy, = — We, a — M,,. Finally, by (18), — OM: OMy Die SSS se Oy z with similar expressions for oy, and gy-. The mean value of the current, in so far as it is due to the magnetization-electrons, is therefore Rot M. It may be called the current equivalent to the magnetization. § 7. It remains to take together the different parts of the second member of (1). Putting D=d+ }, 5 AO tos eee > and R — Rot [P. io ee mente A OMte (24) we have $=S+154+C64R + Roem. Now, we might understand by the current in the ponderable body the whole of this vector. Conformly to general usage we shall however exclude from it the last term. We therefore define the current as the vector so that Ce hop it. fens ake oo, (20) We may call 9 the dielectric displacement in the ponderable body, and &B the displacement-current. As to the total current ©, the for- mula (25) shows that it is composed of the displacement-current, the conduction-current ., the convection-current © and the fourth vector X, for which Porncarté has proposed the name of Rdntyen-current, because its electromagnetic effects have been observed in a well-known expe- riment of RONTGEN. § 8. We shall now write down the equations that arise from (I)—(V) and (1) if every term is replaced by its mean value. In order to obtain these formulae in a usual form, we shall put i ee eek ee ae bn a) ee ek a ee (8) al) (eee 8 i i er mere 215) these quantities being the magnetic induction, the magnetic force in the ponderable body and the electric force in the body. Beginning with the equation (1), and writing @ instead of @, for the (measured) density of electric charge, we find Divd = o — Div }, whence Die — Oar fame a ea oe (K) We may further deduce from (1), taking into account (Dy and (1D, Div &§ = 0 ‘ and consequently Div 8 = 0. Now the expression /o/ we have found for the current that is equivalent to the magnetization, shows immediatelY that the distri- bution of this current, taken by itself, is solenoidal. We conelude from this that Vio G0) 5 es se oe From (Il) we may deduce, if we introduce the value (26), Rot S=4aS-+4% Kot M, or, taking info account the relation B= H+4am which results from (27) and (28), Rot f= La. 3 22a) ee eee Finally we find by (LV) Rot = — 2, ee and by (V) Diol 10) oa belie oe et We have thus been led back to the equations of the cleetromagnetie field in a form that has long been known. In this form we may use them without even thinking of the individual electrons. As soon however as we seek to penetrate into the mecanism producing the phenomena, we must keep in mind the definitions that have been given of the different quantities appearing in the equations and the manner in which they are connected with the distribution and the motion of the elementary electric charges. The formulae (27) and (28) e. g. show the precise meaning that is to be attached in the theory of electrons to the terms “magnetic force” and “magnetic induction”: The equations (I‘)}(V') may be applied to all bodies indifferently. It is otherwise with the formulae expressing the relation between S (or D) and &, and that between B (or ®) and §*); the form of these depends entirely on the particular properties of the bodies con- sidered. I shall not here diseuss these more special formulae ; in order to deduce them from the theory of electrons it is necessary to con- sider the forces acting on the electrons ina conductor, the “molecular motion” of these particles and the circumstances which determine the electric and magnetic moments of a single molecule or atom. 1) See Voier, Electronenhypothese und Theorie des Magnetismus. Nachr. d. Ges. d. Wiss. zu Gottingen, 1901, Heft. 3. — eo LP lL ee 207 Astronomy. — “Preliminary investigation of the rate of the standard clock: of the observatory at Leyden Honwt V°. 17 after it was mounted in the niche of the great pier.” Byers Beh. VAN DE SANDE BAKHUYZEN. 1. In a preceding paper on the clock Houwt 17 I communicated the investigations I had made on an inequality of a yearly period noted in its rate which does not depend on the actual temperature. Besides the periods 1861—1874 and 1877—1898 | discussed also the period 1899—1902 when the clock had been mounted in the hall of the observatory in a niche cut out for this purpose from the ereat pier. From the mean daily rates during periods of about a month each, I derived formulae for the rate in two different ways, and this research clearly brought to light that during this period the rate of the Clock had become considerably more regular than before and now satisfies high demands. Since that time the same formulae have been compared with the daily rates observed during much shorter periods and an investigation has been undertaken about the barometer coefficient, for which purpose the monthly rates were less appropriate. The latter calculations have so clearly shown the excellence of the elock also with regard to its rate during periods of a few days, that it seemed to be of interest briefly to give here the results to which they led. 2. The results we obtained from the previous investigations may be resumed thus. Under all the conditions in which the clock Honwt 17 has been placed, its rate, after correction for the influence of the temperature, has always shown a residual yearly inequality. As the former influence had been derived from the yearly variation of the temperature, the residual inequality must necessarily show a difference of phase of three months with respect to the temperature. If the influence of the temperature had been derived and accoun- ted for in the form c, (#—t,) + ¢, (4-#,)?, whether we had found for ¢, a small negligible value, as in the period 1862—1874 or an obviously real quantity as in the period 1899—1902,, the residual inequality could with sufficient accuracy be expressed by a simple sinusoid. If on the contrary only a linear influence of the temperature had been accounted for, while an investigation of c, showed it to have an appreciable value, the residual inequality showed a half- yearly term besides. This could be expected; for as long as only the 1S Proceedings Royal Acad. Amsterdam, Vol. V. YOS yearly variation of the temperature is concerned, a quadratic influence of the latter and a half-yearly inequality are completely equivalent, 3. For the rate of the clock during the period 1899—1902 I derived in the first place the formula: DD. Ro = — 08.169 + 04,0140 (4 — 760). — 0*.0253 (¢ — 10°) + 0.00074 (¢ — 10"). a a3 PORDAES cor Or eo oe secondly the formula : D. R. = — 07.157 ++ 0°.0140 (4 — 760). — 02,0220 (¢ — 10°) + Suppl. inequal. . . . . ITD) The supplementary inequality in the second formula was repre- sented by a curve. Yet it can as well be represented by a yearly and a half-yearly term. We then find: Apr. 29 Suppl. Tnequ. = = = + 03,0471 cos 2a —— T — Apr. 16 — 05.0198 cos 4x 2 2 ie BTS) From the term depending on the square of the temperature found by the first method of calculation and from the yearly variation of the temperature in the clock-case, which is approximately represented by T— May 4. t= -+- pO Sere Ve 5A sin oe :) ; 365 we derive for the haif-yearly term di — May 4 —‘0°:0148 cos 4. 365 which is in sufficient agreement. The two formulae must however give different results, as soon as the accidental variations of the temperature become of importance, and therefore it was of interest to compare the rates during short periods with either. 4. Hence two comparisons were made for the three years 1899 May 3—1902 May 3. *) T — June 9 30d *) In this and the following calculations the supplementary inequality for for- mula II was read from the curve. 1) For the next term we find: + 09.55 sin 4= ( 269 ) / Within that period [ could) dispose of 182. time-determinations at average intervals of 6 days, giving I8l values for the daily rate. We can assume as mean error of the result of a time-determination, largely accounting for systematic errors such as variations of the personal errors of the observers, + 0+.04. I do not give here in full the results of the comparison of these ISI observed rates with the two formulae and only lay down the mean values found in both cases for a difference: observation—com- putation. ‘ I found: , Formula | M. Diff. = = 0s.0333 Fi Il =+ () .0344 Hence this mean difference is nearly the same for the two for- mulae; indeed, if the three years are kept apart, it is found to bea little greater for formula I in two of the three years. We may therefore say that the two are in equally good agreement with the observations and for the investigation of the barometer coefficient it was sufficient to use either. I chose formula IL (linear influence of the temperature) and I proceeded in the following way. The rates reduced with that for- mula to 760 m.m. and 10° and freed from the supplementary ine- quality were divided into five groups according to the barometric pressure and for each group the mean of those reduced rates was calculated. The results are laid down in the following table, where the first column gives the number of rates from which each mean has been derived. Number. Barom. Reduced. D. R. | O.—C. | | 17 | 752.8 — 08.174 — 0s .002 31 | 757.6 162 | a 02 OS 762.6 | 154 + OL 14 707 4 145 | a 02 21 | 772.2 | 141 td OD From these results I derived as correction for the barometer coefficient: Asb= + Os OOLT 18* 270 ) while T found for the daily rate for 760mm. — O*.160, With these values we obtain a very good agreement with the observations as appears from the differences obs.-comp. contained in the last column of the foregoing table. Hence it appears that the value for the barometer coefficient == -+- O°.0L57 is determined with great precision '). For the constant term of the formula we find from all the rates O8161, while, if we put = + 0°.0157 also in formula I, the constant term here becomes 0.173. 5. With the formulae thus modified : D. R. = — 08.173 + 08.0157 (h—760). 08.0253 (10°) + 08.00074 (—10°)?. + Supplementary inequality... . . (Ia). D. R. = — 08.161 + 08,0157 (h—760). 0*.0220 (¢—10°) + Supplem. inequal. ., (Ma). we have again compared all the observed rates and this time the comparison has been extended to 1902 Sept. 20 i.e. till almost five months after the period from which the formulae were derived. Besides the observations have been compared with a third calculation. This we obtained by applying the formula Ila so that we did not use the actual mean temperature but that of five days earlier. It is obvious that in doing so also the value of the supplementary inequality must be altered. An assumed lagging behind of the influence of the temperature of five days is equal, so far as the general variation of the temperature (as found above) is concerned, to 0.27 X the yearly supplementary term. Hence the latter had to be diminished by this part of its amount. The formula thus modified I call II. The results of these three comparisons are given in full in the following table. The first column gives the dates of the time determi- nations, the next column gives the mean temperature for the period between the date of one line above and of that on the same line, while the third, fourth and fifth columns give the differences between the observed rates for those periods and the computations Ia, a and II/ respectively. These differences are expressed in thousandth parts of seconds. 1) According to the investigations of Mr. Weeper a value little different from this follows for the period 18S82—1S98. a ee BO bss mObssamObssa | |imacmnein | "| Obs. | Obs. | Obs. Temp.| — — — | | Yerap.| — —a Ia Ila | I Ta IIa | Id 1899 | | 1899 May 3 Nov. 12 |-++-192.6 | — 12 | — 14] — 98 pe A210 5 a te AO fe > 9 980|) 44.0) 9 3)]) = sie 3 > «6 47 | 12.0) 4+ 33/4+ 93) 4+ 91] » 28] 10.8 | — 42} — 51 | — 63 » B80] 419.7 Cueto talline 7a 10. k =» 9.) —.99'| — 49 June 3) 13.0) —417)—32}—40}] » 13] 6.8/4 83) + 83 | +140 > 8| 14.8]+ 43})+ 33] — 3 » 16 3.7 | + 76 | +4103 | +170 » 44] 14.8) +97} +44]/+293]7 » 19] 3.0 Hes 19 | + 46 | + 52 Be 2201) 45 4 |b 136 |) 99) a 93)| 2:3)) — 24 | on | Se Bh » OF} 16.5) +290} +14)/+ 574] » 31 3.1 | — 52 | — 419)) — 38 July 7 16.5)/—+ 7)/— 3)+4+ 7 1900 | » aI 16.4 | —17 | — 29 | — 298 ]] Jan. 8 RON |e —— Oe en Ob OD » 44) 184 )-4+57)4+57)/4 4137] » 2] 5.4] — 44] — 29 | — 36 p «AT | 18.6) + 56/4 60)4+ 99}] » 2%] 6.0} — 36] — 36 | — 62 » 1] 19.6/+ 78) +91) 4 7 |] Febr-4] 6.4 12 | 9 | 2 pe) Bl |! 19.67] + 39) + 50). col] » 8 Oa) Gt atatne Aug 3] 19.4 | + 30) + 38/4 45 |] » 20] 43)—98|— 9/4 8 » 9| 19.6) + 66) +76 | +71 |] March2| 69] — 4 0 | — 28 > 44) 191/42) 4+ 98) + 41] » 9) 6.3] —48}— 7] 4 93 bee] 418.7 | + D6:) 4. 30. | =e 34 |], 46-| 6.7.) — 40)| — 30) — 34 » 26] 17.7]— 3) — 4/+4 42 » 20} 6.8] — 30 | — 20 | — 10 Sept. 3 18.3) | +47) + 25 | + 11 my |) OG |) 5) | — 71) ) = » 8) 18.3) + 9]+292/+ 18 ]] » 30 MeEItlie=Lesrisiog) Weg p43) 17.7 | + 34 | + | + 50 [f April 2] 6.0 | — 52 | — 39 | 8 Rouen 16.3 | oa) 9} + 7 eae | 6.4 | = 38) 19) = 41 Oc 5] 14.4) — 35) — 32) — O24 ]) » 12) 7.2/—12) — 4] — 41 > 9 i84|4 3 + 71+ 15]/ » 418] 9.0) — 99] — 99} — 49 5 SA ec || eae 9.9| 4.37 | + 34] 4 95 » 49] 41.4 | — 42 | — 37 | — 30 » +24) 10.7 | +47|/4+ 9|—11 » 4 10.9 | — 419 | — 14} — 417 >» 28 | 10.1 | — 16 | Oh 1 Pama ait sa eA || 194) 35 | May 1| 9.8| +44] 440] +35 Nov. 5| 12.3/4 4/4 6|— a1 | » 4) 10.4) — 71 | = THs 83 Obs, Obs, Obs, Obs, Obs. Obs. -- Temp. — _— — lle Ih 7] Ila Il4 10) 1M) May 10 442.4 | — 42) — 22) — 43 ]] Oct. 19 12.6 7 +) + D 14 114.7) — 46 % | - , » 2 11.6 9 ee } » a 1.2); —19;— 30 | — 12 Nov. 3 114.8} —— 5O 48 | — 67 5 43 se June 2 13.0 | — 27 | — 40; —- 43 wees) 10.3 | 2)+ 6 » 9 9s) —— 19' 1 == 49 4A p 2] 9.2) -+4+ 22) + 90 | + 99 » 12 16.3 | — 26 ee oe » 8.8 re 19° |= 44) ee oe D Is 17.3 | + 33 | + 33 | + 15 |] Dec. 7 8.3) +21) +4147 | +44 | a +- _ + +++t+ | G = ~~ = ~I ae t- | ae ir oie ts eee eee =. + Temp.) — Obs. Obs. | Obs. Obs. Obs. Obs. Ta ia ee la Pe nity 1901 | | | | 1901 Apr. 20-1 9.3 Ae ay Nov. 4 |441.9|/+ 6/+4 8 » 93} 10.5 | +42}] »° 4) 10.6} + 96} + 99 | fa | + » 99 | 44.6 | | =f + = » 20 F | Tune — BD} SZ.) |S als) SE) |) as: 1902 | = ; 4 =A D) 7 16.4 + 17 | + 414 0 Jan. 5 | 6.6 | = Oe le es | | ) [Srl Sao) — oO e—— Ol — 10) » 11 8. 20 aS) H | | i + | SOD. ues Sele oR eee gO! It ig pe Sele Cea || 19k | 0) | 30) | sae . | 9, | , 98 = 9 | fe : = July i] | 16.8 | — KF Nea DA — 38 » 98 | 7.9 “bE Is + D + 5 = || | < | » 10 727°) — A9 |. — 99) — 30 Febr. 4 | 6.4 + 36 | + 37 + 70 | a) + + + tS 2 bo | | is Pest 2022) =) 4 Ae | ho co | ea | t2 to | Z | | + oe ee veer + P16) 494] — 4)4 7 3) March 4-| 5.6] — 44] + 4 | — 95 ee tS, | eae 30) | ON AO | ON) == A kg |p 98 eee Se en al ne » 44 7.4)+ 9|-+46 | + 95 Sipe 5 | 16.8/—%]—27)— 71)» 49] 7.7} +449) 4 45) 4 49 B 4G) 45.8 | = 92) - 93] —96.]] Apr. 3) 8.3] + 19} 144] 4 94 + + —e + + + + » Y6, 16.2 20 pea) 7 » 12 Se lee ay eT 8 : , | =F ( fi + Oct | 16.7) —- 5)/+ 9 | = > Is 9.3 | + 32 | J 3 AG | Dee edo eta Gn) elaeigs |= 30 p25) |) 439) 44 | = 34 | -E 40 | mye AGS ABE! at) | AE), || IES) » 8] 12.4 | + 37 | + 99 | + 96 | | ! ; yh RIT ee) Gi PEN oy 1] Tha Ce) a [ sas See OMG) | 12 29 Obs. Obs, Obs, Obs, Obs. Obs, Temp. -- Temp. + = -- lv | We | ite le | Is. | Wh 12 1902 ; } } May 2% 440.4 | — 10 1s 9 || July 31 |447.4 | — 50] — 63 | — 55 » ! 12.714 26 +42) —13]] Aug 5] 16.8} —54| —o8|— June 41] 45.9] +37] 4392] 4 46]] » 41] 16.9) — 40] — 58 / — 56 » 17 14.6 34 | 48 19 » Wb 16,0 | — 521 — 70) ae » 93! 45.4) —49]—90}—36]l » 20} 46.51 —44 8 — 38 » 81 46.8) 4 7 0 Ril » | 46.8] —49|—55 | — 66 July 5| 48.4] 4+ 44] + 48 O]] Sept. 8) 47.4 | — 16) — 19 | — 36 » 12] 17.9/—9/—%/— 7][ >» 8] 178 _ 95 | 4g | it [Spied 7 ae) — 31 |) — S81) — oF » 4144) 16.7 | —49 16 | — 8 >» 8 47.7) —% | — 32 7H] » 29! 45.9} —97|-—98|— 7 From these differences we derive the following mean errors of a rate computed by means of the three formulae: : : = Form. Ta. Form. Ia. Form. IIb. | 1899 May—1900 April...... | E 08.0348 E (0s .0345 05.0424 1900 May—1901 April... . | Bo | 387. | 447 1901 May—1902 Sept...... | py | 266 | 274 | | 1899 May—1902 April...... + 0.0314 + 0.0327 | + 0.0385 1899 May—1902 Sept...... | +o.0011 | + 0.0339 = 0.0382 First let us compare the mean errors of the three formulae inter se and with the corresponding values formerly obtained for the for- mulae IT and Il with the uncorrected barometer coefficient. Then it appears in the first place from the values for the period 1899 May—1902 April that the correction of the barometer coeffi- cient has markedly improved the agreement with the observations. *) Secondly it would appear that the quadratic formula now represents the observations a little better than the linear formula, and thirdly we find that the supposition of a lagging behind of the influence of the temperature markedly impairs the agreement. 1) Each of the three years separately also leads to the same result. ( 275 ) A consideration of the differences obs.—Il@ and obs.— II shows however, that the latter conclusion does not equally hold good for all parts of the year and that the agreement with formula HH is especially bad in the winter months. In order to investigate this more closely, 1 divided the observations into groups of two months and calculated for each group the mean value of the differences, first for each year separaicly, then after combining the corresponding groups of the different years. The latter values follow here. } Form. Ila. Form. Ip. ee Panuary., Mebruarya.asemie sete a # 0s .0402 + Os .0549 WEEN s\n Foon eas oopcbdscpocudas 208 214 Nikiyg HMB edosssebebasse psc soc00K 285 284 Util h oad AD 0 Ce ora neater Stereo pce e 43 368 September, October..........-..... 215, | 932 Noveniber; December .............. 369 | 559 They lead to the singular result that during the four winter months formula Il 6 agrees much less with the observations than Ia, whereas in the middle of the summer the agreement with II/ seems to be better, and in the other months both formulae may be said to agree equally well. In this respect the different years practically lead to the same conclusion and hence we cannot say that this has been brought on by entirely accidental causes. However this may be, we are not entitled yet to assume a lagging behind of the influence of the temperature. Let us now consider separately the results for formula Iw, which seems to represent the observations with the greatest precision (those for Ila do not essentially differ from them). It will be seen immediately that during the last seventeen months the rate has been considerably more regular than during the first two years’); a smaller M.E. has been reached although the 5 last of these 17 months were not included for the derivation of the formula. Thus the feature observed before, i.e. the gradual improvement of the regularity of the rate after the mounting of the clock, shows itself once more. The mean result for the whole period (M. EK. = + 08.0311) may already be regarded as very satisfactory, and the great regularity represented by a mean difference of + 0%.0251 between a daily rate from a 6 days interval and a relatively simple formula gives us a high sense of the supe- 1) Already at the beginning we had left out the first 4 months after the remounting. ( 276 ) riovity of Honwi 17 in its present state. That this regularity markedly surpasses the one reached formerly is shown also by the results of an investigation of the vears I886—87, which are among those of the greatest regularity in the period IS77—159s5. This investigation was made in a similar manner as the present one, the mean interval between the time determinations used was 5 days and the mean error found was + 0.0365. 6. We may also investigate the rates of a clock in such a manner that only the irregularities of a very short period are considered, A simple process for attaining this is to calculate the mean value of the difference between two consecutive reduced daily rates. Applying this method to Honuwié 17 during the period under consideration ') | found: Mean difference 1899 May-—1902 Sept. + 0*.0315. ; i 1901 May—1902 Sept. + 05.0253. From these mean values considered in connection with the mean errors of the rates in 6-daily and in monthly intervals formerly found we can draw some, albeit rough, conclusions about the amount of the perturbations of longer and shorter periods. The values found, as well those for the whole period as those derived for the last year only, are given in the following table. The columns -1 contain the values found directly, the columns / those diminished by the amount that can be ascribed to the errors of observation, assuming + 0.04 as the total mean error of a time- determination. M.E. 8 of a 6-daily rate stands for the total mean difference from the formula Ia, found above, M. E. @ represents the error derived from the mean differences between two consecutive rates. The mean errors of the monthly rates differ a litthe from those of my previous paper as they now also refer to formula Ta. L899 —1902., 1901—1902. AS AEGAN oaths B. | M. Diff. of two G d. r.| = 0s.0313 | = 08.0967 | = 0.0953 | + 0s.0193 M. E. z of G6 d. rv. 189 | 137 M. E. 7 of Od. r. oll 997 ay | I M. E. of monthl. r. 209 208 164 163 1) The rates were reduced by means of formula Ila, but a reduction according to Ia would practically have led to the same result. Although these calculations are inaccurate owing also to the fact that the intervals between the time determinations often differ rather much from 6 days, yet it is evident that the M. E. 8 are much larger than the M. E. @ and hence that considerable perturbations of long period exist, as, indeed, a glance at the table of the obs.—comp. also shows. It would be possible to account tolerably well for the values found for the three different mean errors by assuming, quite arbitrarily of course, that there are two kinds of perturbations, one constant during 6 days and another constant during a month. We should then have to assign for the whole period-an average value to both of += 05.02 and for 1901—1902 alone one of + 08.015. There are not many clocks about which investigations have been published, which allow us directly to compare the regularity of their rates with that of Honwt 17 and most of these embrace but a short period. An investigation extended over 4 years about the standard-clock of ihe observatory at Leipzig Duxckrr 12 has been published by Dr. Rh. Scnumann*). He uses 224 time determinations at mean intervals of 6*/, days and derives for the rate a formula containing a linear influence of the temperature and of the barometric pressure and besides a term varying with the time elapsed since a zero-epoch. As mean value of the difference obs.—comp. he finds + 03.059 and there is no evidence of a residual yearly inequality. I calculated also the mean value of a difference between two consecutive rates and found + 03.055. In the latter respect we possess also data about the four normal clocks of the Geodetic Institute at Potsdam. An investigation by Mr. Wanacw*), about the rates during last year gave the following mean differences between consecutive rates after correction for the barometric pressure, while the temperature was kept very nearly constant: Strasser 95 + 08.054 Rierter 20 + 0 .062 Dencker 27 + 0.047 Dencker 28 + 0.049. These values are considerably larger than that for Honwii 17, but respecting the Potsdam clocks we must keep in view that Drnckrr 1) R. Scuumany. Ueber den Gang der Pendeluhr F. Dencxer XII. (Ber. Siichs. Gesellsch. d. Wiss. 1888). *) Jahresbericht des Direktors des Kéniglichen Geoditischen Instituts fiir die Zeit von April 1901 bis April 1902, pg. 35. 275 27 and 28 had lately been cleaned, while Sraasser 95 during the period of observation had twice been replaced and meanwhile had been exposed to great differences of temperature. For Dexcker 12 at Leipzig also some perturbations from outside shortly before and during the period under consideration are noted, 7. For a clock which is used for astronomical fundamental deter- minations the regularity of the rate during the 24 hours of the day is of the very highest importance, but it is obvious that only long continued observations reduced with the greatest possible care-can — give us any information on this subject. As yet I can only state that we may confidently expect Honwé 17 not to be inferior in this respect to other clocks kept at constant temperature, seeing that, while the amplitude of the yearly variation of temperature has diminished comparatively little in’ its present place, the daily variation has almost entirely disappeared. This will be seen from the following values of the difference between the temperature at 4 o'clock in the afternoon and the mean of the temperatures of the preceding and the following 5 hours in the morning. These differences taken for about 240 days have been combined in 6 two-monthly groups, and their means follow here: Temp. 4h—Temp. 20h Riiuary, Pebrucinys ieeetetee sree +0?.09 Naresh yA prils-< sre ee eee see + 0.13 lity; ule <0, Seer eee + 0.12 als. AO SUSb i) Bsn dee eee + 0.20 September, October. ..2,.5.........- + 0.14 November, December... ....... + 0.08 The mean difference is greatest in summer, but even then very small, while no difference ever reaches to 07.5. (October 22, 1902). KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MBETING of Saturday October 25, 1902. 0 ce — (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeelmg yan Zaterdag 25 October 1902, Dl. XI). SNS AN Gas ANF ARSE H. W. Bakuvis Roozesoom: “A representation in space of the regions in which the solid phases, which oceur, are the components, when not forming compounds”, p. 279, (with one plate). H. W. Bakuvis Roozesoom: “Equilibria of phases in the system acetaldehyde + paraldehyde with and without molecular transformation”, p. 283. L. Aronstery and A. §. van Nrerop: “On the action of sulphur on toluene and xylene”. (Communicated by Prof. J. M. van BeMMELEN) p. 288. Tu. Wervers: “Investigations of gluco-sides in connection with ihe internal mutation of plants”. (Communicated by Prof. C. A Losry pr Bruyy), p. 295. J. D. van pER Waaxs:“Some obs rvations on the course of the molecular transformation”’, p. 303. J. 1D. van per Waars: “Critical phenomena in partially miscible liquids”, p. 307. J. K. A. Wrrrurim Saromonson: “The influence of variation of the constant current on the pitch of the singing are” (Communicated by Prof P. Zerman), p. 311. J. E. Verscuarrecr: “Contributions to the knowledge of van per Wats’ 4-surface. VIL. The equation of state and the ¢-surface in the immediate neighbourhood of the critical state for binary mixtures with a small proportion of one of the components”, p. 321, (with one plate). Continuation p. 336. J. Borke: “On the structure of the light-percepting cells in the spinal cord, on the neuro- fibrillae in the ganglioncells and on the innervation of the striped museles in Amphioxus lan- ceolatus”. (Communicated by Prof. T. PLace), p. 350, (with one plate). The following papers were read : Chemistry. — “A representation in space of the regions in which the solid phases, which occur, ave the components, when not forming compounds.” By Prof. H. W. Baxavis RoozeBoom. (Communicated in the meeting of September 27, 1902). In the course of my researches, I have often made use of special kinds of graphical representations to indicate the limits of the exis- tence of single phases or complexes of phases. It was only after the year 1896, when it could be taken for granted that the general 19 Proceedings Royal Acad. Amsterdam. Vol. V. ( 280 ) character of the equilibria between liquid and vapour in binary sys- tems had become fully understood, that efforts could be made to con- struct a complete graphical representation of the conditions of equili- brium in which solid phases occur. The simplest possible case is found when only the two components of the binary system occur as solid phases. For such a case, | have since 1896 arrived at the representation in space of which photographs are given in the accompanying figures. For the case that chemical compounds or mixed crystals occur as solid phases other figures have been constructed which, however, may be deduced in a simple manner from the present ones. In this figure the length represents the temperature, the breadth the concentrations « of the mixtures which can exist as vapour or liquid, the component A being placed at the left and the component B at the right. The height represents the pressure. The figure does not represent any, particular case, but is so constructed that the different details come out plainly and the dimensions are not too great. We start from the equilibria between liquid and vapour, which researches on the critical constants of mixtures have proved to be capable of representation by a surface of two sheets, the upper part of which represents the liquids and the lower part the vapours. The coexisting conditions of these two must have equal values of p and ¢ and are therefore, situated on a horizontal line which is parallel to the .r-axis. The said surfaces meet at the left side in the vapour- pressure line O4C of the liquid A, at the right side in the vapour- pressure line Og D of the liquid B and in front in the critical curve CD. The points in the space between the two surfaces indicate complexes of liquid and vapour. In the representation, this space is massive, like all other spaces which represent complexes of fro phases. The surface of two sheets for liquid + vapour is so constructed that A is the substance with the greatest vapour pressure. It has further been assumed that the liquids are miscible in all proportions and that no maxima or minima occur in the equilibrium pressure. Descending continuously, the surface would reach the absolute zero if A or B or both did not solidify first. The pure liquids A and B solidify in O4 and Og; from there the vapour-pressure lines O4/ and Og of the solid substances run in the left and right vertical side-plane. Considering now the liquid-mixtures with an increasing amount of B, solid A can only be deposited at temperatures lower than (4. At each temperature there is a definite liquid and a definite vapour ( 38h } which coexist with the solid phase A at a definite pressure which is larger than the vapour-pressure of solid A alone, but the same for each of them. The three coexisting phases are represented by the lines O4G, O4k, O42 respectively standing for solid, gas and liquid. They are situated together on a cylindrical surface, because for equal ft, also p is equal. The part /’O0,/7 is also a limitation of the surface of two sheets. In the same manner we have for the equilibrium of solid B with liquid and vapour the three lines OgH, Ogk, OgF, for solid, liquid and gas respectively, again situated on a eylindrical surface, while the part HLOpF thereof forms below a second limitation of the surface of two sheets. This cylindrical surface first rises from Og but afterwards falls again. The surface of two sheets terminates, as far as the liquid-surface is con- cerned, finally in 1, the gas-surface in /. This liquid and this vapour may exist in contact with solid A (point G) and also with solid B (point #7). As the points G, F, L, H belong to the same values of p and ¢, they are situated on a horizontal line ‘and represent the only possible complex of four phases. To the gas-lme QO ,/ a second gas-surface joins, representing the vapowrs capable of coexisting with solid A, when the quantity of £6 in the vapour increases; also to Ogi’ the gas-surface for the vapours in equilibrium with solid 4 with increasing amounts of A. From the melting points of the pure substances down to the tem- perature of the quadruple-point G / 4H these two gas-surfaces are not in contact with each other, but each of them singly is in contact with the gas-surface of the surface of two sheets. Below that temperature they intersect each other immediately, forming the line /’Z which represents the vapours capable of coexisting with solid A + solid 4. To this belong the lines GW for solid A and HN for solid 6 which are again situated on a cylindrical surface. All complexes of the solid phase A and of the coexisting vapours are situated within the space formed by the gas-surface JO4FL, the surface of the solid phase /O4GJ/ and the two cylindrical surfaces GO4F and MGFL. All complexes of the solid phase B and the vapours which can exist in contact with it, are situated in the space bounded by the gas-surface AOpFL, the surface of the solid phase AOgHN and the cylindrical surfaces HOpF and N HF L. Both spaces extend to the absolute zero if no new phases are formed. The three surfaces representing the equilibria of gas with liquid, with 19% ( 282 ) solid A and with solid B meet each other in the point /. In the same way, two other liquid-surfaces must join in the point “at which the liquid surface coming from higher temperatures ends, namely those which indicate the p,t,c values of the liquids which can coexist with solid A or solid B. The lower limits of these surfaces ave the lines O4H and Ogk which represent the equilibrium of solid and vapour. Set- ting out from these lines the vapour disappears when the pressure is increased. On account of the small changes which the composition of the liquid undergoes with an increase of pressure, the liquid- surfaces O4EPU and OgkPV will rise almost vertically. They ter- minate to the left and the right in the melting point lines O4 V and OgV of the solid substances A and 4, whilst they intersect each other in the line “P which indicates the liquids which at different p,t values can coexist with solid A and 6. To this line belong the p,t lines GQ and HF for the solid phases, which again form a cylindrical surface with EP. In this way we arrive for the complexes of solid A + liquid at the space included between the liquid-surface, the surface of the solid A, O, UQG and the cylindrical surfaces GO4 E and GEPQ. A similar space includes, at the right, the complexes for solid B + liquid. Finally, the region of the complexes of solid A + solid B is situated behind the cylindrical surface GHRQ and above the cylindrical sur- face NHGM. The spaces last described terminate in the figures at the back at an arbitrary temperature and above at an arbitrary pressure. One must suppose that, in reality they continue their course. The remaining space outside the massive parts constitutes the regions of homogeneous liquids and vapours which pass into each other beyond the critical curve. The other six massive parts repre- sent complexes of two phases, the states of matter forming the complex being represented by two side surfaces. They further are connected with each other by four cylindrical surfaces on which three lines are always situated representing the systems of three coexisting phases and these cylindrical surfaces intersect each other in one straight line on which is situated the only possible complex of four phases. If for any system of two substances the figure described were studied completely, it would enable us for each mixture at each temperature and each pressure to read off, of what phases it has been built up and as far as liquid and vapour are concerned it would also show their separate composition. ( 283 ) For the complexes of fwo phases, the relative proportions may also be read off in the figure; for those of three or four phases it would be necessary to also know the relation of the volumes. The figure also makes it possible to ascertain what changes a mixture will undergo, when the temperature, pressure‘) or concentration are changed. Chemistry. — “Kquilibria of phases in the system acetaldehyde + paraldehyde with and without molecular transformation”. By Prof. H. W. Baxkuuis Roozrpoom. (Communicated in the meeting of September 27, 1902). The character of the equilibria of phases is exclusively determined by the number of independently variable constituents — components — of which the system is built up. Sometimes this is equal to the number of the different kinds of molecules. It may also be smaller, if there are among the molecules those which may pass into each other as in the case of associating, ionizing or isomeric substances. If these molecular changes proceed more rapidly than the equilibria of the phases, they exercise no influence on them. Although water, for example, is a mixture of at least two kinds of molecules, its freezing point is quite as sharply defined as that of a single substance. If however, the velocity of the molecular change is small, the system on being treated rapidly will behave like one with more components than it shows if treated more slowly. The effect of this on the phenomena of solidification has already been mentioned by Bancrorr in 1898 and by myself in 1899. So far, however, no suitable example has been found which would enable us to consider 1) It demonstrates, for instance, in a simple manner that on compressing vapour mixtures with a sufficient amount of A, the component B first deposits in the solid state in increasing quantity, but then again completely disappears at a certain pressure to make room for a liquid phase. This phenomenon has recently been observed by Kurnen (Phil. Mag. July 1902) with solid CO, mixed with C3H,. It must always show itself with the component which in the liquid-mixtures is the least volatile: in this case B. When however, the liquid-surface has a maximum pressure as in the instance cited by Kurnen, the phenomenon will be noticed with both components. If the surface has a minimum pressure it can only occur with one of the two. ( 284 ) Fig. 1. | | / MM) 260 N } a) 260) L | 200 | L\ | | | 160 | | } | G | 120) / = i \ = . | Near . 3 80 | v4 eX 5 / ~~ K Fa = 40 eee. ee a s \/Z Feb | Pe Pee —_—— : F eee eet _ E — D —40 —80 | 4 c | —160 aad 2 i00 Mol. %o. Acetaldehyde. the whole of the equilibria of phases from that point of view. Such a system has now been investigated in my laboratory by Dr. HoLuMANn of Dorpat. It is the systemacetaldehyde+-paraldeliyde, which has the further advantage of not undergoing molecular trans- formation except in the presence of a catalyzer and so behaves like a system with two components, whilst it undergoes transformation ‘apidly enough on addition of a trace of sulphuric acid to appear as a system with only one com- ponent. It becomes possible, thus, for the first time to obtain a general insight into the position which equilibria with apparently one component occupy among the sys- tems with two components. The chief results of the research. are the following. First of all the solidification phenomena of mixtures of acetal- paraldehyde were As is well known, dehyde and investigated. paraldehyde in a pure state melts Paraldehyde. & aes: (point b). This melting point is lowered by addition of acetaldeliyde along to the curve BLDC, which continues until the liquid consists almost entirely of acetaldehyde. With the aid of the apparatus of Prof. Kameriincu Onnes *) the melting point of acetaldehyde was determined at — 118°.45 (A). The melting point line of acetaldehyde does not extend further than — 119°.9 (C’) where it meets that of the paraldehyde. C'is therefore a eutectic point, ; Bo + 12°55 E+ 6.48 D— 4.0 C —119.9 A —118 45 1) LapenpurG gave — 120°. Melting point. Oo; 0 Paraldehyde. ( 285 ) The boiling points of the mixtures were next determined at a pressure of 1 atmosphere and the composition of the vapour of these boiling mixtures was also determined by means of a special apparatus. The former form the line “HG, the latter the line 7G of which the following points are the most important : fF 20°.7 boiling point of acetaldehyde IT 41.7 vapour 2.5 °/, paraldehyde Joh are ae G 123.7 boiling point of paraldehyde. liquid 53.5 » " On account of the great difference in volatility of the two components the liquid- and vapour lines are situated far from each other. The vapour of a boiling mixture is much richer in acetaldehyde than the liquid, for which reason the two are readily separated by fractionation. In the third place the critical temperatures of the components and of a few mixtures were determined. (Only that of acetaldebyde had been previously found by Prof. van per Waats to be 184°). Result : Critical temp. °/, Paraldehyde. Li 188" 0 Jed eA 11.0 One 2ate 22.0 IVE 2 OF 50.0 M 286° 100.0 These are the relations when there is no transformation of acetal- dehyde into paraldehyde, or the reverse. If, however, a trace of a catalyzer is added, acids in particular, the iwo molecules can be converted into each other, till the condition of equilibrium corresponding to p and ¢ has been reached *). It appeared that by these means the boiling point of all mixtures came in a very short time to 41°.7 and as this point according to the line FHG is situated at 53.5 °/ the relation of equilibrium in the liquid condition at that temperature » of paraldehyde, it represents and 1 atm. pressure. As the corresponding vapour according to point Z of the vapour line F/G only contains 2.5 °/, of paraldehyde a rational explanation has thus been found of the long-known fact 1) A little meta-aldehyde is also formed but the quantity remaining in solution is so very triflmg that its influence on the system considered may be utterly ne- glected. It must still be ascertained what place meta-aldehyde occupies in regard to the two forms at high temperatures. ( 286 ) that on distilling paraldehyde with a little sulphuric acid, nearly pure acetaldehyde is collected. At temperatures below 41°.7, the equilibrium appeared to be dis- placed along the line HE, which at 6°.5 and 88.1 °/, of paralde- hyde meets the melting point line of paraldehyde. The consequence is that, from whatever mixture we may start, paraldehyde will always erystallise out on adding a trace of sulphurie acid and cooling to 6°.8 and as the transformation of acetaldehyde into paraldehyde proceeds very rapidly even at this temperature, the whole mixture becomes at last a solid mass of paraldehyde. This even proved to be the case when pure acetaldehyde was taken as starting point. On the other hand paraldehyde in the presence of a trace of a catalyzer does not melt at 12°.5 but at 6°.5 owing io partial conversion into acetaldehyde. : We have no knowledge of the equilibrium in the vapour at these low temperatures but something can be said regarding higher tem- peratures. The lines / /7G and F/G have regard to 1 atm. pressure. Simi- lar lines might however, be determined for a higher pressure and in that manner the displacement of the points AZ and / with the pressure would be determined. Finally, we should thus arrive at the critical line 4.1/7 and here the compositions of the vapour and liquid, which indicate the relation of equilibrium, must become the- same. Ii appeared from a series of determinations that the point P? at 221° and 11°/) of paraldehyde is this very point. At these high temperatures, the equilibrium is also reached after some time without a catalyzer. It appears from the position of P that the line which gives the com- position of the liquid when equilibrium is attained slopes in the begin- ning very rapidly, with rising temperature, towards the acetaldehyde side of the figure (portion 7 H A’)*) but afterwards much less rapidly. The line of equilibrium of the vapour certainly does retrograde, for at 41° the vapour still contains 2.5°/, of paraldehyde, at 100° less, and at 221° again 11°/,. In this case the influence of the pres- sure prevails obviously. As paraldehyde is a triple polymer, the influence of the pressure is very marked. If we make a representation in space of the whole figure, like the one mentioned in the previous communication, it willbe noticed that the equilibria where the possibility of the mutual transformation of acetaldehyde and = paraldeliyde is admitted, are lines on the surface 1) The point K has been determined by TurpasBa at 50°.5 and 39.4%. Nw ( 287 ) which represents the case that the two components are not subject to transformation. For this another new representation may be given which consi- ders the matter from a more general point of view. Taking p, ¢ and wx as coordinates, a surface may be constructed which shall represent the equilibrium between the two kinds of molecules in a homogeneous phase, vapour or liquid. Ac. Cone. Par. Ac. Cone. Pai. The general form of such a surface of equilibrium for the system acet-paraldehyde may be readily deduced from analogy with other known equilibria in the gaseous condition, if one considers that paraldehyde requires heat to pass into acetaldehyde and may be reobtained from the same by compression. The general course of the equilibrium line at a constant pressure is indicated in fig. 2, that at constant temperature in fig. 5. [If we now imagine that on the different points of the /, .-line in a_hori- zontal plane, »,.-lines are evected in vertical planes, we obtain a p, & « surface of a very peculiar shape which gives the equilibriam relation between acetaldehyde and paraldehyde for every temperature and pressure. The course may be theoretically calculated for the vapour if the pressure is not too large. With greater pressures and for the liquid state this becomes a difficult matter but the general course remains fairly certain. We might therefore, imagine this equilibrium surface first of all at temperatures higher than those of the critical curve LM. Here, the surface would for some time extend itself undisturbed both vertically and horizontally. At lower temperatures, the surface, on account of its form, must necessarily meet first of all the surface for liquid-vapour; according to the investigation this takes place in the point P. From here to lower temperatures, the ( 288 ) equilibrium surface whieh was at first continuous will become dis- continuous and break up into an equilibrium surface for the vapour state and another for the liquid state. The lines of intersection of these two surfaces with the surface of two sheets are the lines ?/ and PA //F in fig. 1. To these must, of course, also be added lines of intersection with the other gas- and liquid surfaces, which have been mentioned in the previous communication. In this manner, it appears that special equilibria, which oceur When transformation between the two components is possible, may be always considered to originate from the intersection of the general space figure for the equilibria of phases with the surface of equilibrium for the molecular equilibria in each phase. Chemistry. — “On the action of sulphur on toluene and xylene.” $y L. Aronstery and A. S. van Nrerop. (Communicated by Prof. J. M. van BrEMMELEN). (Communicated in the meeting of September 27, 1902.) The researches on the molecular weight of sulphur according to the boiling point method of L. Aronstem and S. H. Meravizen *) showed that this molecular weight was found to agree with the formula S, and this in liquids the boiling point of which varied from 45° to 214°. But when toluene and xylene were used as solvents for sulphur the determination of the molecular weight had given values which corresponded with those calculated from formulae ranging between S, and S,. It was then suspected that this difference might be due to chemical causes. In the following lines we will communicate the results of our efforts to trace those causes. Action of sulphur on toluene. It had already been noticed that on boiling a solution of sulphur in xylene hydrogen sulphide was given off which was shown by means of lead acetate. A similar evolution of hydrogen sulphide was not noticed on boiling sulphur with toluene. As the chemical action of sulphur on toluene at the usually observed boiling point could probably not amount to much, a preliminary experiment was made by heating a solution of sulphur in toluene in sealed tubes at 250°—300° so as to accelerate the action until on 1) Proc. Kon. Akad. Wetensch. 1898. First section VI, 3. (289 ) cooling the tubes no crystallisation of sulphur took place. In the case of a mixture of 2 grams of sulphur and 10 grams of toluene, this lasted 10 days; in the interval the tubes were repeatedly opened to allow the accumulated hydrogen sulphide to escape. The product obtained was freed from undecomposed toluene by distillation; a preliminary investigation of the residual mass showed with certainty the presence of stilbene, thionessal and probably also of tolally! sulphide. As moreover the contents of the tube had a strong odour of merecaptane it was supposed that the action had taken place in one of the following ways. Firstly, benzyl sulphydrate might have been formed by a direct addition of sulphur according to the equation : C, H, CH, + S=C, H, CH, 5 H and this on losing hydrogen sulphide according to the equation: 2C, H, CH, SH= (C,H, CH,),.S + 0,5 might have yielded benzyl sulphide, which according to Forstr ') may yield as final products stilbene, totally! sulphide and thionessal. Secondly, the sulphur, according to the equation: C,H, CH, + 25=C,H,CSH-+H,S might have yielded thiobenzaldehyde or rather (C, H, CS H)x, which’) according to the equation: 2C,H, CSH=C,,H,,+28 might have formed stilbene, which then might have formed thionessal according to the equation: 2C,,H,,+35=C,, H,,S-+ H,S. In order to test the accuracy of these theories 4 grams of sulphur were boiled in a reflux apparatus with 150 ec. of toluene for 120 hours, care being taken that any hydrogen sulphide which might have been formed and the non-condensed benzylsulphydrate were carried off by means of a current of carbon dioxide and passed through an alcoholic solution of lead acetate. Although perceptible quantities of lead sulphide were precipitated during that time not a trace of the well-known yellow lead mereaptide was found. Both the toluene solution and the crystalline mass obtained therefrom were carefully tested for the presence of benzyl sulphydrate and also of thiobenzal- dehyde but notwithstanding the delicate tests for these substances their presence could not be demonstrated. But from the toluene solution we sueceeded in isolating stilbene melting at 124° and from this was prepared the characteristic dibromide (m. p. 285—236°) by 1) Liesie’s Annalen, Band 178. P. 370. ®) Baumann & Kuert. Ber. D. Chem. Ges. Band 24, P. 3307. ( 290 ) means of an ethereal solution of bromine. The result justified the belief that the formation of stilbene had taken place in a more simple manner than was formerly supposed, and according to the equation ; 2C, H, CH, + 2S=C, H, CH: CHC, H, 4+ 2H,8 The thionessal found in the preliminary experiments might then have originated from the action of sulphur on the stilbene which according to Baumann and Kuerr readily takes place at 250°. Fresh experiments in which toluene was heated with sulphur for hundreds of howrs in sealed tubes at 200° yielded as sole crystallisable produet a large quantity of stilbene which was obtained in a perfectly pure condition and of which the bromine addition product with the correct melting point was prepared. In connection with the results of the action of sulphur on xylene to be mentioned presently, we took into consideration the possibility that as a first product not stilbene but dibenzyl might have been formed according to the equation: 2C, H, CH, +S=C, H, CH, CH, C,H,+ H,S and efforts were made to isolate this if possible. As, however, according to the researches of Rapiszewskt'), sulphur converts dibenzyl very readily into stilbene and as we had found by special experi- ments that this already takes place at 200° when a solution of dibenzyl in benzene is heated with sulphur and as we had also proved that this action does not take place at a temperature of 140—145° we have heated sulphur with toluene in a sealed tube for eight days at 140°. As sole product we obtained stilbene besides hydrogen sulphide from which fact we are justified in concluding that by the action on the toluene two atoms of hydrogen are directly withdrawn and the two remaining groups are condensed to stilbene. Action of sulphur on p-aylene. When a solution of sulphur in p-xylene is boiled there is a much more perceptible evolution of hydrogen sulphide than on boiling a solution of sulphur in toluene. If, as in the previous experiment with toluene, the gas evolved was removed by means of a current of carbon dioxide and passed through an alcoholic solution of lead acetate 16 milligrams of lead sulphide (equal to 2.1 milligrams of sulphur) were obtained after boiling for an hour and a half. Here again there was no sign of any lead mercaptide; neither did the xylene solution contain a mercaptane as was plainly shown by the fact that no reaction was obtained with mercuric oxide. We next proceeded to heat one gram of sulphur with 30 ce of p-xylene in sealed tubes for 120 to 160 hours at 200 to 210° similarly to what was done in the experiment with 1) Ber. D. Chem. Ges. Band 8. P. 788. ( 291 ) toluene. On opening the tubes much hydrogen sulphide escaped and from the liquid obtained the xylene was distilled off. The residue became quite solid and apparently consisted of sulphur and a ery- stallised hydrocarbon. To remove the greater part of the sulphur, the hydrocarbon was dissolved in ether which was then distilled off. By recrystallising the residue from alcohol a mass was soon obtained which melted at 81—82°. Two determinations of the molecular weight by the freezing point method with benzene gave, respectively the values 200 and 205. No change took place on heating with hydrogen iodide in sealed tubes and no addition product was obtained on adding an ethereal solution of bromine. The product in fact appeared to be identical with p.p. dimethyldibenzyl p—CH,C, H,CH,. CH, C, H, CH, — p. which Moritz and Wo.rrenstrin *) had obtained by the oxidation of p-xylene with potassiumpersulphate. The result which was not analogous to that obtained with toluene caused us to repeat the experiment which now yielded a crystallised product which unlike the first substance was found to consist of a mixture of hydrocarbons.’ In order to completely eliminate the sulphur the mixture was boiled with solution of sodium sulphite, then dissolved in. ether and after distillime off the same, the residue was treated with cold alcohol. The alcoholic solution again contained p.p. dimethyl- dibenzyl (m. p. 81— 82°) as was proved by repeated recrystallisations. The portion insoluble in cold alcohol was solved in boiling alcohol and by repeated recrystallisation a product was obtained which melted at 176—177°, yielded, on adding an ethereal solution of bromine, a bromine product melting at 208° and proved to be identical *) with p.p. dimethylstilbene p— CH, C, H, CH CH C, H, CH, — p. In order to find out the cause of the difference in these results a further investigation took place. As far as we were aware, the only difference between the two experiments was that this time the tubes had been repeatedly opened thus causing the removal of the greater part of the hydrogen sulphide. The temperature during the experiment was in both cases the same and constant between 200 and 210°; the heating was also continued for about the same length of time. It was now possibie that originally in both cases p.p. dimethyl- stilbene had been formed. Whilst in the first experiment this sub- stance might have been almost completely reduced to p.p. dimethyl- dibenzyl by the action of the hydrogen sulphide, this reaction could only have occurred in a limited degree in the second experiment. 1) Ber. D. Chem. Ges. Band 32. P. 2531. 2) Gotpscummt & Hepp, Ber, D. Chem. Ges, Band 5, P, 1504, 1 292 For this investigation a solution of p.p, dimethylstilbene in benzene was saturated with hydrogen sulphide, introduced into tubes the air of which was totally displaced by hydrogen sulphide and after sealing the tubes, the contents were heated for 40 hours at 200°, From these tubes there indeed was obtained, besides unaltered p.p. dimethyl- stilbene, a product which proved to be identical with p.p. dimethyl dibenzyl. This showed that under the given circumstances the expected reaction might have taken place. On the other hand, dimethyldibenzyl was heated with a solution ot sulphur in’ benzene for 40 hours at 200° and, although it was not yielded in a quantity sufficient to admit ofa thorough purification, p.p. dimethylstilbene was obtained; at all events a hydrocarbon melting between 140° and 150° which absorbed bromine and yielded a product melting between 185° and 192°, whereas the melting point of p.p.. dimethylstilbene dibromide is situated at 208°. From these experi- ments it is, therefore, probable that the formation of stilbene is here the primary and that of dibenzyl the secondary reaction, but we here got no certainty about this. On repeating the experiments on the action of sulphur on p-xylene in sealed tubes some of which were opened from time to time unequal proportions of stilbene and dibenzyl were still obtained, but the result of the first experiment (nearly exclusive formation of dibenzyl) was never again obtained. It should be mentioned here that p.p. dimethylstilbene was often obtained in two different forms. Generally, it was a coarse crystalline powder, but occasionally it consisted of very thin leaflets with a silky lustre and showing a violet-coloured fluorescence. The original form of both was retained after recrystallisation from alcohol. Once we succeeded after a good deal of trouble to convert the coarse granular form by grafting, into the silky condition. The melting point of both forms was identical. On treating them with an ethereal solution of bromine they both gave the same bromine addition product. To see whether this was a case of stereo-isomery, solubility determinations were made of both modifications in absolute alcohol at 25°. In both instances the same solubility value was found, namely 0.21 part per 100 parts of alcohol *). Notwithstanding the difference in appearance which was also retained in these solubility experiments, a stereo-isomery has thereby been rendered very improbable. 1) Evzgs (Journal f. Pract. Chemie. Neue Folge Band 39. P. 299 and Band 47. P. 46) gives the solubility of p.p. dimethylstilbene in alcohol at the ordinary temperature as 0.76 per 100. ( 298 ) Action of sulphur on m.-vylene. Sulphur boiled with m-xylene not only gave a much smaller evolution of hydrogen sulphide than in the case of p-xylene but the amount was even less than that obtained on boiling sulphur with toluene. m-Xylene which had been boiled for a considerable time with sulphur was quite as free from mereaptane as the similarly treated toluene and p-xylene. We now proceeded to heat sulphur and im-xylene in sealed tubes at 200°. After the heating had lasted for 70 hours, the sulphur had totally disappeared and the tubes could be opened. Streams of hydrogen sulphide escaped. From the liquid obtained the xylene was distilled off and the liquid non-crystallisable residue was freed from sulphur by boiling with solution of sodium sulphide. As if was not impro- bable that both m.m. dimethylbenzyl and dimethylstilbene might have been formed (to judge from the behaviour of p-xylene) and as the first named substance is, according to VoLtiratH') and Moritz and WoLFeENsTHIN *), a liquid and the unknown m.m. dimethylstilbene probably a ecrystallisable substance if was tried (although in vain) to effect a separation of these two substances by heating in a current of steam, by fractional distillation at ordinary pressure and also by solvents. The suspected presence of a stilbene in that liquid was, however, soon proved when bromine was added to its ethereal solu- tion and the whole placed in a freezing mixture. A bromine-addition product now crystallised in abundance. The addition of bromine was continued until a small excess was present. The crystallised product after being recrystallised twice from xylene had a constant melting point of 167—168°. A bromine determination according to Carus gave 44.02 °/, of bromine, the calculated quantity for dimethyl- stilbene dibromide being 43.50 °/). The dibromide was used to prepare the hydrocarbon itself. For this purpose it was dissolved in xylene and boiled with molecular silver or sodium wire for 6 hours m a reflex apparatus. From the xylene solution obtained the xylene was removed by distillation ; the residual liquid crystallised on cooling and the crystalline mass could be readily purified by recrystallisation from alcohol. The substance is very diffi- cult to burn; the combustion only succeeded by intimately mixing it with lead chromate and potassium bichromate. The elementary analysis gave the following result : HOM Aes, parka Mion? tote ont OL OAD fee TROL. */, Calculated for Gi Ho. «= C492130:°%, JH 7.70) %/, 1) Zeitschr. f. Chemie 1866. P. 489. 2) Ber. D. Chem. Ges. Band 32. P. 2532. (294) The melting point was constant at 55— 56’. That the obtained hydrocarbon was really m.m. dimethylstilbene was proved by adding bromine to its ethereal solution which imme- diately yielded crystals of the dibromide with the previously found constant melting point of 167— 168°. The ethereal liquid from which the dimethylstilbene bromide was precipitated, contained, of course, free bromine from which it was freed by treatment with aqueous potash. After distilling off the ether, the liquid was submitted to fractional distillation when hydrogen bromide was evolved owing to the presence of brominated products. The hydrogen bromide present in the distillate was removed by treatment with aqueous potash and the liquid distilled once more, When it appeared that this distillate, passing over between 298° and 302° was not vet free from bromine it was dissolved in toluene and boiled for three hours with sodium wire which completely removed the bromine. The liquid then showed a constant boiling point ot 298°. On analysis was found : ( 91.38°/, H. 8.64°/, Calculated for @; Hig". «72, 40 914 3t/s eso ae Two determinations of the molecular weight by means of the lowe- ring of the freezing point in benzene gave 201 and 199; calculated 210°. All data agree with those of VouLratH and those of Morrrz and Wo rrensteIn for m.m. dimethyldibenzyl. Only the boiling point was found to be two degrees higher. From this it, therefore, appears that m-xylene on treatment with sulphur yields stilbene as well as dibenzyl as discomposition products. To ascertain whether stilbene was here also the first product, m.m. dimethyldibenzyl was submitted to the action of sulphur by boiling it with this in a reflex apparatus. The product of the reaction dissolved in ether and treated with bromine did not yield a trace of the characteristic m.m. dimethylstilbene dibromide. This sub- stance could not even be recognised by means of the microscope. From this we think we may come to the conclusion that during the action of sulphur on im-xylene the first product is most proba- bly stilbene and that dibenzyl is a secondary product formed by the reducing action of hydrogen sulphide. The results of this research are, as we believe, a confirmation of the opinion expressed by Aroystrery and Meinvizen in their treatise on the molecular weight of sulphur. A trifling action of the sulphur on toluene and xylene must cause a derivation of the molecular weight in the direction previously found. One mol. of sulphur causes the formation of 8 mols. of hydrogen sulphide and 4 mols of stilbene. ( 295 ) Although hydrogen sulphide is volatile and most of it escapes during the boiling, the increase of the number of molecules formed during that action (however small this may be) is large enough to account for the observed difference. The fact that the deviation has been found larger in the case of toluene than with m-xylene as solvent is also in agreement with the observed fact that more hydrogen sulphide is evolved in the first than in the second case. Our research on the action of sulphur on p-xylene was not conducted merely with the idea of confirming the researches of ARONSTEIN and Meravizen (we were not quite sure whether the j-xylene then used had been completely free from p-xylene) but also to throw more light on the mechanism of the process and particularly on the ques- tion of the primary formation of stilbene and the secondary forma- tion of dibenzyl. Chemical Laboratory of the Polytechnical School. Dever, September 1902. Physiology of Plants. — “J/nvestigations of Glucosides in connection with the Internal Mutation of plants,’ by mr. TH. Wrevers. (Communicated by Prof. C. A. Losry pr Brvyy). (Communicated in the Meeting of 27 September 1902.) The purpose I had in view in this investigation was to trace for some plants, whether the amount of glucosides remains unchanged during the development or not; and to investigate in the latter ease by what conditions these changes are determined. At the same time the manner in which those changes took place formed another subject for study: whether glucosides were trans- ported as such, or whether a decomposition could be stated, and in the latter case what were the components in which this took place. Salix species and Aesculus hippocastanum lL. were especially used for the investigations; Gaultheria procumbens L. and Fagus sylvatica were also submitted to a prefatory study. The glucosides to be mentioned here are salicine for the Salix species, gaultherine for Gaultheria and Fagus, aesculine and more- over some glucosides not yet chemically determined for Aesculus hippocastanum. As for salicine the quantitative valuations were made as follows. The salicine was entirely extracted by boiling water from the parts to be examined and the extract treated with basie lead acetate. The 20 Proceedings Royal Acad. Amsterdam. Vol, V. ( 296 ) surplus was removed by dinatriumphosphate and the liquid then obtained reduced to a definite volume. In this two estimations of sugar were made, one before, the other after: allowing emulsine to work in upon it for 48 hours. Prefatory experiments with pure salicine had proved that in this way it was completely decomposed: the increase of the reduction after inversion was to be attributed only to the glucose formed of salicine. ’). From this increase of the glucose the quality of the salicine could then be calculated. This same method was followed in order to state the salicine in various parts of the plant; then however, after inversion the liquid was extracted with ether, so that saligenine might enter into it. This substance is easily recognised by the physic qualities of its crystals and by the substitute of bromine obtainable with brominewater and moreover by its salt of copper. The efforts to point out salicine in the tissue itself were unsuccessful; the method formerly used by THEoRIN *), namely that of adding concentrated sulphuric acid, proved impracti- cable, as it during the produced erroneous results. For the above mentioned Salix species salicine is found in the bark of the branches, but not in the wood; young buds are rich in it, likewise the assimilating leaves. It appears in young ovaries but disappears during the process of ripening. Although an inverting enzyme was not to be extracted, it proved necessary to kill the parts immediately in boiling water, otherwise considerable alterations in the quantity of salicine presented them- selves. Thus e.g. after slow drying 25 pCt. disappeared out of the bark. The following series of determinations for the purpose of invest- igating the quantity of salicine during the budding period, was made with one specimen to exclude individual differences. The total quantity in various successive stages was calculated by taking a branch with a definite number of sidebuds as object. The weight of the different parts of this branch together with the procentic values of the quantity of salicine in corresponding parts of the same object in the suecessive stages gave the total quantity of salicine of this branch in those stages *). 1) Before inversion a solution of salicine does not reduce even with boiling ; neither does saligenine formed by means of inyersion at the same time as glucose. 2) See Theorin Ofversigt af Kongl Vetenskaps. Akademiens Férhandlingen 1884. No. 5. Concentrated H, SOQ, gives with salicine a coloring of red. 5) In corresponding parts of one object was an equal quantity. (291% 3) Under observation were only branches without genitals ; those with catkins gave a different result *). Branches of 1'/,—4 mM. diameter (wood and bark together). March 24% 3.2 pCt. ”) April 17 2 I May 21s 04 , Branch of 4—8 mM. diameter (only bark; hence the quantity is higher). March 24% 4.1 pCt. April 17% 2.8 » Wey | PAIRS gil For Salix Helix L. the figures for the bark of branches were March 24% 4.4 pCt. April) Aye 2a The quantity of glucose is a little variable ; however, it does not rise above 0.5 pCt.; the quantity of fecula diminishes when budding from 9.5 pCt. to 6 pCt. In the young buds of Salix purpurea there is before the budding 4.4 pCt. and of Salix Helix 6.2 pCt. During the budding this quantity decreases greatly, disappears even for 5. purpurea entirely (17 April) but rises again quickly, when assimilation begins, to 3.7 pCt in leaves and 3 pCt. in young shoots (21 May). Of the absolute quantity of salicine in a branch with 300 buds + 36 pCt. disappeared from 24 March—17 April aE 18 TT Ti 17 Mareh—21 May, the assimilation, begun already before May 21, having given rise to new salicine. Experiments with branches placed in the dark in water*) showed the following : After the roots have been formed, a number of long etiolated shoots bud forth, consuming by their development besides the fecula also a great quantity of the salicine in the bark (+ 70 pCt.). At first the young shoots contain a great quantity 7.2 pCt., this, however, keeps on decreasing; the absolute quantity calculated for 100 young shoots also diminishes : for 100 young shoots long 18 mM. there is 25 mG. salicine " " " Gf AU if fe Ldn Sr " 1) The quantity of salicine is at the same instant lower in branches with catkins than in those without; the salicime diminishes more quickly. 2) These procentic values are calculated for dry weight. ‘) These were branches of 6—10 m.M. diameter, the young shoots coming from sleepmg buds. 20% (298 ) These quantities are small compared to the entire quantity consumed + 330 mG. for 100 young shoots. When the young buds were budding forth saligenine was found in them, the branches were immediately killed in boiling water, the extract after cooling down extracted with ether; so all influence of enzyme could be excluded. It becomes very probable that the salicine is analysed before the consumption, on account of saligenine being found ; the quantity, however, is so small that if really the analysis of salicine were to take place as indicated, and a decomposition to precede the consumption, saligenine can only be an intermediate stage. Either the aromatic half disappears as such, or another aromatic substance must be the definite product of the decomposition. In the young leaves developing normally, salicine soon makes its appearance again after having disappeared for a moment; we can expect that this increase is connected with and due to the assimilation, as etiolated shoots do not show it. In order to state whether the leaves were really the place of a new formation and the light really had a part in it, the quantity of salicine before and after darkening was compared. The quantity in the leaves was determined in the evening after sunset and in the morning before sunrise (one specimen). Likewise in the evening leaves were halved, one half with midrib left on the plant, the other half analysed. The following morning the remaining half was cut off from the midrib and also analysed*). Provided that a suflicient number, 100 or 200 leaves were halved, a comparison could very well be made. For a small-leafed specimen a 100 leaves 8 P. M. 7 Aug. 47.5 mG. glucose 87.2 mG. salicine 4 A. M. 8 " Dee: " " 60.2 " " For a big-leafed specimen a 100 leaves 8 P. M. 7 Aug. 80 mG. glucose 177.7 mG. salicine. 4A. M.S 9 “sid yn 142.7 So in both cases we see a decrease during an 8 hours’ summer night of respectively 30 and 20 °/, of the salicine in the leaf in the evening. For experiments with entire leaves of one specimen : 8 P. M. 7 Aug. 4.6 °/, salicine. AS ASCSM: 8-7 SAR ap SAM 8. 4 Se wes 1) See Lotsy. Mededeelingen *s Lands Plantentuin XXXVI. " " ( 299 ) Thus here too a decrease of 30 °/, during the night followed up by an equal increase on the following day. If branches on the plant 0 are enveloped in black waxed paper the decrease amounts after 48 hours only to 35 °/,, no great difference with that of 8 hours; increase, however, did not take place, so light proves to be a necessary factor. The experiments of etiolating told the same. If this quantity of salicine disappearing from the leaves was removed to the bark, an increase would have to be observed there. This was indeed the ease, for branches rich in leaves the increase of the quantity of salicine of the bark amounted in one night to 2.5 °/,; for branches with few leaves to 1.1 °/,. From the etherextract prepared in the above described manner, of the parts of Salix purpurea still another substance could be isolated by means of subliming. According to the micro-chemic qualities this was a substance resembling phenol and qualified by its compound of lead and of lime, besides reaction with tetrachloorchinon as an ortho- derivate *). The substance did not show Aldehydreactions. The further micro-chemical qualities corresponded to those of the simplest ortho- phenol, catechol. After a repeated crystallisation out of benzol the melting-point proved to be 104°. Elementary analysis and determina- tion of molecular weight confirmed the fact, that it was catechol. As the material which furnished the substance was quickly killed both in boiling water and in boiling aleohol and the etherextract already showed the erystals before sublimation, influence of enzym ?) is not probable and formation out of resin is not possible. Treatment with ferrichloride followed by additon of natrium hydro- carbonate also furnished in the tissue the reaction of catechol. The red colour was clearly visible in the unopened cells of the sections of the bark, young etiolated shoots showed them faintly, older ones more. Catechol is like salicine only to be found in the bark *). The supposition was aroused that catechol might be the aromatic substance, remaining there as definite product of decomposition of the salicine. In order to test the accuracy of this supposition, an investiga- tion had to be made whether the quantity of catechol of the parts of Salix purpurea were varying. For a quantitative determination of the catechol the method of 1) According to an investigation of Prof. H. Brarens which will shortly appear, communicated to me by Miss GrurTerink. 2) The black colour of the dying leaves is caused by the influence of a “tyrosi- nase” on catechol. 8) Catechol was also obtained out of Salix Helix L., 5S. babylonica L., 5. vitellina L, Populus alba L., P. monilifera Ait, sometimes only very little. ( 300.) Deoener (Journal f Prakt. Chemie 1879) could not be used on account of a flavon-like colouring matter not closer examined, and also precipitated by a basic leadacetate. So the method of Prof. Bearens to determine Indigo was followed. The sublimate of a solution of ‘atechol of a known strength in absolute alcohol was compared with that of the alcoholic solution of the remainder of the ether evapora- ted dry. Now it was examined how much this liquid had to be diluted to obtain an equivalent sublimate. The sublimation was performed by means of the brass table described by Prof. Wissman. Under certain precautions the determination could be accurately made to milligrammes. The quantity of catechol of the leaves was in the evening 0.6 pCt. ) with one " "on no onw on 2 » 9 morning0.1 , | specimen 2 : with the " ” " " vn on bark » won evening0.6 " : N same " noon it no " » » » MorningO.4 : specimen. So the quantity of the catechol here proved to change in reverse order as that of the salicine. In the leaves the salicine diminishes in the night, the catechol increases, and in the bark the catechol dimi- nishes and the salicine increases. Is there any connection between the extent of these changes ¥ For that purpose for one and the same object catechol was deter- mined as well as salicine. 200 halves of leaves 8 P.M. 225 mQr. salicine (4.5°/,) 32 mG. catechol (0.65°/)) ~~ I » «£ A.M. 162 , - (3:3°/)) se 52) s (1.059) So 638 mG. salicine less, 20 mG. catechol more. The proportion of these values, given the degree of accuracy of the determination of catechol, pretty well agrees with the proportion of the molecular weights. A comparison was also made of the change in salicine with that in catechol for leaves budding forth in the dark. 17 Gr. bark before budding 851 mGr. salicine 36 mGr. catechol 17 " " after " vow " " 55 7] " budding etiolated shoots SBy Vi r Ae, it (a great increase in the bark, in the voung shoots only a small part of the catechol thus formed to be found) 64 mG. salicme was used, 23 mGr. catechol was formed. These two values stand in the ratio of 36 to LOO, the molecular weights in that of 38 to 100. So it is very natural to assume here a decomposition of the salicine into sugar and eatechol with saligenine as intermediate stage (see ( 301 ) above). For this then a CH, group out of the lateral chain would have to be decomposed, as saligenine is orthodxybenzylalcohol and catechol is the orthodiphenol. Corresponding to this the quantity of catechol of the bark is large in May(1.1 pCt.), a greater part of the salicine then having disappeared, much lower in July (0.3 pCt.) when the loss has been repaired *). Where now has the decomposition taken place ? Prnrrer says Kap. VIII, Pflanzenphysiologie 2+ Auflage: ,vielleicht dienen die esterartigen Verbindungen der Kohlenhydrate mit Phenol- kérpern zur Herstellung von schwer diosmirende Verbindungen bei deren Zerspaltung im allgemeinen der Phenolkérper in der Zelle intact verbleibt, wm fernerhin wieder zur Bindung von Zucker benutzt zu werden.” The facts are excellently explained in the following way: The decomposition of the salicine takes place in every cell, the glucose is conveyed in the direction of the green parts, the catechol remains in the cell and binds glucose, coming from cells situated closer to the bark, to salicine. Glucose is transportmatter and salicine is transitory reservematter. The glucose being comsumed in young parts in greater quantities than its supply is, catechol must be found, but only so much as corresponds to the decrease of the absolute quantity of salicine. 100 young shoots 18 m.M. long 28 m.G. salicine, traces of catechol. 100 " " 85 m.M. W BALA m.G. " 2 m.G. " 6.4 m.G. salicine corresponds when calculated to 2,5 m.G. catechol, when observed to 2 m.G. This correspondence adds great strength to the hypothesis. *) In the bark the loss of consumed glucose is not repaired, so eatachol increases greatly. As for Aesculus, here it was especially the germination which was studied. The glucosides found in the ripe seedlings being not yet chemically determined, it was only necessary to base the method of the quantitative definition on the quantity of sugar formed by inversion. I had to trace whether the quantity of sugar bound in glucoside decreased during the germination. To this end the seedlings were ground and extracted with methy]- aleohol, of this extract the alcohol was evaporated, and the watery liquid 1) IT here mean the quantity in the bark of thicker leafless branches where no difference between night and day is obseryed. 2) Also the facts observed at the change of night and day can be excellently explained in this way. ( 302 } extracted with ether to get rid of oil and resin. The extracted liquid served as definition of the reduction before and after inversion by boiling it for 2 hours with HCL *). From the difference of this reduction the quantity of reducing sugar originating from the glucoside could be calculated; it amounted to 13 pCt. During the germination this quantity deereased in cotyledons by 60 or 70 pCt. Feeula and albumen by 70 or 80 pCt. The germinating plants contained only L or 2 pCt. of glucose bound in the shape of glucoside, the consumption of the glucosided sugar during the germina- tion could be regarded as proved by the 70 pCt. decrease of the absolute quantity. The localisation of aesculine was observed by fluorescence of its watery solution, to be seen when there are not too few sections. Aesculine was to be found in ungerminated seeds only sporadically in the plumule; when germinating it appears in greater quantity in the stalks of cotyledons, not in the cotyledons themselves. Stalk and hypocotyledon internodium contain aesculine when germinating in the dark as well as in the light, so light is not necessary for the formation. The stalks of the leaves show the aesculine only when developing in the light and not in the dark; this seems to point to the fact, that the aesculine of the normal germinating plant originates from two sources : that it is formed for the greater part by reforming of substances out of the cotyledons and side by side with this, that it is prepared inde- pendently in the stalks of the leaves from substances assimilated by the leaves. Experiments with full-grown plants, in the light and in the dark, with coloured and with normal leaves made this the more propable, but full certainty can only be given by means of later quantitative definitions. Studies on Gaultheria procumbens showed what changes took place in the quantity of the gaultherine, the investigations have however not yet been bronght to an end. The method of quantitative definitions was founded on the observation of the quantity of methylsalicylate Which could be formed out of it. This was redistilled with vapour out of the parts, caught in alcoholic potash and saponificated with it. The kaliumsalicylate formed in this way was determined according to the method of Mrssincer and VortMann *). For smaller quantities the colorimetric method of determination was used with Fe Cl,. 1) After inversion and neutralisation the liquid was treated with leadacetate. *) Messincer and Vorrmay, Zeitschrift f. Anal. Chem. 38 bl. 292. Ber. d. deutschen chem. Gesel|schaft. Berlin. Bd. 22. 2313. ( 303.) With Fagus sylvatica where Tattievr ') found methylsalieytate only in the germinating plant, the latter method showed that it was also present in the full-grown plant. Methylsalicylate is to be found sporadically in the buds of the beech shortly before budding, during that process it is found in the young leaves and shoots as well as in the branches of the preceding year. Young long branches are richest in it, 0.02 pCt. As soon as the leaves have unfolded, this substance begins to disappear again and is nowhere to be found in a week’s time. Further particulars to be looked for in the dissertation to appear shortly. Physics. — 4Some observations on the course of the molecular transformation.” By Prof. J. D. van prr Waats. As is well known, acetic acid may be considered as a mixture of simple and double molecules and we find a decreasing number of double molecules when we investigate the saturated vapour of this substance at increasing temperature. The same applies also to NO,. We are apt to conclude from these two best known instances of molecular transformation that this course is the only one that is possible. We may, however, easily convince ourselves that also the Opposite course may occur, and it appears to me that we may conclude from figure (1) of the communication of Prof. H. W. Baxuuis Roozmsoom in the Proceedings of the previous session, that for the transformation of acetaldehyde and paraldehyde this opposite course perhaps occurs. Let us take the equation for the molecular transformation, as it oceurs Cont. II, pag. 29, namely : CaO ey ED) 4 (lear ng ame Se te co The quantity 1—v of this equation represents the quantity of the substance expressed in grams which occurs in the form of simple molecules, v therefore that which occurs in the form of double molecules. If molecules were formed consisting of 7 simple mole- cules, the equation would be modified into the following one: log (Ct eee _ Hh aaeas ~ (l—a)r fly It is true that we only find the equation in this simple shape if ') Tatteur, Comptes Rendus A. Sc. Tome 132 p. 1235. 304 | Wwe make suppositions concerning the quantities « and 4, whieh can only be satisfied if the multiple molecules may be considered to be mere complexes of simple molecules, which can be formed without further radical modifications in the structure of the molecules them- selves. But as I will apply the given formula only in the ease of saturated vapour at a pressure which is not very high, in which case the influence of the quantities a and 4 may be neglected, we may consider it to be sufliciently accurate for our aim. We may deduce from it: 1 dv ‘ du (1 n A OY at ar (a v aa) = aes For saturated vapour at a pressure which is not too high, we have: —] pe eT (: wwe «) n from which follows: n—l1 de dp i dv _1 n at pal ' wdT T n—1 = ac nu : 1 dv If we substitute for sar the value found above, we get the s equation: _ dx il T dp A DP ee dl n—1 pd 7 x (1—z) (1— z) nt Whether the number of multiple molecules in the saturated vapour increases or decreases with the temperature, depends therefore on the fact whether the value of the expression: T dp ae) A is more or less than — a is , = d Z ; cr For a normal substance —— is approximately equal to 1+ P For a substance in which molecular transformation takes place, the factor 7 is to be modified and this factor will even vary more or less with the temperature. But if a perfectly accurate numeric deter- mination is not required, and if we only ask: Can both ways in which « may be thought to vary with the temperature occur? then we may state what follows: —————————— ee ( 305 j “When the heat developed by the combination of 7 simple mole- cules to a complex one is so great, that it far exceeds the quantity (n—l1)7 Ti, as is the case for acetic acid — then the saturated vapour will at higher temperature be associated in a lower degree. If on the other hand that quantity of heat is much smaller than (a—1) 7 7,,. then the reverse will take place.” When we proceed to saturated vapours of greater density and when Wwe approach the critical temperature, then this difference in the course will no longer exist. If we consider in the equation : 1 T adv , 1 n da: A CS rT 2c AMS Peay Tide the value of — rer | for ihe saturated vapour at all temperatures vU— OE between O and 7;,, we see that this quantity has a minimum value for a certain value of 7. For very low temperatures it may be 7 ihe, equated to 7 oye and for the absolute zero it is therefore infinite. But also for 777", it will be infinite, for — is infinite in the ¢ critical point. The value of 7 for which this minimum value occurs, would for normal substances be the same fraction of 7’... For sub- stances with molecular transformation we find a different value for this fraction. It may be calculated for many substances from the experiments of Srpyny Youne at least approximately. T dv A Above the temperature for which ————_—~— for acetie acid v—bdT vf day, ¢ i : . ; also pene ee positive. For substances which behave as acetic : = acid therefore a minimum value of x occurs. The fig. (1) of Baxauts RoozeBpoom presents in fact such a minimum for paraldehyde, and from this would follow, that this transformation is of the same type as that of acetic acid. Yet it seems possible to me that an accurate direct investigation would prove this minimum not to exist. If it really exists, then it will probably occur at a much higher value ot <2’. But even if this transformation would also prove to be of the same type as that of acetic acid, vet it seems not superfluous to me to point out, that also the other type may possibly occur. The abnormality of substances as the alcohols, water, etc. is ascribed to a possible molecular transformation, and yet the saturated vapour ( 306 ) of these substances appears to follow the laws of the perfect gases the more accurately as the temperature at which it is investigated is lower. So the density of saturated vapour of water at 100°, appears to be 2'/, pCt. higher than would follow from the applica- tion of the laws for perfect gases; whereas the saturated vapour of water at ordinary temperature presents a density which does not deviate noticeably from that, which follows from the laws of Boye and Gay-Lussac. If for molecular transformation the type of acetic acid were the only one which could occur in nature, then the supposition that water is also subjected to this transformation would involve that the deviation would be found to increase when the temperature is lowered. It is highly probable that the deviation of 2°/, pCt. of saturated vapour of water at 100°, which cannot be accounted for by the ordinary deviation from the laws of Boyte and Gay-Lussac which also normal substances present, must be ascribed to the presence of more complex molecules; but at the same time we must then assume, that the heat of transformation lies below the limit which we have indicated above. The equation which we have used here, is taken from Cont. H, p. 29 and there it had been obtained by the direct application of the principle of equilibrium, according to which a given quantity of matter at a given temperature in a given volume will arrange itself in such a way that the free energy is a minimum. It is therefore that we had to take a fixed quantiy of the substance, e.g. a unit of weight, which might be divided into 1—v grams simple, and x grams double molecules. When # varies, the total quantity of the substance remains constant. We may, however, also consider a mixture, consisting of a number of 1—x simple and 2 multiple molecules and then we may apply the thesis that, when equilibrium is established the thermodynamic potential for a molecular quantity of the multiple molecules must be n times greater than that for the simple molecules. The linear function of wz, however, which in other cases may be omitted, must in this ease of course be preserved. If we then put: $= MRT {u 4+ (1-2) 1 (1-2) + ala} + Tia (1-2) 4+ Ba}+ y(-2) + de then we have: S—wxr — MRT {u—— this formula does not seem to be very plausible. <€ I have also tried a quadratic expression connecting the steadying resistance with the frequency, but this did not give satisfaction. At last I found as the most simple formula and agreeing best with the observed results : logp—atbl, in which @ and / are constants, p the frequency and / the constant current intensity. I found for series 1: ( 317 ) ( 318 ) loy P — 3.23522 of O.2165 I log p (cale.) | log p (obs.) f | p (eale.) | p (obs.) 1.9 3.64757 3 65514 | + 0.00857 4432 4520 2.2 3.74152 3.71850 +. 0.00698 DIAT 5230 2.6 3.79812 3.77525 0.02287 6282 | 5960 2.8 3.84142 3.80956 — 0.03186 Gos1 | 6450 ee BT 3.92802 3.90309 — 0.02493 R473 SOOO 3.7. | 4.03697 4.01662 | — 0.01965 10871 | 10390 4A | 4.49987 | 4.14364 | -++ 0.02077 13270 13920 ’ for) eee ! The mean error of /og p being: [ve Y (o)? = 0.02272 the error- 6 factor of p is 1.053 and the mean error of p is 5.3 °/,. Considering that 3 galvanometer readings are necessary which individually ought to have errors of much less than 0.5 °/,, but which are to be taken all at the same time and therefore are more inaccurate, a mean error of 5.3°/, in the result, representing an interval of less than a tone may not be called extravagant. For series 2. I find: log p= 3.47786 + 0.18453 J. [ log p (cale.) | lag p (obs.) P p (eale.) | p (obs.) ey 3.79156 3.79239 + 0.00083 6189 6200 2.4 3.92073 3.91009 — 0.01064 8332 8130 2.8 3.99454 3.99211 — 0.00243 9875 9820 30 4.3145 4.04929 + 0.01777 10751 11200 3.5 4.12371 4.13322 + 0.00951 13296 13590 3.1 4.16062 4.14551 — 0.01511 V4A75 15980 1 on= pre = (0)? = 0.01228 5 the mean error of one observation being 2.867 °/, 319 Series 3. logy p= 3.84563 + 0.17062 7. vi | log p (cale.) | log p (obs.) | F | p (cale.) | p (obs.) | 1.9 | 4.46981 4417464 | 0.00483 | 414785 14950 2.3 | 4.93806 | 4.93654 0.00152 | 17300 17240 2.6 4 98997 4. 27462 0.01465 19466 48820 2.9 4.34043 | 4.34635 0.00592 | 21900 299/00) 353) | 4.40868 4 AQ4S8 0.04620 | 95626 26600 3.6 | 4. A586 f. 44963 0.01023 IS831 28160 (a 4 DADIT 4 ADB 0.00014 85089 35100 eer om = fue Y (0)? = 0.01085 mean error of one observation 2.412 °/ 0° Series 4. loy p= 3.80102 + 0.31641 /. l | log p (cale.) | log p (obs.) p (eale) | p (obs.) 1.9 440290 | 4.40140 — 0.00080 25247 25200 | | | 2.4 | 4 56280 | 4.56585 + 0.003805 36542 36800 27 4.65582 | 4.64640 | — 0.00892 A529 | = 44300 34 4.78189 | 4.74468 — 0.03721 GUS1I9 | SanS0 34 4. 87681 | 4. 92788 + 0.05107 75303 84700 3.7 h. QNT4 | 4.98989 + 0.01815 93700 97700 3.9 | 5.03502 | 5.00217 — 0.03285 108400 | 100500 == Om Lae (Or = 0.02994 mean error of one observation 7.14 °/, ( 320 ) Series 5, log (= 3.98960 + 0.17902 J. / / | log p (cale.)| fog p(obs.) p p (cale.) p(obs.) 1.9 4.32974 £35025 + 0.02051 21367 29400 2.2 £. 38344 4.39270 -+- 0.00926 24179 24700 2.6 4 45905 4 42651 — 0.02854 98513 26700 2.9 4.0876 4. 50243 — 0.00633 32267 31800 3.2 | 4.56246 4.56820 | + 0.00574 36514 37000 | 3.6 4.63407 4.61490 | — 0.01917 43060 441200 SP 4.65197 4.63949 — 0.01248 ‘A871 43600 £2 4.74148 4.77232 -+- 0.03084 dd 141 AN200 ; om = ie > (9)? = 0.02024 7 mean error of one observation 4.77 °/,. Series 6, log — 4.31949 + 0.22466 /. I log p (cale.)| log p (obs.) p p (cale.) | p fobs.) 24 4.79128 4. 78746 — 0.00382 618+ 61300 24 4.85867 4.85673 | — 0.00194 72299 719.0 29 | 4.97100 4.96199 | — 0.00910 = 93540-91600 3.6 5.12827 5.11394 — 0.01433 134360 130000 4.2 5.26306 5.29296 + 0.02920 183257 196000 i See VAS > (9)? = 0.01702 mean error of one observation 4.00 °/,. The empirical formula represents fairly well the observed results in the range of the experiment. But it does not give more than that, I do not think that it may be used for extrapolating. This will be directly seen, when we extrapolate for the intensity = 0. We cal- culate for the frequency at the intensity = 0 in the 4" series: 6324 d. v. and in the 3° series: 7009 d.v. Theoretically the frequency in series 4 should be exactly V2 times higher than in series 3. A more exact method may perhaps give numbers from which a better formula might be deduced, and which at the same time might give us some insight in the phenomenon. I have tried to get more exact numbers by means of the Kunpr dust-figures but I did not succeed, though others might. Yet the oscillatory discharge of a Leyden jar through an inductive resistance easily gave regular dust-figures. The reason why the Kunpr-method proved refractory with the singing are, is not easy to be understood: Lean only suppose that the intensity of the sound is not large enough. Physics. — Dr. J. KE. Verscnaree.t. “Contributions to the knowledge of VAN DER Waals’ yp-surface. VIL. The equation of state and the y-surface in the immediate neighbourhood of the critical state for bimary mixtures with a small proportion of one of the components’. Communication n°. 81 from the Physical Laboratory at Leiden, by Prof. H. KameriineH ONNEs. ') (Communicated in the meeting of June 28, 1902). Introduction. In Communication n°. 65 from the Physical Laboratory at Leiden *) I have given the first results of a treatment of my measurements on mixtures of carbon dioxide and hydrogen *) by the method which KAMERLINGH ONNuES *) alone and with Remeanum *) used for the measurements Of KUENEN on mixtures of carbon dioxide and methy! chloride *). They confirm KAMmERLINGH ONNzEs’ opinion that the isothermals of mixtures of normal substances may be derived, by means of the law of corresponding states, from the general empirical reduced equation of statefor which he has given in communications nrs. 71 *) and 74°) a development in series indicated in communication 59a. In this empirical reduced equation of state | DS) ) = — sid 4 ? av +r Redz + 1) The translation of the first and second part of this article are treated as a whole, hence some minor changes in text will be found. 2) Arch. Néerl., (2), 5, 644, 1900; Comm. phys. lab. Leiden, n° 65. 3) Thesis for the doctorate, Leiden, 1899. +) Proc. Royal Acad., 29 Sept. 1900, p. 275; Comm. 59a. ®) Ibid. p. 289; Comm., n°. 59d. 8) Thesis for the doctorate, Leiden, 1892. 7) Proc. Royal Acad., June 1901; Comm., n°. 71. 8) Arch. Néerl., (2), 6, 874, 1901; Comm., n°. 74. ( 322 ) where %, % ete. represent series of the powers of the reduced abso- lute temperature ft, with co-eflicients which like 4 are the same for all substances, we then put: T P v ger pat File ee T*, pax and vy standing for the eritical elements of the mixture with molecular composition .7, if it remained homogeneous, while = oes tad Tk It must therefore also be possible to find expressions for the = critical quantities of a mixture — these are the elements Psyl, Uxpls T,, of the plaitpoint and pe, vx, T.? of the eritical point of contact — in which only the co-efficients of the general empirical reduced equation of state and further the quantities characteristic of the mixture viz. Tix, Pre, Vek, Occur, or the co-efficients of the develop- ments in series of these quantities in powers of z. In the case of mixtures with small values of , it may, exclusive of exceptional cases, suffice, to a first approximation, to introduce the co-efficients: Ty oi MAES 1 dpi = — -and p = — —. ie acur pr da a A first step towards realizing this idea of KamertincH Onnes has been made by Kersom*) who took for his basis the general equations by whieh van Dek Waats in his Théorie moléculaire and following papers has expressed the relation of the critical quantities and the composition; he has found what these equations would become for infinitely small «-values and has introduced into them the co-efficients aand 8 mentioned above, besides others which might be derived from the co-efficients of the general empirical equation of state. I have now tried to work out this idea in a method which is more closely con- nected to the treatment of the y-surface, namely by developing the co-efficients of the equation of state and the equation of the y-surface in the powers of 2. On account of the great complication involved by the introduction of the higher co-efficients into the calculation, I have confined myself to the lower powers of 2. However, the method followed by me can also be used to find the co-efficients of higher powers. As I have confined myself to states in the neighbourhood of the critical point I could use instead of KamertincH Onnes’ empirical reduced equation of state ihe more simple one which it becomes within narrow limits of temperature and volume on developing the different 1) Proc. Royal. Acad., 28 Dec. 1901, p. 293; Comm., n°. 75. (323°) terms in powers of the small quantities ,—1 and ¢—1. According to Van per Waats’ method‘) I wrote this new equation: ee or 1) (t—1 1 a — (t— ala) aie) ia = [ oa . e . p= i+. (1) + sae OD 1) + () ee, dy 07 F ; é ; where the eo-efficients =, —— ec. Can be immediately derived from Ot Oydt : those of the above mentioned empirical reduced equation of state. 1. The p,v, T diagram for a simple substance in the neighbourhood of the critical point. In order to limit the number of the continually re-occurring factors as much as possible, I shall not write the equation of state of the pure substance in a reduced form, but thus: p=, + k, (e—vz) + &, (o—vz)? + &, ey)? +... =f (rv). ~ (2) where /;,, /:,, /, ete. are temperature functions which can be developed in powers of 7—7; as for instance: (yy SY a (Ea ee and it is evident that £,,—= pz while %,, and k,, are zero. We might clearly find the equations of several curves in this diagram, such as: the border curve, the curve of the maximum or minimum pressures, the curve of the points of inflection ete. I shall derive the former only, chiefly in order to apply to a simple case the method of calculation to be used afterwards for finding the pressure, volume and composition of the co-existing phases with mixtures. If v, and v, represent the molecular volumes of the vapour and of the liquid, co-existing at the temperature 7’ under the pressure p,, then these 3 unknown quantities will be determined by the equations: jy ACE a — ei (OE) even hie ixnew Lem nlacdt (O) and by Maxwe.w’s criterium pi(y—n) =f pao. aap sheen | cy, ok oat (A) Yh The two unknown quantities v, and v, I shall, however, replace by the pe ean opal 1 two infinitely small quantities 5 C+) —n=2 and 50 )=Fi 7) is therefore the abscissa of the diameter of the border curve for chords parallel with the v-axis, and g is the half chord. 1) Zeitschr. f. physik. Chem., 13, 694, 1894. ( 324 ) fquation (4) after division by 2 g yields: ] ] Prk thy DEAD gh, DUD LG) Eh (D4 2G" +. Gp) 4 (5) ' v0 where for completeness I have not regarded the order of the differ- ent terms. Also taking equation (3) once for v, and once for v, and adding together, yields: Py hy Hh, PHA DP? +?) +h PUD? +3") +h, (Pt +6 by? +¢') +...(6) and subtracting and dividing bij 2 gives Ok, +24,044,3 DP? +9)4+4h4, OP? +g)4+ . . . (9% while the, at least to a first approximation simpler equation : 2 ] Oph bahytb4k,( d+ Sgt) ale, ee follows from (5) and (6). The equations (6), (7) and (8) now determine the quantities 2, g and p,—pe; for we find: ky, r aad g=— (2 Ty) = ie Se kyo D a (fay Mae areca pte 10 ob — — — | —-k, — =——_ —Tlpr)y— athe Ee 8 eer oe oO” Pike =, (T—T) +. ee Along the border curve v =v, + ®+ 4, so that we may write the equation of the border curve: 0 = (v—v,)? — 2 (v—ve) B+ D?—GQG,. . . . (12) and to the first approximation this represents a parabola *). 1) Just as v. pv. Waats (Arch. Néerl. (1), 28, 171) from the reduced equation St 3 elt ; i of state p = og ae has derived 3 (v.—»,;) —=2V2(1—1), I have also derived }(*9-+-»,) from the same equation by means of the reduced formula (10) and have found for it: 3 (v9 + 4) =1+7,2(1—2), whence, if ¢; and ¢, stand for the liquid and vapour densities : _ Fo) = pe (1 +0,8 (1—h)] From Amacat’s data for carbon dioxide I find: A=3 (2 +) = 0,464 + 0,001181 (TE — 7), or reduced 1-+ 0,775 (1—t), and for isopentane (S. Youne’s data) A= ¢r[1+ 0,881 (1—+)]. The above equation of state, therefore, represents the diameter numerically ina satisfactory manner. 2) The same problem with regard to 2 has been treated by v. p. Wats (loc. cit.) in a somewhat different way; only 9 is determined accurately by his method and the border curve can be derived from his formulae only to a first approximation. ( 325 ) 2. The p, v, T diagram of a mixture with a small value of x near the critical point of the homogeneous mixture. From the consideration we have started from it follows immediately that we obtain the system of isothermals of the mixture by moving that of the pure substance to an infinitely small amount parallel to itself so that the critical point (p,, ve) is brought on to the critical point of the homogeneous mixture (per, Urk), and at the same time by expanding it infinitely little parallel to its co-ordinates in multi- Prk , 3 ke 2 Vol: ; plying the ordinates by —and the abscissae by —. Moreover an isother- k UL mal, belonging to the temperature 7 in the first system will belong to the temperature Hi after we have moved and magnified the system. We put again: p=, +1, (e—vxt) + 1, (even)? + 1, (0)? + . + (13) where /,,/,,/, ete. are once more functions of the temperature, thus: Uy yy + lay (L— Tan) + bog (L—Tat)? + + - - « (18) According to the derivation from the reduced equation of state by means of 774, prt, Vze the co-efficients /,,, J,,...-.4,,., 4, ete. are only functions of z. Putting: pee i, (lyre aa to) Doe pe (l Be Bat e..)) os 2 sl A) Urk = 4 (1 + yo + y'z? +....) where y=a—B, y'=a'—f'—oaB+8 ete, . . - . (14) we find Io PH + Bot...J; by) =ho[1—(a—B)e+...]s lyg—=kyal1—(2a—A)e...Jyee- 0 4, =, ,[1—2(a-B)a-+...], lyk, [1 —(8a-28)aL...Jye-- f.=0 ,l,,=h, ,[1—3(e-B)at...],... Lj=hyg! 1— (8a —48)a-b ose. ]yene ji cei ee TA aS Pale a OG) where all co-efficients 7 are expressed in co-efficients 4 as well as in KAMERLINGH ONNES’ a’s and (’s. From the values of 7%, por, Vox, With mixtures of carbon dioxide with small quantities of hydrogen for z= 0, «= 0,05 and « = 0,1, ') I find : 1) Comm., n°. 65, Ta = T (1 — 1,17 « + 1,58 o°) Prk = pe (1 — 1,62 e + 2,45 27). . . « . (16) vst — vp (1 + 0,62 w — 0,95 «?), ') while from (14') would follow: Vek = vy (1 + 0,45 w + 0,08 «?). Although the agreement between the two expressions for v,, is not quite satisfactory, it vet by no means indicates that the law of corresponding states does not hold; it may very well be a result of the uncertainty of the critical data of the homogeneous mixtures, chiefly of the v,,’s. Besides from the second formula for v,, I find: for «= 0,05 v,. = 0,00432 and for z= 0,1 v,. = 0,00441; and these values deviate from those determined directly (0,00434 and 0,00444) not more than the amount of the error that can be made in these determinations. Besides, since the law of corresponding states does not hold entirely with pure substances, it is not likely to do so for mixtures. 3. The p, v, «, diagram for mortures with a small value of 2, at a temperature differing little from Ty. We shall now consider different mixtures at the same temperature 7’; the system of isothermals in the p, 7, « diagram, at that tem- perature is represented by the equation of state (13), where, however, T must now be taken as constant and « as variable. We will now put this equation in another and more suitable form. Among all the mixtures there is one for which the critical tempera- ture would be 7’ if this mixture remained homogeneous; the com- position «7, of this mixture, and also the critical elements p 7, and ry ave determined by equation (14). (In this equation we must put: i — ae — ip Pxk = PTk and v= v7,). Hence we find to a first approximation T—T,, Pk (a-2) a ae pre= pe + PM (0 Tr), om = ee : ae Tj). (17) It will be seen that to a first approximation a value wz, is either positive or negative according as 7’— 7), and « have the same or opposite signs, that is to say a>0 a0: figs. 4, 6, 10 and 12 2) Comp. also Keesom, Joc. cit., p. 12 Grau a) Although from a physical point of view x can only take positive values, in these considerations even the case v7, < 0 is not impos- sible; for the point pre, v7~ has only a mathematical meaning. In general, equation (13) may now be written thus: pam, + m, (v—vrk) + m, (v— vr)? + m, (e—vTK)? ++ (18) where m,, m, ete. are functions of « which can be developed in powers of «—v7,; for instance: m, =m,, +m, (ew—«rm) + m,,(c—er)? +.--. - ~ (18/) The co-efficients m are functions of the temperature which is here considered constant; it will be obvious that m,,—= pre, while m,, and m,,—=0. By equalization of (18) with (13) we can express all the m’s in the #’s, and in KameriincH Onngs’ e’s and ’s; for we find: kn 7 Palys aes Eyed (ra 7 en ee Tra mn = — kno [na — (n+ 1) 8] — fini Tea — (x + 1) kn tiyjo(a— 8)v;-+..., ete. (19) so that to a first approximation : MK 302 Mao ae Cagis ss) ss m,, = prb-k,, Tha, m,, =-k,, Tha, m,, =—k,, Tra-3k,,vj,(a-B), ete. (19') HarTMAN ') has given a diagrammatical representation of the p, v, « diagram. This representation completely resembles a p,v, 7’ diagram; but this resemblance is not necessary. It follows directly from the p,v, T diagram that £,, is positive, while £,, and &,, are negative ; in the p,v,« diagram m,, is negative, but according to (19), m,, and m,, may be either positive or negative. The circumstance 7,,<.0 does not indeed influence the general shape of the diagram; it indicates that the isothermals of the mixtures lie below those of the pure substance as is the case at the upper limit (c = 1) of Harrman’s representation ’). But while in the p,v, 7’ diagram the isothermals with maximum and minimum pressure occur under the critical, the opposite may be the case in the p,v,x diagram, if m,, and m,, have the same sign. The four cases which may now present themselves, leaving out very particular values of the coefficients, are given in the following table: 1) Thesis for the doctorate, Leiden 1899, p. 6; Journ. of Phys. Chem., 5, 425, 1901 _ 2) From a mathematical point of view we may imagine the p, v, x diagram to be continued outside the limits s=0O and «— 1. It is also obvious that a, if diffe- ring little from 1, means the same as x infinitely small and that x > 1 means the same as x < 0. 22 Proceedings Royal Acad. Amsterdam. Vol. V. ( 328 ) Tk eee 49 m,, >0 or a>0O | figs. 1 and 2') figs. 7 and 8 | m,, < 0.0r Oi) L figs. 3, 4, 5 and 6 figs 9, 10, 11 and a HarrMan’s diagram represents at the lower limit the case m,, >0 and m,, <0, at the superior m,, << Oand m,, >0. The case «e >0 will in general occur when the second is less volatile than the first substance; this for instance is the case when methyl chloride is added to carbon dioxide 7). On the other hand we shall find the case a<0 when the second substance is the more volatile, when for instance hydrogen is added to carbon dioxide (comp. formulae 16) or earbon dioxide to methyl chloride *). A p, v, v diagram based on observations has, so far as 1 know, not yet been published. A diagram of this kind which I have drawn from my measurements on mixtures of carbon dioxide and hydrogen perfectly resembles the p, v, 7’ diagram after Harrman, so that in the neighbourhood of pure carbon dioxide we must have m,, >0 and m,,< 0; according to formula (16) @ is really negative, while with &,, =—1,61° (comp. Kersom /oc. cit., p. 14) I find m,, = 454, and positive. For carbon dioxide with a small quantity of methyl] chloride‘) a = 0,378 and 8 = 0,088, and hence m,, <0 and m,, > 0; and for methyl chloride with a small quantity of carbon dioxide, ¢ = — 0,221 and p= 0,281 so that m,,>Oand m,,< 0. At temperatures between the critical temperatures of the two pure substances, the p, 7, « diagram for mixtures of carbon dioxide and methyl chloride will probably correspond to Harrman’s drawing. While two neighbouring isothermals (7, 7’+ d7) never intersect ree 0p in the p,v, 7 diagram (the (54) never being zero) this may be the case in the p, v, « diagram for two neighbouring mixtures 1) Figs. 1—13 represent diagrammatically p, v, © curves for infinitely small values of « and 7—T:, such as they appear in reality for finite values of 2 and T—T;. They are moreoyer theoretically extended into the imaginary region 7 < 0. All lines lying within the region of negative 2 are dotted; the isothermal =O is represented by a dot-dash line. The line «=. (erroneously marked xv -in figs. 1—12) would be the critical isotherm of the homogeneous mixture. *) Comp. KamertincH Onnes and Retcanum, loc. cit., p. 39. 3) Thidem. *) Comp. Keesom, Comm. n°. 79, p. 8. i a ( 329 ) (vandw—+ de). If this point of intersection is situated at a finite distance from the point pre, vrg, it lies outside the limits we are con- sidering; but if it lies infinitely near this point, then it practically co-incides with it; then m,,—0O and all the isothermals in the neighbourhood will intersect each other approximately at the point pr vr This case is shown in fig. 18, where I have also supposed «<0 and V< 7Z;. The isothermals intersect in pairs, and the curve formed by all the points of intersection of two consecutive isother- mals, also passes through the critical point (p7,, vr); this is repre- sented in fig. 13. The connecting line of the points of contact enve- lops the isothermals; ifs equation is found by eliminating « from Op equation (18) and from =i) where we also put m,, 0; hence Ow we find to the first approximation : Domes, ae P—PTk = — — (v—v7k)’- 4 my. This parabola is turned upwards (as in fig. 13) if m,, is negative. 4. The y-surface. In order to find from equation (18) the phases co-existing at the temperature 7 I shall make use of the properties of the y-surface of van per Waats. The equation of that surface is: y= | pdv + RT| «log # 4+ (A—2) log A—z) |, where #& is the gas constant for a gramme molecule, hence the same quantity for all substances. Neglecting the linear functions of 2, we may write: 1 if 1 wp = — m, (v-v TK) — 5 (v-v 7p)? - 3 m, (v-v7,)* — 4 m, (v-v7K)* +... 1 1 “EL OL ee Sescatia > a oc SENG SB let “nt Gnu iaies. (40)) 5. The co-existing phases. The co-existing phases are now determined by the co-existence conditions : ow ra Ow ow ae Ow at, 3 (3). = (30), - feels) nt ee (ure Oe A) if w represents the thermodynamic potential : 22% ( 330 ) Instead of the third condition I find it however better to use an- other which follows from all three, viz. Pee My st!) PPR a, where ow 0 M= wp — (v—vm) Wa TF (w—27%) a. . Corresponding to a former transformation now I write b(r, +0.) —erne=® and 4(r,—v)=y and equally $(v,+2,)—«#7.—=— 8 and }(«,—z,)=6§, and I consider the infinitely small quantities ®, g, 2 and § as fune- tions of the same variable, viz. p,—pze. Thus I find to the first approximation ‘) A a \{dens m,,m i: m, Pi:— PTE p—— i ol 01 = sae). 1 ae Rr" R +5" “5 wget Fe +m.) eee fe = Moro “TL (22) 2RTm,, 3 RT Rs oak B= 1 [im Pi—PTk m : 01 1 01 =—— Bi 2 eee y ee Mor RTm,, @8) gatos . (24) Mo, m Pi PTE and p= Tip | h Pm ten; ¢ 343 RT M,, where x7, and pr; may be replaced by their expression (17). 6. The plaitpoint. In the plaitpoint the co-existing phases become identical. If we represent the elements of the plaitpoint by xz,), pz: and v7z,) then 1) The four equations from which I derive the relations (22)—(25) are: op) (ow nes dy) (dy Ow dw @)=@)—* GG) r—1G) GF ; x The two first equations contain the expression /og = as all the other terms are beat | ae : eae oe as infinitely small, this must also be the case with Jog —*, in other words, the rahe zy 1 can differ only infinitely little from 1; § must therefore be of a higher order than =, s a = : - so that also Jog —* may be developed in a series in powers of —-——. x, Ete Sm at that point = v7, —o7,, gy = 0, F= eri—wxre and § = 0, while Pi=pri: thus we obtain, from the equations (22), (23) and (24), RTm,, HOS SEES SE ela ea a ms P Tpl = PTk — m?, - RTm,, UT ss . . . (2 7) and a My, 2 m7 53 : : USCS yer cee ome GONE Oe Scone » fone C8) If x7, pre, and vz,z are replaced by their expressions (17), the elements of the plaitpoint are thereby determined to the first approxi- mation as functions of the temperature 7; R7m,, may then be replaced by R7Tim,,. From equations (26) and (27) follows immediately : ar ae Sat eee eS ee han (29) LT pl — &Tk In order to see how this relation holds for mixtures of carbon dioxide and hydrogen I consider the temperature 27,10° C. at which the mixture «= 0,05 has its plaitpomt (pr; = 91,85 atm.); at that tem- perature «7, = 0,011 and pr, = 72,4 atm. so that ane 500, &Tpl — &Tk in good agreement with the value 454 which I have found for m,,. It follows from equation (26) that #7,. can be positive or negative. As «7: <0 is not impossible, this is equally the case with a7z,,. It is true that from a purely physical point of view the w-surface, only exists between the limits «—0O and «= 1 (in our case x > 0), but from a mathematical point of view we can imagine this surface to extend also beyond those limits *). If we consider a temperature lying above the critical temperatures of the two components of a mixture, then there are, exceptional cases excluded (Harrman’s 34 type), no co-existing phases, that is to say the real y-surface does not show a plait, although formula 26 shows that there is a plait- 1) If we take the value of x7, from the equation (26), insert it in (27) and (28), and finally introduce the k’s, «’s and 6's, the formulae (27) and (28) become Keesom’s formulae (20) and (2c) (Gomm. n°. 75), while (26) corresponds to Kersom’s formula (2a). 2) Outside the limits 20 and «=1 y is imaginary owing to the presence of terms with log x and log (1—<). Although this is the case the co-existing phases beyond those limits are real, as the co-existence conditions contain the necessarily = Hy i — Lp real expressions Jog — and log ——. xy —2X, = 332 ) point on the imaginary part of it. If the temperature is lower than the critical temperatures of the two components the plait oceurs between the limits «—0O and «1, but, except for mixtures of the second type, according to formula 26 the plaitpoint lies outside these limits. Hence the case is physically not without significance, but the plaitpoint cannot be observed. Equation (26) may be written: 271 = Ppa —— (T— Ty), aes, a eee “el and this form shows that «7, will be positive or negative as T—T, and R7*,k,,a@—m’*,, have different or the same signs. RT?, k,,@>m’,, is only possible if ¢e< 0; R17? k,,a< m*,, will always be the case if «@ >9, but may occur with @< 0. The different cases that may occur are shown in the following table. RT*, k,, a > m’,, || Rk @ 2re > 2Tpl | °Tk > tty > 0 Tp > 0 > 2Tr af fe Tr j Zot figs. 5 and 11 | figs. 1 and 7 | figs. 3 and 9 |- = a3 LTpl > 276 > 0.0 > LT yl > LT, | 2TE >= 0 => LTpl TT, ' figs. 4 and 10 | figs. 6 and 12 | figs. 2 and 8 7. The border curve in the p,v,« diagram at the temperature T. Along the border curve v=v7y.+ 7+, so that the equation of the border curve may be written 0=(v—r7n)*—2 P(v -v7m) + P?—-g?. . . . (80) where @ and g must be replaced by the expressions as functions of p,- To the first approximation we can take therefor the expres- sions (22) and (23) and neglect 7*; the equation (30) then repre- sents a parabola of the second degree. The apex of this parabola does not, as in the p,v, diagram of a simple substance co-incide with the critical point (prz, vy), but with the plaitpoint. Along that parabola dp 2 m,, m,, RT; 2m, 1 Aso RT, ae 7 % m*,, + RTym,, ~ RT, k,,a— m? ty ; ( 383 ) This expression is either positive or negative; that is to say that the border curve may be turned with its convex side towards the v-axis, while in the p,7, diagram for a simple substance the bor- se enidape Ft ae der curve is always concave to the v-axis. on will be positive if m and R7?,k,,a—m’*,, have different signs, and will be negative in the other case : eee am. D4 Bs ; ~ RI, k,, a@< m0, | m >O figs. 5 and 6 | figs. 1—4 | | oa ewe cee | Ne = — — | —— + mm, | «+ —— 27, - + (33) Ube ato Ms and ie — oe) (Cr) Pie Nel cl Ms, fc tbe (95) 1) Wien. Ber. 98, 1159, 1889. 334 ) Now we may again write for the equation of the connodal line 0 = (vo—vm)*—2 F (vp—v 7) + P"—g®. . . . (86) To the first approximation along this curve x 2m,, RT; 2k,, RTE ae a = = — : (37) dv* m*,, + RT, m,, RT*, k,,a—m’,, and this expression has the opposite sign to 7°, k,,a—m’*,,. Here therefore we distinguish only two cases. Pa : F ; 4... Fol He aS mn", 3 7 9 i.e. the connodal line turns its do concave side towards the v-axis (fig. 14); Mex y eee el A ee = > 0 and the connodal line is convex to v the v-axis (fig. 15). 9. The critical point of contact. The characteristic of the critical point of contact is that there the two phases with which the condensation begins and ends coincide. If x7,, pr, and v7, represent the elements of that point we have there @' = v7,—vTm, ¢' —0, D'=pr-—pm 2 = Vand «= 27,. and from (338) it follows that RT), m,, m+ RT, mi, STG sot eta ee i — that is to say to the first approximation the composition at the critical point of contact is the same as at the plaitpoint (cf. 26). The diffe- rent cases which may occur now follow. A RI, bk, a >> m*,, (ig. 14): a). T >T).; x7, is negative and there is no connodal line inside the region that can be observed. This corresponds to the position of the border curve in figs. 5 and 11. 6) T= T,; x7-=0 and the formula (30) represents a connodal line which touches the v-axis. c) T< Ti; «r->O and there is a connodal line in the region of positive z, (see also figs. 6 and 12). 2 WaT ka < meg eee ‘a) T>T:; xr->>0 and the connodal line lies entirely within the region that can be observed; (figs. 1, 3. 7 and 9). b) T=T;; xr-=O0 and the connodal line touches the v-axis ; c) T'< T;; z7->> 90 and the connodal line can only be completed ee ee ee eee ee ae ea ee eee ee ee eS OE es eee Te 1. = +. ( 335 ) by prolonging it in the region of the negative w (fig. 2,4, 8 and 10). Equation (34) gives : m* TMS RT a “nny. o. (B38) OT, = PTk + m,, (eT, — &7Tk) = pT so that also to the first approximation p7, = prpi eu: equation 27). And from the equation (82) we derive in connection with (38): 1 Mine MyM, UT, == UTE | m,, + —-— ] wre, - - (40 ; Tet 3 m,(m,,+RTypm,,) : Ina lyp ) from which by comparison with (28) we find 1 Lei 1 ky, m o1 ’ UT — UL pl = ———— «7, = —— (7— Tx) . (41 Psst an eOM eT 2 RTtk,, ce The difference vp,—vz7,, may be positive or negative, that is to say the critical point of contact may be situated on the vapour or on the liquid branch of the border curve (or of the connodal line). In the first case, as it is well-known, we have retrograde conden- sation of the first type for all mixtures comprised between x7, and x7y,|, in the second case retrograde condensation of the second type : eS. en GU tCs Us ties. me and’ | De T,. vn Ze PTs 2. c. i; figs. 2, Lan » TU TS rc. 11; figs. 38, 1Oand12, on Demir c. i figs. 7 and14| Expressing that the plaitpoint and the critical point of contact lie on the connodal line and subtracting the equations thus obtained we find to the second approximation : 3 2 il ne Ua LT;—2£T, — SUE GRe ate ae (ae mae ae ARTs a a (m? RT, m,,) ae (#2) this expression is positive if 27?,.4,, ¢ > m?,, (fig. 14), and negative if RTck,,a 9 Be < 9 RI”; k,, « > m,, |ptr << pty; figs. 5 and 6) pr, > pry; figs. 11 at nd 12 | = eee | RE? pike am", (ptr > pry; figs. 1—4. | PT pri; ues. 7—10 } a. y | = = = ——| (To be continued). 336 j Physics. — Dr. J. E. Versonarrenr: “Contributions to the knowledge of VAN per Waats’ w-surface. VIL. The equation of state and the w-surface in the immediate neighbourhood of the critical state for binary mixtures with a small proportion of one of the components.” (Continued). Communication n°. 81 from the pliysical Laboratory at Leiden, by Prof. IH. Kamertincu Onnes, *) (Communicated in the meeting of Sept. 27, 1902). 10. The border curve and the connodal line in special cases. lL. When m,, = 0, i.e. peB =k, Ty, @, all isotherms intersect one another nearly at the critical point (pz,, 7”) as we have seen in § 3; according to the equations (26), (27) and (28) the plaitpoint coincides in that case with this eritical point. Besides from (31) it follows that d?p dp | Oo ; this value however belongs to a only to the first approx- imation (i.e. at the critical point itself), or the border curve is a parabola of a higher degree than the second. In fact we find in this case: (le 3 My, and therefore the border curve to the first approximation becomes a parabola of the fourth degree; the equation of that parabola is: m* lm,,m | a Yb — (Me — 3 mus Tet ony) m 11 30 The connodal line, however, remains a parabola of the second dix 2k degree, on which — = — : dv? Teka 2. A second remarkable case is that where R7,m,,+m’?,,—0; for then the term p,—py, disappears from the expression for g? (equation 23), so that g becomes of the first order with respect to p,—pre. We then find : 1 /m, Pi—=PTE i Ma FL 2 m,,m p—— a 5 a Od oa oe RT +” re See PONS tae en 30 and 3 My 1 (5 mm, msm 4 = ww ThLE-— — i Ms ie 30 2 RIL = RT em,, + mm 5 atta _ 7 in (eer, uw 13 = = 3 m ™m 1) Comp. Proceedings Royal Acad. of Sciences Sept. 1902. in the last term I shall express the co-efficient of (,—r)’ for con- venience by K. Substituting this in equation (80) we obtain to the first approxi- mation an equation of the second degree, which now no longer represents a parabola but an ellipse or a hyperbola. The coordinates of the centre are: Mo, 1 2 My, My \ Pe=—PTE and vw = vr, — ee ( 1, Jere while the straight lines P—piT and wv -- & are conjugate axes. With respect to these axes the coordinates of ihe border curve are g and p,—p, so that the equation of the border curve with respect to those axes is: 2 i 2 Mary ky, it Merry gy? — K (p—pr.y? = — 2#Te = — xa (T—T;). Meso 30 In the same case the equation of the connodal line is: > k 7 ’ g', — Km’,, (e—«7,)? = — ae (T—T;), 30 with respect to the conjugate axes : Le, and v=v744 ©&; - : aan Pre: where ®' is obtained through substituting «—«7, for in @. m 01 We must now distinguish two cases. a. K 0) of the y-surface. We find two plaitpoints of which only one is in the real y-surface and two eritical points of contact co-inciding with the plaitpoints (at least to the degree of approximation considered here, i. e. to the order V(7T—T;,); the coordinates of these points are: 1 Uae LT) (= & 7, = &7 EE a Kh. (7 —T;,) O1 ARE 3 Sie Smee Vee T_T, Pili PTh Ke, | 3) 1 Mien A cA kh. —-_—— v a - “mM, === (Ih sha ts a9 My, —( heli: aes Kk ( t) 30 If T=T;, the border curve and the connodal line shrink to one point, the critical point of the pure substance; and if 7 > 7%, there is no longer a border curve nor a connodal line. 338 ) b. K>O; the border curve and the connodal line are hyper- bolae; the asymptotes are: g=—+(p—pr)V A(bordercurve\andg'= +m, («—«7)V K(connodal line). If 7 > TT, g (or g’) is the real axis; only that branch of the hyperbola which lies above the axis p= jp7,% can be observed as border curve; in the case of the connodal line it is only the branch lying above the axis «—.2#7, which can be observed; again two plaitpoints are found of which only one can be observed, and the coordinates of which can be expressed by the same terms as used for the ellipse. If 777), the border curve and the connodal line consist of two straight branches meeting at the critical point of the pure substance, which is therefore a double plaitpoint. Lastly, if T< 7, there is no longer a plaitpoint; we observe two branches of the border curve and the connodal line lying to the right and the left of the point pzz, v7~; each phase on one branch co-exists with a phase on the other. 11. The border curve in the p, v, T diagram for a mixture of composition «x. In equation (86) of the projection of the connodal line on the x, v-plane, if we consider «2 as constant and 7’ as variable, that equation will express how the volumes of the phases, where the condensation begins and ends depend for the same mixture on the temperature. It therefore may be considered as the projection on the v, T-plane of the border curve on the p,v, 7-surface for the mixture of composition 2. This projection, can be written in the following form, corresponds to (36) 0 = (v—vzt)? — 2 ©" (v—v,x) + Bg", . . . (44) where 1 ns pl = 5 (vite) — vn = © + v7, —rz = (to a first approximation) iL Mo, (Mos 2 mo, 4m,, m’*,, he ae pm Dray. + Mi, a0 On Ors a ae Ee Pa Dm wv + 2m,,| RT, \ RT; 3 eT bm, AT; ee tT) + 1 | (Ge tm) tS Tr 2m,, |m,, \ RT, es ont] T— Tak \ ; (45) Do Ms, aTy, and 1 1 m,, T—T2 (eee aes Sep ees Pal Cie Z = == 46 g Z ('>,—-v,Y=¢@ RTyn,, es. ae (46) 339°) To this can be added 1 ry yy Tt Oo (sn) SH = hoy (ad) ee oe ae (47) and x! = Ipemelsiy pie . (48 a Ta i) gp" (48) To the first approximation equation (44) represents a parabola, of which the apex determines the elements of the critical point of contact for the mixture v. For we know that in the case of the critical point of contact v',=v',=v,, so that g"=—0 and &" = v,z,— vx. Hence it follows that‘): 7 r m* ol Ln SS Lp RI h,, St Age at a eS ES ceed ee (49) Hes tip < Por = Pak — RTE, Sk: Ra ee ieee (50) trea t| ma: pee “en (Mam ra” ») |e ae Oe In order to derive from this the equation of the border curve in the p,v, T-diagram, we must express 7’ in terms of p and v by means . of equation (13). Then we find: 0 = @—2)? — 2B" (wv) + P — Gy" 2 2. (52) where Gl! — il Me [Maa ve 2 my 4 TUE Dae ate ea OU A Teg ta SRT Do mee Bere v(a—PB 1 m,, (m* 2 4 m,,m, qe Be pat) +; Sa ea a ee k, aT. PV ac 3 5 pie ne fut |e (53) ky, al). and m? m,, DP—Drk == ae aa 4a P eee q aa 6 as) (O49) RI; Ms, Heaven AOo Liye To a first approximation (52) is a parabola on which as in the case of the border curve of the pure substance. The apex of the border curve is the point of the maximum co-existence ') We obtain the same formulae if we replace in equation (26) 27% by its value (17), put T= T:, and %7,=<, solve Tz, and substitute it in (39) and (40). ( 340 ) pressure '). Let Pim Yen Tra, be its coordinates, then we find by putting CU and @®" = vy, — Usk Tas Ta er . te eee Hence to the first approximation Pon = pe and Ty, = T,,, but Vx — Yzp = — : et Fons acre cries b5)o for real mixtures, that is to say «> 0, the latter expression is neces- sarily negative, so that the critical point of contact is always situated on the descending (right) branch of the border curve. We cannot call it the vapour branch, because here the apex of the border curve is not the plaitpoint as in the p,v,«-diagram. The critical point of contact is situated thus, because the critical isothermal touches the border curve at that point, and because on that isothermal and hence also at the critical point of contact 7',,>> 71, (at least for real mixtures), Op therefore 5 <0 for the border curve. This corresponds to a diagram- a matical representation of a p, v, T-diagram for a mixture given by KvrNen ?) and also with the experimental diagram for the mixture : 0.95 carbon dioxide, 0.05 hydrogen which I have given in my thesis for the doctorate. In spite of the small value of .z, terms of higher order appear to have such a great influence in the case of this mixture that the apex of the border curve lies far outside the area investigated, and the border curve at the critical point of contact is no longer concave towards the v-axis but convex. The plaitpoint elements for the mixture of composition x are found by substituting 7. for ZY and « for «7p, in equation (26), by solving 7’); and substituting that value in (27) and (28). Then we find : m? ,, + RT pm m* T= 7; | 1 oe SS eS eee eee zpl | aly RTwm.,, «| zk Rk,” (59) key ym* oy Kym", Pe ; t=Pu— Sy ee Papt = Pk+) PKB +> Ral fea Roe (60) 1) Comp. Haran, Journ. Phys. Chem., 5, 437, 1901. Communications Leiden Suppl. N° 3 p. 14. 2) Zeitschr. f. physik. Chem., XXIV, 672, 1897. ( 344 ) ee : mi, [2 Im*..m, , x 1 Urpl = Urk + | m 01 Ue (@—B) =e By ft 3 ora aS RT, SL RT ym —,(61) BY pv c yy aut Kl which formulae, after some reductions, can be put in the form in which Kerrsom has given them (Comm., n". 75). Also the following well known equation ‘) results directly from equations (59) and (60) Pxpl— Prk = ky, (Lpi— T xk) a a 3 Ie va G(r) which also according to equations (49), (50), (55) and (57) holds for the coordinates of the critical point of contact and for the apex of the border curve. From the coordinates of the plaitpomt of mixtures of carbon dioxide with a small proportion of hydrogen *) («= 0, 0,05 and 0,1) I derive the following formulae TV yp1= T, (1 — 0,30 & 4 a?) | Papl = pe(1 + 4,424 112?) | > 6 6 ee (G35) Urpl = vz (1 — 0,40 e — 82’) In connection with the formulae (16) I obtain directly from these : Ion =) ols wal } Bie BETES GG (te 2c), Pepi — Ts I: in good harmony with equation (62) (4,, = 1,61) *). Using the value k = — 513"), I moreover find that the formulae (59) and (60) applied to mixtures of carbon dioxide and hydrogen become: Txpt = 7; (1 -+0,03 «) and Pxpl = Pk (1 +6,4 2); . (63') hence the agreement with the formulae (63) is decidedly bad, as has also been remarked by Kesrsom (loc. cit., p. 13). We cannot, however, draw any conclusions from this; it is improbable that the imacecuracy of the data should cause this great deviation ; but from the fact that terms of higher order produce such a great influence in the mixture « = 0,05, we see that quadratic formulae are very unfit for this comparison *), the more so as it appears from 1) Comp. v. p. Waats, Versl. Kon. Akad., Noy. 1897. It also follows directly from the equation of state (13) in connection with (15), by expressing that the elements of the plaitpoint satisfy this equation and by neglecting terms of a higher order than the first. j 2) VerscHarrett, Thesis for the doctorate, Leiden 1899. 3) Comp. also Keesom, Joc. cit., p. 14. 4 RT; 0?x *) Derived from ——- ——- = — 32,2 (Keesom, p. 12). PRUE OWOT 5) By intreducing the values for «0,2 (comp. Verscuarrett, Arch. Neerl., (2), 5, 649 ete., 1900, Comm. n° 65, and Keesom, loc. cit. p. 12) they certainly will not become better. 342 ) Keresom’s calculations (p. 18) that tolerably small variations in the values of @ and ? greatly influence the values of aT out and BPsot =. Vix de da Accurate observations for mixtures with still smaller compositions are therefore highly desirable. As the v,,;, and also the coordinates of the critical plaitpoint, are known with less certainty than the 7’,,; and pi, & Comparison of the theoretical and the experimental values for these quantities is practically useless. Again from the preceding equations pyi=per, Ti Ty to a first approximation, and es 1 vas : Urpl— Vzr ss aR Tun, RT, + a mS (G4) Hence the plaitpoint may lie either to the right or to the left of the critical point of contact; for positive « we have kage RT", k,, a> m?*,, | Vzpl < Dares Mh ea Vzpl > Urs B.C HI | L t | } RI*;.k,, @ |) Uzyl > Usps PLGA |) Vent 0 or 0m, ae a ~ + ms) and 3. . the left of the apex when Nor SS ky, (a 4 ‘ m)> 0 or >E (Ge = mm) > ma In the p, v, T-diagram the plaitpoint has no geometrical meaning. The expression that the coordinates of the critical point of contact and the plaitpoint satisfy the equation (44) gives, to the second approximation : r Piao ais mor , eu - (65) apl — Lar = Te RT yk, ,k a RT, pat |, Wee rey ee o ( 343) The right side is necessarily negative and therefore we always have Pr > Ti, which also necessarily follows from the meaning of the critical point of contact. In the same way we find by means of equation (52) : Lika Migy (203 moh, 1/m’,, a Pipl > Par = —* as 5 apqp +m, Ta hay RT». + m,, x. (66) 2 ky, RT, WRT ko, 2\ AT, 12. The condensation. The line which indicates the relation between the pressure and the volume during the condensation, the so-called experimental isother- mal, extends between the two points p’,, 7’, and p’, ,v’, (the points where the condensation begins and ends) but we can also imagine it to extend beyond those two points, although there it has only a mathe- matical meaning; for beyond those two points the quantity of one of the phases would be negative. In order to find the equation of the experimental isothermal we must seek at each volume for the pressure at which the two phases into which the mixture splits, can co-exist. For this purpose I return to the projection on the «, v-plane (§ 8) of the y-surface belonging to the temperature 7. If v,, v, and v,, @, ave the phases into which the mixture v splits when the volume v is reached (», >v>v,), the point v, # hes on the straight line con- necting the points v,, 2, and v,, 2, and hence we have this relation : —upE— P ses sree (5. toe Wan Meg ee B7) Se L£—27T-— where ®, 2, gy and § have the same meaning as in § 5. If p, is the pressure at which the two phases v, and w, co-exist then we obtain the equation of the experimental isothermal by expressing the quan- tities ®&, =, y and § of equation (67) in p, by means of the equations (22), (23), (24) and (25). That this experimental isothermal passes through the two points v’,, v and v’,, wv follows directly from the way in which its equation has been derived ; we also obtain it from the substitution of v’, , «’, — or v’,, 2, — for v, x, which involves the substitution of v’,, 2’, iOELY, 2, — Or Of v',; 2’, for v,, 2,. By successive approximations (67) is brought to the form : Mm 9 . PP, =PpTe + m,, (eu —27E) — =— (e—v7R) ae +..-.-3 - ~ (68) RT. if we consider only the three first terms, this is the equation of a straight lime, hence of that connecting the two phases where the condensation begins and ends. In connection with (18) we find, neglecting terms of higher order, Proceedings Royal Acad. Amsterdam. Vol. Y, ( 344 ) m? P—P, = ™,, (e—vre) (e—a7%) + (v—v7,) « + m,, (v—v7¢)’, RT, and according to (33) this may be written P—P, = 4; (v—v7e) [((e—ore)? — "]. We see that in this form the experimental isothermal intersects the theoretical at three points’), viz. »x=vr7_y+ 9’, v=vmR—y’ and v = v7, (all to the first approximation) ; the two first points are the points at which condensation begins and ends (#’ has been neglected as being of higher order than g’), the third lies between the two first. When vy + 4%’ >v >v7, that is to say at the beginning of the condensation, p> p, and the theoretical isothermal lies above the experimental ; when v7; >v > v7, — gy, ie. at the end of the con- densation, » > p, and the experimental isothermal is the higher *); this, indeed, follows necessarily from the s-shape of the theoretical isother- mal, and the approximate straightness of the experimental. According to thermodynamics the two areas enclosed by the theoretical and the experimental isothermal must be equivalent *), that is to say: v's fo-r dn'=20: vy +,’ fer) dem =0, =, and this actually follows from the form, found just now for p—p,. This has only been proved for the terms considered here: but obvi- ously it must also be possible to prove this for terms of higher order. or 13. The p, T diagram. a. The vapour pressure curve of the pure substance. We have found to a first approximation : Py = pet’, (T—T»). As &,, is positive, this straight line rises and terminates at the 1) Comp. for this Hartway, Comm., n°. 56 and Suppl. n°.3 p. 25; Journ. Phys. Chem., 5, 450, 1901. *) Here the proof is only given for mixtures with small composition. For a general proof comp. Kvueney. Zeitschr. f. Physik. Chem., XLI, 46, 1902. 3) It has escaped Briimcxe’s notice, who mentions this theorem in 1890 | Zeitsechr. f. physik. Chem., VI, p. 157) that it occurs already in a treatise of van peR Waats of 1880 (Verh. Kon. Akad., Bd. 20, p. 23). (eee) point pe, T,. T; is a maximum temperature, so that this curve lies in the third quadrant (S’O, fig. 16.) Fig. 16. b. The plaitpoint curve. According to equation (27) me oe T-T', RT yk, ,m,, oy PTpt—=Pk+| PrB-—,— = Pit Monae TEN ly Mae Mia RT;, mM, aT; m+ RT pm, This curve may have all possible directions. If we consider only real mixtures (v > 0), it extends only on one side of the point p;, 7%, namely that corresponding to such values that 7—7), and m*,, + RT, im,, have the same signs (according to equation 26). With regard to the position of the plaitpoint curve we distinguish the following cases : 1. m,,=0. pri=pe+h,, (7—T;,), hence the beginning of the plaitpoint curve will lie either in the direction of the vapour pressure 23* ( 346 ) curve of the pure substance or will eo-incide with it as T > 7, or T< T,, that is to say, according to (26'), as a is positive or negative. In the first case (1a), therefore, the plaitpoint curve will lie in the first quadrant (OS fig. 16), in the second case (14) in the third quadrant (OS'). We have noted that then the plaitpoint elements of a mixture co-incide with the critical elements which the mixture would have, if it remained homogeneous, hence the mixture behaves like a pure 07 substance. This is the case on =O already discussed by VAN DER Ox Ov Waats'); in this ease there is a mixture — here it must be the pure substance itself — for which the vapour tension is a maximum or a minimum, and indeed it follows from the expression for p,—pi- ree. : Op, in this case *) that | — =D: Ox, 2,=0 2a.m,, > Oand m’?,, + RT; m,, > 0. — k,, so that the plait- point curve lies in the angle SO Y because 7— 7), must be also positive. dp: Tyl __ dT ning of the plaitpoint curve co-incides with OY*). Thus we have here the second special case of the shape of the plaitpoint curve investigated by van per Waats, i.e. where there is a maximum or minimum temperature, here the critical temperature of the pure substance. Really in this case (§ 10,2), as pry—pe is of higher order than p7,:—pr, 2b. m,, > Oand m?,, + RT, m,, = 0, = + o, and the begin- ery he WN be a os (PTpl—px)* 11 hence (7 = 0. T > T;, that is to say 7; is the minimum plait- dp ty point RAIS when A > 0; this is the case where the border curve and the connodal line are hyperbolae (mixtures of Hartman’s third type). And 7’< 7, that is so say 7% is a maximum, when K < 0; in this case the border curve and the connodal line are ellipses (mixtures of the second type). = 2e. m,, > and m’*,, + RT. m,, < 0. 1) Arch. Néerl., (1), 30, 266, 1896. *) Comp. preceding communication, p. 267; to the first approximation ==. 8) Not with OY', for, as in this case pri—pz and cry are infinitely small with respect to prpi—px and Xr: (§ 10,2), according to (29) prpi—pr = Mp, XZ, so that for x > 0, pr: > pe. 9, = < k,,, but T—T;, >0, and hence in the angle SOY’. 3b. my, < 0 and m*,, + RT; m,,=0. The plaitpoint curve touches OY’ *). Compare moreover 25. 3c. m,, << Oand m?,, + RT; m,, <0. = so k,,, but T—T;, > 9, hence in the angle S’O }”. d v ci From this it appears that oe can take all possible values. Accor- ¢ ding to vAN pbER Waats’*), however, this is not true and the case gre mee for instance could never occur. But it should be borne aL - bye in mind that this rule of van per Waats does not rest on an ex- clusively thermodynamic reasoning, but also on special suppositions about the form of the equation of state, which naturally corresponds to special relations between the co-efficients introduced here, and as a matter of course it is always possible that the numerical values of the coefficients are such, that one or more of the cases considered are excluded. ce. The critical point of contact curve. To the first approximation PTr=Ppr7,), so that the critical point of contact curve to a first approximation co-incides with the plaitpoint curve and the conside- rations in 6 hold also for this line. Equation (43) shows moreover that to a second approximation : 1 lie a Po 4 RTjm,,(m?,, + RT pm, ,) eee from which it follows that the critical point of contact curve lies above the plaitpomt curve when m,, and m?,, + R7;m,, have the same signs; this occurs in the cases 2a and 3c just mentioned, hence in the angles SOY and S'O¥". In the other cases the point of contact curve is the lower. Moreover the two curves also co-incide to a second approximation if m,, =O and even if m’?,, + R7.m,, = 0. dp nies dp T; eae he to the second approximation. PTr— PTpl = — == S5 » ) although in that case PI:e—PTypl 18 not zero d. The border curves. This position of the critical point of con- 1) Pr < pe for x >0; comp. preceding note. 2) Arch. Néerl., (2), 2, 79, 1898. - ( 348 ) tact curve with respect to the plaitpoint curve corresponds to the position of the critical point of contact with respect to the plaitpoint on the border curves, represented in an exaggerated way in fig. 16. To the second approximation those border curves are parabolae which touch the plaitpoint curve and have a vertical tangent at the critical point of contact, but to the first approximation they co-incide with the axis which is conjugate to the vertical chords and the equation of which according to (47), is: P= pek + ky (T—T xk) = papt + &yy (T—T spl). Hence these straight lines are parallel with the vapour pressure curve of the pure substance and terminate, on the plaitpoint curve, in the plaitpoint of the mixture to which they belong. 14. Continuation of § 9: the critical pomt of contact. Mr. Kersom kindly informs me that the method given by him in Comm. N°. 75 and which leads very easily to the constants of the plaitpoint presents difficulties when applied to determine the constants of the critical point of contact. He however succeeded, by means of the method used by me in § 9, in deriving the constants of the critical point of contact from the formulae '), given by Korrrewre in his paper “Ueber Faltenpunkte”, Wien. Sitz. Ber. Bd. 98, p. 1154, 1889, and proceeded thus. It has been shown in Comm. N°, 59°, p. 367) that instead of deducing the coexistence-conditions by rolling the tangent-plane over the y-surface, we can also obtain them by rolling the tangent-plane over a w-surface, the latter being deduced from the y-surface by making the distance, measured in the direction of the y-axis, between this surface and a fixed tangent-plane the third coordinate perpendicular to and vr. We can go a step further in this direction by deducing a y'-surface by means of Korrewre’s projective transformation *) Nee a , (ow dae Ge ee (=), a! =2' —me' vp! =y' Here y= pp — Hr, 2 =2 — zh ov =v — vp : ') The simplest way of proving that the case c, = «in Kortewec’s formula (4) does not influence the present deduction, is by notins that the area over which the development is applied is infinitely small in comparison with xT,.. 2) Proceedings Sept. 1900, p. 296. 3) See Kortewee |. c. equation 38. ( 349 ) “Oy” dy” as al =) 4 dy” a ae), =e), ? , (ow , (ow hi cawr , ow" 5 ca lag sm) ee aa Weg? Coe 3 (ee i when ‘oy -(* ; (aa) = 1 da! , A ie it is also possible to obtain the coexisting phases by rolling a tangent- plane over this w'-surface. y” as function of wv’ and v" presents the form py’ ea? 4 d,x"v'? + ev" (Kortewne’s equation 4). Hence for the connodal curve Korrewse’s deduction may be applied, and we find for the equation of that curve ee (equation 8 1. ¢.). d, m is now found from OhatD O7w — — 0 (equation 34), c i Je Gs), el where the differential quotients are taken for the plaitpoint, so that for a substance with a small proportion of one component, to the first approximation 1 Op = ———— | a Plc MRT), \ 0a )y7 —? Further we may put, leaving out terms of higher order, according to equation (39) fee WON Pana oe ie sunt; (el para : oe ome?’ i ie ike Using the property that for the point of contact > =—w Oe) this Ose i 4. MRT (ss) 4 k are UT pl (RT)? (3 =) Ox JyT Oxdr r\ dv yields : U,—UT;|—o - and 9 ~ (MRT;). 3 On ) oy op’ wy ( Otp oe tee 0p ( ) wae ( 5 han Ov" dey, dae7,t ; AL gy > -AT zpt ar. aT da de dp, — Ipryl de =F da point of contact curve and the plaitpoint curve touch at the ends. We find further that with the same wv: 63) § r T ) 2 . 2 ek ae Ee + MRT. ies at, } 2 rf ‘0*p 0p Ow oT Owdv T (MRT;)'. = aes dv* )\ dvd T from which p,,—p,,, can be easily found. 1 Paypl J If, as in Communication N°. 75 (Proceedings Nov. 1901), we So that for «=O: , from which we easily derive that also so that in the p7-diagram the introduce the law of corresponding states, we find: 2 Ox mae arise) aa\ IS 9 (PER By UL y1— “eeu =| = (so ) x Pe hea? ‘aaeo =o. yon tel ‘\dw?)/ > *\ dwdr Physiology. WOn the structure of the light-percepting cells in the spinal cord, on the neurofibrilae in the ganglioncells and on the innervation of the striped muscles in amphiorus lanceolatus.” bv Dr. J. Borkr. (Communicated by Prof. T. Pracr). In connection with a former note’) I mean to describe here some points of the histology of the central and peripheral nervous system of amphioxus lanceolatus, especially to follow the neurofibrillae in their arrangement and distribution in the cells and in the musele-plates. This paper is the outcome of observations begun in 1900 in the Stazione Zoologica at Naples. but then not carried any farther, to study the structure of the pigmented cells ef the spinal cord. During 1) Proceedings of the Royal Academy of Amsterdam. Meeting of April 19, 1902. . 351) a stay at the Zoological Laboratory of Prof. Sr. Apxruy in Kolozsvar once again | took up the theme, with some excellently fixed material I got through Prof. Aparuy’s kindness. Finally the researches were curried on in the Histological Laboratory of Amsterdam. A. The structure of the light-pereepting cells (eye-cells). In 1898 Hussn') showed, that the peculiar pigmented cells, which are found in the spinal cord grouped round the ventral wall of the central canal, and. which after beginning at the third segment, are arranged segmentally through the whole medulla, are each of them composed of two cells, one of them a big ganglioneell without pigment, the other a cupshaped cell, filled up entirely with dark brown pig- mentgrains; the last cell covering the greater part of the firstnamed cell and hiding it from view. The big unpigmented cells Hesse called eye-cells, light-percepting cells, the cupshaped pigmented ¢ells he called the pigmentecup (Pig- mentbecher), and the whole complex he compared with the cupshaped eyes of the Planarians, that are equally composed of two cells, and attributed to it the function of light-perception. The arrangement of these two-celled eyes in the spinal cord is strictly segmental. They begin in the fourth segment, with two eyes ; from there each segment is furnished with about 25 eyes. In the region of the tail the number lessens, until a segment has only one eye or none at all. The eyes lying ventrally of the central canal are always looking down, their line of vision, if we may call it so, being directed to the ventral side of the animal, those at the left side of the central canal look upward and to the right, those at the right side look down and to the right. The pigmenteup consists of one cell, the nucleus, when distinguishable, Iving at the concave side of the cup. The eye-cell is coneshaped, the base being covered by the pigment- cup, the top being drawn out into a thin process. At the basal side (turned towards the pigmentcup) the protoplasm. is differentiated into a layer of fine small rods, placed at right angles to the cell- periphery, and continuing in the protoplasm as a network of very thin fibres. Another layer of minute rods may be seen close against the pigmentcup. Between those two layers a clear space is formed, Which is not caused by a shrinking of ihe cell. W. Kravcse') did not agree with the results of Hesse. He still mnaintained that the pigmented cells in the spinal cord consisted ') Zeitschr. f. Wiss. Zoologie. Bd. 63. 1898. p. 456. 1) Anat. Anzeiger. Bd. 14. Pag. 470. Zodl. Anzeiger. Bd. 21. p. 481.- ( 352 ) each of them of only one cell with the pigmentgrains Lying only at the periphery, just as Heimans and v. bp. Stricut') had said in 1898; by Brrr’) and Scaneiper*) the description given by [esse was taken for right and contirmed. As to the arrangement of the pigmenteells in the spinal cord in the first place, the observations of Hesse are not complete. They do not simply lessen in number going from before backwards. In young pelagic larvae there are to be seen very distinctly two groups of pigmentcells, one in the cranial part of the body, the other in the candal half. Between those groups there are much less pigment- cells in each segment. In later stages however these two groups become fused, and then the arrangement is in the main as it is described by Hesse. As regards the position occupied by the pigmentcap on the eye- cell, I’can in the main confirm ‘the observations of Hesse. The eyes at the ventral side of the central canal are always looking down, those at the left are mostly looking upwards and to the right, those at the right mostly downwards and to the right. The histological structure of the eyes seems to me to be slightly different from the one described by Hesse and Scunerper. The nucleus of the pigment-cell is never lying at the concave, but mostly at the convex side of the cupshaped cell; sometimes the nucleus is found in the middle of the pigment-cell, where often a clear pigmentfree zone of protoplasm may be distinguished. According to Hessk the pigment-cup consists always of only one cell. Now sometimes in young animals, where the pigment is of a light-brown colour and the nucleus may therefore be seen very clearly, I found two nuclei in the pigment-cap, and so it seems to me that there are sometimes two pigment-cells with one eye-cell. So the form of the pigment-cap in fig. 3 seems also to point to the pigment-cap being composed of two cells. As a rule, however, there is only one pigment-cell in each eye. In the eye-cell, lying under the pigment-cell, Hesse describes a double row of small rods, lying close to the pigment-cell. This double row of small rods exists, but the two parts of it are not separate, but continuous at both ends, in whatever direction the cell is cut through. So a flat oval body is formed, with a striated wall, lying close to the pigment-cap (fig. 1.@), and following in its shape the form of the cap. This body seems to me to be homologous with ') Mém. couronn. de l’Acad. roy. de Belgique T. LVI 1898. 2) Wiener med. Wochenschrift 1900. 8) Lehrb. der yergl. Histologie der Tiere 1902. ( 353 ) the 4Glaskérper’ with a striated wall, as it is found in the eye- cells of the Hirudines. As is the case with those eye-cells, here in Amphioxus too the vitreous body seems to be filled with a granular- looking substance (coagulation ¥) but this was not always clearly to be seen. Between this body (@), that lies close to the pigmented cap, and the nucleus (fig. 14) lying at the other side of the eye-cell, there is in most cases to be seen another beanshaped body, that does not possess a striated wall, but by a clearer tinction with protoplasmic dyes and a more homogeneous substance may be distinguished from the darker and more granular-looking protoplasm of the cell (fig. LO). This body seems to be connected with the perception of light by the eye-cell in the same way as the vitreous body described above. The arrangement of the neurofibrillae in the eye-cells seems to point to this conclusion. Enterme the cell at the ventral side of the nucleus, there, where according to Hrssk the eye-cell is drawn out to a point, the neurofibril forms a loosely biuilt network round the nucleus. From this network large neurofibrils ascend through the cell and take the beanshaped body (4) between them (fig. 2, fig. 3). Between this body and the pigment-cap these neurofibrils anastomose again and form a second net, which seems to enclose the vitreous body (a) with the siriated wall. How the further course of these fibrils is between the vitreous body (7) and the pigment-cap I could not deter- mine with any accuracy. To obtain good results with the chlorid of gold-method of ApatHy the sections may not be very much thinner than 10 u. Now for the study of the eye-cells it is necessary to make sections of about 6 to 7 uw, because in thicker sections the black pigment of the capshaped cell embraces the greater part of the eyve-cell and shuts it out from view. It is therefore not possible to get those deep black neurofibrillae, which may be seen so distinctly in the prepara- tions of ApaTHy (the more so as the neurofibrillae of Amphioxus are thinner than those of Hirudines); and even in sections of 6 to 7 w that part of the neurofibrillae-network, which is lying beneath the pigment-cap is entirely concealed by the pigment-grains. Probably the. network is continuous and anastomoses at the other side with the more ventrally lying network. In what manner the neurofibrillae leave the eve-cell I could see only in a few cases. The fibril seemed then to proceed horizontally for some time but could not be followed any farther. 4%. The neurofibrillae in the ganglion-cells. On the neurofibrillae in the ganglioncells I ‘Il say only a few words, ( 354 ) Ii would lead us too far to go into details about the arrangement of the neurofibrillae in all the different types of ganglioncells, and besides, that would not be possible without many plates and drawings. I will therefore confine myself here to the following statements : According to Berner‘) in most of the ganglioncells of the vertebrates the neurofibrillae pass through the cellbody without branching or breaking up into a network. Only in the spinal-ganglioncells and in the cells of the lobus eleetricus of Torpedo marmorata Berne observed networks of the neurofibrillae, and according to this author networks possibly occur in the basal part of the cells of Porkisse in the cerebellum and in the cells of the cornu Ammonis. According to Bocurxrk*) it is on the other hand probable, that in the vertebrate ganglioncells the neurofibrillae form a very fine network with small meshes. The very dense reticulum of neurofibrillae, he was able to demonstrate in the ganglioncells of Hetix, forms according to BocHENEK an intermediate stage between the coarse net- work in the cells of Hirudines and Lumbricus, and the very fine network in the vertebrate ganglioncells. In accordance with the statements by these two authors, we should expect to find in the ganglioncells of Amphioxus either a dense reticulum or a mass of disconnected interwoven very fine threads, passing from one process through the cell-body into another process without branching. This is not the case. In most of the ganglioncells the arrangement and distribution of the neurofibrillae in the ganglioncells resembles very much that which is described by Aparny in the ganglioncells of Hirudines and Lumbricus. Sometimes we find cells as the one shown in fig. 4, where the neurofibrillae pass through the cell-body without interruption, but. this is only to be found in a few cases. In the bigger ganglioncells, which are lying in the dorsal part of the spinal cord and in the dorsal group of ganglioncells behind the brain-ventricle, there is always a network of neurofibrillae branching and anastomosing with each other. After having entered the cell in most cases the neurofibrillae form a network round the nucleus (partially distinguishable in fig. 5). From out this reticulum radial fibrillae go through the cell body to the periphery (often branching on their way) where they form a second network. With this network are connected fibrillae, which pass through one of the processes of the cell (out of the cell or into it?) — in short, a distribution of 1) Arch. f. Mikrosk. Anatomie, Bd. 55. 1900. P. 513. *) Le Névraxe. Vol. Ill. Fasc. I, 1901. P. 85. (Sh) 9) the neurofibrillae very much like that described by Apatuy in the smaller ganglioncells of Lambricus. The fibrillae however in Amphioxus are thinner, and the reticulum finer. In other ganglioncells there are not two networks (one round the nucleus and one more at the periphery), connected with each other by means of the radial fibrillae, but the neurofibrillae enter the cell, form a network round the nucleus and leave the cell at the other side, without there being any trace of a more peripheral network to be seen. A connection between different ganglioncells by means of the neurofibrillae, I could not yet state with a sufficient amount of certainty. In the colossal ganglioncells the “Kolossalzellen”, lying just in the middle of the spinal cord, the arrangement of the neurofibrillae is very peculiar. From out the colossal nerve-fibres, the axons of these cells, a thick bundle of very thin neurofibrillae, arranged very regularly and equally in the whole axis cylinder, enter the ganglioncell; in the cell-body they pursue their way as a thick bundle that passes round the nucleus, turns upon itself, forms a sort of vortex and then seems to condense itself into a few thick (composed of a great number of elementary fibrillae) fibrillae. Where these fibrils go to, I could not state accurately. In the axons the extremely thin neuro- fibrillae are closely set and parallel to each other, and so a striking resemblance is formed with the “sensorische Schlauche” of Hirudines and Astacus. During the course of these nerve-fibres through the spinal cord the neurofibrillae are seen fo pass one by one every now and then in an oblique direction through the wall of these nerve- fibres; then they are lost in the nervous network without, and could not be followed any farther. Perhaps they are connected there with other ganglioncells, which should be in concordance with the character of the colossal ganglioneells as connecting cells (“Schaltzellen’’). (. The innervation of the striped muscular tissue. According to Ronpr’*) the motor nerves simply enter the muscle- plates there where these end, and there is no trace of a motor nerve endplate; according to HEYMANs and vAN DER Stricut*) however the motor nerves of Amphioxus terminate each in a shovelshaped end- plate, that lies itself against the muscle-plate just as the motor nerve endplates of the higher vertebrates do. According to their descrip- tions and drawings the endplates of Amphioxus are thick shovel- shaped plates without branchings, without further differentiations (Golgi method). 1) Scunewer’s Zoologische Beitrige. Bd. II, 1888. *) Mém, couronn. par l’Acad. roy. de Belgique 1898, Now Apstay and Rerrint') were able to demonstrate in homo the existance of “ultraterminal’ nerve-fibres, that is to say nerve-fibres which grow out from the branching and thickening of the motor nerve known as “endplate”, and enter the musele-fibre (this could not be made out with absolute certainty) pass through it and in many cases are connected with other endplates. Only a few cases are described but they are sufficient to show that the so-called nerve end-plate is not always to be considered as the real termination of the motor nerves. The following observations seem to point to the same conclusion. The thin muscle-plates of Amphioxus (fig. 6a) present in longi- tudinal sections a beautiful cross striation. Each isotropous dise (7) is divided into two dises by a delicate, but distinct membrane of Krause; each anisotropous dise (g) is composed of two dises, separated by a thin layer, that takes but a faint stain with chloride of gold, the median disc of Hensen. In the middle of this transparent portion there is sometimes to be seen an extremely deiicate line, the membrane of HENSEN. The membranes of Krause form, as is known, crossnets, which bring the fibrillae of the entire muscle-plate in connection with each other. In the adult animal real muscle-cells ave not to be distinguished, there are only the thin flattened muscle-plates to be found, which however in hardened specimens sometime appear to be broken up into rows of flat bundles of fibrillae. This is nothing but an artefact. In longitudinal sections of Amphioxus in which therefore the musele- plates are cut in the same direction, but mostly appear not as plates but cut obliquely as bundles of muscle-fibres (fig. 67), there are to be found, in case the sections are coloured after the chloride of gold method, in many places just there were the anisotropous and isotropous discs meet, minute black dots, or small corpuscles; seen under a microscope of the highest magnifying power these dots appear as very delicate cross lines, thickened in the middle, running just between q and 7. In these discs belonging to the same muscle-plate these dots are lying in adjoining discs one just beneath the other, so that rows of black dots running parallel to the myofibrillae are formed. In each muscle-plate such longitudinal rows seem to be distributed with some regularity. These black dots were always found only at one side of the anisotropous disc, and, so it seems, always at the same side of gy, viz. at that turned caudal. The black dots lying in the same muscle-plate in the same longitudinal row, are often 1) Rivista di Patologia nervosa e mentale. Vol. V fase. 10. 1900. ( 357 ) found to be connected with each other by means of very delicate fibrillae, which are running parallel to the myofibrillae. This could be stated in many cases with great clearness. In some cases these fibrillae were straight, in other cases more or less undulating. In fig. 6a a longitudinal section through the muscular plates (cut obliquely) is drawn greatly enlarged. The small dots and fibrillae are easily to be seen. In transverse sections the same rows of fibrillae and black dots were also to be seen, and here they are seen to be distributed more or less regularly on the muscle-plates (fig. 64). At both ends of the black dot here too a delicate black line may be seen, extending for some way along the muscle-plates but then being lost to view. By playing up and down by means of the micrometer screw of the microscope in cross sections too a longitudinal fibril may be made out extending upwards and downwards from the black corpuscle; this fibril is identical with that, which in longitudinal sections was seen to run parallel to the myofibrillae and to connect the black dots of a longitudinal row with each other. So we find here in the muscle-plates of Amphioxus an apparatus, which brings the anisotropous dises of the same muscle-plate in con- nection with each other, which seems to be distributed with some regularity over the whole muscle-plate, and which gives the staining reaction of the neurofibrillae. Although I could not find the connection of these fibrillae with the motor nerves, still these facts seem to point to the conelusion, that we may regard these fibrillae and their knobshaped thickenings at one side of the anisotropous discs as representing the real innervation-apparatus of the striped muscle-fibres. Sometimes I saw one of the longitudinal fibrillae near the place of attachment of the myofibrillae to the myosepts bend off from the muscle-plate; but it was lost almost immediately between the myofibrillae in the neighbourhood and could not be traced any farther. When we consider however the constant position of the small knob- shaped thickenings at one side of the anisotropous dise, the fine often undulated connecting fibrillae, the dark-purple tinction with chloride of gold (Nachvergoldung Ap\riy) so characteristic for neurofibrillae, then, I think, it is difficult to avoid the conelusion that they are neurofibrillae. This seems to me to be important from a general point of view. Although the structure of the striped muscular tissue of Amphioxus differs largely from that of the higher Vertebrates, yet the same type of cross. striation, that is, the same strueture of the myofibrillae, is present in all. ( 358 ) ‘ Where now Hrymans and vas per Strricur found a motor nerve endplate identical with those of the higher Vertebrates and at the side of this structure can be seen an innervation of each anisotropous dise, as I have attempted to show, there is room for the conclusion that in other vertebrates too the so-called motor nerve endplate is not the ending of the motor nerve, but that from here neuvrofibrillae enter the muscele-fibre, and that every anisotropous disc is innervated, The truth of this surmise, however, must be tested by further study. Amsterdam, October 1902. (November 20, 1902), KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday November 29, 1902. — <> (Co—_— (Translated from; Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 29 November 1902, Dl. XI). ClOENB EEN, ses SS: J. J. Buanksma: “The intramolecular rearrangement of atoms in halogen acetanilides and its velocity’. II. (Communicated by Prof. C. A. Losry bE Bruyy), p. 359. S. L. van Oss: “Five rotations in S; in equilibrium”. (Communicated by Prof. P. H. Scuourr), p- 362. J. Wreper: “On interpolation based on a supposed condition of minimum,” (Communicated by Prof. H. G. van pr Sanpe BAkuuyZzEN), p. 364. The following papers were read : Chemistry. — , The intramolecular rearrangement of atoms in halogen acetanilides and its velocity,’ Il. By Dr. J. J. BuANksma. (Communicated by Prof. C. A. Losry pr Bruyn). Communicated in the meeting of October 25, 1902). t2) In a former communication’) it was shown that the conversion of acetylehloranilide in acetic acid solution under the influence of hydrochloric acid proceeds like a monomolecular reaction. In continuing this research the object was to study the influence of: Ist. The dilution of the acetic acid with water. 2d. The quantity of added hydrochloric acid. 3°. The solvent (besides acetic acid, alcohols ete.). 4th Different catalysers (H Cl, H Br, H, SO,). oth. Different groups in the nucleus and their relative positions. 6. The temperature. First of all the influence of the dilution of the acetic acid was studied, varying proportions of hydrochlorie acid being also added. afterwards a few experiments were made in alcoholic solution. 1) Proc. Royal Acad. Amsterdam. June 29, 1902. 24 Proceedings Royal Acad. Amsterdam, Vol. V. S60.) The modus operandi was as follows: A delinite quantity (38 to 4 grams) of acetylchloranilide was dis- solved in respectively 100, 150, 200 and 250 ¢.c. of 100°/, acetic acid; to this were added 10, 15, 20 or 25 ¢.c. of 28,67 °/, hydro- chlorie acid and the mixture was finally diluted with water to 500 c.c. The experiments were then conducted as described in the A previous communication; by applying the formula 4 = ; l the Ai—@ k’s were calculated; ¢ is expressed in minutes. The following results have been obtained : in 500 of solution, 10 15 20 25 c.c. hydrochloric acid. | — é eee 0.00973 | 0.0189 0.0241 { | 100 0,00506 150 | 0.00846 | 0.0186 0.0318 0.0460 200 | 0.0157 0.0335. | 0.0588 | acetic acid, »C. c 250 0.0359 0.0719 300 O.0836, in 500 of solution. 10 15 20 c.c. hydrochloric acid. ry a kee S| 200 | 0.00883 | 0.0201 0.0341 | "- | | 2 - ——————_| = ees, | 3 | 250 0.0158 0.0358 | 0.0591 | 35 | | By means of these figures curves may be constructed either by taking the figures from a horizontal row or those from a column. The first row for instance shows how the velocity of reaction (con- stant) increases in 20°), acetic acid in the presence of a varying unount of hydrochloric acid (10, 15, 20, 25 c¢.c.) ete. In this manner the different series may be represented by the lines A, B, C and D. The first column shows how the velocity of reaction changes with different concentrations of the acetic acid if the amount of the catalyser is constant. These columns are represented by the lines EL, Fy Gand H. The alcoholic solution has been represented in the same manner (A’, B’; C”, D’, E’). These curves show: ist. That the velocity of reaction, both in acetic and alcoholic solution, is decreased by addition of water. ( 361 ) 2ed_ That the velocity of reaction is much accelerated by increasing the catalyser. 3rd. That the curves all end in the origin of the co-ordinates which means that the velocity of change in water without hydro- Always chloric acid is zero so that the substance is stable therein. on condition that light is excluded, (compare first communication) |. On comparing the two tables it will be also noticed that the velocity of reaction is greater in acetic acid than in alcohol; for instance, in a mixture of 200c.c. of acetic acid and 15¢.c. of hydro- chlorie acid, k =0.0835; when usine 200 ¢.c. of aleohol and 15 e.e. hydrochloric acid k = 0.0201 *). If we compare the curves /, /. G and H we notice that on decreasing the concentration of the catalyser, the curves begin to approach the abscissa axis which again shows that, in the absence of hydrochloric acid, the velocity of change in acetie acid or alcohol is zero or in any case very small, which may also be seen from the curves A, B, C and D. A A00c.c. acet.acid with water to 500c.c. GAO ¢.c. HC! in 500 c.c. solution. B 150 » » > » St, Sy ps acy) ) ye ay ) C 200 » » » » Se DIED G20 » » De ey . D 250 » » » » » » Dd H2% » y ) ) ) ‘ cchCl bs 10 1S 20 25 cece aceatic acid 1) If we calculate number of mols. of alcohol or acetic acid to a given number of mols. of water we see that this difference in velocity of reaction is still greater. 24* 362 ) A 200 ¢.c, alcohol +- water to 500 ¢.c, © 10 ec, HCL in 500 ¢.c, solution, B 250 » » + » HOO » DAD » » " PW » v » » Dp v 10 15 ZecHCl alcohol. Mathematics. — “Five rotations in S, in equilibrium.” By Dr. S. 1. vAN Oss, Zaltbommel. (Communicated by Prof. P. H. Scnovurr). In a previous paper (these Proceedings, Vol. 1V, p. 218) the investi- gation of the elementary motion in S, was reduced to the consideration of the elementary motion in S, by making use of a principle to be read as follows: A system of rotations about planes a// passing through one and the same point is in equilibrium when their inter- sections with an arbitrary S, are in equilibrium. Here we mean by section of a rotation with any S, the rotation of the intersecting space caused by its component about the plane orthogonally cutting this S, in the intersection of the plane of rotation. As an immediate result of this principle we can state the conditions under which three to seven planes through ove point can be the planes of a system of rotations in equilibrium. Thus i.a. the con- dition for four planes, that they must belong to a hyperboloidic pencil, etc. ete. We now wish to extend this principle in order to arrive by investigation also at the case, that the planes do not pass any longer through one and the same point. It goes without saying, that if a system of rotations is in equilibrium, its section with every S, must be in equilibrium. The question (363) ) here, however, is to find out how many of those intersections will have to be examined before we can conclude about the system being in equilibrium or not. To this end we direct our attention in the first place to the case, that a system @ has two sections in equilibrium, namely with the spaces A and Jb. If the section @/A is in equilibrium, then £ must necessarily be reducible to a single rotation about a plane in A; likewise, if 2/5 is in equilibrium, then 2 can be reduced to a single rotation about a plane in the space LB. So from the equilibrium of the sections it does not yet follow that the system itself is in equilibrium, for the possibility remains that it may be reducible to a rotation about the plane common to the two spaces of intersection. If, however, we can point out three spaces S, not passing through the same point, their sections being in equilibrium, then the equilibrium of the system itself is guaranteed. Let us now apply this result to determine five planes which can be the bearers of a system of rotations in equilibrium. The neccessary condition which these planes must satisfy is that they be intersected by three spaces S,, not passing through one and the same point, in rays of a linear congruence. In other words: They must intersect three pairs of straight lines, the director lines of these congruences. Now we know that in S, there are just 5 planes intersecting 6 given lines. They are the five ‘associated planes” of Srare (Rend. di circ. math. di Palermo, t. U, 1888). Now we have the necessary condition; we shall show, that it is also sufficient. Let 2 be a system of rotations about 5 associated planes, A an S, so that 2/A is in equilibrium. If 2 were not in equilibrium itself, this system would have to be equivalent to a rotation w about a plane @ in A. If we reverse the direction of the rotation about this plane, then the combination (£2—w) is in equilibrium. If we now consider a second intersecting space 6, not through a, then the planes of 2 are intersected in 5 rays of a congruence and the plane of @ in a line not belonging to this congruence. The section of 5 with the combined system £2—w would, however, have to be in equili- brium. This is impossible, unless w is equal to naught, i.e. unless 2 is in equilibrium. Nothing remains but to determine the ratios of the intensities of the rotations of 2. This should be done as follows: ( 364 ) We consider an arbitrary S, which intersects the planes of 2 in the axes of rotation of the section; the determination of the ratios of the intensities belonging to them is a well known problem. If, finally, we notice that between the intensities @ and w’ of a rotation in S, and its intersection with a space A the relation w' =o sin (Aw) exists, then in this way the intensities of the rotations about the five associated planes have become known quantities. Mathematics. — “(On mterpolation hased on a supposed condition of minimum.” By J. Weeper. (Communicated by Prof. H. G. VAN DE SANDE BAKHUYZEN.) For the reduction of the daily rates of the standard clock in the Leyden Observatory I have developed a method of interpolation, which may perhaps also be profitably used for other investigations. The following is the problem we have to deal with: a variable quantity, here the correction of the clock, is given for a series of instants, during a long period, with unequal intervals; how can we find an intermediate value of that correction at any moment. First I tried to solve this problem with the limiting condition that for all the intervals of time which enter into the caleulation there is a smallest common divisor, which we take as unit of time. 1. Let S (clock correction) be the variable quantity, and g (rate) the amount by which it increases during a unit of time. Let S, and | > be two successively determined values of S separated by mm units See ee of time, then-’——* is the average inerease per unit; that increase m is represented by Qn,. Hence the m quantities Ji Ja: ++ Jia > Ju OF ae =m ; interval considered depend on the relation + g;= S, — Sp =m Os 1 and a similar relation exists for each interval between two con- secutive determinations of S. In order to determine the quantities g, I put the condition that the sum of the squares of the differences of the first order for the whole period of observation should be a minimum. This condition of minimum was selected with a view to the special case where we have to interpolate between the clock corrections, but I doubt whether in all cases these interpolated values will be the most probable ones. Leaving aside for the moment these considerations, | go on developing the problem in hand. The quantities which cor- respond to an interval of m units occur only in the following terms of the sum which according to this condition must be a minimum: (9:9) + (9.—9)" 0195 M0 =F (9m — 9m 1)? + (9g—9m)? » gp vepresents the rate preceding S, and gy, the rate following ‘Sy. If to this quantity we add: 2hm (9, + Ia +++ + Ji +++: + 9m—1 - Jn) their sum J will also be a minimum for the same values 7, 10 dyn, im because S g,= S; — Sp = mQn is constant. — 1 These values 9, ---fm are found by means of the condition that each derivative of (7 taken with reference to each variable shall be zero. At the same time we must assign a definite value to /,, in 0 . order to satisfy the equation © gj= mQn. I—I Thus we obtain the following equations: — ih +294, —g9, thn=0 SR SRC i Ge — gi-1 -= 2 Hie ato S| =e Hi Ost rn fat Gas, 3p (A) — Jn—2 4. 2 Gn—\ =. 9m + 0 mI +. 2 In ame + nO) Bij taking the sum of these m equations, each multiplied by ¢ (m—), we eliminate 9, ,4i, gm. the coefficient of each g; of that sum being i=m equal to 2; hence the sum of the terms is 2 Y g;= 2 mQn. ==l\ The coefficient of 4, is: FF; mn eaee m (m-+-1) (m+2) —I erate: Hence the sum of the multiplied equations is: 1) ( 2 — m gp a8 Ona On. — mga 4 is m (m+ — ) = 6 6 (Ip a= Ui = 2 Qn) whence [ie (m + 1) (m + 2) Then we determine the values of g; by multiplying the m equa- tions by the terms of the following series: 1(m—i+1), 2¢m—i+1),...i—1)(m—i+1), t(n—i+1), im—d)..., 12, 21 366) and taking their sum; in the resulting equation all unknown quan- tities J, ... dm except gi are eliminated. That equation got by sum- mation is: ] — Og (Qnm—i t 1) + (m-+-1)o; - iy -f- ; i (m—i-4-1)(m +1) ky»= 0 which yields: m—t+1 1 i i (m—i-4-1) OC) | i Q,.— i, F m+] tg +1" : 2 - m 1 ] hence i w+ Iq — 5 ™ An m-+-1 m+1 2 1 ue m 1 j an Im = ——— Jp + —— 9g — = Mi - aye Wee eo Gea a The quantities g, and g, are still unknown and depend on the quantities @ of the neighbouring intervals; they may be derived from them by means of successive pers It gives some advantage to determine eto) ) and — = (gn) by approximations, because then we shall have to approxi only one quantity for each |S. The approximation may be made : 1 il in the following way: we _ put 9 Yota=% and 9 Yat Ig=Ce then we obtain: kn = a (¢ op se ar 2 Qn) 3m 2m?+1 m—l1 ——— — Q, +-{ 1 + ——— Je —--- I m? +2 Qn = ( oe Sea Bek. m(m? + 2) bs 3m m?—1 2m?+1 99 = aig Oe a ae ara nea (a+ ‘ as) For the next interval of 7 units of time between the determinations So and SS, we have the following equation: Paz Qn? ; n?—1 In = a5 Qn + (: a8 = n(n*--2) < AS gy +4m=2c¢, we obtain when finding the summation of the two last equations a recurrent equation containing 3 consecutive quantities c, so that c, can be expressed in c, and c,. This equation ‘an also be written thus: \: 2m?+1 antl | m? —1 4 3m Get 2 A Sa De Ce | m(m? +2) n(n?+2)) 7 m(m?-+-2) * m? +2 3 7__] Sige yay ee 8 n?-+-2 n(n? +2) For the first interval considered here the first of the equations (A) is g,—9,+hn=0. This equation may also be written in the general form by putting — g, + 29,—g, +m =9, thus assuming that the value of y preceding g, and ¢ belonging to the first observation are both equal to g,. In the same way c belonging to the last observation is equal to the last g of the last interval. Between each three consecutive quantities c, therefore, a relation exists of the form (,) and two other equations are added to the beginning and to the end of this series, each containing only two values ¢ derived from the formulae for g, and g,. Let cq and cy be the first two and ec, and c: the last two quantities c, then we obtain by substituting ¢c, for Jp =p and cy for c, the first condition, and by substituting c. for Jy =, and c, for c, the last condition of the series which determine the values c¢. If the lengths of the limiting intervals are represented by mw and vy these equations are: (Qu?+1)e, = + 3u°Q, — (’—1) cs (2p? 1) ¢, = + 3n*Q, — (v?—1) ¢, The series (6) and these two equations determine all the quantities c. If we solve them by approximation our purpose is soon gained ; 2 , ; n Qn +mQn we assume to the first approximation cg = ——-—— and ¢q and ec. m+n equal to the values of @ of the first and the last interval respectively. From the equations (4) we derive the first corrections 4, ¢, A, ¢y, ete. and A, cy is derived from the formula: 2m?+1 Bean oc hset m—1 Ath bree nN m(m?+-2) — n(n? a | nese) a“ n(n?+2) + In this interpolation we determine g; and |S; of an interval of m units according to the formulae: 1 Ss =) 2+ a Tere IL Cre om 1 Cy —Cq ce i= Gs m kin 4- Sp + Om ie e 2. In the previous section the observed and the interpolated quantities S, occurring in the problem discussed, form a series of ( 368 ) discrete values corresponding to an arithmetical series of the argu- ment; now I will remove the restriction of commensurable arguments and will make this mode of interpolation applicable to a continuous varying quantity and an arbitrary argument by putting for the ratio of that series the infinitely small value df, The condition as\? of minimum then becomes | ( 3 dt = min. 0 The formulae for this continuous interpolation may be derived independently, but it is shorter to derive them from the corresponding formulae of the discrete interpolation developed above. For the present I shall put for the lengths of the intervals between which we have dS to interpolate m’ and x’, for the derived values 3 of the interpo- lated function y’, to distinguish them from the letters we have used in the former problem. ’ m n' ; Instead of m and 7 we have and —; for ¢p, Cy, Cr we must dt dt substitute the quantities g', dt, g'g dt, g', dt, and for Q, and Q, the ss S38 5 : 3; — Sy quantities ———* dt and ——— dt or Qydt and Qy dt. m vu After dividing the relations (2) by d@# and omitting the infinitely small values we have: DIES Rt Leesa 3 ig 5 9g So eo m n m m vu n from which, after dropping the accents, we get: 2Qm = mQ, n(Qm — Gp) ; m(Qn — 4dr) mtn 2(m+n) ' 2(m+n) to which we must add as first and last equations : Q, —9Jb Q—a Ja = Q. + ng eee oo Sp 2 2 . ©) = 6 For k, we substitute — (9'p>+9', — 2 Qn’) (dt)? ; for 7 we substitute m oie : : ‘ an if ¢ represents the time between the last preceding observation at the moment for which we interpolate. These substitutions in the formula for S, yield a formula for S,, which, after the omission of infinitely small values and accents, is: ( 369 ) S = S, + gt — le Gu + Gq —2 On) + = pit, i Rata om 2m m By substituting in the above formula m—t' for ¢, we obtain for S; a formula developed according to the ascending powers of ¢’, the interval between the moment for which we interpolate and the moment of the next observation. It is simpler to find the same formula by imagining the interpolation to be made in the inverse direction, so that the quantities g and Q change signs and the indices p Phas places. Hence : 2 2Qn 13 ri 3 —99 Ip+9q— Si — St, y— Jat + iP + 9g— 2Qmn) = aa ae = m For WS, to be ene in the following interval we use: 2n 2n n? 5 re Se = Sy + yt — i (y+ gr = 2Qn) + =| Pel a at Therefore the formulae on either side of each observation are different. If in the latter formula ¢ is negative and —f?' is substituted for it, the resulting formula differs from the preceding one only the coefficients of the terms of the 3"¢ degree. The coefficients of the terms of the 2"¢ degree have become equal by satisfying the relation (C). Therefore we also obtain the interpolated function if, by starting from a value (S,) derived from observation, we represent the values of S_, and S4, for the moments between that observation and the next preceding one and those between that observation and the next following one by the formulae: S_, = Sy — gat + gt? — ent® and S42= Sy + gat + cgt? + ent Taking this as basis, we find: +4)-3Qm +294 aes = 299 BQn-gr _ Ip 9a- 9q- —2Qn mag +9r-2Qn S =— en = en = m n m it 2 =(dS\* ate The integral af a) dt, which becomes a minimum through this a nterpolation, is equal to the sum of the integrals between two con- secutive observations, and each of these integrals can be expressed in the coefficients of the interval in the following manner: Pike =) (F ya _ 3g r= 2Qn)* 4 a= 9" ne (ode 2s rn nL 4 or: Lives il (c7g + Cg Gr + c,). 370 For the total integral Y /, we can also derive a simple form by integrating partially : =a? S\3 ; “dS d?S “dS dS ; ( t = —— ‘ t | (ae ) alt dt? | | dt de a “ a a For the first moment @ and the last moment ¢. zg “=0, as follows ‘ from the first and the last equations belonging to (C). For each ES interval between two observations rT is a constant quantity. Hence we find: = = 6 & (S, — S,) where the summation extends over all the intervals between the observations. We can easily find a simple expression for the differential quotient of 7 according to each of the observed values, which may be useful when we want not only to interpolate for an intermediate moment but when at the same time we have to determine the most probable values of the observed quantities. For then the difficulty presents it- self how to find the best method for diminishing the amount of the minimum value / by applying corrections to the observations, of which corrections the mean value is known. In doing so heed must be taken that these corrections, being errors of observation, sliall satisfy the law which determines their probabilities as functions of their magnitudes. I have not yet reached a satisfactory solution of this problem. The following remarks, however, on this subject seemed important enough to be communicated. 3. Let L,, Ly, L, be the observed quantities, free from errors of observation, and f/f), fy, jf; the errors themselves. If we have developed the interpolation by means of the quantities L and / separately, we obtain the formulae: hn=L,+ Gyt4+C,?4 £,t haf eee e By means of the summation of these two formulae we get: Si= Sq + ggt + og? + ent’. “EL yf . de" dt dt, we get: If we apply a partial integration wf a @L df aL dt, dt he dt a a dL df "dL df or Cee cee | A Peay brdt dt. | (hee wali: e a a In either case the integrated parts are equal to O, because at the on CL ae ip beginning and end — and — are zero. a dt™ dt? In this way we find the relation : = Ep, (fo—Tr) — = En (L,—L,). In the same way we find the relation: > en (fo—Sr) = = én (Sy—Sr)- By applying the corrections — §/, the minimum /s becomes the minimum J; = [s—f. Ls — f= = 6 (Gn—en) (Sg—fg— 8; hr) = == be, (Sy—S,) —— OE, (S7—S,) — = 6 e, (tq —fr) + = 6 & (fa—Sr) which expression by means of the latter relation may be reduced to: Is — f=I1s — 12 2 ea (fg—sr) + = 8 & (fq—Fr)- For infinitely small values 7, the last term in the expression ; dls given above becomes of the order 7? so that we find Ot es This result enables us to determine the set of small corrections, which, when applied to the quantities S, diminish Js by the greatest amount. These corrections will be proportional to the abrupt changes The variations in the interpolation coefficients g, c, e, resulting from these corrections are found by repeating the interpolation, with this sole difference that for the observed quantities S we sub- BS stitute the abrupt changes of aa As a rule a set of corrections of this kind will not show the character of the errors of observation and therefore be dissimilar to the set of errors which actually exist in the observed quantities S. We may also determine a limit which should not be passed in the rectification. If the quantities 7 represent the real errors, we have: ig= f+ = 12 #, (fa—Sr) + 266, (Ja—Sr) The coefficients # of the interpolation formula between the correct quantities Sand the errors f being as a rule entirely independent, we must assume that in 12 4, (f,—/;) the positive and negative terms neutralize each other for the greater part. Hence the difference /s T;, does not exceed Y 6, (f,—f,), the value of which depends only on the errors and the lengths of the intervals; the mean value of this expression for every possible distribution of the errors of the observations may be derived from the mean error of those observations. This is the utmost limit to which by means of corrections to the observed quantities S we can diminish /s, lest the interpolation curve found should assume a less sinuous form than would be probable with regard to the results of the observations and their precision. Here follows an example of the computation. The annexed table contains the interpolation coefficients of a part (period 1882 June 8 to August 30), taken from a longer series of observed rates of the clock Hohwii 17. Therefore the coetlicients at the limits of this period are not in accordance with the boundary- conditions supplying the formula (C). We compute the interpolated clock corrections by means of the formula: h B29 t lig Sp = 9q + tl Iq 7h eg — + ne, = n a S, is the clock correction of the last preceding observation and the coefficients gy, mcg, Wen are given in the columns 5, 6 and 7; they are expressed in the unit 0°.001. The values g, and neg to be used are placed a little above the horizontal line corresponding to the length of the interval expressed in days, which interval contains the moment ¢ for which we interpolate. Because of its connection with the constant derivative of the third order of the interpolation curve within each interval, the coefficient n’e, for each interval has been placed on the horizontal line of that interval. The 8 column contains the coefficients ¢ and the 9" their differ- ences 6 by passing from one interval to the other. For each of these differences I have calculated the variation 46, of a given 6,, as the corresponding correction of the clock , increases by + 03100 while the other corrections remain unmodified; they are Og given in the 10% column. By the increase 4S, = — «< 05.100 Oy the difference 6, becomes zero, so that by means of thiis ines we obtain the same result as if in the determination of the interpolation curve we had omitted the observation S,. Hence the correction of the clock S, derived from this interpolation is equal to the observed Duration of the SES s =i g > = |e : oP i 2 Sl = Chee “=O Z = 5) bs 5 ° x 3S I > am es iS = _ ren = == _ = = BS 2 Cis iS) +2 Ss Fa) SE xa 5 eee (ee S| 0S = BS |i = ms : E+ -o male e H > of oS el ee te ee ae |S s Se hors aS) 2 Sie Pees 5 Bios || BS ax > s Ses SO = 2 Il : be = | 3 | ra Se S) b 2, D lo a = Ss! ~ 2) rs) mo) a © I = Os ‘e) xt IS aS 3 og cS) \| sq |o° = = 2 & qd | | s 118 —03 | 445 63 — 7.0 5.4 | —0.13 b | 435 | " —43 |— 2.7] ins 110 02 |-419) |= ‘69 +4.94 4.01 40.42 4 O86 ge +36 ++ 2.2) iy a 106 —10 | C96 |-+ 44 — 3.1\-+ 3.9 | —0.08 4 126 | —14 |— 0.9) 126 16 | 142 | 04 | — 0.3/-+ 3.7 | —0.01 4 | 126 a Coa Eo 49 i | | 102 —12 | 090 |— 68 | + 3.2-+ 3.0 | 40.41 5 | 073 | +51 | 9.0 | c 108 —Ol | 4107 | 52 — 5.34 4.4 | —0.43 3 |: 4199 | sO = 3-3 199 —Ol | 491 |— 94 H- 494 3.3 | 40.45 7 | 104 +77 |-+ 1.6 156 +08. | 164 |4+ 18 —20 64+ 26.0 | —0.08 | 163 | —19 |—-19 | 443 00 | 443 |—450 | j+23.4\1 99.3 | 10.08 4 | O64 | 74 |4- 4 Aes fue sa | O81 —2 | 056 |+ 46 — 5.3/4 6.5 | —0.08 3 | 094 | —08 |— 0.9 410 | +44 | 124 |4 32 — 0.6/+ 5.6 | —0.01 4 132 | —2% |— 1.5 113 03 | 446 |— 50 2.5/4+ 3.0 .08 5 | 090 | a +94 aah rs a ; 089 —O1 | 088 |4- 44 | | — 244+ 4.2 | —0.06 3 | 089 | —13 |— 1.4 | 082 —05 | 077 |— 4 +29/-+ 4.3 | +0.07 5 | 070 +38 |++ 1.5 a 095 +06 | 101 | 43 — 5.3/4 4.6 | —0.12 3 | 440 | —34 |— 3.8 093 —08 | 08 |— 78 | +7.7/+ 6.4) 40.12 4 | 070 +163 |+- 3.9] i leo G 5 | 418 |4 28 | |\—25.9|-+ 57.0 | —0.05 1 124 | | —22 |—292 | 106 +02 | 108 |— 38 +39. |4467 0.02 | 087 | S77) | av 090 —07 | 083 |+ 31 | |—21.2|+ 85.0 | —0.03 2 | 097 | =17 |= 4.9 | | 401 | —O07 | 094 |— 98 i+ 8.8\+ 21.9 | +0.04 ae A407 | + | 4.6 n 153 +08 | 4161 [+ 33 —29.6\-+ 57.8 | —0.05 1 | 469 | | | —25 |—25 148 404 | 152 |— 84+ 34.2) 4414 0.03 2) 405 | +37 |+ 9 ft ae | 106 —l1 | 09 /+ 81 | —11.0+ 10.6 | —0.10 6 | 140 —66 |— 1.8 | 054 +05 | 059 |— 77 + 3.9+ 2.6 | 40.15 4 | 016 34 Ly 2.41 ! o | —14 | 007 [4 95 | 22) 5 3-8 0.07 } 374 GC, = ns ‘ : ’ << 08.100, These differences Obs.—¢ omp. given Oy in seconds of time, are contained in the 11% column. S, diminished by From the developed formulae | derived for these 24 intervals the 4 value Js= = ites (eg? 4+ eger + ¢-?) = 69500, while for all the dif- ferent manners of distribution of the errors of observation the mean of all the values Z7= 2 6 & (fy—/r), which values depend only on the magnitude of the errors and on their distribution is equal to 30500. In the computation the mean error of the observations has been put 03.028, which value must be regarded as the smallest that can be assumed on the strength of other investigations. Therefore the sinuosity of the interpolation curve must be ascribed for a great part to errors of observation. (December 24, 1902). KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday December 27, 1902. Ce ed (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 27 December 1902, Dl. XI). GS) AS) ao) ae Np aa Se IL. W. Bakuvis Roozenoom: “Tin amalgams’’, p. 373. J. Porrer van Loox: “Benzidine transformation”. (Communicated by Prof. C. A. Losry pr Bruyn), p. 377. K. FP. Wesexenacn: “On the duration of the compensatory pause after stimulation of t? « auricle of the mammalian heart®. (Communicated by Prof. C. A. Pexenirvnina), p. 378. J. Carpisain: “On the geometrical represontation of the motion of variable systems”, p. 886. J. KW. A. Werrienr Sarosoxson: “A new law concerning the relation between stimulu and effect’, (4th Communication). (Communicated by Prof. C. Winkirr), p. 492. M. W. Bevrrisex and A. van Derpen: “On «a colourless bacterium, whose caibon fooa comes from the atmosphere”, p. 398. L. H. Sirerrseaa: “The caleulation from the magnetic rotation of the plane of polari- m = I I sution, for substances without an absorptionband in the visible spectrum". (Communicated by Prof. H. Kawerrixci Onnes), p. 413. The following papers were read: Chemistry. — “7% amalgams’. By Prot. H. W. Baxuvis RoozeBoom. (Communicated im the meeting of November 29, 1909). As the number of properly studied amalgams is still very small I directed Dr. vax Hernrex to conduct an investigition on tin amalgams in connection with the research on cadmium amaleams by Dr. Bun. The more important results ave communicated here. In the liquid) condition tin and mercury ave miscible in all pro- portions. From the different mixtures a solid phase is deposited at different temperatures. The points at which solidification begins are mdicated in the accompanying figure by two lines AC and CB 25 Proceedings Royal Acad. Amsterdam, Vol. V. 37 Which meet each other at C (0.3 at. °/, Sn and $4.5) in a sharp angle. As the line (B ends in the melting point of tin, the solid phase Which deposits on cooling must be either tin or mixed crystals in Which ordinary tin occurs as a component, On analysis, the solid phase whieh has separated from the liquid amalgam at 25° was found to be composed of 94 atom °/, Sn. On account of the difficulty of obtaining trustworthy results in oO \ 2g" 90) ao Oo b Yo fo gO foo LINE BC. At. 0% Sn. | Temp. | At. 0/) Sn. Temp. 400 231° 6 90 37 902° 0 89.95 O16 10.79 | 79 .7 76.62 | AS3 7 5.17 | 65 .S 61.44 | 4155 .2 1.20 25.0 49.99 433 4 35.33 | 107 .4 98.96 | 99 .0 this manner, measurements of the A. J/. 7. were also made at 25 of amalgams of 0.001—100 atom °/ o/ mos » on against an amalgam of 16 atom These measurements led to the results that the wisaturated amalgams have a /2. MM. F. rising with the amount of fin until at 1.2. atom °/, saturation sets in. From this concentration up to 99 atom "/, the potential remains unchanged, consequently two phases of unchange- able concentration must exist between these limits; one of these is the liquid one of 1.2 °'/,, the other the solid one containing 99 atom °/,. At 25° the crystals deposited therefore consist of nearly pure tin which is the case in a still greater degree at higher temperatures. By a comparison of the values of the 42 1/. /. for amalgams of which the whole mass was liquid at 25° and 50° the heat of amalgamation could be calculated. The introduction of 1 eram-atom of Sn into a liquid amalgam with O.01—1.00 atom °/, Sn, therefore nearly pure He, absorbs about 8000 calories. The line (4 may also be considered as the line of the solutions saturated with Sn. It takes a very peculiar course. The part from 120° up to the melting point of tin is nearly straight, the centre part shows a very rapid increase of the solubility with the tempe- rature, the lower part, however, an exceedingly small increase and also an exceedingly small solubility so that the line approaches very closely the Hg-axis. In the lower part of the figure (p. 374) this part with ifs course towards the melting point of He has been drawn on a larger seale. 376 The extraordinarily great curvature of the central part of the line would lead to the supposition that the liquid mixtures of Sn +- Hg in the absence of a solid phase would on further cooling separate into two layers. On cooling below 34.55 a change takes place in all amalgams from 0.8 to 85°" decrease of volume. With increasing concentrations of Sn it first accompanied by a decided evolution of heat and increases but then decreases in intensity. The maximum lies near 50°). This change occurs in the figure on the line (') which therefore 1uns to at least 85°). The change causes a new phase to appear which also belongs to the second solidifving-line (4. The maximum in the intensity of the change on (YD at about 50°, would lead us to suppose that 0 mixed crystals having about this composition are formed. The modi- fication of tin therein contained must differ from ordinary tin. Between —34°.5 and —38°.5 these mixed crystals continue to be deposited from the mother-liquor (which moves along the line CA), this is accompanied by expansion. This change in volume diminishes 0 jor as the amount of tin’ present increases and dies out near 75 The solidification point of pure mercury and also the final solidifi- cation point of all amalgams containing up to about 60"), Sn, lies at —38°.6 (line 17). As the line CA of the saturated solutions also ends here it would seem that at the solidifying point of Hg, the solubility of tin has decreased to O, so that instead of a eutectic mixture only the remaining mercury solidifies. Still, the point A bears quite the characteristic of a eutectic point as not only the line AV is horizontal, but all mixtures up to 60°, Sn also remain a shorter or longer time at this temperature which proves that a residual liquid is solidifving completely. A great uncertainty still exists as to the nature of the tin-modifi- cation which occurs in mixed crystals below —34°.5 chiefly because it has so far not been possible to discover the part played in the amalgams by the grey modification of tin which may occur below 20° C. But from the change in volume which takes place in the different transformations at and below —34°.5 we may argue that the specific volume of the tin must be smaller than that of the grey modification and larger than that of liquid and, therefore, also of ordinary tin, Chemistry. “Benzidine transformation.” By Dr. J. Porrur vax Loon (Groningen). (Communicated by Prof. C. A. Losry pe Bruyn). (Communicated in the meeting of November 29, 1902), It is known that hydrazobenzene when treated with a dilute mineral acid is converted into benzidine and diphenylene, benzidine being, however, the main product. | endeavoured to ascertain the proportion in which the isomers are formed and in how far this depends on the temperature and the concentration of the acid and | farther attempted {0 measure the velocity with which the transformation takes place under definite circumstances. Benzidine was obtained pure by recerystallisation from water and distillation in) vacuo; the melting point of this substance was 128° which is in agreement with the statements of Mrrz and Srrassmr. (Jour. f. Pract. Ch. N. F. 60. 186). For the preparation of hydrazobenzene, azobenzene was used as the starting point: this was purified by distillation and then reduced with zine dust in an alcoholic alkaline solution. The hydrazobenzene so obtained was dissolved by warming in alcohol and the still yellow liquid deeolorised by means of ammonia and zine dust: the filtrate deposited pure white crystals of hydrazobenzene whieh could be separated unaltered from the liquid. A determination of the melting point gave as result 122°. For the study of the transformation it was necessary to have a method for the quantitative determination of benzidine. It was found possible to do this gravimetrically by adding potassium sulphate to a solution containing not too much free acid and so precipitating the base as sulphate which was then collected on a weighed filter, According to my experiments, the slight solubility of benzidine sulphate amounts to 5—6 milligrams per LOO ce. of water at the ordinary temperature and consequently a correction should be applied. To ascertain in what proportion the two bases are formed during the transformation of hydrazobenzene, weighed quantities of this substance were put into bottles of about 120 ce. capacity and then shaken with a definite solution of an acid until all had dissolved. The benzidine present in the solution was then estimated, as directed, and the proportion calculated from the two data. At the ordinary temperature, W/LO hydrochloric acid used in this iInanner causes 84 per cent of the hydrazobenzene to be converted into benzidine. Normal hydrochloric, hydrobromic acids convert 90 378 per cent of the same into benzidine, Ata higher temperature the proportion is another, for in four experiments with one-tenth normal hydrochloric acid, nitric acid, sulphuric acid and hydrobromie acid the proportions ala Loo were respectivel G64. 67.3, 63.1 anid 65.5 per cent, therefore, much lower. To get some data respecting the velocity of reaction a beaker with 50) per cent aleohol whieh contained hydrochloric acid in’ tenth- normal concentration was put into a thermostat and while stirring violently and passing a current of carbon dioxide over the surface a few grams of hydrazobenzene were introduced into the liquid: in which that substance is but litthe soluble. At 25°, the velocity appeared to be dependent on the concentration of the acid and it) inereased more rapidly than the concentration. The experiments ave being continued in the two directions indieated above. (Chem. Lab. Univers. Groningen). Physiology. “On the duration of the compensatory pause after stimulation of the auricle of the mammalian heart.” By Prot. kK. F. Werxckepacu. (Communicated by Prof. PEKELHARING). (Communicated in the meeting of 29 November 1902). When an extrasystole is set up by artificial stimulation of the ventricle or auricle of the beating frog’s heart, this extra-systole is followed up by a pause longer than the pause succeeding a spon- taneous systole. This long interval was studied by Margy, Dastre and others, and called a compensatory pause, because the longer quiescence of the heart was regarded as a compensation for the extra activity of the heart muscle. And it was not without reason that the word “compensation” was used, because the pause after an extra- systole is of such length, that the following spontaneous contraction just commences in the moment when it would have set in if, instead of an extra, a spontaneous systole had preceded. ENGELMANN (6) has given a simple and exhaustive explanation of the pause: the normal, physiological stimulus to contraction reaching the heart from the vena cava and causing it to contract finds, after an extra-systole auricle and ventricle in a refractory phase and so it cannot cause a contraction. It is only the following stimulus which finds the heart again in a condition in which it can react on that stimulus; the contraction (the “post compensatory”’) then Commencing, presents ( 379 ) self precisely in the moment in which it would have commenced if the heart’s action had been disturbed; so the rhythm of the physiological stimulation is not disturbed. In fig. I") the case is represented schematically. An artificial stimulus ¢ reaches 17. When the second stimulus arrives it finds the ventricle still refractory ; so one systole is missing, but the following third stimulus, causes just at the right time again a normal systole. So the pause following the extra systole is with regard to its duration just compensatory ; the time taken up by a spontaneous systole + extra systole and pause is just equal to that of two normal systoles. If, however, we stimulate the froe’s heart at the vena cava where the contraction always sets in, the compensatory pause is entirely missing and the following spontaneous systole succeeds the extra systole after a period equal to the normal period of contraction. In Fig. [| the second artificial stimulus Y reaches the vena cava; the following spontaneous contraction sets in after the usual interval 20, a compensatory pause is missing. Whilst the imterval between the systole preceding the extra systole and the one following the extra- systole after stimulation of the ventricle (or of the auricle) was double the normal period = 40, the same interval is here only P90 = 39. From this ensues that the stimulus is not rhythmically induced from 1) In these schemes answering to those used formerly by Exeetmayn and by me the lime is indicated on the three abscissae, and this is done for the duration of the phase and the stimulation of vena cava (Ve), auricle (A) and ventricle (V’). j= physiological stimulus, Y= artificial stimulus. The perpendicular lines represent the contractions of the heart-cavities. The slanting lines connecting the base points of the systole-mark indicate the direction in which the stimulus is conducted. If these lines are dotted the conduction does not actually take place. The duration of the spontaneous period is put at 20 abscis units (= 1 mM.), the interval from the moment of the physiological stimulus to the ventricular contraction (Ve — Vs) =5 units. sso outside to the vena cava, but that it originates in that place in a definite period. It is certainly the most natural and the most suitable explanation of the phenomenon to assume that at the venae cavae fas is known to be the ease in less degree in the other parts of the heart) continually stimulating matter is) formed, fill this obtains such a strength that a contraction is caused. When however, the musele fibres contract the stimulating matter seems to have been used up or at least to have been destroyed, so that every time afier a con- traction the same time is wanted to produce new stimulating matter to such a strength that again a contraction follows. This destroying of the stimulating matter (dissociation in Tons, chemical changes or whatever this may be) always takes place when there is a contraction, whether the systole is caused by the stimulating matter itself or caused by a stimulus induced from elsewhere. For it is a well-known fact, that by artificial stimulation of the auricle or the ventricle, more frequent than the spontaneous rhythm, the latter can be entirely overpowered. Another explanation is that at the vena cava there is a continual stimulation constant in’ strength, expressing itself periodically in systoles, because with each systole irritability, contractility and con- ductive power of the heart muscle are neutralized; so if a systole has taken place it always again lasts a certain time before the heart has recovered itself in’ so far that another contraction is possible. ENGELMANN objects to this, that the explosion bronght about by the contraction in the molecular system of the muscle cell will destroy the stimulating matter in stock together with the other properties of this muscle cell, (irritability, contractility and conductive power); moreover did) ENGELMANN show that the period of the formation of the stimulus can be changed independent of the irritability in’ the wall of the vena by chronotropic nerve influence. So we must assume that the systole destroys the stimulating matter and that every time the latter must again develop itself after every systole to active power. The law of the preservation of the physiological period of stimulation dominating the duration of the compensatory pause and all the important data come to light by means of “the method of the extra-systoles” for the frog’s heart have been traced by Cusnyy and Marruews (1) for the mammalian heart. These in- vestigators showed that the mammalian heart obeys the same laws as the frog’s heart, that its activity is dominated by the same fun- damental properties of the fibres of the heart muscle, that the same theories hold good for both. Only in one respect they found a difference: when the anricle is ( 381 } artificially stimulated, the compensatory pause after the extra-systole is not as in the frog’s heart truly compensatory but mostly of too short a duration. Sometimes it was completely Compensatory, it was never entirely missing, if was generally shortened and then at any rate not equally shortened. They say on this subject (l.¢. page 226): ,,As long as the interval “A— AL is of considerable length the compensatory pause in the “auricle is truly compensatory, that is the interval between the last “spontaneous contraction and the post-compensatory is equal to two “auricular eyeles. When however the stimulus falls earlier in’ the “irritable period, no true compensation occurs, the post-compensatory “contraction being premature,.... when A,—A. is short the com- “pensation (of time W.) before the first natural contraction is always “imperfect.” The explanation of this difference is according to them: ‘either “the contraction wave passes from the auricle to the great veins “and there sets up a forced contraction which returning to the “auricle causes the premature systole, or the irritability of the auricle “oradually increases until it} culminates im a contraction whieh is “independent of the great veins and initiated me the auricular muscle “itself. As to which of these two is the correct explanation we are “unable to give any opimion and feel that it would be useless to “balance probabilities before the movements of the great veins have “been examined.” Formerly | myself expressed the supposition, that the mammalian auricle might, possess a greater automatic irritability, because in the phylogenetic development a part of sinus and vena would be taken up in the auricle. H. EK. Hnriva (2) has also been able to establish the difference described for the first time by Cusuyy and Marrinws; he says: “The earlier the moment of stunulation falls in the irritable period “of the auricle, the shorter the artificial bigeminus is Gnterval between “last spontaneous and post-compensatory systole); the later it falls, “the more the duration of the artificial bigeminus approaches that of “two normal cardiac periods.” He continues: “the pause (after the “extra-systole of the auricle) lasts longer according to the moment “of stimulation falling earlier in the irritable period.” So here too he assumes the law of the conservation of the physiological period of stimulation: ‘aber die Beziehune ist keine so einfache wie am Ventrikel”, We had all overlooked, that Mackrnzin (3) had become convineed already in 1894 after a careful analysis of the venous and liver pulse B82 that also in the human heart a “premature” contraction coming from the auricle is often succeeded by a too short compensatory pause. The possibility. of distinguishing in this way between auricular and ventricular extra systoles had not eseaped his attention. When reflecting upon the consequences which extra systoles coming from the auricle must have on the action of the heart and the cir- culation of the blood of man, | found the following simple explanation of the above mentioned phenomenon, an explanation from whieh ensues that we have not got anything to do with a difference in principle between the frog’s heart and the mammalian heart and that it is founded on an anatomic difference between the two hearts. ENGELMANN (5) has shown that in muscular tissue of equal com- position the stimulus to contraction is conducted also at an equal rate in all directions. So when an artificial stimulus is given to the auricle, a contraction stimulus and with it a contraction wave will pass from the stimulated point not only to the lower parts of the auricle and to the ventricle, but also to the higher parts of the auricle and to the vena cava, so to the place where normally the stimulus is formed and the contraction begins. ENGELMANN (6) has already pointed to the importance which this ‘‘antiperistaltic” move- ment may have for the action of the heart, Cusuxy and Marrikws have also seen the possibility of it. When a stimulus is applied late in the irritable period of the auricle, so just before the moment when the following physiological stimulus was to come from the vena cava, the stimulus (and the contraction) will not be able to reach the vena cava any more before the physiological stimulus has had its effect there: auricle and ventricle will obey the extra stimulus, the spontaneous contraction already begun will not go on, but the rhythm at the venae is not disturbed. If the extra-systole sets in a little earlier, the extra contraction might reach the vena cava just at the moment that the physiological stimulus had developed to the necessary intensity ; then also auricle and ventricle obey the extra stimulus, the physiological stimulus is neutralized or it finds the whole heart refractory, but here too the rhythin of the formation of the stimulus is not disturbed and_ the pause of auricle and ventricle is completely compensatory. When however the auricle is stimulated still earlier, the extra contraction will reach the vena cava before the moment, in which the stimulus to contraction forming there, had attained at sufficient strength to cause a contraction. The stimulating matter found there at that moment will be destroyed by the extra contraction : from this moment (oom 1) new stimulating matter is being formed and affer a certain time equal to the normal period it will have obtained enough intensity to cause another contraction. So the following spontaneous systole will not fall in the moment it would have done so if an extra systole had not been set up, but just so much earlier as the extra contrac- tion reached the vena cava before the moment in which the following spontaneous contraction would have occurred. In the diagrams Il and IIT an attempt has been made at making these observations clear for a particular case. ae u l | ate! In fig. II the auricle is artificially stimulated respectively 18, 15 and 12 units of time after the previous spontaneous contraction; auricle and ventricle follow the extra stimulus; in the first two cases the extra contraction moving to the vena cava intercepted the spon- {aneous contraction coming from the vena cava. In the third case it arrives in the vena cava just at the same time as the physiological stimulus becomes active. In all these cases the rhythm remains un- disturbed and the compensatory pause is complete for the auricle as well as for the ventricle: the interval between the systole preceding the extra systole and the one following it is double the period of the heart, in this ease = 40. In fig. IIT an earlier stimulation of the heart is shown, 10, resp. 8 and 5 units of time after the preceding systole the auricle is stimulated. The extra systole formed by the first stimulus arrives in the vena cava 4 units before the following spontaneous contraction. The stimulating matter present at that moment is destroyed and a certain time — 20 has to pass before the stimulus has increased to sufficient strength. So the interval of the spontaneous contractions is not = 40 but = 16 + 20=— 36. According to the extra auricular contraction falling earlier, this B84 interval must become shorter, a fact which goes without saying, in fig. HI resp. = 35 and = 34. From this ensues, that when the stimulation ¢ effected late in the irritable period the COM pPeHSAlory pause is complete and farthermore, the earlier the stimulation ts effected the shorter the interval betiveen preceding systole and following spontaneous systole. Another influence is still at work, which also governs the length of the pause. The earlier the stimulation is effected in the irritable period of the auricle, the slower the stimulus is conducted through the wall of the heart, for the conductive power of the cardiac muscle returns but gradually after the preceding systole. So the interval 1.— Ve, will be longer according to the stimulus being effected earlier and as this interval also dominates the moment in which the stimulating material is destroyed by the induced extra contraction it| will also influence the length of the auricular interval. In fig. Il] where the slower conduction when the stimulus is effected earlier is taken into account this influence is illustrated. And in’ this way it is to be explained, that the titerral is longer after an auricular eatra-systole according to the moment of stimulation falling earlier in the irritable period of the awicle following quicker upon the preceding systole. The differences in length of the compensatory pause after stimu- lation of the auricle are in this way easily explained and it appears that the rules established for the amphibian heart hold good for the mammalian heart, in the sense however, as Hrrinc says, that “die Sezichung keine so einfache ist’. The peculiar modifications in the course of the extra contraction when the auricle is stimulated, derived by Mackkyxziz from the venous pulse, by Cusnyy and Marrurws from the tracings of the auricular movements, will probably find their explanation in the way in which, as is proved in fig. II, the contraction waves meet here in the auricular a Le ~~ (Bish) ) wall and the differences will depend upon the spontaneous or the extra contraction being the most considerable. The question must however now be put: why does a complete compensatory pause always (or almost always, ENGELMANN ") follow the extra systole of the auricle in the amphibian heart and why in the mammalian heart only under certain conditions ¥ The answer may run as- follows: In equally built up parts of the heart muscle the stimulus is also equally conducted to all sides, but where for whatever reason the state of the muscle fibres is not everywhere the same, the conduction of the stimulus will neither be the same. This is the reason that the conduction of the stimulus of the auricle on the ventricle, in general of one division of the heart on the other, takes place much slower than inside the wall of auricle or ventricle. When conduction takes place in the direction opposed to the normal, this distinction will not make itself less felt. And just as the slower conduction may be the cause that extra-systoles of the ventricle never recede quickly enough to have a disturbing effect on the rhythm of the great veins, the differentiation between veins, sinus and ventricle in the frog@’s heart will be the cause, that here a stimulation of the auricle is not quickly enough conducted through the transition places to disturb the rhythm at the venae cavae. Moreover this possibility seems so much the slighter, because in the froe’s heart muscle fibres with a strong automatic irritability ascend high up in the vena cava and so cannot be reached so easily by an extra stimulus. As this differentiation of the cardiac muscle between vena cava and atrio-ventricular limit is missing for the mammals, it is no wonder that the disturbing influence on the for- mation of the stimulus at the vena cava occurs just in the mammalian heart. If finally this explanation is the right one, the place where the auricle of the mammalian hearth is stimulated, will have its effect on the length of the compensatory pause: perhaps it will be possible to establish for not too small hearts and where the conduction of the muscle has already somewhat slackened, that for auricular sumulation far from the vena cava the compensatory pause is longer or even complete, whilst the pause becomes shorter according to the auricular stimulation taking place closer to the vena cava. For such an experiment the stimulation would always have to be effected exactly in the same moment of the heart period, every time equally long after the preceding systole. ( 386 ) LITERATURE: 1. Cusuxy and Marrirws, Journal of physiology. Vol. NX, 2. H. KE. Henne, Piliiger’s Archiv. Bd. LXXXIL. 3. d. Mackenzie, Journal of Pathology and Bacteriology. Vol. IL 4. K. FP. Wenckepacu, Zeitschrift fiir Klin. Medicin. Bd. XXXVI. 5. Ta. W. Exeeumany, Sur la transmission réciproque et irréciproque. Archives Néer- landaises XXX. 6. TH. W. Excemany, *Onderzockingen” Physiol laborat. Utrecht. 1V Series, Il Vol. IS. Mathematics. — “(n the geometrical representation of the motion of variable systems”. By Prof. J, CARpinaat. 1. In two communications ‘) some theorems have been developed by me, relating to the motion of variable systems. Also in this sub- division of the doctrine of motion the method of the geometrical representation occurring so frequently in Mathematics can be applied. The following communication has in view to mention some parti- culars on this subject. The representation in question is treated *) by R. Sturm. From this treatise [ derive the short stummary, which must needs appear here as an introduction to the subject. 2. In the quoted considerations two complexes of rays played an important -part, namely the tetrahedral complex formed by the directions of the velocities of the points of the moving system and the rays of a focal system belonging to it; the latter consists for the motion of an invariable system of the normals of the trajectories of the points and for a projectively variable system of rays whose construction took a great part of the considerations. ‘The purpose must be to obtain a simultaneous representation of complex and focal system; it will prove desirable to give the foremost place to the representation of the focal system. 3. Let thus be given the focal system A sitnated in the space Y. According to the method of Sytvester let us suppose two planes Sand § with two projective pencils of rays situated in them with their vertices V’ and VY situated on the line of intersection §§' —.r, 1) Proceedings of the Kon, Akad. van Wetensch., section of science, vol. IV, pages 489 and 55s. 2) Die Gebilde ersten und zweilen Grades der Liniengeometrie, 1, p. 257. ( 387 ) wv being an homologous ray of both pencils. The rays of A are the transversals of two homologous rays of (.YS’) and (NY’S). Let us now take two sheaves of rays in the space SY, with the vertices VY, and \’, and establish a projective correspondence between these sheaves and the pointtields $ and $’, in such a way that the pencil of planes through the axis VA’, is homologous to the pencils (V§’) and’ (Y's). Let 7 be a ray of A, cutting two homologous rays of (.Y§’) and (.Y’S), to which in the homologous plane 2, a ray /, out of VY, and a ray /’, out of XV’, correspond; /, and /', intersect each other in a point 4,. This point is homologous to the ray /. So a projective correspondence is established between the points of the space Y, and the rays of the focal system 4. As is the case with every representation, also here the knowledge of its principal curve cannot be dispensed with. It is a conic X,? » and XX” homologous to the pencils of rays of 4 situated in planes through .. through the points VY. situated in a plane §,. [ts points are The plane §, (principal plane) itself is homologous to ve. To an arbitrary pencil of rays of 1 a right line corresponds cutting er X,?7, to a hyperboloidic system of focal rays a conic having two points in common with -Y,*, to a linear congruence belonging to .1a quadratic surface through X,’. 4. Let a projectively variable moving spacial system be given ; let as before PQRS be the tetrahedron of coincidence of two sue- cessive positions and let the corresponding focal system 4 be deter- mined by PQ and RS as conjugate polars and the conic A’* touching PR and PS in FR and S. According to the indicated method the focal system can be represented in the space *,; for the tetrahedral complex of the directions of the velocities, however, we need an- other representation, which can be taken in such a way that the same principal curve is retained; we shall succeed in this if we do not represent the complex itself, but its section with the focal system 4. This gives rise to a congruence (2,2) which we shall first investigate more closely. 5. Let A be an arbitrary point, @ its focal plane; at the same time A is the vertex of a quadratic cone, geometrical locus of the directions of the velocities through A, but of which only one is the direction of velocity of A itself. This cone will cut in general @ into two rays belonging to the congruence (2,2); in this way we can construct the whole congruence. By this we have determined the construction, but not the geometrical character of the congruence ; this can be done in the following manner; 388 Let the direction of the velocity a of a point 1 intersect the plane of coincidence ?RS in L; now the focal plane of 1 interseets this plane in’ the polar p of / with respeet to the conic A*. The rays of the complex, at the same time rays of the conjugate foeal system, are situated in the focal plane «@ of 1; from: this ensues that these rays intersect the plane ?/2S in two coincident points, at the sume time conjugate with respect to A%; so these rays will intersect K* and now ensues the theorem : “The rays of the congruence (2,2), which is the section of the complex with the foeal system, have a point in common with the conie A?; so they are found as rays of 4 cutting A?” So the congruence (2,2) arising from this belongs to those con- eruences, not possessing a focal surface, but a singular or double curve), geometrical locus of the first series of foci of the congruence. 6 The congruence can be constructed as a whole out of points of the conie A?; for these points have the property of being the points of intersection not only of two but of a whole pencil of rays of the congruence (2,2), situated in’ the focal planes belonging to each of the points. These focal planes envelop a quadratic cone )*, with the vertex ?: so the congruence must touch the cone. From this ensues the following construction : “Let a point 1 be taken on A®, the focal ray PA be drawn, cutting A® for the second time in 1. Let the two tangential planes to P2 be brought through PA; each of these planes contains a pencil of rays of the congruence, the vertex of one pencil being .1, of the other 1.” 7. We now proceed by giving some visible properties of the con- eruence (2,2). a. The two foci of each ray are the points of intersection with A? and the point of contact with ?*. The focal surface of points hecomes (??; the focal surface of tangential planes consists of the tangential planes of A®. b. All rays of the congruence (2,2) belonging to a congruence of rays (1,1) of A cut two conjugate polars of 4, and cutting at the same time A? they form a ruled surface of order four with a simple conic and two double lines. ce. The rays of the congruence (2,2), lying on a hyperboloid of 1) Gongruences of this type are ranged in the “Index du répertoire bibliogra- phique des sciences mathématiques” under V?1¢2 and placed by R. Srurm in a separate division; see “Liniengeometrie’, I, p. 323. A, pass through the points of intersection of the latter with A’, so they are fow in number. d. Let A?® be real and let P be situated within A®; all focal rays through ?, the focal point of plane PRS, now cut A; so all pencils of rays are real. If P lies outside A® two tangents out of P can be drawn to A*; these tangents are the lines of intersection of the cone P? with plane PAS. The planes touching /?? according to these lines of intersection are focal planes, in which two pencils of rays have coimeided; rays through 2, not cutting A’, give rise to imaginary pencils of rays of the congruence (2,2). Further ensues from this : “If A* is real and all the vertices of the tetrahedron of coinci- dence likewise are real, the congruence (2,2) is built up of real and imaginary pencils of rays, where as a transition two are double ones; if A® is real but the vertices 7? and S are imaginary, all the pencils are real.” e. The cases in which A® is imaginary, or also those in which all the vertices of the tetrahedron of coincidence are imaginary, do not sive real congruences; so they are not under consideration. 5. We now pass to the representation of the congruence (2,2) by which the image is obtained of the connection of focal system and tetrahedral complex. a. The congruence containing 2 pencils of rays which are represented in , by straight lines having a point in common with X,°, the whole congruence is represented by a ruled surface passing , In XY, a hyperboloidic system of through Y\*. To a straight line / focal rays corresponds, which has four points in common with A®; so if contains four rays of the congruence and the representing sur- face S\* of the congruence (2,2) is a ruled surface of order four. 6. An arbitrary pencil of focal rays of .1 contains two rays of the congruence; the straight line in +, corresponding to them cutting AX,* has another two points in common with S,‘; so .V,* isa double conic of Sy‘. ¢. To the pencil of rays in > with P as vertex and. PRS as plane a straight line p, in S, corresponds, cutting V,*. Each ray of the pencil P/PRS belonging to two pencils of rays whose vertices are points of intersection with A®, in all points of p, two generators ot S2 concur; from this follows that SS," is a ruled surface havine as doubie curve a conic with a straight line cutting it: with this the type of S\* has been established. 26 Proceedings Royal Acad. Amsterdam. Vol. \ 390 ) 9. A closer acquaintance with the form of SS,‘ is obtained by tracing the pinchpoints on the double curve; there can be two of them on py and two on NX,?. Those of p, depend on the position of P with respect to AY. a. Let P be outside A*. When a ray through 7? cuts A? in two points, we get two pencils of rays of the congruence, to which two real generators of SS,‘ correspond, concurring in a point of p,. For the tangential lines out of P to A? these two generators coincide, so the point of S,*, from which they are drawn is a pinchpoint; so for this position there are two real pinchpoints on p, ; from this ensues : “If P lies outside A’, p, has one part appearing as double line and another which is isolated; two pinchpoints separate these two parts.” hb. Let P lie within A*. All focal rays through P cut A?*; there ae no tangents to A’, so there are no pinchpoints on p,. So the double line p, is in its whole length really double line. Besides the pinchpoints on p, the surface S,* has also pinchpoints on X,*. To find these we must keep in view that the points on _X,? correspond to the pencils of rays whose vertices lie on VX’ =a, which are thus situated in planes through 2. Let y be a plane through « and (C its focal point; the pencil of rays (Cy) has two rays cutting K* viz. the two rays connecting C and the points of intersection Band B of y and K*. These two rays are represented in 2, by a single point B, of X,*. Now CB belongs still to another pencil of focal rays, viz. to the pencil whose vertex is and whose plane is the plane C6P—3. The latter pencil belongs to the con- eruence (2,2) and is thus represented by a straight line through B, lying on S,*. In a similar way it appears that also a second straight line of S,* passes through 6,, namely the one which is represented by the pencil of rays (5'3) lying in plane CB'P. Now again two principal cases may occur: a. « cuts the plane ?RS in a point 7’ outside A?. The pencil of rays 7 lying in this plane has rays cutting A’? in two points, touching A’*® or having two imaginary points in common with A’®. In this case these are parts of Y,* through which two generators of S,* pass, which have thus to be regarded as points of a double curve, and parts which are isolated; the transition is formed by two pinchpoints, through which two coinciding generators pass; and these last correspond to the pencils of rays, having their vertices on the tangents drawn from 7 to A®. 4. The above mentioned point of intersection 7’ lies within _X,’. All rays through 7 cut A*; through each point of Y,* two generators pass, so the whole conic .X,° is a double curve. ( 391 ) 10. Among the particular sections of S,‘ the conies of this surface come into account. These conics have two points in common with X,?; so (8) to these must correspond in + hyperboloidic systems of focal rays of A. These can be constructed in the following way : Let again a point A be taken on A’’, its focal plane @ be deter- mined, moreover the second point of intersection A’ of @ with A’? and the focal plane a’ of A’. If now a pencil of rays be drawn in a’ through A (which rays are not focal rays) and likewise through A’ in a, the pencils (A,@’), (A’,@) consist of conjugate polars of 4 between which a projective correspondence is established by means of the focal rays. In connection with Y,* each pair of conjugate polars causes a hyperboloidic system of focal rays to appear. These two pencils generate them all, so their number is 2. 11. Finally a few particular cases ask for ow’ attention. a. The line of intersection « cuts the plane PRS in a point of the tangent plane PR. The pencil of focal rays in the plane PR has as vertex this point of intersection; to this pencil corresponds a pinchpoint on -Y,*, but at the same time this pencil of rays has more- over a ray in common with the pencil of rays in the focal plane of the point #; so the obtained pinchpoint is at the same time a point of p,; from this follows that in the point of intersection of .Y,* and p, two pinchpoints have coincided; so through this point only a single generator of S,* can be drawn. 6. Application to the motion of an invariable system. In this case K? is imaginary (the imaginary circle in the plane at infinity); so the congruence (2,2) consists entirely of imaginary rays. The pencil of rays P/PRS, however, remains real; so the representation in becomes an imaginary ruled surface oS,‘ with real double curve con- sisting of a straight line and a conic intersecting it. The same obser- vation can be made for other cases where A’ becomes imaginary. ce. Another particular case occurs when the ray VX’ —.v is taken in such a way that it cuts the conic A,*; by doing so the character of the congruence does not change, but its representation does. If we now consider a pencil of rays in a plane brought through «, it is apparent that always one of the two rays of congruence to A’? coin- cides with wv. Of the two rays cutting in Y, the double conie V,? only one is situated on S,*, the other one passes into a ray situated in &, ; from this follows: “When the focal ray w cuts the conic A? the surface St breaks up into §, and a cubic ruled surface S,* of which p, is a doubie line; so this gives a simpler representation of the congruence ‘2.2) 26* ( 392 ) Physiology. “A new law concernuny the velation between stimulus and effect.” By Dro do WK. AL Wreeriitin: S\LoMoNson, Commt- nicated by Dr. CO. Winkier. (Communication LV), In three papers, bearing the title 4a new low concerning the relation between stimulus and effect 1, Tl and UL, LT have tried to prove that by increasing a stimulus, the effect too will increase in a detinite manner. The relation was expressed by the formula E= AN—e—-)) OS ee In deducing this formula L assumed that the transformation of chemical substance caused one and only one well-defined effect. In most cases however from such a transformation several conse- quences will result, constituting together the total effect: e.g. a mecha- nical, a thermal, a chemical, an electrical effect may be caused simul- taneously by some changing of the protoplasma. The question arises, whether our mathematical expression may be applied as well to the different parts of an effect as to the total effect. In order to obtain an answer to this question, we have to con- sider again the differential equation: — d= BER oT tadae 2 eee (2) expressing, that by an infinitesimal increment of stimulus an infini- tesimal proportional part of the transformable substance was trans- formed, and at the same time stating the quantity of this transforma- tion. The quantity —(// represents the increment of the effect. In the case of the effect being composed of several different parts, : 1 the same equality will prevail for any of them, e.g. the — part, and at so we shall obtain for a partial effeet the equation —— db = BEGR~ =... ec i ee ioe nt in which n > 1. From this formula we get the expression B= at) — e-Bay. ee eee wherein @ represents another constant than A, and wherein » is a number larger than 1. This formula for a partial effect is identical to the formula for ¢ ( 393 total effect the only difference being that the exponential constant in the case of a partial effect is larger than in that of a total effect. The muscle may be taken as an example. Every contraction brings about a mechanical effect, whilst at the same time an electrical response is given. Finally the production of heat may be taken for the total effect, at any rate in the case of isotonic or isometric contractions where the mechanical effect is afterwards converted into heat. Thence we are justified in presuming that our statement about the formulae for total and partial effects, may be applied to the thermal effect and mechanical effect of muscle-contractions. I have tried to ascertain whether the numbers, given for the thermal- effects by different authors are in accordance with our law. In Daninewsky’?) I found several series of numbers, from which ihe following tables were calculated TAUB LAR Te Daninnwsky, lc. pag. 184. lsometrical contraction. Initial load 40 gram fig. 1. A == 23 B= 0.03 (C= Wes, Rh Ey cal. Pee 20 (54) AF 30) 6.97 4D 40 11.09 11.4 ) 14.18 16.2 so | 49.38 | 419.9 100 | 21.00 | 49.8 300 | 22.98 20.5 600 | 93. | 92 S00 93. | 24.9 In this table, as in the following # represents the magnitude of ihe stimulus; /, observ. the thermal effect as observed by DanxiEwsky. ') B. Danitewsky. Ergebnisse weilerer thermodynamischer Untersuchungen der Muskeln, YV.e. A. Fick. Myothermische Untersuchungen 1889. 394 /}, cale. the thermal effect, as calculated with the constants given at the head of each table. T 2B Ib. Initial load 80 Gr. fig. 2. A = 24.2 B= 0.0324 C20: R Ew cale. Rest observ, 30 6.7 6 D0 15.3 IS 100 29.4 oo 300 24.2 24.8 ° TABLE Te Ib. Initial load 300 Gr. fig. 3. A=20.8" B=00217 “C=16-42 R Ew calc. | ee 0 TES: LD 100 | 474 | 48 400 | 20.7 | 20 800 | 20.8 | 21.5 The first of the next-following tables, which are much more important, is also taken from the experiments of DanitEwsky l.c., ( 395 ) whilst the observations in the 5 and 6 table have been published by Nawanicuin'): the school of Hemrnnain and that of Fick are both represented. The higher importance of the series given hereafter, consists chiefly in the fact of their having served to determine as well the mechanical response as the thermal effect with stimuli of increasing magnitude. In the series of Daninewsky a double thigh-muscle-preparation of the frog after the method of Fick was employed, whilst NawaLicHin made use of a single gastrocnemius. The muscle contracted isotonically, whilst simultaneously the thermal and the mechanical effect of each contraction, were recorded. As it has been proved with sufficient accuracy in our first papers that our formula may be applied to isotonie twitches, these may now serve us as a means of control. In the following series the magnitude of stimulus is again indicated in the first column by #&. The second column contains the calculated height of twitch, the third column the observed height; the fourth column the calculated and the fifth the observed thermal effect. The constants A,, B, and C,, were used for calculating the thermal effects, the constants A;, 2, and C), for calculating the heights of the contractions. TABLE IV. Danitewsky l.c. Load 60 Gr. fig. 4. A; = 40 155), == (0X0 (C7, == 14a! Ay = 14.55 By = 0.02 Ch SS Wt | Pe ee ApEn | Li | = Lw Rh | ix cale. | observ. | fw tale, observ. | | DOE 9277 ono See Aes OFT, 30 | 21.6 soa im cone 4 | | BOe|t 88095 | ae iP yeaa vey 1) Nawattcuty, Myothermische Untersuchungen. Pfluger’s Archiv, Bd. 14, p. 297, NAWALICHIN loc. pag. 297. Load 30 Gr. fig. 5, Aj, = .6.25 By, = 0.0036 Cp = 205 i, ee B,.—= 0.00085 C,.= 205 I M0 observ. Ei f Ewe cale. observ. Rh F% calc. 40 3.47 3.9 2 60 3 450 3.66 Saat 3.20 3.5 500 £208 4.2 3.78 4 600 4.74 4.2 4.84 4 S00 a2 2.4 6.75 7 1500 6.48 aT 11.34 10.5 2000 6.23 0 13.30 B.D 2500) 6.25 6.2 14.60 15 2500 6.25 6.3 14.60 1% PSN J bald Wl Ib. Load 90 Gr. fig. 6. FA ean ee B, = 0.0185 Oy, == ol) lp == WAS By = 0.008 C= 660 R yy, cale. I Ei Ew cale. Boo . observ. observ. 700 3.40 3.5 4.70 es) 750 5.97 es) 8.80 9.5 900 6.42 | 6.4 14.61 12 1000 6.50 6.5 16.00 16 {500 6.50 6.5 GAS aaN7 | | | Considering that the degree of accuracy with which the thermal effects were measured is not very high, we have some cause for satisfaction about the results of our caleulations. Though only a first approximation has been effected throughout all these series, the errors remain wholly within the limits of the mean errors of observation. Moreover in some cases if is even possible to apply a correction. Looking at series VI, we see immediately that the observed numbers ( 398 corresponding to the stimulus 900 are rather too small, as well for the height of twitch as for the heat-production. Calculating from the observed lifting-height the corresponding magnitude of stimulus, we find SLO instead of 900. Now taking this number 810, to caleulate the heat-production, we obtain 12, in perfect accordance with the observation. The supposition that the number 900 is an error and that 800 was meant is not very hazardous. From the communicated series we may draw firstly this conclusion that the heat-production, considered as total effeet, increases virtually with increased magnitude of stimulus in the manner indicated by the established formula. In the three last series 2,, the increment-constant for the thermal effect, proved to be always smaller than the 4, corresponding to it, a fact predicted already in our deduction. We found for the number B, Dy pan = n = in series IV, V and VI the value 2.5, 4.23 and 2.31. Though of course even by this fact our deduction may not be deemed absolutely proven, it nevertheless affords a valuable support for considering the deduction proposed by me as a most useful working-hypothesis. Bacteriology. — “On a colourless bacterium, whose carbon food comes from the atmosphere.” By Prof. M. W. BrigsertNck and A. vAN DELDEN. We give the name of Bacillus oligocarbophilus*) to a colourless bacterium, whose carbon nutrition in the dark (and likewise in the light), takes place at the expense of a not vet well-known atmospheric 1) It is probable that W. Herarvs (Ueber das Verhalten der Bacterien in Brunnenwasser sowie tiber reducirende und oxydirende Eigenschaften der Bacterien. Zeitschrift f. Hygiene, Bd. I, pag. 226) already in 1886, has had cultures of B. oligocarbopnilus before him. He says the following: .... ,Ausser- ordentlich auffallend war das Ergeniss dieser Versuche in der Hinsicht, dass eine Vermehrung der Bacterien in einer Fliissigkeit eingetreten war, welche keine organische Verbindungen sondern nur Salze enthielt. Ein unansehnliches, kaum sichtbares Piinktchen von Bacterienzoogloeén hatte sich im Verlaufe vom zehn Tagen so stark vermehrt, dass die ganze Oberfliche der Liésung vor: einer dicken Haut bedeckt war.” Analytical results are not given, and the remark makes the impression of being accidental and is lost among insignificant observations, — Wixocrapsky’s statement, concerning the accumulation of organic carbon in nitri- fying solutions, evidently refers likewise to this microbe, but his description suffers of indistinctness (Annales de l'Institut Pasteur, T.4 pg. 270 et 462, 1891).-- In the experiments of Gopieswx (Bulletin international de 1’ Académie d. sc. d. Cracovie, Dec. 1892 pag. 408 et Juin 1895 pag. 178), the vanished CO? is not, as he thinks, absorbed by the ferments of nitrification but by the Mg O.Mg C05. ( 399 carbon compound (or compounds), from which the energy, wanted for the vital processes, is also derived *). The culture of this bacterium on solid media or in nutrient solutions, containing soluble organic substances has not yet succeeded, which may, of course, have been caused by an erroneous choice of these substances. On the other hand, pure cultures on solid and in liquid substrata, without soluble carbon compounds, are easy to be made. lL. CRUDE CULTURES OF BACILLUS OLIGOCARBOPHILUS. Bacillus oligocarbophilus is obtained by the following accumulation experiment, which, because of the purity of the thereby resulting vegetation, may be called a “perfect accumulation experiment.” Into a large Ervenmnyer-flask a thin layer is introduced of a nutrient liquid of the same composition as used for the water culture of higher and lower green plants, but with alkaline instead of acid reaction. One takes for instance : Distilled water 100 Kaliumnitrate 0.01 to O41 Dinatriumphosphate — 0.02 “Mineral solution” 1 drop. This “mineral solution” contains in one drop: 8 Merms MesO, . 7 H,O 0.05 1" MnSO, . 4 H,O 0.05 ” FeCl, . 3H,0 If from this liquid nitrogen, phosphor, kalium or magnesium is left out, special experiments have proved, that no, or but an insigni- ficant growth is obtained. As to the necessity of the likewise added elements sulphur, manganese and iron, there still exists some doubt. The inoculation is made with a not too small quantity of garden- soil, the flasks are closed with a cotton plug, or with filter paper, without impeding the entrance of air by diffusion, and the culture is left in the dark at 283—25° C. After two or three weeks, the fluid, which itself remains perfectly clear, is seen to cover with a thin, white, or feebly rose-coloured, very dry film, difficult to moisten, and macroscopically resembling a J/ycoderma-tilm, but consisting of minute bacteria, microscopically often invisible without staining, and sticking together by a slimy substance. This is Bacillus oligocarbophilus. 1) We also found another, rarer species, belonging to the genus Streptothria Cony, with corresponding properties. It will not, however, be further discussed here. ( 400.) The growth of the film continues for months, whereby a considerable accumulation of organic carbon may be observed, which is not only visible to the naked eve by the vigorous bacterial growth, but can also he proved by direct weighing, and by a comparison of the perman- gvanate numbers found before and after the experiment, of which some instances are given below. As there is reason to admit that our bacterium is generally dis- tributed in garden-soil, and was without doubt always present in the crude material used for the inoculation, the failing of the film-for- mation in some of the flasks must necessarily result from the chosen culture fluid being less favorable to the feebler germs and not allowing their growth. So we observed that water, distilled in a copper apparatus, caused many more failures than when distilled in glass; we there- fore afterwards always used the latter. In other cases monads, which immediately devoured the bacteria, were cause of the failure; by transfers and by the use of pure cultures, these voracious organisms could be rendered harmless or removed. When the distilled water is replaced by fap-water, the number of flasks remaining without growth after inoenlation with the same quantity of garden-soil is much smaller. If once a pellicle has formed, transfers into the said culture liquid, prepared either with distilled or with tap-water, come easily and without exception to development. 2. SOURCE OF NITROGEN REQUIRED. In the above mentioned nutrient liquid we have chosen kalium- nitrate as source of nitrogen. As well, however, kaliumnitrite or some anorganic ammonium salt may be used. Very good results were obtained with: Distilled water 100 Ammonium sulphate (or NH, Cl) 0.01—0.1 Dikalinmphosphate 0.02 “Mineral solution” 1 drop and with: Distilled water 100 Kaliumnitrite 0.01—O.1 Dikaliumphosphate 0.02 “Mineral solution” 1 drop. As both these liquids answer to the conditions of life of the microbes of nitrification, the formation of nitrite or nitrate is actually to be observed when using them, and when inoculating with garden-soil or with crude cultures. With the easily produced pure cultures ( 401 } of B. oligocarbophilus, of which more below, a good development of the film is possible, by which experiment it can at the same time be proved, that this microbe itself does not nitrify. Hence, ammonium salts or nitrites, added to excess can, even for a year or longer, continue unchanged under the luxuriantly growing pellicle of B. oligocarbophilus, whereas, in the presence of nitrifying ferments, they completely disappear in a few weeks, being then found back as mitrates. If the ferments of nitrification alone are present, there is no question of film-formation and the nutrient solutions remain perfectly clear. Not only the nature of the nitrogen-furnishing substances, but also their quantity can in these experiments, as already inferred in’ the recipes, vary between fairly wide limits, and the same may be said concerning the conditions for the water culture of higher and lower green plants. The limits allowable for B. oligocarbophilus, have not yet been precisely fixed, but they certainly have a broader range for this organism (circa O.1—10° pro mille) than for the higher plants (0.5—5 pro mille). By many experiments if was established, that in absence of kalium, phosphor, and magnesium, a still shehter growth occurs, than when no nitrogen compounds are given. Evidently 2. oligocarbophilus tinds in the almosphere, in a condition fit for nutrition, a quantity of nitrogen, which, although insufficient, should not be overlooked. If the distilled water in the artificial solution is replaced by tap-water, a somewhat higher rate of organic substance is produced. As in tap- water a small quantity of nitrogen compounds occur, — here, at Delft, about O.4 milligrams of combined nitrogen per litre, Whilst it contains the other necessary elements (phosphor and kalium, of course, excepted) in an obviously favorable form for the nutrition of our mikrobe, one can simply use for its culture: Tap-water 100 Dikaliumphosphate — 0.02. It should, however, be kept in view, that the productivity in bac- terial substance, in consequence of the film formation, is not deter- mined by the volume, but chiefly by the extent of the surface of the medium, which is in free contact with the air. Henee, in a very thin layer of ‘ap-water, the nitrogen may soon be consumed, whereas, with fee same amount of nutrient liquid, but with asmaller surface, corsequently in a thicker layer, the provision of nitrogen will suffice for a longer time. Therefore, in order to obtain from a flask of determined size, the maximum production of 2. oligocarbophilus, a © 402 ) nitrogen compound should be added when a small quantity of tap- water is used, which addition is not necessary when cultivating im a greater quantity in a flask of the same size. 3. PURE CULTURE. Our bacterium does not grow at all or only to a slight extent on the commonly used bacteriological media, these containing too much organic food. But it is easy to produce pure cultures on solid media, when observing the same precautions which I deseribed in the Meeting of the Academy of 27 June 1892 for the pure culture of the ferments of. nitrification on agar-plates*), and to which I referred in the Meetings of 30 March 1901 (Proceedings p. 586) and 25 May 1901 (Proceedings p. 5) when discussing the culture condi- tions of the oligonitrophilous Cyanophyceae. In all these cases it is necessary as completely as possible to remove all soluble organic substances from the solid medium, which is to be effected by a prolonged washing with distilled water. The agar thus prepared, with the required nutrient salts, for instance in the proportion : Distilled water L100 Agar 1.5 K HPO, 0.01 KNO, (of NH,CI O.0O1 is boiled and plated, and used for strew-or streakcultures originating from a film of B. oligocarbophilus. Very soon the common saprophytic bacteria which never lack in the film, are seen to develop on the plate and when these by their growth and respiration have consumed the soluble carbon compounds, which were not yet removed from the agar by the extraction with water, 4. oligocarbophilus itself begins to grow. This is usually the case after 14 days. Then, however, the colonies become easily recognisable, our bacterium being the only species which in the given circumstances can feed on the atmospheric carbon, and so go on growing, whilst the growth of all other species soon comes to a stop. Even the colonies of the nitrifving ferments, which, as I have demonstrated before (1. ¢.), can grow fairly well on this medium, when instead of nitrate an ammonium salt is used, remain very small, never exceeding 1 mM. or less. On the other hand, the colonies of B. oligocarbophilus attain dimensions of 1 ¢M. and more and may then easily be transferred in a pure condition into test-tubes 1) Nature, Vol. 46, pag. 264, 1892. ( 403 ) on the said medium. They grow on the agar as thin, snow-white or rosy-tinted, very dry, flatly extended layers, which strongly remind of the pellicle floating on the liquid. Also on silica plates, prepared in glass dishes, which, after extraction of the chlorides are soaked with a nutrient solution, 2b. oligocarbophilus can produce yery fine cultures, appearing after some weeks, as snowwhite colonies with indented margin, and which by a right selection of the salts, can finally spread over the whole plate. Then the remarkable phenomenon is observed, that the silica liquefies a little in the centre of the colonies and sinks in by evaporation. The silica plates are made as follows. A commercial solution of potassium silicate, diluted with a known quantity of water, is titrated with normal hydrochloric acid. As the solidification is much favoured by an alkaline reaction, a complete neutralisation at the preparation of the plate should not occur, and as a plate, with a high percent- age of silica, contracts strongly after coagulation, and expresses much water, the dilution must be sufficient for this contraction to be delayed. Into a small beaker-glass was introduced, in a certain case, 5 cM* of potassium silicate diluted with 25 cM* of water, and into a second glass the required quantity of hydrochloric acid, amounting to 10 cM* of normal acid. The acid is mixed with the diluted silicate and the mixture poured into a glass dish. The solidification delays the longer as the mass is more diluted, but it is easy, after some practice, to make very solid plates. The plate is first freed from the chlorides by streaming tap-water, then washed out with boiled water, and afterwards treated with the solution of nutrient salts. When these have sufficiently diffused into the plate, the glass dish is gently warmed at the underside, until the adhering water has evaporated and the plate shows a “dry”, glossy surface. The surface is flamed in the Bunspy-burner, by which only a partly but sufficient sterilisation is to be attained. Not only B. oligocarbophilus, but also the ferments of nitrification grow on this medium very well. By mixing of the diluted solution of the silicate with chalk, magnesium carbonate, or ammonium- magnesium phosphate, snow-white plates may be obtained, which are particularly fit for the culture as well of all these microbes as of several lower algae. Even earth-diatoms, of the genus Nitzschia will grow thereon. Once more it must be observed, that in the silica plates organic substances must be absent, even fragments of cork, fallen into the silicate solution, may disturb the experiment. The pure cultures, obtained on agar or silica plates, are as well fit 404 ) for the further experiments on liquid media as the erude cultures, of which many experiments, continued for years, have convinced us. Every thought of symbiotic relations on which the carbon assimilation by our bacterium might repose is thereby excluded, so that at least the biological side of this part of our problem is clear. Concerning the further properties of our bacterium in pure cultures, we can be brief. In the films, as well as on in the colonies on the solid) media, it) consists of minute, thin and short rodlets, probably always immobile. They are ca. 0.5 4 wide and 0.5-—4 4 long. The length however is) very variable and frequently particles are seen O.5 a wide and 0.7 —Ilu long. Often, when not using reagents, such as dyeing substances or acids, no structure at all is to be observed, neither in’ the colonies nor in the flowing pellicle, but the bacteria at once become visible by staining the preparations. The thick cell- walls form the chief constituent of the colonies; albuminous matter is only present in a slight quantity in this bacterium. 4. THE NUTRITION WITH ATMOSPHERIC CARBON, A good appreciation of the carbon accumulation may be had as well by a direct weighing as by the permanganate method. For both determinations it is possible, to suck off the fluid, which is. practically free from bacteria, wholly or partly from beneath the film, so that the quantity of the culture material, destined for the filtration or the determination of the permanganate number, is not too voluminous, In our experiments there only resulted a precipitate of caleium- phosphate or calciumearbonate, when we had used our tap-water, which is rich in lime, and when kaliumphosphate to excess had been added. These precipitates can, however, be dissolved beneath as well as in the film by dilute acid, and then the acid can be expelled by further washing. The film is so dry and wetted with so much difficulty, that all these manipulations may be effected without much loss of material. The permanganate munber was determined after Kupeu’s*) method. In relation to the quantity of organic matter found by direct weighing or by the permanganate method and formed from the atmospheric carbon, the following should be well observed. As B. oligocarbophilus grows only on the free surface of the 1) Tremans-Gartyen’s Handbuch der Untersuchung der Wasser, 4e Aufl. pag. 255 1895. ( 405 ) medium, and not in the depth, the thickness of the layer of the nutrient solution and consequently its volume, is, as already observed, actually indifferent. That is to say, by enlarging the surface of the solution, a bacterial film of any dimensions is to be obtained, which circumstance is of importance for appreciating the productivity of a certain quantity of a nutrient solution, the more so as the thickness of the bacterial film is usually only one cell-layer. How very thin the required thickness of this layer can be, growth being still possible, may be derived from the fact, that, especially when using distilled water with nutrient salts, the film can mount at the appa- rently dry glass-wall from 1 to 1.5 decimeter high, and not seldom extends on it nearly to the cotton plug. Only in certain vinegar bacteria I observed the same. As it seems that our bacterium forms no compounds prejudicial to its growth, so the only circumstance, which governs its increase relatively to a given volume of liquid, provided its surface be of a sufficient extent, is the lack of one or more elements necessary for the nutrition. Carbon cannot be among the number, our experiments being made with free entrance of air. Although it is thus established, that only the number of bacteria, produced in a certain time per surface-unit, indicates the rate at which the atmospheric carbon is assimilated, we will yet give the quantities in relation to the volume of the solution, because then a comparison can be better made with the numbers found by other authors for polluted waters. 5. HOW MUCH CARBON IS ASSIMILATED. First we determined by an experiment, in which, after vigorous shaking, a culture was divided into two equal portions, how much one half contained at direct weighing, of bacterial substance, whereas the other half was titrated with kaliumpermanganate. We used for this a three months old culture on: Tap-water 100 Na, HPO, 0.02 KCl 0.02 KNO, 0.02 The film from the part, destined for the weighing, was separated trom the liquid by filtration, washed out on the filter with strongly diluted hydrochloric acid, and subsequently with distilled water, to remove the chlorids. Subsequently the filter with the film was 27 Proceedings Royal Acad. Amsterdam. Vol. VY. 406) dried, first at 40°—50° C. and then at 100° C., until the weight remained constant. So we found that per litre 180 milligrams of bacterial matter were produced, and that, after deduction of 14 milligrams, used by a litre of our tap-water itself, the corresponding permanganate number was 94. We can thus, with an accuracy sufficient for our purpose, accept that the relation between the two figures is as 2:1, that is to say, that the doubling of the permanganate number gives the weight of the dry bacterial substance, and, as this latter number is much more quickly to be found than the weight, we have contented ourselves with it in most of our further determinations. We shall now give some more figures. Like the preceding they all relate to bacterial films produced in Ertenmeyer-flasks on 100 ¢M?’. liquid with a free liquid-surface of about 80 cM?, By weighing we found in one case on: Tap-water 100 KCI 0.02 KNO, 0.02 K, HPO, 0.04 after 5 months’ culture 235 milligrams per litre. On: Distilled water 100 KCl 0.02 KNO, 01 K, HPO, 0.02 ‘Mineral solution” 1 drop after 5 months 220 milligrams per litre. Some numbers, found by the permanganate method follow, and in the first place some relating to tap-water. The greatest production which we had, was obtained with tap- water 0.02 K,HPO, and 0.02 KNO,, after a year’s culture and amounted to 250 mgrs. of permanganate per litre, nearly corresponding with 250 & 2 = 500 milligrams of dry bacterial substance. After a shorter time the production is likewise smaller; so we found in a culture on: Tap-water 100 Na, HPO, 0.02 KCl 0.02 K NO, 0.02 after 5 months’ culture (January to May) 202 mgrs. of permanganate, corresponding with 404 mers. of bacterial matter per litre. ( 407 ) If the tap-water was replaced by distilled water, the production of dry organic substance was commonly smaller, which cannot, how- ever, result from the nutrition by substances in the tap-water, oxidisable by kaliumpermanganate, for the 14 mgrs. of permanganate, which our tap-water consumed per litre, we found quantitatively back, at the end of the cultivation period, im the clear liquid beneath the pellicle of B. oligocarbophilus, which liquid can easily be sucked off with a pipette, without any considerable bacterial contamination. Moreover the experiments with distilled water have likewise exhibited ereat divergency in production, and though the cause has not been established with perfect certainty, we still think it probable, that these differences result from the greater or smaller density of the cotton plugs, by which the speed of air entrance is greatly influenced. We base this supposition on results obtained with flasks, only differing in the width of the mouths, and to which we shall refer later. It is furthermore certain that we have not to do here with the infection of other bacteria, or with monads, for the pure cultures displayed as considerable divergency as the crude ones. Neither can the chief cause be attributed to a change in percentage of the air in gaseous carbon compounds, the differences being observed simul- taneously in cultures placed side by side in the same locality. But we now give some further numbers. In an experiment with: Distilled water 100 K, HPO, 0.02 KNO, 04 KCl 0.01 “Mineral solution” 1 drop sterilised and inoculated with a pure culture of B. oligocarbophilus, were found, after 37 days’ cultivation (2 Jan.—19 Febr.) at 23° C., 66.6 mers. of permanganate, corresponding with circa 133 mers. of dry bacterial substance per litre. In another experiment with: Distilled water 100 Na, HPO, 0.02 KNO, 0.01 “Mineral solution” 1 drop likewise sterilised and after a culture of 40 days, at 23°C. the per- manganate number amounted to 60 mgs., corresponding with 120 mers. of dry bacterial matter per litre. ‘ 408 ) In a third case in: Distilled water 100 Kener O, 0.02 (NH,), SO, 0.02 Na, CO, 0.01 “Mineral solution” 2 drops after cultivating from 5 May to 1 Dee., 155 mgrs. of permanganate per litre were found. In a culture in: Distilled water 100 Na, HPO, 0.02 KCl 0.02 KNO, 0.02 “Mineral solution” 1 drop from 1 June to 1 Dee. we found 165.5 mers. of dry bacterial sub- stance, corresponding with ca. 83 mgrs. of permanganate per litre. As we see, the differences are considerable. When a little natrium acetate was added to the anorganic solution, and when using a pure culture for inoculation, we could neither state an augmenting nor a diminishing of growth. Thus we obtained in: Distilled water 100 KCl 0.02 KNO, OA Natriumacetate 0.02 K,HPO, 0.02 “Mineral solution” 1 drop by means of weighing, 220 mgrs. of dry bacterial substance per litre, corresponding with 110 mgrs. of permanganate, which figures are not exceedingly high and might likewise have been producedi n the same time (4 months) from the air alone, without acetate. In all these experiments with distilled water, the free surface of the liquid was also 80 cM?, and the air had to pass through a dense cotton plug, with which the Erteneyer-flasks were closed. Already before we drew attention to the importance of the way in which the flasks are closed; be here still mentioned that we made some special experiments, which proved that a very narrow opening of the flasks, slackens the growth of B. oligocarbophilus, so that years may go by before the film has vigorously developed. We could not, however, expected anything else, for the considerable volume of air, required for the growth of the said quantities of bacteria, can oniy very slowly diffuse inward and outward through the narrow canal. ( 409 ) 6. CARBONIC ACID CANNOT SERVE AS FOOD. Various experiments were made to establish what may be the volatile atmospheric carbon compound which renders the growth of B. oligocarbophilus possible. That it cannot be carbonic acid, whether free or combined, resulted from the following experiments. In closed culture-flasks with the best nutrient solutions, and arranged in such a way, that at times a little free carbonic acid mixed with pure air, could artificially be introduced, it was not possible to get any growth. This experiment, which seemed of particular interest, has been so frequently repeated, and so long continued under different conditions, that we consider it as quite certain, that free carbonic acid cannot serve for the nutrition of B. oligocarbophilus. For testing the influence of combined carbonic acid, cultures were made, iirstly in the following solution: Tap-water 100 Dikaliumphosphate 0.01 Kaliumnitrate 0.01 Natriumbicarbonate — 0.1 When cultivating at the free air surely a luxurious growth was obtained, but it Was by no means more vigorous than when the bicarbonate was left out. If in this liquid the nitrate was replaced by an ammonium salt, the result was quite the same. Secondly, the bicarbonate was replaced by common natrium car- bonate, the same quantities of the different salts being used. But in this case the action proved rather injurious than favorable. It is true that the film had become considerable after a few months, but it was directly to be seen that the growth was so much inferior to that of cultures obtained in the same circumstances but in absence of car- bonate, that the determination of the permanganate number seemed superfluous. Here, too, the replacing of nitrate by an ammonium salt or by a nitrite caused no change. As a remarkable fact it may be mentioned, that in these experi- ments, in our large flasks, containing a litre of air, the thin bacterial film mounted very high up the dry glass-wall, which is likewise often observed in the solutions made with distilled water, and may repose on the absence of dissolved lime salts. If the tap-water was substituted by distilled water, the addition of natrium carbonate did not cause an increase of bacterial growth either. We found, for instance, in: . i= 410» 4 Distilled water LOO K HPO, 0.02 ; (NH), SO, 0.02 Na,CO, O.1 “Mineral solution” 1 drop after 7 months (5 May—1 Dec.) 155 mgrs. of permanganate, corre- sponding with ca, 3800 mgrs. of dry bacterial substance per litre, which production is less than that, obtained in other cases under the same circumstances but without carbonate, so that here also, the action of the carbonate, the long time of cultivation being taken . into consideration, was not favorable. Quantities of carbonate, smaller than 0.1 ° The resulis of this examination can be thus summarised, that for the growth of B. oliyocarbophilus an atmospheric carbon compound is actually consumed, but that this cannot possibly be free carbonic acid. Furthermore, that also combined carbonic acid cannot serve for its nutrition. a were neither successful. oe 7. NATURE OF THE ASSIMILATED ATMOSPHERIC CARBON COMPOUND. “ If the carbonic acid of the air cannot be the food of B. oligo- carbophilus, what other atmospheric carbon source might then come into consideration? ~ It is clear, that we should think here of the carbon-containing component of the air, discovered in 1862 by the botanist Hermann Karsten '), and recently discovered anew by French experimenters, especially by Mr. Henrret*). It is true that the chemical nature of this substance has been hitherto unknown *), but yet it is certain that we have here to do with an easily oxidisable compound (or com- pounds), for a prolonged contact with alkali and air will already suffice to split off carbonic acid from it. Furthermore, according to the statement of the French investigator, the substance probably P contains nitrogen. This latter circumstance gives rise to the question whether this 1) H. Karstey. Zur Kenntniss des Verwesungsprocesses. Poggendorff's Annalen Bd. 191, pag. 343. 1862. To this place, as also to the not unimportant older literature on the carbon compound of the air, my attention was drawn by Mr. G. van ITerson. *) Comptes Rendus T. 135, pag. 89 et 101. 1902. 8) Heyriet thinks that the substance must be a monosubstituted formamid with the formula HCO.NHR, where R represents a still unknown alkylrest. But then it is not easy to understand, why the production of carbonic acid takes place so readily. It might then rather be expected that, with an alkali a formiate would , ; result and no carbonate. ( 441 ) nitrogen, like the carbon, is fit for assimilation by our microbe. Though this question has already partly been answered in the negative by the preceding experiments, it should still be remarked here that in nutrient liquids, without an expressly added nitrogen compound, for instance in: Distilled water 100 Kee Oe 0.02 Mg, 5, Mn, Fe traces. Or still better in: Tap-water 100 KH, 0.02 without any further addition, a not inconsiderable growth of B. oligo- carbophilus may occur, so that at least traces of an assimilable nitrogen compound may be drawn from the air by this bacterium, whereas, for the possibility of assimilation of the free atmospheric nitrogen no indications were found. We now turn to another question, which the assimilation of the atmospheric carbon gives rise to, namely: How great is the quantity of the volatile substance wanted for the formation of the bacterial film produced in our cultures? This question is closely connected with the following: How much of the compound is moreover consumed by the respiration of our bacterium, escaping as free carbonic acid? For answering these questions we have to measure the quantity of the carbonic acid corresponding with a determined weight of dry bacterial substance, granted that the carbon percentage of this sub- stance be known. Our experiments relating to the measurement of the quantity of carbonic acid produced, are not yet closed, but as to the first part of the question, we give the following calculation to tix the volume of air wanted for the production of the carbon, actually accu- mulated in the bacterial films. We hereby make two chemical suppositions which, to be sure, are fairly well in accordance with truth. First, we admit that the carbon, freed from the unkown compound, as carbonic acid by a prolonged contact with alkali, is consumed quantitatively by our bacterium and, secondly, that the bulk of the bacterial cells consists of a substance possessing nearly the composition of cellulose *). 1) If accepting that the composition of the bacterial cells corresponds with that of albummous substances, then, instead of 449/)C., 52 to 55°/, C. should be brought into account, and in this proportion the volume of the air should be augmented. ( 412 ) Let us now consider the case when, in */, litre-flask with 100 eM’, of fluid and a free surface of 80 cM’, after a month's culture a quantity of 20° megrs. of dry bacterial substance is formed, which, calculated as cellulose, contains 44 °/, C.; we then find in the 20 mers. of dry matter 8.8 mers. of carbon. According to Henrie the atmos- pheric carbon compound, present in a certain quantity of air, under prolonged action of alkali, gives out as much carbonie acid as oceurs already in a free state in the same volume of air, that is per litre 0.35 ¢M?.= 0.6 mers., in which 0.163 mers. of carbon are present. Thus, for 8.8 mers. are wanted 55 litres of air. Consequently, in the course of a month these 55 litres of air must have diffused through the cotton plug inward and outward of our */, litre-flasks, in order to produce the found quantity of carbon, that is 76 cM*. hourly. Though this figure should not be considered a priori as impossible, it still appears to be very high, and the difficulty of accepting it increases, if still the addition has to be made of a yet unknown, but apparently considerable amount consumed for the bacterial respiration, which, as remarked above, seems necessary. We therefore think that it must be admitted that the quantity of the atmospheric compound (or compounds) assimilable by B. oligecarbophilus, is much larger in our laboratory atmosphere, than in that of the Paris boulevard, analysed by Henrretr, and that we have here: to do with an extremely variable factor. The circumstance, too, that we have not as yet been able in our greenhouse, where the air, in the common sense of the word, is surely much purer than in the laboratory, to obtain a vigorous growth of BL. olgocarhophilus pleads for this view. But here we could not always keep the temperature high enough, so that we consider our experiments in this direction not yet closed. Besides, we should observe, that in an empty, isolated room of the laboratory, the quantities of combined carbon drawn from the air, were as great, or only little less than in the laboratory itself. where the air was certainly impurer. We are accordingly conscious that further experiments, with fresh atmospheric air are wanted to decide, whether the carbon compound occurs in the atmosphere in a constant or in a varying percentage. Only thereby it will be possible to ascertain the distribution of this compound, by which, at the same time, the signification of B. oligo- carbophilus i nature will become clearer. As to this signification, the question arises whether our microbe in substrata containing sufficient mineral nutrients (N, P, K, Mg, S, Fe, Mn), but being poor in organic substances, is able to build up the latter in the dark from the volatile carbon compounds oceurring in the ( 413 ) atmosphere of the surrounding medium. And furthermore, whether carbon nutrition takes place exclusively in the floating dry films, — hence, in the earth, only on the relatively dry surface of the earth particles, — or that also in the depth of fluids growth and carbon assimilation be possible. The hitherto gathered experience about the self-purification of rivers and the biological purification of water in general, seems to exclude the latter hypothesis, and our own experiments too, render it not probable. The result of these experiments consists, in our opinion, in the very discovery of a microbe, which, in consequence of the film-formation, has the spe- cific faculty, to absorb for its nutrition and multiplication, from a gas, namely the air, traces of volatile carbon compounds, by which the struggle for existence with the rest of the microbic world can be successfully sustained. The biological purification of water would, according to this view, find a counterpart in the biological purifie- ation of the air by Bacillus oligocarbovhilus 2 . . é , . . Physics. — “The calculation of — from the magnetic rotation of mm the plane of polarisation, for substances without an absorption hand in the visihle spectrum.’ By Dr. lL. H. Strtsema. (Com- munication No. 82 from the Physical Laboratory at Leiden by Prof. H. KAmmErLINGH ONNES). Starting from Firzgeraip’s') simple explanation of the magnetic rotation of the plane of polarisation derived from the Zeeman effect, and also from the supposition that the result of the magnetic force is only shown by the displacement of the dispersion curve of the medium (7=/ (a) ) over a distance d, Hatno *) finds for the magnetic rotation @ Where 2 represents the thickness of the medium. HaLLo’s investigations are concerned with the parts of the spectrum in the neighbourhood of an absorption band and for these we are justified in making the above supposition, as appears from a formula derived by Vorer ') Firzeeratp. Proc. Roy. Soc. 63 p. 31. *) Hato. Diss. Amsterdam 1902, p. 7. ( 414 ) from a more rigorous theory’). If, however we want to apply it to points at a greater distance from an absorption band, as is the case with the magnetic rotation of transparent substances, we must turn io Voier’s more general formula * De ent a &, 0 (» —9#taR ®) (9°— 9) + o, R9)* + 94 9 If we may assume that only one term occurs under the summa- tion in the second member, and also that ¢,/ and %,' are small compared with &, a simple reduction shows that the new dispersion curve may be derived from the original one by moving each point oe over a distance ‘/,e, —, which depends on % and hence also ov on the wave-length. In this case Hatio’s relation will hold, if d is not supposed constant, but proportional to 2’. Though it is uncertain whether for a given transparent substance we are entitled to accept the formula for # with only one term under the summation, we may investigate to what results this would lead. From the elementary theory of the Zeeman effect it follows that Che i bf he i : m Aa whence for the displacement of the dispersion curve tea ee e AT Vipas a. HF mecnere mame as Eon) ge This value has been derived for the absorption band. From the above considerations it follows, however, that we may apply it for each wave-length, and hence we find 2% e ae tdn e ’ dn ze 1 = — 2H —— —., 2 m AxV di m2V di 2 lan @ =— Whence follows for the rotation constant @ = = e Aa dn 0 5 == SS > om. Daa which formula corresponds with one, given by Vorer*), if we replace the & occurring there by: 1 a ke 2 1) Voret. Wied. Ann. 67 p. 351. 2) Vorer. Wied. Ann. 67 p. 349. 3) Voter. Wied. Ann. 67 p. 351. which value may also be derived directly, if we equate the magnetic . 1 ; : : : displacement 5 Ch R after Vorar with that resulting from the elemen- tary theory. The dispersion of the magnetic rotation expressed by this formula is the same as that resulting from BrcoquErEL’s *) relation and found by him to be confirmed in the case of carbon disulphide and creosote. . . . é The relation found for g enables us to compute — as soon as we mm : ‘ hp constant @ and the dispersion Z of a substance an know the rotation for the same wavelength 2. For we have —-= o—. m A hp We shall make the calculation for some substances at a value of 4=589 we. The rotation constants 7 being usually expressed in minutes we have 2a wee, == - : = 3 360 X 60 and hence we find > 9 Ve é va. 10 22 i ible Stace ay at Garey Oa ceals yy 5 (Sin) 589 360 X< 60 dn dn mm D03.10—*, PERRBAU °) teen LOOSKG 20.3.0). finds for the refractive index at (1 atm., 0° C.) A= 644, n—np = 85.10—8 538 88.10—§ I have found 2) 7 < 10%, on an average 0.61 10°. dd whence = 0.65 10° and 0.58 an Supposing “—1 proportional to the density, it follows that for air (100 kilogram, 13°.0 ©.) di/dn = 0.648 10° and we find: < 103 1) BecquereL. C. R. 125 p. 679. *) Stertsema. Comm. Lab. Leilen. Suppl. N°. 1, p.&6; Arch. Néerl. (2) 2 p. 376 5) Perreau. Ann. de Ch. et de Ph. (7) 7 p- 289, ( 416 ) * — 0.89 >< 10°. m 3. Hydrogen (85.0 Kilogram, 9°.5 ©.) Y= 456) Soau da/dn (1 atm., 0° C. == ALOF (85.0 KG,, 9°.5 C.) = 1.31 & 10°, — = 1.77 >< 10". Vit 4. Water. From refractive indices of Durer‘) and the magnetic rotation constant O".OL30 we get “ — 1.25 107, mn 5. Carbon disulphide. In the same way with + = 0.042 we find from VAN pER WILLIGEN’s 7) refractive indices “ = 0,745 X< 107. m ‘ 6. Quartz. r=0.01684 *). By means of VAN DER WILLIGEN’s refrac- tive indices we find © = 1.25 >< 107. Mt e a It may be remarked that the values of — found here correspond m in order of magnitude with those found in other ways. 1) Durer. Bull. Soc. Minér. 8 p. 218. *) V. vp. Wituieen. Arch. Mus. Teyler III. 1. p. 55. 5) Bonet, C. R. 128, p. 1095. (January 24, 1903). KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday January 31, 1903. ————DOC— = (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 31 Januari 1903, DI. XI). (S (©) any Gata ANT BE Se A. Smuts and L. K. Worre: “The velocity of transformation of Carbon monoxide”. (Com- municated by Prof. H. W. Bakuvis Roozenoom), p. 417. J. J. vay Laan: “The course of the melting-point-line of solid alloys or amalgams”. (First communication). (Communicated by Prof H. W. Bakuvis Roozrsoom), p. 424. J. J. VAN Lar: “On the potential-difference, which oceurs at the surface of contact of two different non-miscible liquids, in which a dissolved electrolyte has distributed itself”, (Cont municated by Prof. 1. W. Bakivis Roozenoom), p. 431. : J. J. Harro: “The value of some magneto-optic constants”. (Communicated by Prof. P. ZEEMAN) p. 438. j jolt: A. Werte SALOMONSON : “A new law concerning the relation between stimulus and effect”, (V). (Communicated by Prof. C. Wiykier), p. 441. c ye Plainoints ne : Te ; PD. J. Kortewec: “Plaitpoints and corresponding plaits in the neighbourhood of the sides of the ¢J-surface of vAN pER Waats”, p. 445. (With one plate). AS H. Sinks: Some: remarkable phenomena, concerning the electric cireuit in clectrolytes”. (Communicated by Prof. H. A. Lorentz), p. 465. i The following papers were read: Chemistry. — ‘The velocity of transformation of Carbon monowide.” By Dr. A. Sirs and L. K. Wonrr. (Communicated by Prof. H. W. Bakuuts Roozesoom). (Communicated in the meeting of December 27, 1902). From the researches of Boubov Arb!) > equilibrium 2COSCC ) parch oe UbDOUARD') on the equilibrium 2¢ OSCO,+C, where use was made of the accelerating action of the metals Ni, Co, Fe, it follows that they do not modify the equilibrium but only ') Ann. de Chimie et de Physique [7] 24, p. 5 (1901). \ 28 Proceedings Royal Acad. Amsterdam. Vol. V. ( 418 exercise an influence on the velocity and are, therefore, catalyzers. It was shown by Bovupouxrp that, whilst CO, in contact with © is practically totally converted at L000" into CO, the amount of CO, in the gaseous mixture in equilibrium increases at lower temperatures in accordance with the sign of the heateffeet CO,+C=2C0—42000 eal. until at 445° the CO is practically completely converted into CO, and C. From this follows that below 445°, CO- exists in a metastable condition, INVESTIGATION, “a. Preparation of the catalyzer and preliminary experiments. lL. The following research was instituted with the object of determining velocities of reaction in the metastable region in presence of a catalyzer. The apparatus employed by us was in the main the same as that used by vant Horr in his research on the velocity of transformation of detonating gas into water. The reaction vessel, however, was filled with a catalyzer obtained in the following manner, Pumice stone was broken up into small lumps, drenched with a solution of Ni(NO,), then dried, ignited and finally reduced in a current of hydrogen or carbon monoxide. This reduction, it was observed, takes place in two stages. The grevish-black surface of NiO: first turns yellow owing to the formation of a suboxide (Ni, OF)') and afterwards on complete reduction again becomes dark-grey. When operating at a high temperature, reduction with H, or CO. gives apparently, the same material. If, however, the reduction takes place in a current of CO at 445° a layer of carbon is deposited on the reduced nickel. 2. The experiments with nickel-pumice obtained by reduction with either H, or CO at a igh temperature gave the following result ?). At 310° (boiling point of diphenylamine) the activity of the catalyzer did not appear constant. Successive fillings continually gave smaller diminutions of pressure in the same length of time. 1) Mitier, Bell (Chemical News 20, 258). *) Coating the inner wall of the reaction vessel with nickel did not appear to affect the result, probably because the surface of the glass wall was very small as compared with the surface of the catalyzer. ( 419 ) We found for instance : el Ome Diminution I\lling. in mM. He. during 10 minutes, —— Ist 5,68 2nd 5,00 3rd 3,80 ect. As we suspected that the retrogression of the activity of the eatalyzer was due to the ever increasing layer of C, which deposits on the catalyzer during the experiment and fillings, we next used a nickel-pumice which had been reduced at 445° and was in consequence already coated with a layer of carbon, Although at first there was still a perceptible diminution in the activity, the differences in’ sue- cessive fillings become gradually smaller and finally, the activity ‘ ie ; Was constant as seen from the following table: 31 (0); Diminution Filling. in mM. He. during 10 minutes. Ast 1,88 2nd 1,80 3rd 1,78 4th 1,74 Sth 1,75 6th - 1,74 7th 1,74 Being satisfied with this result, we started our investigation with the catalyzer of constant activity obtained in this way. bh. Measurements concerning the order of the reaction. For the determination of the order of the reaction the method of van “t Horr was first of all applied. It is given in this case by the equation: Aoher =) loa = 5 ‘ ( (One ihe 2 = SS log (¢, = €,) 28% ( 420 ) The determination was made at 310°, In the first experiment the pressure of the CO) was 786,8 mm. He at the commencement; after 80 minutes the pressure amounted to 739.9 mm. He. The diminution of pressure in 80 minutes there- fore amounted to 46,9 mm. Hg. de : J F If we take for the diminution of pressure per minute then dt de ~s becomes 1,56. at In the second experiment the pressure of the CO) was 5385.3 mm. Hg at the commencement and after 30 minutes the pressure had come down to 501,7 mm. Hg. Here, the diminution of pressure de in 380 minutes amounted, therefore, to 33,6 mm. He or 7 = fies ( C,=aver. of press. at beginn. and end at the 1st experim.=763,35mm. Hg. OR PTY 9 Pk ” noe ny 2d py —= 00,0 a et If from this we caleulate 7, we find n = 0,86, from which it is apparent that the reaction is a monomolecular one. In order to make more certain of this, the order of the reaction was also determined at two other temperatures according to the method given by Noyes. In this case 7 is calculated from the following formula: t log— t, A oo —.— Cy log C, in which ¢, and ¢, are the times during which the same part of the original quantity is converted when starting from different concen- trations c, and ¢,. At 256° we obtained the following result: At 256 g ( 421 ) The observations at the three temperatures 256°, 310° and 340°, therefore lead to the conclusion that we are really dealing here with a monomolecular reaction. c. Determination of the reaction-constant at 256°, 310°, 340°. These determinations were conducted with the same reaction vessel and the same catalyzer. 256° (boiling point of amyl! benzoate). Time in minutes. | Pressure 1 5 =a in k= log— | Dies I 2, mm. He a 0 761.0 — 5 0 758.9 0 OO0464 10 TET 8 0.000381 10 756.4 0 000987 20 754.4 0.000276 30 Tse | 0.000277 AO 749.3 0.000278 average 0.000279 The following may serve to elucidate this table: At 256° the catalyzer seemed to. still perceptibly absorb the CO, which caused the diminution of pressure during the first 5 minutes to be excessive. The values for / are, therefore, not constant when we start from the pressure corresponding with the time O, but they gradually diminish which may be seen from the first two figures in the last column of the table. To eliminate the error caused by absorp- tion, we have, when calculating /, started from the pressure corre- sponding with the time 5 minutes (column 2) and, therefore, have called this pressure P,. As the CO) concentration had diminished very little in 5 minutes the error thus introduced could be disregarded. The values obtained for / ave found in the last column beneath the dotted line. The following table relates to the temperature 310°. 49 310° (boiling point of diphenylamine Pressure | P Time in minutes in mom, Hy ee 0 786.8 10 769.8 0.00192 A) 754.8 0.00184 30 739.9 | 0.00184 40 725.6 : 0.00184 average 0.00186 As was to be expected, the absorption at this high temperature was scarcely perceptible and in the following table, which shows the results obtained at 340°, no absorption whatever was noticed. 340° (boiling point of phenantrene) Pressure 1 P Time in minutes in — mm. He 0 791.4 10 7TAGA 0.0524 20) 7035.9 O.CO0527 30 668 7 000536 50 612.7 0.00521 average 0.00527 In order to make sure that the activity of the catalyzer had not diminished during these three series, a series of experiments was finally taken at 310° with the following result. | Pressure 1 P, Time in minutes in k= — log a mm. He 0 805.5 10 788.3 | 0.00189 20 leeet23-0) | 0.00183 30 | 757.8 | 0.00182 40 | 742.8 | 0.00184 average 0.00184 The activity of the catalyzer had, therefore, undergone during these measurements, so that we were justified in the temperature-coefficient from the results obtained. The as follows: | Kitio Temperature. k | _ = t 256° 0.000279 S 1,4 310° 0.00186 her } 1,4 340° 0.00527 d. Mechanism of the reaction. no change calculating result was What idea are we to form about the mechanism of the reaction if this takes a monomolecular course 2 If we assume the formation of Ni(CO), with an immeasurably large velocity and the subsequent breaking up of this according to the equation Ni (CO), = Ni+2C0, +2C we must also accept the equilibrium Ni (CO), S Ni+4CO of which the constant is given by the equation: K= i Nico), compound This would then necessarily lead to the conclusion, that the velocity 424 of reaction should be proportional to the 4 power of the CO-con-° centration whereas if appears to be proportional to the 1" power of the CO-concentration. Rejecting this hypothesis two further sup- positions remain. Firstly : l. CO C+ 0 (with measurable velocity) IH. CO+ 0 = CO, (with unmeasurable velocity). Secondly : I CO+Ni=C+Ni0 I. CO + NiO = CO, + Ni. In the last case it need not be assumed that one of these reactions takes place with tmmeasurable velocity, but only that the second one proceeds more rapidly than the first. As regards the nature of the catalyzer we think we may conclude from the result of several experiments, that it is not the carbon but the finely divided nickel which possesses the catalytic action. Amsterdam, Chem. Lab. University. Dee. 1902. Chemistry. — Professor Bakuuis Roozesoom presents a communica- tion from Dr. J. J. vay Laar on: “The course of the melting- point-lines of solid alloys or amalgams.” (First Communication). (Communicated in the meeting of December 27, 1902). 1. In the researches of vAN Hereren*) on Tinamalgams a mel- tingpoint-line occurs *) of a kind, which has not as yet been studied over such an extended course (from 0 to nearly 100 atom °/, of mercury). This is chiefly due to the fact, that the temperatures of fusion of the 38.6°. In consequence the meltingpoint-line of the tin meets that of the mercury practically at 100 atom °/, mer- {g=282° j os Hr two metals are so very different; tin 231°, mercury cury, so that the meltingpoint- line of the mercury has not even been observed. We therefore see for the first time a melting- mercury tin point-line in its full course, and the question arises whether the course, found by van HETEREN, may be predicted theoretically. The answer to this is in the 4 affirmative. Let us, to start r=1 r=0 with, take the most simple view Fig. I. as regards the molecular poten- 1) Dissertation 1902. (also Report Meeting 29 Noy. 1902), 2) lc. pg. 18. tials mw of the tin as solid substance and «, of the tin in the liquid amalgam, namely that uUmee-—e if | ee Riana). 2+ tog, DD In this it has been assumed, firstly that the tin, crystallised from the amalgam, does not consist of mixed crystals, but of pure tin — a suppo- sition, which has been proved by experiment to be nearly correet — and secondly, that the energy-quantity e is no function of «. Later on we will drop this last simplified supposition, and demonstrate, that au more accurate calculation of the function gt, affects the course of the meltingpoint-lines quantitatively, but not qualitatively. Then it is our object to demonstrate at once, that the entire qualitative course, as represented in the figure, follows from the equations (1) in con- nection with the course of the logarithmic function of 1—w. By putting the two potentials equal to each other, we obtain: (e, — e) — (ec, —¢) T = — RT log (1—2), or calling e, —e=q (the heat of fusion of the solid tin, when passing into the amalgam), and the quantity ¢,—c = q — yf = — RT log (1—2), from which follows: oy LL ee Ue y—R log (1—z) This is then the most simple form of the meltingpoint-line. On introducing the temperature of fusion of pure tin 7’,, 2 becomes O, and we obtain: eee Y so that we may also write: gal Te LE ERT Ee wake Pate 1 — —— log (1—2) : qd ms : esl if we abbreviate —— to 0. q We notice at onee, that on the development of the logarithmic function, the formula, for very small values of wv, passes into ryy 4p! E> eh a oe Re 1+ Eo q 426 ) feat, that is to say into fis ft 2; ‘4 the ordinary formula of vax ‘tr Hore for extremely dilute solutions, If, however, the solutions are no longer extremely dilute, we can no longer be satisfied with one or two terms in the development of log A—w), but log 1—) must remain. I will now show, that the approximative relation a | hemp : 1—@ log (1—.r) d7 gives indeed the observed course qualitatively. For we find: a dT cp 0 da (i—d log (1—«))? ee Whilst 7’ itself, for «=O, passes into 7’ o? and for «= 1 into 7’ = 0, which already agrees with the steadily declining course — it eecar: appears from —-, that this quantity, for «=O, becomes: ae dT é RT, —}/ => -7d0=——, ty da Py q the limiting value of van *r Horr, whilst for uw=1 it passes into —a. It may now still be asked, whether there will be a point of inflection or not. In the case, examined by van HerereN, a point of inflection plainly occurred at about « = 0.8, but it may also be possible, that the course was like the one in the following figure, without point of inflection. Let us therefore determine | LT Fig. 2. dix? LT 2T, “ Ty Te OF Oe dz? (1—Olog (1—«))? (l—a)? N? (1—2)? - N? =a)? | WN “4; Evidently “—_ —(), when 20 = N, that is to say, when ar 1—J@ log (1—wx) = 20 log (1—«) = 2 — 0) SS | SS : 0 As 0=—— will be positive, we see, that the point of inflection can 7 1 only occur if @ is situated between '/, and «. For d='*/,,7=0; for O0= ex we find on the other hand «= 0.865. A point of inflection further than «= 0.865 can only occur with negative values for 7 G=—o till 0=0; when «= 0.865 till «=1). But there is no point of inflection if O <'*/,, that is to say, if Geo T Go ALL... In our case therefore, where 7, = 505 — when ¢g > 2000 eram-eals. or in gram-eals. 0 This last conclusion will however be modified, when we apply the necessary correction to the approximate formula (3). But the fact of the possible occurrence of a point of inflection may already be completely explained by the simple formula (3), and this by the course of the function fog (L—2). Il. We now proceed to write down a more stringent relation than (8). Assuming an equation of condition of the van pur Waans’s kind, the value of w, (the molecular potential of the component 7,) becomes as follows: = — 4h, T (log T—1) — RT (log (V—0) — 1) + (2 -- )) - Sie | 0 hh Sq, +0, 4,+-.)4+RTlogn . . . . For 6 has been written: Diet) Ohe SUps Skeier whilst for a@ the quadratic relation = 0N> Whe SeWAlln We Une a Oe has been taken. Now, log (V—+) can be supposed to be independent of «, whilst the expression Pie hod f, 2 RT 2 Vos 1 Sp tn hs) = aay b,— =e — x)a,,+-wxa,,) in regard to 7 will become not of the order.7, but of 2. Let us, to prove this, rather start from a more general expression for the total poten- tial § (in our case we have only to deal with two single components nm, and 7,), namely = Wat sn aad ni U jue) ei, pe N, + 2, + RT (" log Bint nC + n, og") b n +n, n,n, 428 We then find: EN 1 i Ande KM, = On, fy ~ (n, +n) xf | hy - on, Ny lly, + Ny Mss) 4 9 n i RT log —. t n +n, ~ (ny Hy, =F n 2 ly.) <3 af ETE With n, +2, =1, », =1— 7, 1, = we obtain: H,=(4,)o-[(1-2) "4, , + 21), + e+ Ley + eu, | UT log(1- a), or after simplification: ty = [ede + tad — 27 try — 2 tag # tas) + RT log (1 — 2). In analogy with (4) we may therefore write: Bp, =e, —¢, 7 4+ a, 27+ RT log (1—2). The terms with 7’ /oy T have not been taken into consideration, because they disappear on account of the equality of the quantities k and R in the liquid and in the solid phase. If, for the sake of a closer approximation, we take up some higher 1 powers of «, we finally get: (solid tin) oer ‘ (tin in liquid amalg.) #,=e,—¢, T+ (@,07+ 8," +y,2 Piri: (9) Equating, we then find as in § 1: q, —y T=— (a, +8, 2? + y, 2) — RT log (1—a), or pat +(4, wet Bix +724) (6) y—Rlog 1—~) The heat of fusion of the solid tin in the amalgam is now plainly : g=q.+ (¢,2° 4+ 8,0 +Yy, 27) 2°. Se (7) For «= 0, (6) passes into T c= pee ee sO we may again write: 1 a+ Bey ‘ q Tg ht eae Tet. 1 — — * log (1— w) To Parmiee ee or with ~ = «@, Bs aS ee ve To yi qo _ op LHe? +80 +724) 1—@ log (A—x) (8) and this is the more aeeurate formula, which has taken the place of the simple relation (3). Ill. We will now show, that the above formula quantitatively yields the values, found by van Hereren for 7’, in a satisfactory manner. dT , : As — (=) = T, 0,0 may be determined with great accuracy from A 0 the beginning course of the meltingpoint-line. From the values, found for 7’ (on pg. 16 of the dissertation) for “= Oatom'"/, of mercury (pure tin), .« = 0,1005, « = 0,1716 and 1 = 0,2338, the average value, IT j ie. obtained for — — is = 200. From the determinations of Huycock and Av Nevitie between «=O and w= 0,1 it also follows, that — — —= 200. AX For 7 we may therefore take (7, = 505): I ealenlated the values of @, 8 and y as follows: C0320 Se ep —— ey al. Formula (8) thus becomes: 140,825? —1,11a3+ 1,338.24) saa ~ 1—0,4log(A—z) and so we find the following values for 7’. : The agreement is as good as can be expected : the difference between the calculated value of 7’ and the observed value generally amounts to fractions of a degree, average O°,8; as regards to the absolute temperatures the deviation is only average 0,2 °/,. Only the two last values are too low (the last 3°/,), but then the influence of a small inaccuracy in the determination of the coefficients 6B and y makes itself strongly felt. If we except these two last values, the calculated meltingpoint-line fully coincides with the observed line in the scale of the figure in the dissertation. And by means of a slight alter- ation in the value of 8 and y we might perhaps cause the two last observations to agree. Let us not forget, that the formula (8) always remains an approximate one. In the last values of a the composition of the separated tin must also make its influence felt. For this is no longer pure tin but contains certainly 1°/,, or perhaps even 6°/, of mercury. As regards the value of ¢ (the heat of fusion of tin, when passing into DRIP MOA) EG ee = 2550 gram-cals. At 25° our formula is no longer available, as the amalgam) — when «= 0, q = q,, that is to say = ( 480 5 x oa - a — log(\-#) Numer, Denon. atin Se ——— O.1005 0.01018 0.00101 0.00019" O1059 10023 41,0424 249.4 21,6 0,8 O171G6 O0R948 0.0050 0.000893 OTSS83 10051 1,0753 108.0 1O8,6 03 0.2338 0,0546° 0,01278 00020") 0.2663 10076 11065 0 186,7 183,77?) 3,0? 0.2969 O,O881® 002617 0.00777" O523 10099 | 11409 173,8 17,0 0,8 OS856 OF487 0.0573" 0.02211 OAR72 LOU 11940 155,4 55,2 0,2 OSO00L O50) O1251 (0.0625 0.6933 1,0256 | 41,2773 | 4132.3 13:34 —4,1 05973 OBS68 | OBL 01273 0.9095 1,0488 3638) F15,2 15,2 0,0 O.6467 Of4182 0.2705 01749 10404 10682 41,4161 107,7 107,4 O38 0.6754 Of562 O08 O2O81 11252 10830 44501 104,0 103, 4 0,6 O,6813 04642 0.3162 02155 11435 10866 01,4574 103,35 102,4 0,9 07104 05047 0.3585 0.2547 12393 W047 14,4957 99,8 99,0 0,8 07155 05119 0.3663 0,2620 1,2570 11083 41,5028 99,2 98,8, 0,4 0,7477 | 0,5591 | 0,4480 0.3126 41,3772 14,1385 | 41,5509 95,9 95,4 | 0,5 0,7547 | 0,5696 | 0,4299 0.3244 1,4053 | 41,1393} 45621 95,1 94,0 3 Fy 0,7963 | 0,6341 | 0.5049 0,4021 10912 | 14,1805 41,6365 O14 90,0 | “Fp 0.8189 0.6706 05492 04497 14,7087 1,2064 | 41,6835 | 88,7 88,4 | 03 0,8921 | 0,7958 0,710 0,6333 2,2266 | 1,3128 | 41,8906 77,5 79,7, |—2,2 0,9483 0,8993 | 0,8528 0,8087 9.9693 | 1,4912 | 21849 | 55,3 according to up to about or that is to say the above 65,2 yj 9,9 table it only yields trustworthy values for 7 90°. At 90° «= 0,8, and then, according to (7), we have: | — Lo | 1 =i (a uv + ity x ai if w*], Y= J (1 4- 0.325 vw? — 1.11 2° 4 1.33 «*], q = 1.185 g, = 3020 eram-cals., whilst van Hereren (at 25°) found + 3000 gram cals, by means of electromotive measurements '). The concordance is absolute. We, finally, wish to remark, that according to the determinations of vaN Hereren and of Heycock and Nrvitin, regarding the lowering of the temperature of fusion of tin on adding small quantities of mercury, g, vist be = 2550 cals. We therefore see, that the value, assigned by Person, namely 14.25 & 118.5 = 1690 gram cals., is much too small. In a later communication | will show, that the heat of fusion of mercury, given by Person, is also many times too small. Dec. 1902. 1) Dissertation pg. 49. ( 434 ) Chemistry. — “On the potential-difference, which occurs at the surface of contact of tivo different non-miscible liquids, in which a dissolved electrolyte has distributed itself” By Dr. J.J. vAN Laar. (Communicated by Prof. H. W. Bakiurs RoozEBoom.) (Communicated in the meeting of December 27, 1902.) 1. It has already been demonstrated by Nernst) in 1892, that a potential-difference must occur at the surface of contact of two liquids, which lie together in layers, such as for instance water and phenol, on account of the unequal distribution of the neutral molecules and the Llons of a dissolved electrolyte. It is true, that his expression for the electromotive force relates to the case, that one of the two phases is a solid solution, but it will be perceived at once, that the sane formula also applies to our case *). There is, however, at present no prospect of obtaining direct measurements of this potential-difference *). But as Rigsenrenp *) has lately been experimenting on the subject, although in another direc- tion, it may be as well to give the exact theory of the phenomenon, which I worked out about a year ago, when engaged in writing a book on electro-chemistry, which will be published later. Suppose we have a solution of KCl in the solvents A, and A,. A, A, erat cil : KCl, CuK KCl, clk | If now equilibrium has been established between the non-dissociated, electrically neutrai portions of the dissolved KCI in the two phases, there need not be equilibrium between the /ons in the two solvents. Indeed, equating the thermodynamic potentials for equivalent quanti- ties of the non-dissociated portions in the two phases (equilibrinn of partition), we get: ee a a Meer, 5) (0) But the two dissociation-equilibria give: = -L ; = A= vice OIE! exch = Meo er, Cro, — Me, Me, (=) Consequently it will suffice if : = zi 3 SiG 4 0) a a a = 1) 1) Zeitschr. fiir Physik. Chemie 9, 13 2) Compare Riesenretp, Wied. Ann. ( 5) Tbidi; kf c: ‘) Nernysr und Riesenrerp, |. c. p. 600—G6OS8; Riesenrerp, 609—615 id. Inaug. Diss., Gottingen 1901; Hirrorr, Wied. Ann. (4) 9, 243—2 917 (1902). : 616—624; 45 (1902). ( 432 ) and it would be a sheer accident if we also had: ye — Uy + i= Mey There exists therefore as a rule no equilibrium of partition between the /ons in the two solvents. For example there may be in the second solvent relatively too few K-lons, too many Cl-lons. Since a system out of equilibrium tends to pass into a condition of equilibrium, K-lons from A, will migrate to A,, and remain there in the boundary-layer, while the corresponding liberated Cl-lons remain in the boundary-layer of A, (inversely Cl-lons will migrate from A, to A,, whilst the corresponding liberated K-lons remain in A,. Both add theniselves to the above mentioned similar ions in the boundary-layer). The consequence is the occurrence of an electrical doublelayer and therefore of a potential-difference. And it is this potential-difference, which will restore the originally non-existing equilibrium between the Tons. All this may be put into a very simple mathematical form. Let V, be the electrical potential of A,, Vy that of A,, so that 4= V,—V, represents the potential-difference at the boundary (in the case we are dealing with, 4 is therefore positive), then the formula for the equilibrium of the K-lons will be: He Uy i Bg, a Rae =: & which is at once obvious, when we consider the virtual passage from the left to the right over the boundary of such a quantity of K-Ions, that the quantity of electricity transported is de. As the quantities je relate to equira/ent-quantities, and as these do not cor- respond with one electric unit, but with ¢ (= 96530) electric units, He Ug must be divided by «. For the equilibrium of the Cl-lons we find in the same manner: Pate Foy Pes cy Vey — Ade=0. é The sign at 4 is now negative, because on account of the negative charge the change in the electrical energy is — 4 ¢e. We therefore obtain from the two relations, after dividing by de: * é That these two equations for 4 are not conflicting, is at once apparent. For the relation, resulting therefrom Oe nk As leads at once to (3). If we introduce: uw + RT loge, in which ¢ is the concentration of the Ions, we may also write: ecole RT log “RE ora ieee) 1, Ae tog CK ] i he (5) 1 Cell Ul ' ig Al 2 == eo RE log — me & (« Cls u cr) ieee eg Crete Il. Now everywhere ex =cc (only in the boundary-layer an excess of positive or negative Ions is present, owing to the for- mation of the doublelayer), therefore also Gig ECE CK, coy, and so we find‘) by addition of the two equations (5): i | 1 (es ' ae | oy (peas > ase c erate) ar Agent a Siesad Ginn u From this last relation it follows at once, that in di/ute solutions, where the quantities w are almost independent of the concentration, the potential-digference & will be also independent of the concentration. Whether much or little KCl is distributed through the two solvents, we will always notice about the same potential-difference A. If we deduct the two equations from each other instead of adding, d ‘ CN, Oh, then we obtain | observing that —~ = —— ]}: CK ca Ky Ch, Reolog | eae ies ta aaa (7) LOC == Le —= . . . mens 9 | 4 car cr, em aad G Ky If now we put Wee = RT log ie : (a) (Ge Hy = RT log ie | in which Ag and Ac are quantities, which depend on the nature of the two solvents (and which in dilute solutions will only be fune- fions of temperature) — they are the so-called partition-coefyficients of the positive and negative Ions — then (6) and (7) pass into Tid TGs <== log —— (6a) en! ae a K Cr 2 K (2) = Kk xX Ke x (7a) °K ') The formula (6) was given already, though with a somewhat different notation, by Lurner [Z. f. Ph. Gh. 19, 537 (1896)]. The first thermodynamic theory of the equilibrium of partition was given by me ina paper of 1895 (Z, f. Ph. Ch. 18, 264 —267). 29 Proceedings Royal Acad. Amsterdam. Vol. V. ( 434 ) Nernst’s formula for 4, obtained in a different manner, is identical with our formula (5). (As Nernst’s “= V\—V,, our 24> — F). For if we replace re by RT loy Kx and wy Hy hy K; RT log Ky, then (5) passes into . Bis slat A= — se loo KK Wak = ts log Ke Se ; é CK, & CU, and this is Nerxst’s expression. As has already been observed, the quantities Ay and Ay; are the so-called “partition-coeflicients” of the positive and negative Lons. For instance for the positive lons we should have, when equilibrium of partition occurs ; By by = 0, or ; aad be + RT log “a = 0; 1 ee ORG 3 3 t so that we obtain —~ — Ax. The same for the negative Ions. CR The relation, given by Nernst ') C - - lv Ke Kx X Ka= 7 X Kxet, 2 in which Age is the coefficient of partition of the neutral KCI- molecules, and (, and C, are the dissociationconstants in the two phases, follows directly from the thermodynamical meaning of these quantities. For if we write this relation in the form RT [log KK + log Kei] = RT [log C, — log C, + log Kx); it passes, taking into account equation (a) and the relations 7h au TA 4 iia Bl a Fp ea ey “ RP log KKC1= ey, eK} RP log Cy = cy ee aa RR log, = l ' ' ko, “x, “oy immediately into the identity ' ' ' ’ ' ' ' = =s —= — —") os TE) + (Hey, —# oy) (Hey HE en) ' ' ! ' ' a {¢ Ke ye Ka cu) <= (u Ken AC 1 Not the formula (5), but the formula (6) or (67), derived by us from (5), deserves however the preference, becanse the concentrations of the Ions have been eliminated therein, and an expression has been obtained, in which only the coefficients of partition Aq and Ay; occur. Ill. If the dissolved electrolyte has now distributed itself so, that 3) Z. f. Ph. Ch. 8, 138 (1891). ( 435 ) the total concentration is c, in A, and c, in A,, we shall have: ce Ce) eae which the quantities ¢, and c, may be found by chemical analysis, and «, and @, by determinations of the conductivity. As soon as & : Ko ean be determined by experiment, Kz, may be caleulated from the K equation (6a), and Ax X Ay from (7a), and we can therefore get to know separately the quantities Ay and Av, consequently also the quantities | wk,—ewK, and wc, — u'ci, - From (6a) it further follows, that 4 will be positive (as supposed in the figure), when Ko > Kr - Only when by accident Ay; =A, A can be 0. In general a potential difference will always occur between tive non-miscible solvents, when an electrolyte is partitioned between them. This potential-difference is given by (6a). From the equation (7a) it follows, that the relation of the concen- trations of the /ons in the two solvents in the case of di/ute solutions will be practically independent of the total concentrations. This equation may also be deduced directly from (3). For this, being a result. of (1) and (2), that is to say of the equilibrium of partition and the two equilibria of dissociation, may be written : ! at Cor (WK) + He Hy) = — BP | ba oe = + log i OG elt and this after substitution passes at once into (7a). For OR, eG CK Oe NG log og ——= "2 6g) $= = log) | ——_}) - I: L L Ky Cor, CK The equations (6a) and (7a) moreover lead to an important conclusion. As the quantities Ay and Aq are, in the case of di/ite solutions, specific quantities, we must therefore find about the same values for these quantities in the case of other salts, when employing the same solvents A, and A,. For NaCl for instance we will have : Jiedhs TkKGe Gre JON = SS fir) a ( am Nas CS he GN from which by experimental determination of 4’ and the quantities fv, and vq, , the two quantities Aya and A may be determined. The value, found for Ay, from KCl-solutions in A, and A,, must then be practically ¢dentica/ with the value for Ay,, determined from solutions of NaCl in these solvents. ) = Kiva < Kor, 29% ( 436 ) The quantities 4 will show an almost complete additive character, on account of Ay and Avy being independent of the concentration in the case of dilute solutions, For instance, in the same solvents A, and A, we must find: Axci—4yact = SKno,—A4ONaNo, « And the same for other combinations. The above considerations may be readily extended to the case of non-binary electrolytes such as CaCl, ZnCl,, ete. In the different equations the valencies » of the Tons will then also occur, because the fundamental relation (4) then passes into the more general one: IV. The question in how far and in what manner the value of 4, given in (6) or (67), is still dependent on the concentrations of the Ions, can only be answered, when we calculate the values ofp’. 1 ete. with the aid of an equation of condition. If we accept the equation of VAN DER WaAats as also applying to liquid-phases, we obtain for instance for the molecules Np: V—b lp = — k, T (log T—1) — RT (1 —— 1) + [(¢).—T (np)o] + ny pe 2 ee Mp + RI Vos by— 7 (n, ap, + 2, @y, +--) + RT log a 1 n, stands here for the molecular number of the solvent. For 4 and a@ we write: b=, 0, -- mb ee ee ts a=n,'a,, + 2n,n,a,, +2, n,a,,+..- Let us now calculate the value of ' ’ ' ' ' — — (wv -—u,_), ( ch! cr) (Ht x) or, What amounts to the same, of ' ' ! ' (Hy) — UH ey): If we indicate the solvent by the index 1, the non-dissociated KCI, dissolved therein, by 2, the two Ions by 3 and 4, we obtain for ay xpressio! UE oy the expression Sgr (k,-k,) 1h (log T-1) + [((ex)o—(?a)a) -T ( (%]3).)-(4)o) | + Sn 2 we (G,-4,) — pln (45 ,-44,) ar N (43-44) +n, (4,,-4,;) --n, (4, ,-a,,]- RT +RT— ‘ ( 437 ) Remembering, that ,—=7,, a,,—=4,,, the last term may be simplified to 9 2 Ty ral (a,,—4,,) + %, (@;,—4,,) + 2; (@;,—4,,)]- For We Pal itch we find a similar expression. In this, however, the quantities ee k, Sr heat-capacities of the same lons, at infinite volume) and (@5),, (€4)o> Qla)o> (%4)o (the ene) IOV and entropy-comstants of these Ions) will be exactly the same. @,,,4,,, @,, and @,, will also 1 1 Ay . ‘ » » ] ay as ‘Pp ! — \ ee L — f remain unaltered, so that for the difference (HE) (u Ko cn) we may write: tra e705 nl (@3,—@41) if AG @ 5 a a',,) RI e les -b, ae yy Os —b! oe a| (= A a iden — ) ut os (a,.—@,,) io = =) + (a,,-4 cay iG 3 Hii: The quantities, relating to the second solvent, are indicated by accents. We may now go a step further and accept as a first approximation: Neat eee If we then also write V V' = = 5) 0) 5 nh, — 2 (L—a)i, — =e, etec:, i a = f (3 (b= Nol = Cc a y= ee saat oS) BA (antares) [ a a 2) ) feo & v v v U : 1l—a)c As, im consequence of the equilibrium of partition, aay — jc constant, A will have the form A — Le ate 7 (l—a)e, 3 4 aS ze As ac)? or since, on account of the equilibrium of dissociation, (ae = —Q)c constant, also the form A=A, +7 (0 Whether 4 will be positive or negative, depends chiefly on 4,. If ! ' ,,— a 7 CU 31 41 al 41 ae Se, : v A will be positive. We also see, that A—A, will increase or decrease with the second power of @c, that is to say in the ease of strongly dissociated electrolytes, where @ is nearly 1, almost with c’. Dee. 1902, 438 Physics. — Dr. J. J. Hato: “The value of some mayneto-optic constants.” (Communicated by Prof. P. Zeeman). In my doctoral thesis, on The magnetic yolation of the plane of polarisation in the neighbourhood of an absorption-hand *), Thave eal- culated the values which three of the constants, occurring in Vorgr’s theory of magneto-optic phenomena, assume ina particular case. 1 did not then know as yet, that Drupe had already tried — in his Lehrbuch dey Optik (Leipzig, 1900) — to make some estimate as to the order of magnitude of a constant 7, introduced by him, which is connected in a simple manner with one of the constants of Vorer’s theory, of which I have determined the value. Therefore | beg to be allowed to mention here my results and those of Drupr, and to examine in how far these results agree. If ¥, 9, 3 are the components of the electric polarisation in some medium, Voicr assumes that every one of these components exists of a part X, JY, Z, relating to the free ether, and a series of other parts X;, 9), 3), indicating the state of the ponderable matter. He therefore assumes: = X-+ > Fj, ete. A representation of the phenomena of selective absorption, in which the influence of a magnetic field with components 1, 4, C is also taken into account, is gained when the sets of veetor-components A, B, C ave subjected to the conditions: OX), 07x), Od; 03; x =i - b, — , C= h+ % a + bn ie ale ns ( The constant 4; appears to be equal to 7,°/42°, if zt, is the vibratory period of a free vibration of the absorbing medium; I have derived the values of the constants a), ¢c, and & for the line VD, from the results of my measurements in a particular case (for a flame whieh contained very much sodium); the values | have found are (vide p. 85 of my thesis) : et RS PWS Che Ore mee e7 — Weos Oe The constants a, and ¢, depend on the density of the sodium- vapour in the flame, the constant c, does not so far as we know. The data which served for the calewlation of these constants are the following: a, was calculated from the width of the absorption- 1) Amsterdam, 1902. ( 439 ) band, which is proportional to it; this width was about 1 Angstrém Unit; ¢, was calculated from the magnitude of the Znuman-effect ; for this magnitude in the field which I used of 9000 C. G.S. Units — I took */,, part of the interval between the two sodium- lines; €, was caleulated from the value of the rotation of the plane of polarisation in the neighbourhood of the absorption-band; on the magnitude of this rotation as a function of the wavelength, for dif- ferent intensities of the magnetic field and different widths of the absorption-bands, I have made measurements of which the results have been recorded in the tables given in my thesis. From these tables I shall quote one series here, giving the numbers from which the above-mentioned value of & was deduced (vide p. 42 of my thesis, table 241): J x J x 15 8 | 50 bai 20 54 55 1-40 95 Sty. | 160 9 30 93 65 8 35 18s OEM) 6 | | 40 Aa Ss aap rN 2, AB 12 | Here d is proportional to the difference between the wavelength of a given kind of light and the wavelength which corresponds with the middle of the line D,; the coefficient of proportion may be found from the fact that the difference between the wavelengths of the two sodiumlines corresponds with a value d= 130; x .represents the rotation of that particular kind of light in my experiments, expressed in a unit of which the value is determined by the fact that a rotation of 180° corresponds with a value ~= 105. Thus we read from the series, given above, that for a value of d corresponding with Sb iiss 18 sa, <6 A.U. the rotation of the plane of polarisation is — >< 180°; 130 105 from these corresponding numbers the value of «, is deduced in the way which I explained in my thesis. Drupr, in his Lehrbuch der Optik which I mentioned above (p.353), in his version of the theory of dispersion gives the equations of motion of an electron in the form: 440 ) m os =eX— andl § — neres ; or v ot Here m is the mass, ¢ the charge of the electron, § its displacement parallel to the axis of Y from a position of equilibrium, X the com- ponent parallel to this axis of the external eleetrie force acting on the electron; 7 and # are positive constants, In working out the theory it appears that Vorer’s constant a, is identical with the expression rd/42 of Drupe. Now the value of 3 was calculated by Drepr himself (p. 490) from the vibratory period of the sodiumlines; he finds the value of this constant to be 7,6. 10-25; from this value and that of Voiet’s constant a, which | mentioned just now, we find: r= 1650; here we must bear in mind that this value applies to the particular sodiumflame to which my measurements relate; 7 must, as well as a), depend on the density of the sodiumvapour in the flame. Drvpe tries in his book to fix limits, between which the value of r must lie. He finds a lower limit by deducing from theory the proportion between the quantity of light, which the absorbing sodium- flame itself begins to emit under the influence of incident radiation, and the quantity of incident light which is absorbed. This proportion he finds to be 0,126/r. From the fact that reversal of a sodiumline is possible, he concludes that this proportion must be considerably smaller than 1, and he therefore fixes the lower limit for the value of 7 by assuming: FLO. A higher limit-is found by Drupr from the consideration of the phenomena of interference. He deduces theoretically the value of the coefficient of damping y of the free vibrations of the electron and finds for this: a UEP cris A eee Now this coefficient must be small, as with great phase-differences interference-phenomena can still be observed. With sodiumlight inter- ference-phenomena have been observed with a phase-difference cor- responding with 200000 wavelengths; therefore 200000 y must still be smaller than 1, therefore in this case: *< 100. It is evident that this result is not at all incompatible with the value of ¢ which I calculated above. In order to observe interference- phenomena with such great phase-differences it has been necessary to use a source of light showing very narrow sodiumlines; with ( 441 ) the width of the sodiumlines to which my measurements relate (which was about 1 Angstrém-Unit) the greatest phase-difference with which interference-phenomena can be observed is one corresponding with 3000 wavelengths; the higher limit is therefore raised to TOOO, so that 7 must in this case le between 10 and 7000, which it really does according to the calculations given above. Some further deductions which can be made from the comparison of Vorer’s equations with those given by Drupn, have already been given on pp. 90—95 of my doctoral thesis, with reference to LoRENTz’s paper in the Report of the Congres International de Physique, held in Paris in 1900, and I will here only refer the reader to that part of my thesis. Physiology. — “A new law concerning the relation between stimulus and effect.” V. By Dr. J. K. A. Wertaem Sacomonson. (Communicated by Prof. C. WinkiEr.) From the law connecting excitation and effect, i ean =O) a eee 8 CL) we may obtain by differentiating ue ith) dk or also LE eee eC eat th nah Beck BoM C2) AB Introducing differences instead of differentials, with this limitation that the differences should be very small, and taking according to Frcuner, Oy, the differential sensation-threshold as a constant quan- tity, we obtain Dusky BUG) hs Oe 3) or, by putting the constant e—~2°k, =k Revie BPC mba eh) ht ca) the latter formula containing an expression for the absolute differen- tial threshold-value. We might employ this formula for psychical impressions of peripheral stimuli, if the peripheral stimulus had caused excitation of only peripheral neurones with equal stimulation-constarits 4, and moreover if all these neurones had been uniformly stiniu- lated. Under a similar limitation we might also admit the validity of the formula for the relative differential threshold-value deduced from (4) by dividing both terms by #&; we then obtain: 442 AR eR ea Re As a rule, however, this formula may not be applied in’ the ¢-1 veS hc) Ake case of psychical processes, because the above-stated conditions have not been fulfilled. It is impossible to suppose the case of a peripheral stimulus hitting only one single peripheral neuron, or of one single group of neurones being exposed uniformly and with equal foree to that stimulus. Let us see, what happens when a sense-organ in the living human organism is subjected to a stimulus. For instance we may consider the action of pressure on the skin. Suppose the compressing object to be in contact with a limited surface of the skin at the moment the pressure commences. We may fake it for granted that all end- organs situated within the limited skin- surface in direct contact with the com- pressing object, undergo an equal and uniform pressure, and that in the case of this pressure being increased, its action will remain uniform. To the neurones con- nected with tlie nerve terminations @,4,4,4, our deduced law (5) may be therefore applied. As soon as the pressure increases the skin-surface will undergo a change of shape and be compressed (see fig. 1). This implies that nerve-endings 4, 4, situ- ated outside of the originally compressed surface, will also enter into an excitatory state. If this deformation be a slight one, only the nearest end-organs 4,4 will be . fn) sy increased pressure the more distantly situated ones compressed. | c, ¢, d, d ete. will also be stimulated. To all these end-organs, situated outside of the originally compressed surface, impulses are given, which are conducted to the central nervous system. From all the combined impressions finally results the sensation by which our judgment is decided. The neurones connected with 6,4 ¢,¢ d,d-ete. will likewise obey the law of stimulation and effect. The intensity of stimulus however is different for all these neurones, and also different from that for the neurones a,a,a. Therefore, whilst for the neurones aa, the expression dR eBR ae K aed R ( 443 ) might be employed, we must use for the neura b,4 c,c d,d ete. the expression eBn eBrs Bry 0, = K—, o;, = kK—, o, = K— ete. r) Lig Ts As the stimuli 7,, 7,, 7, ete. are proportional to #, we may sub- stitute for these m,R, mR, m,R ete. The question arises next: how shall we psyechically combine these impressions in order to make use of them for the special purpose aimed at by our experiment, i.e. to decide whether two stimuli are different from one another? Summation or addition is out of the question: this would be in contradiction with the experience that by fixing our attention on a definite sensation, other sensations are weakened. It is clear that we will conform our judgment to that part of the sensation that is best fit for our purpose. Starting from this fact we may continue to treat the question mathematically. In the first place it ought to be taken into consideration, that by increment of a stimulus not a small number of new peripheral neurones are stimulated, but generally a great many. In the case of a pressure e.g. not only nerve-endings lying sideways of the compressed surface, but also more profoundly situated end-organs will be acted upon by increased intensity of stimulus. For every individual neuron we shall have to put in another coefficient m. If Fig. 2. we construct therefore a great many curves @,, ,, 0, all these curves will only be different on account of the constant mm being changed. We now suppose the final judgment fixed each time by a part of a farther situated curve. Thence it may be concluded, that the ( 444 ) enveloping curve Will represent the manner in which a judgment about the final result originates. To obtain the envelope of the eB group of curves 9 = A >» if the constant m is changed, we put: med pmBR KF=o—K Se ce ek mk : : : . ol } Calculating the value of mm corresponding to = 0, and substi- i} tuting this value into the equation #’ = 0, we find the formula for the enveloping curve. We may state: nd , ye of fA. A ne mBR—| Lo. ee Om hk m From which follows m= mt which substituted into “= 0, gives: v 0: REBEL AO see See proving that the relative dijerential thresholdvalue is constant. By this process we have deduced from our formula the law of WEBER. From our deduction may be inferred that the area, wherein the law of Weer prevails, is a limited one. The validity of this law commences within the area of the enveloping curve, and a look on the figure 2, will make it clear that the first part of the whole sensation-curve is given by the descending part of the curve eDR ale 5 or. o—kK—. The horizontal part then represents the area within 1 the limits of which the law of Wesrr prevails, whilst in the case of very great intensities of stimuli the ascending part of the curve ebnk j= Kk will appear. mR adie There remains still another conclusion to be drawn from our deduction. This latter was founded on the supposition that the increment- constant B was the same for all stimulated neurones. This, however, is highly improbable: in the most favourable cases we may only suppose that the /-coefficient of the homogenous neurones will possess approximatively the same value, from which follows that we may admit the law of Wereper at best as an approximation. Finally it may be mentioned here that apart from the above- demonstrated correction for obtaining an approximation in the direc- tion of the law of Wreer-Frcnxer, probably still another means of correction exists in some of our sense-organs; I shall prove this ina later communication. ( 445 ) Physics. — “Plaitpoints and corresponding plaits in the neighbour- hood of the sides of the y-surface of VAX puR Waats.” By Prof. D. J. Korrewna. (Communicated in the Meeting of December 27, 1902). First Descriptive Parr. 1. As in my “Théorie générale des plis’') 1 wish to precede in this paper the demonstrating part by a short summary of the obtained results. As we know a plaitpoint may occur on the side =O of the w-surface of VAN DER WaAAzs,*) which is represented by the equation : w= — MRT log( v—b,) — a + MRT {vlog e+(U—w) log (1—.)} . (1) 5) where: a=, (1l-w)? +2 a, e(1—-«)+ a, v7? =a, +2(,a,-a,)e+ (4, 4,-2 ,a,)u?, . . (2) b,=b,(1-«x)? + 2 ,b, a(1-«) +6, w?=b, + 2(,b,-b,)e+ (6, +6,-2 ,b,)a7, . . (8) This oceurs only in the case that the temperature 7’ corresponds with the critical 7), of the principal component; but in that case it occurs always. This plaitpoint coincides with the critical point of the principal component for which v= 34, and which in our figures we shall always represent by the symbol A; the plaitpoint itself will be represented by LP. If the temperature varies, the plaitpoint and the corresponding plait can in general behave in two quite different ways. It will namely either, as is indicated by the jirs¢ four cases on fig. I of the plate, on which the (v,.2) projections of the sides of the y-surface are represented, at increase of temperature leave the v-axis and move to the inner side, therefore entering the surface, and disappear from the surface at decrease of temperature, or it will as in the last four cases of that figure, enter the surface at decrease and leave it at increase of temperature. 1) Archives Neérlandaises, T. 24 (1891) p. 295—3868: La théorie générale des plis et la surface ~ de van per Waats dans le cas de symétrie. See there p. 320—368. 2) We take here the equation of the J-surface as it has been originally derived by vAN perk Waats, so without the empiric corrections which seem to be required to make the results agree quantitatively better with the experimental data. So is, for instance, @z considered to be independent of the temperature, and all the results and formulae mentioned are founded on this supposition. It would not have been difficult to take such empiric corrections into account, as has really been done by VerscHArreLt and Keresom in their papers, to which we shall presently refer; but then the results were of course not so easily surveyed. Therefore | have preferred to leave them out of account, at least for the present. ( 446 ) And this different behaviour of the plaitpoint will necessarily be accompanied by a different behaviour of the connodal and spinodal curves. For they must always cnt the r-axis at decrease of temper- ature, the connodal in the points of contact of the double tangent of the awye-curve of the principal component, the spinodal in its two points of inflection; at increase of temperature above the critical temperature of the principal component, however, they get quite detached from the v-axis. In connection with this they turn in the first four cases of fig. 1 their convex sides, in the last four cases their concave sides towards the side «=O of the y-surface as is also indicated in the figure, where the connodal curves are traced, the spinodal curves dotted. Fig. a. At decrease of temperature a figure originates in the first four cases as is schematically given here in Fig. a. At increase. of temperature, on the contrary, in the /ast four cases, the spinodal and connodal curves disappear from the surface at the same time with the plaitpoint itself. Besides to this different behaviour it appeared however desirable, to pay attention to two other circumstances. First to the direction of the tangent in the plaitpoint, whether if prolonged towards the side of the large volumes, it inclines to the imner side of the y-surface, as in cases 1, 2, 5 and 6 of fig. 1, or whether it inclines to the outer side, as in the remaining four cases. For on this it will depend which of the two kinds of retrograde condensation will eventually appear *). But besides we have to pay attention to the question whether the plaitpoint, entering the y-surface, either at decrease or increase of temperature, will move towards the side of the larger volumes as in cases 1, 3,5 and 7, or whether it will move towards that of the smaller volumes as in the other cases. In connection with this question we may point out here that the line AP in fig 1 of the plate may everywhere be considered as a small chord of the plaitpoint curve of the v,r-diagram and accordingly indicates the initial direction of that curve, which it has when starting from point A. The three different alternatives, which we have distinguished in this way, give rise to the eight cases represented in fig. J, and we may now raise the question on what it will depend which of these eight cases will occur at a given principal component with a given 1) See on these two kinds of retrograde condensation inter alia, the paper of van DER Waats: “Statique des fluides (Mélanges)”: in Tome | of the “Rapports présentés au congres international de physique, réuni a Paris en 1900", page 606—609. ( 447 ) admixture; of course only in so far as with sufficient: approximation the conditions are satisfied on which the derivation of the equation (1) of van per WAALS rests. 2. The answer to this question is given in the graphical repre- a sentation of fig. 2. If appears, namely, that the case which will oceur, a: h, is exclusively determined by the quantities = = and Zot which 1 1 have already played a prominent part in my above mentioned “Theorie générale des plis.” In accordance with this a x and a y-axis are assumed in fig. 2 of the plate and the regions where the points are situated whose x- and y-values give rise to the appearance of each of these cases, are distinguished by different numbers and colours. For instance the white region 1 indicates the x- and y-values for which the plaitpoint enters the y-surface at rising temperature, moving from A to the side of the large volumes, while in the well-known way we can derive from its situation on the connodal curve on the right above the critical point of contact # (for which the tangent to the connodal curve runs parallel with the v-axis) that the retrograde condensation will be eventually of the second kind (i.e. with tem- porary formation of vapour) and also that the temporary vapour phase will have a larger amount of admixture than the permanent denser phase. : In the same way the blue field 5 indicates the x- and the y-values for which the plaitpoint enters the w-surface at decrease of temperature, moving towards the side of the large volumes; whilst the retrograde condensation will be of the first kind and the temporary denser phase will show a smaller proportion of admixture than the permanent vapour phase. 3. When examining this graphical representation we see at once "that one of the eight regions which were a priori to be expected, region 8, fails. From this follows that for normal substances the combination of retrograde condensation of the second kind and of a plaitpoint which enters the surface at decreasing temperature and moves towards the side of the small volumes, is not to be expected. All the other seven regions, however, are represented in the graphical representation. 4. Further the point x = 1, y=1, is remarkable, where no less than six regions meet. This point represents really a very particular ( 445 ) case, namely that in) whieh the molecules of the admixture, both with regard to volume and to attraction, behave towards the mole- cules of the principal component exactly as if they were identical with these latter molecules. If at the same time a,=a,, b,=,, which is of course not involved in the above suppositions, it is easy to see that at decrease of temperature below the critical temperature the plait would suddenly appear all over the whole breadth of the y-surface. Now it is true that every deviation from these equalities a, =a,, h,=h, will prevent such a way of appearance, but it is evident that then the behaviour of plaitpoint and corresponding plait will depend on a, and /,, i.e. the first approximation for which the 2 knowledge of x and y is sufficient and which everywhere else suffices to make this behaviour known to us up to a certain distance from the side of the w-surface, fails here. And also already in the neiyhbourhood of the combination of the values x=1,y=1, this first approximation will be restricted, to the immediate neighbourhood of the point A’ and of the eritical temperature 7% of the principal component. When we are not in that immediate neighbourhood the influence of «a, and 4,, — of the former of these quantities specially, — will soon be felt. On the contrary for values of x or y sufficiently differing from unity the considerations derived from the first approximation will probably be of force within pretty wide limits, at least in a qualitative sense. 5. Before proceeding to a discussion of the border curves between the different regions, we will shortly point out that we cannot attach an equally great importance to all the parts of the graphical representation. So all points lying left of the y-axis relate to negative values of ja ponent and admixture should repel each other, which is not likely to occur. 2) i.e. to the case that the molecules of principal com- In the same way the negative values of y, so of ,/,, of the points below the x-axis, should be considered as having exclusively mathe- 1 matieal signification. If the relation, ,/,=— (6,+6,), should. still be =4 applied also for very unequal values of the 4’s, then y would even rema to | — 1 always larger than > and so the part below the line y = would lose its physical signification. 6. With regard to the border curves between the different parts, we have first to deal with the parabolic border curve separating the ( 449 ) rezions containing blue (blue, green, purple) from the others. — It 1 BA ve! touches the y-axis in the point x=0, y=-. Its equation is: “ (2y—8x+ 1 —8(y or if we transfer the origin to the point y=1, *= 2) a0) 1 and therefore introduce the new variables: x’ =z—1; y’ =y—1, which brings about a simplification also for the other border curves, we get: (Qin Sizel) a = B'( —aet— O8 a s (4) Then we have everywhere inside that parabola, so in the regions Dee Ount: (2 yi Sie iy —%) <0 and outside it in the regions 1, 2, 3, 4: (2 y' —4 x')? — 8 (7'—x') > 0. In consequence of this it depends on the situation inside or outside the parabola, whether on the corresponding y-surface the plaitpoint will enter the surface at decrease of temperature or at increase of temperature and whether the spinodal curves turn their convex or their concave sides to the side «= 0. Fig. b. For points ov the parabolic border curve the plaitpoint occurring in the point A’ at the critical temperature of the principal component, is to be considered as an homo- geneous double plaitpomt at that moment. The projection on the v, wv-surface appears then as is indicated in fig. }. How the transition to this condition takes place may be made clear by the subjoined fig. c, which represents the same projection for a temperature slightly below that of the critical temperature of the principal component for the case that the z- and y-values indicate a Fig. c. point, which is still situated in the green region 6, but on the verge of the border curve of the yellow region 2. Very near the plaitpoint we find here already a second plaitpoint ?’, which at further decrease of temperature soon coincides with 7. If now the point in the green region approaches the border curve of the yellow region, the two points / coincide nearer and nearer to the critical temperature of the principal component and to the point A. On the border curve it takes place in the point A itself. Beyond the limit, in the yellow region, the plait of P does not develop any more and P’ takes the place of 7. 30 Proceedings Royal Acad. Amsterdam. Vol. \ 7. As second border we get in the graphical representation the straight line: 27—Diee = 0, .. ey) wy eel) ae ee It separates the regions containing red 3, 4 and 7, — for which 2 y’—-3 x’ 0. In the former case the tangent AP to the plaitpoint-curve of the (v, z)-diagram is directed to the side of the small volumes, in the second to that of the large volumes. If we, however, examine, whether e.g. at decrease of temperature the plaitpoint moves towards the large or towards the small volumes, the parabolic border curve acts again as separating curve. It appears then that the plaitpoint moves towards the large volumes at decrease of temperature in the regions 2, 4, 5 and 7, at increase of temperature in the others. Se ( 451 ) 9. The following table gives the characteristics for the diffe- rent regions. Region 1 (2y'-3x')?-8(y'-x') >0; 2y'-3x'>>0; (2y'-3x')*-4(4y'- 3x')(2y'-3x') + 16y">0 2 ” S07 a0; . <0 3 a SU ee 0: “ >9 { e S02 cs i. <0 5 = <0 ae ees e >0 6 % 0s. 4 ee ? where : ee ara a ares Pe’ ee Le a(S) a, b, A similar tabular survey of the physical properties of the regions seems superfluous, as these properties may be immediately read from the illustrations of fig. 1 of the unfolding plate. 10. It seems not devoid of interest to know how the breadths of the regions change with regard to each other, when continually increasing values of y’ are considered. An inquiry into this shows at once that the blue region 5, measured along a line parallel to the x-axis, has 2) a limiting value for the breadth of 5 All the other regions mentioned, however, confinue to increase indefinitely, and do this proportional with y' and in such a way that the yellow and the red region get gradually the same breadth and in the same way the green and the purple one, but that the breadth of the two first mentioned regions will amount to 0,732 of that of the two last mentioned. If we also take the white region (reckoned e.g. from the y-axis) into consideration then we find its breadth at first approximation to be proportional with y', so that it exceeds in the long run the other mentioned ; the orange region keeps of course an infinite breadth. The limiting values of the ratios may therefore be represented as follows: white yellow __ green blue purple red orange es = = Se SO equi O752, 9. 1 0 1 ON7S2 0 Pcs We may see that if we keep x constant and make y to increase we always reach the white region, while reversively increase of x with constant y leads finally to the orange region. Strong attraction between the molecules of the admixture and those of the principal 30% ( 452 ) component promotes therefore in the long run the relations of case 4, large volume of the molecules of the admixture promotes those of ease 1. 11. We may conclude this deseriptive part with mentioning some formulae which we have obtained in the course of our investigation, and which will be derived in the second part. We do not, however, give them as new, as they must essentially agree with similar equations obtained by Kresom’) and Versciarrent), if the simplifying hypotheses are introduced on which the original equation of the y-surface, used by us, rests. Nor does the way in which they are derived, in which the method of the systematic development into series is followed, differ considerably from that of VerscHnarre.r. In these formulae we have restricted the number of notations as much as possible. They only hold at approximation in the neigh- bourhood of point A’ and of the critical temperature 7), of the principal component. We shall first give expressions for the radii of curvature R’,,, and R’ conn. Of the projections on the (v,.7)-surface of the spinodal and connodal curves in the plaitpoint; from which appears that the radius of curvature of the connodal curve in the neighbourhood of the point K is at first approximation three times as great as that of the spinodal. 3 r ' ' Ry. = g by" [27-32 —8(y'—#)] - =: 6; See ame Bom, => by? (27 —3e))—8(y'- x)J=3Ry, (IY) These radii of curvature are here considered as being positive when both curves turn their convex sides to the r-axis as in the cases 1—4 of fig. 1 and negative in the cases 5—7. We may shortly point out here that the corresponding radii of curvature on the y-surface itself, on account of the strong inclination of the tangential plane in the neighbourhood of the v-axis, are quite different and much smaller, though the relation 1:3, of course 1) W.H. Keesom. “Contributions to the knowledge of van per Waats's 4-surface. V. The dependence of the plaitpoint constants on the composition in binary mixtures with smajl proportions of one of the components”. Proc. Royal Acad. IV. p. 293—307. Leiden, Comm. phys. Lab. N°. 75. *) J. E. Verscuarrert. “Contributions to the knowledge of vay pen Wats, +-surface. Vil. The equation of state and the ?-surface in the immediate neighbourhood of the critical state for binary mixtures with a small proportion of one of the com- ponents”. Proc. Royal Acad. V, p. 321—350, Leiden, Comm. Phys. Lab. N®. 81. ( 453 ) continues to exist. They even become zero when the plaitpoint coincides with the critical point A, so that both curves have then a cusp. 12. The knowledge of the radius of curvature /?,,,,, 1s of importance specially because it may be used in connection with the formula: Fig. d. 1 tg b= 2 = — (27'— 32a 4b, through which we know the small angle which jen © the tangent of the plaitpoint forms with the v-axis, to calculate in a very simple way the differences in density and volume between the phases of the plaitpoint P? and the critical point of contact & at first approximation *). According to fig. d we have, within the indicated limit of accuracy : day » 0, = PQ=PR= ER com =! 27-32) (27/32)? — Bly»), -- (13) P h 8 P 1 ke 1 Onna 1 ote ar a, —# p= RQ= 5 Oe TR or BA (2y'—3x')? | (2y'-3x')? — 8(y'—x )]a* (14) 13. We proceed now to give the formulae relating to the plait- points phase at a temperature 7) which does not differ mueh from the critical temperature 7% of the principal component. They are’: 4 (PIP av —— a . . . . . 15 “P (2y' _ 3x!) Say ae Tr. 2) v,, —3b,= —F, t (2y' — 3x!) —4(4y'— 3x) (27'—3x') 4 16y'} « . (16) Ripieme lee - = { (2y'— 3x')?4y'+ 22! de ye esa cee (le) Pk P By means of (15) we may transform (13) and (14), so that they become : Cle ee ee Sg, i team on =i5 (27 ed aie Se Alpeetn Stace aus) and oe 9 B54’)? fT 19 @y— Xp: 160% apr ~ eg 1a (AS) 1) A similar method is given by Kersom at the conclusion of the before-mentioned paper of VeRscHAFFELT. 454 io which we add: Pp—Ppr 1 9 1—T; = — 7, (27'-3x')* (0-0 p) @p = — g By-Sx')’ w (20 Py ay, 1 ™) Opp) *p g Oye) Fp (20) 14. We shall conclude with giving some formulae relating to coexisting phases, where the index one refers to the liquid-, the index two to the gas phase. Where the index fails, we may arbitrarily take the value for the one or for the other coexisting phase; either because it is indifferent at the degree of approximation used, or because the formula will pie hold for either state. 0, = 3b, —3b, Te ay 3x)? —B8(y'—x')Je . (21) v= 3b, +3), Sere Sx)'—8y'—x)}e- (22) — pI: T—T rok = = Sa)2" . 3 > ee Pk 1 U ’ &,—2, —— (2y'—3x')(v,—v,)27. . . . « « (24) Ab, 1 54 LU y 7 ’ ‘ ’ (e+e) 36, = — > b, T+ 88,) = [By 3x) 8 (ya) + 2 5 Ty 5 i g [27 Se) 24 (7/2!) 2y'—Bx) + 16 (87—2x)] @ . - 2B) in which formula (23) holds also for non-coexisting phases. SECOND DEMONSTRATING PART. Transformation of the y-surface and preliminary development into series. 15. We begin with a transformation of the y-surface by intro- ducing the following variables : v—s3b T—T). 1 : wu v= — eS jot —= 5. sos dye BIB} Bb, Ty, MRT; which means that we henceforth measure the volume v’ from the critical volume and with that volume as unit, the temperature in 8a, 27b, MR the same way with regard to the critical temperature 7 = and the free energy w’ with MRT; as unit. = If we moreover put: a eres es ea! ; ies ust (ann) b, a b we find easily from (1), (2) and (3) for the equation of the new surface : '): yw’ =e (i +t) log ob, (by' -v ') = a ote (1+¢#’) fa log a +- (1-«) log (1-2), (28) 1 1 where Wo es Shae. Ae 2 a? 99 pin Tre AG eo oS id oh AS) 2 2 1 Bee ame ediyrt a eta t ot Wes (80 pay vetsr—sa (30) further : dw MRT; oy’ 8 Oy’ Se 8 — 31 of PY 3h. Oe 3 Pk Oy ) 16. For investigations in the neighbourhood of the sides it is desirable to develop the expression for wp’ so far as possible according to the powers of w. We write therefore: yp = (14+?) e« WARES A Ca te aeUCt Se bod.) 1a oe (B74) where in ne form *) Xo = — (1b) log b, (24-30! Se eens XGA. ee (25) pea (eam oe 34 p= 049 (sr —)\-ao- (34) Dy'2 9 (ib =. f! 1 9 pe Siar, —— oS mE +| sr Aes ae ee a (35) 1) If we wanted to consider a, as function of the temperature, the simplest way of doing this would be by writing the second term of the second member : 0 ' iP} (Cee a ee a The formula 7 = MES would continue to 1+7' 27 6, MR hold unmodified for the critical temperature of the principal component. provided we take for a the value it has at that critical temperature. With Crausius’ hypothesis that ds is inversely proportionate to 7, we should get _;=—1; -:.=-++1. Also (29) continues to hold and the modifications in the developments into series and in the formulae derived from them would be easy to apply. 3) In this form they may be used for investigations concerning the conditions at the side of the p-surface at temperatures greatly differing from the critical tem- perature of the principal component, as are made by Kersom: Contributions to the knowledge of the -surface of van per Waats. VI. The increase of pressure al condensation of a substance with small admixtures. Proc. Royal Acad. LV, p. 659— 668; Leiden, Comm. phys. Lab. N°, 79, 456 or, after development into series with respect to the powers of v's: 9 ‘oe a] +] 9 Xo —(1 ++) log 26, — FI ={ “fy ye + —t'y?— — ty? + 8 2 5 8 9 a 6B : 9’) rt — a a ieyn of) ae to, the!) Re re j + Gy t+see" — F504 (36) rt) ( 3 m2=0+0('—) — 7 #7 | er—3 R)+2y't |r+ 9 9 + {| ety e|—5 (By’—2. a) oF Es. hs on g 3 u 9 >.,! ' hx ' ' ’ oF Osher « %=50 +O —7V +9) +6 (2x’—2A \—gl4r *_4dy'4-2d'+ 62'-32')e'+ ..(38) for which last expression we write: %,=6,+6,t+o6,v"+4... = th too Determination of the plaitpoint and classification of the different possible cases. 17. For ealeulating the coordinates wD and Lp of the plaitpoint we have the following relations: *) mm ne ——f Pe wv 0? w' 0?’ —_— |.___ — ee ee ee ee Pie ee oy du" a ale O° y’ dy deel |.” Oe data, ates Ope where mm represents *) the tangent of the angle formed by the (v’, 2)- projection of the common tangent of spinodal and connodal curve in the plaitpoint with the r’-axis. If by means of (32), (36) and (37) we introduce in these equations everywhere the values of the differential quotients at first: approxi- mation, in which, as appears, wi, tp and vp may be treated as small quantities of the same order, we find: m 3 ———(2y'—3x)=0 ..... . (48) Fe 4 1) DP. J. Korrewee. Ueber Faltenpunkte. Wiener Sitzungsberichte, Bd. 98, Abt. JL, (L889), p. 1171. *) See 1. c. p. 1163. ae Ole GEL gx, eer hey t Brlnhesg Clare) Cia oye (44) me 2 SRC a eae area hee = =< = == — t —2 i) 5 oo at CEE E> SG tal RS CN a ay “a from which it is easy to deduce : 3 ! « U . fee NE ae A re - (46) : t (47) 5 2 y'—3 Ss 8(y'—x') aes iL 7 é: 1 Py U < LA U < ! ! € ' aot vp =F [(2y'— 3x’) —4(4y'— 3x’) (2y'—3x') 4+ 16y |e): peer (48) The formulae (12), (15) and (16) of the first descriptive part of this paper may be derived from these formulae by means of the reverse transformation into the original y-surface with the aid of the formulae (26). Applying equation (31) we may also derive formula (17). In the course of this we get first at formula (23), which is given at the end of the descriptive part as serving also for the calculation for coexisting phases. The last statement might be objected to, because for those phases not »’ but v’? is a quantity of the same order as SOR aa oe _ dy’ wand ?t’; but this objection loses its foree when we observe that in — v no term occurs with v’? alone. 18. From these formulae (46), (47) and (48) follows now imme- diately the classification of the plaitpoints according to the eight cases and all the particularities of the corresponding graphical representation, as described in § 2—9. It is only necessary to say a few words about the construction of the cubic border curve. (2y'—3x')? — 4(4y'—3x') @y'—3x') + 16y'=0. . . (49) A closer examination of this equation shows, namely, that the curve possesses a double point, i.e. the point at infinity of the straight line 2’ 3z’=0. A simple parameter representation is therefore possible and it is really obtained by putting Dia ae een at tat east 0150) from which follows: oA gi(eeoy) ts Gyo 00 eee. ee 2 (61) hence: ; s?(s—4) : s®§—8 s?718s —— > *£ = as ; 8(s—2) 12 (s—2) ( 458 ) The points of the left-side branch are then given by the values of s between + @ and 2, those of the right-side branch by the others. For s=2 we get the two infinite branches belonging to the asymptote ; A — 3 % 2 be? ip? els | edn oe 19. Nor do we meet with any difficulties in the caleulation of the breadth-relations of the regions for very large values of 7 men- tioned in § 10. For the cubic curve we may put: Six! == 2 OR ee da. dee oe through which its equation passes into: (—P+4+8)Vy7+16—4h#=0 ... . (55) from which appears that for very large values of y’ we find —2y2, 0 and + 2V 2 for /. We get therefore for the leftside branch of the cubic curve approximately : 9 9 | Sgt YD ay oe t,o od aire gp red V7 (56) and for that on the right-side: 2.5 AB diel We La FT Vi2Vy sie Ye eee or eee while of course the middle branch with asymptote corresponds with &£=0O. For this branch we have: 2 2 ee ay NS) Ch tee Se ee act) ig (58) In a similar way we find for the parabolic border curve: 9 2 ied = VOY ae) i ce ene Taking this into consideration we may equate the breadth of the 2 yellow region at infinity to = (3_V3)V2.Vy’, that of the green , that of the purple w| no 9 one to av B-Mt that of the blue one to 2 2 one again to ae Cae and that of the red one to 9 8 V3V2Vy' from which the relations of equation (9) easily follow, while V3 —1=—0.732. uo —————E os ( 459. ) The spinodal curve. 20. The equation of the spinodal curve is found by elimination of m from (40) and (41). We must, however, take into account, when writing these two equations, that v’ along the spinodal curve must be considered to be of the order Vw, so that the terms with v must also be taken into consideration. We get then: m Bi BV) Be ee Weegee (0) Bsp 4 Sp- and 9 27 9 9 =F Oy —Be)m + tt ee ty Ge) ey =O - (61) from which follows for the equation of the spinodal curve: 1" Oem ns oe aioe 4 Usp. a 3 [(y —3x)?’ a 8 (y —*x)| Usp. = 3 Ye tp (62) This is, however, its equation on the w’-surface. In order to know it on the original y-surface, we must transform it with the aid of (26) into (ep. — 8b,)? — 3b,” ((2y’ — 8x')? — 8 (y' — *)] ey. + 120,27 = 0. . (63) For that of the cirele: (v—3b,)? + (e—R—d)? = R’*, (d small) we may write with the same approximation : (v—3b,)? — 2he + 2hd — 0, from which we may immediately derive the expression (10) for the radius of curvature of the (v, 7) projection of the spinodal curve. The two jirst connodal relations. Equation of the connodal curve. 21. We shall now take P, (,,v,) and P, (v,,v',), for which v, >v,, as denoting two corresponding connodes. We put then: Sons 8 es ee" — Sy; ie, =e! + Sys. (64) hence : " 1 ! 1 f " 4 omen .e v= Zeit) y= 5 C.2%)i 2 => Pst) S== = 8 (8) a a a v Vy where therefore (w", v") indicates a point halfway between the two connodes and § denotes the tangent of the angle which the projection on the (v', 2)-surface of the joim of the connodes forms with the v'-AXis. 460 ) It is then easy to anticipate, and it is confirmed by the caleula- tions, that all these quantities ¢, 2" and § with the exception of %, we of the same order with each other and with ; on the contrary not 9 but 9% is of this same order. 22. Taking this into consideration the jirst connodal relation : ——— 43 ( ) Soe) ae yields at first approximation : ” = 3 U ' ” f ”" E 3 U , ” log (a" +-§)) - re (2y'-32') (ve +-9)) = log (w"-§r)) - ri (2y'—3x') (v"-9) . (67) or also, subtracting on either side log 2": 57] 3 log (: + =) aay (2y'—3z') 4 = log ( — ae “ $7 or, as — is a small quantity of the order of 1, we get after deve- wv =) : lopment into series and division by 7: had 3 ’ ' ” $= 7 Gy—8) 2 Hoe Oe in which we shortly point out that this formula passes into formula (46) in the plaitpoint, and further that it leads immediately to for- mula (24) of the descriptive part. In the same way the second *) connodal relation : oy’, ow, er op 0) see yields at approximation: — SS ep Le (ebay (oa)? — > Cy 8x) (2-4 E+ 8 2 4 16 4 9 3. 3 9 9 l- > edt? 9) ea aot Sis t (v"—4) + 16 Cis 9 2 3 . ' ” —_ U U ” ” ” et (2y'—3x’) («" —§y) +— (y'—’) (v"—7")av",. 2 www. (TD) or, after reduction and division by 7: 1) We must here have recourse to the terms of the order ¢' or 2), as all those of lower order cancel each other. For the sake of clearness we have kept (¢" + 7]) and also (¢" — 1) together, though it is evident, that we may write e.g. for (v" + 4)8 at once 75 on account of the difference in order of v” and 1. ( 461 ) 9 ' 9 3 ' . ! en! t ' " Le] 2 t + 8 4? — 5) (2y ox) § +} 9 (y ora) ae =F . ° (72) from which follows in connection with (69): 4? — [(2y'— 32’)? — 8 (y’—x')J eo" + 4¢=0. . . . (73) 23. This formula yields at once the radius of curvature of the (v, x)-projection of the connodal curve. We need only observe that according to definition : fae 5 Vieonn. = 0 = 3 Lconn, — @ Se $j; Sa ay «oe went so at first approximation : = 2= ton = BATE, Mae Et oe ee Meet od ae eal (TLD) Substitution of these last relations in (73) now yields immediately the equation of the connodal curve and in exactly the same way as for the spinodal curve we find from it the value of the radius of cur- vature Reon, given in formula (11). A further explanation of the way in which the knowledge of this value leads to the formulae (13) and and (14) need not be given here, nor need we explain the derivation of the formulae (18) and (19), (21) and (22). But the derivation of formula (20) will detain us for a moment; we require, namely, for it a more accurate expression for p than that given in formula (23). If we therefore develop (31) as far as needful for the purpose, we find *): 8 3 3 9 3 9 jira (- ease? ¢ 7 ty! — re (2y'-32') a 5 (7-2) (76) Or: PP, ——— = 4#— 6tv' 4 2 (2y'—3x') « — 12 (y’—#') ve, . (77) Py thence : Pp—Pp Sion toe hye ara E we =- 6t(',- 2) +2 (27-8) (@, — © ,)— 12 (y'-*/) @, - v' ,)@ (78) for, with regard to the last term, the difference of wp and xp is slight compared to that between v'p and v'p. 9 1) It might appear as if y¢_%'> ought also to be inserted in the following ex- pression, but it is easy to see that this term leads to a small quantity of higher order than those that will occur in the final result. ( 462 ) It is now easy to find: 1 3 ‘ _— = — Pas —— Dy! am 320") i fog! 70 ep vp 5 m (, U R) 3 (2y ba')ic , (t ae ) - (79) either by paying attention to the fact that we have in Fig. d, § 12 (see the first descriptive part), if applied to the (»’, .r)-diagram, witha sufficient degree of approximation : 1 PQ Wit 3", PQ sm, to) 1 RQ= PQ.tg RPQ= PQ. - 4 = or by application of the formulae (13) and (14), observing that ,—°*p= 34, (e Se rR” This yields by substitution in (78): Pp— Pr wu 3 9.,! 2. c ' ' ' ' ee — Ob, -]- rn (27 —Sx)e, 12 ('—a).e, Jen p? 8%) or finally substituting for ¢’ its value from (47): i ee (8 y'-3x'Px 27'— 3x’)? (0, _ ») »(81) ' = ] ¢ P 7 a u p= a 4b, from which we immediately derive formula (20), applying (18). The third connodal relation. 24. We have now obtained the principal formulae. For the sake of completeness, however, we shall treat here also the third connodal relation, the more so as this leads to a new determination of the formulae (47) and (48), which puts the former to the test. This third relation reads: dy’ dy’ ay’ Oy’, i: 2 — 7, = yy, — 2, — — 7, ——: - 62 a * Our, 4 Oe", va % Our ma Or’, ©? if AON OU Re ‘atte We first transform y'—« at ae with the aid of (32). It proves we v to be necessary to keep all terms up to the order # or 7°. So we find : _ oy Oy’ ie ey 9s Wo eS St eat 2 ee - (83) From this follows: ' Ow’, , Oy ao, wn 9 > ”" Wits a Ms “ = -(1+4#')(e"+ §y)-(1-+ #') log 26, - 5 - gf (a + 20"y) + 22 9 ae 27 . Ae we iReader e sal +40 Jagr, 7 : [(2y'—3x') 4 2y't \(qt-v") (e"+Sy) — 2 sev — 5-22 + 2e"ayle" +80) + BY Ben! -0,(0* 4 2e"Sn) 20,0 (84) ( 463 ) If we equate this to the corresponding expression for PeOe st.» 8 wy —eu vs " Oz, = ov’, which is obtained by changing 4 into — 4, we get, dividing by 1: PEE ir) eee Nahe oe (ott gen oN gato SESE ie see mend align T5 (2y'— 8x) a+ dy'tal 3 : ie: aa ahs 2y'— 32) v"§— 9 (y' — x) § 7? — 18 (y' — z’)) vo" a" + 27 ao 77 (iy — 2i ej a —— ee 6 —— 4 Os (85) At first approximation this yields: = Ti (2y'— 3x!) a". This relation is, however, identical with the relation (69) which is derived from the first connodal relation. So we cannot draw any further conclusion from equation (85) without bringing it into con- nection with the first connodal relation; but for this it is required to introduce a further approximation for the latter. Second approaimation of the first connodal relation. 25. From the first connodal relation in connection with the equation 0 ' a = 14t+(1+4) logia-\-y,-2y,0-1-. 6 3.) - (86) the following relation may easily be derived, if we take into account the terms up to the order ¢? or 7°: 1, ve (1+ #’) log — SS (2y' —3x')j—3y'yt' + 9(7'—x')o"aj — —- (By'— 2’) 3 + 1 Sr 4 av SATO NG Tipo a4 On tie Oem aun Lise Gals Meda tabiomce. Mi. vs. Use sl (8m) Within the same order of approximation we have however: 47) i hesiaeel An Gh SE EGP log g Sra 3 pil 7 L vO: 1 at el v v & In the second term of the second member of this equation, however, we may safely make use of the first approximation furnished by equation (69). Taking this into account (87) passes after multiplication with w and division by 4 into: iu 3 et! —By'a't 25 sh Set at ee key em) Te ey — oe tt + Oy —x')0 ae" — 9 ' - ” oO 25 (Sy'—2x')yru” + 4a,§e" +4+- doy’? = 0... «. » « 2 es (88) Further veduction of the third connodal relation. Derivation of equation (25) of the first descriptive part. 26. By addition of (85) and = we find: *) 9 9 27 at 2 4 a 8 +5 20) =a —9(y' — 2!) $1)? —9(y'— x! w"e" 4- 3 9 + 2y'—Bx)o'S + 5 [(2y'—Bx')* + 16 (8y'—2x'))ne” = 0... (89) When we add to this relation (72), which is deduced from the second connodal relation, after having multiplied it with 7”, we can divide by 77 and we get: 9 9 63 ' ad 9 ' . ' ' " —t'— — vo" + — 7-0 y'-x')§ + — [(2y'-3z')? +168 y'-2%’)]Jc"=0 . (90) 2 4 20 52 Making use of (69) we may solve the quantity +" from this equation : 7 1 ae eee ~ [(27-32!)?-24(27'-3x') (y'-2!) + 16 (8y'-2)]2", (1, o o or finally with the aid of (73): att =e — 3z')? — 8 (y'—z')] + 1 = ' ~ 7o_) ' " -}- = [(2y' — 3x’)? — 24 (2y' — 3x’) (7' — z') 4+ 16 (By — 2')] \" . (92) from which equation (25) follows immediately with the aid of (65) and (26). In this way we have found the starting-point of the curve in the (v, .x)-diagram described by the point halfway between the points which represent coexisting phases. The tangent in that starting point also is now known. 1) Remarkable is the disappearance of the terms derived from 7 «2, which makes Ao Dy also }’ and a’, 1. e. re and b, disappear from the result. We have tested the truth 1 1 of this in different ways. = = -_—~ ( 465 ) A new determination of the plaitpoint, independent of the preceding one. 27. It is now easy to obtain such a determination with the aid of (73) and (91). For in the plaitpoint we have: " H= 003 (ae Sap 3 8 ap. From (73) follows immediately (47); from (91): 1 Up = Ot + = [(2y'— Bx) —24 (2y'—Bx) (y'—n) 16 (8y'—20/)]err;- (93) from which in connection with (47) we find again (48). Physics. — “Some remarkable phenomena, concerning the electric eurcuit wn electrolytes’. By Myr. A. H. Strxs. (Communicated by Prof. H. A. Lorentz). On etching of metal-alloys by means of the electric current, as communicated in the proceedings of the meeting of September 27, 1902, I met with a great difficulty. In some cases the hydrogen developed at the kathode was very troublesome, namely when, instead of escaping immediately it divided itself in small bubbles through the liquid and stuck to the object to be etched used as anode. This obstacle was overcome by surrounding the kathode with fine brass-gauze, so that the gasbubbles were compelled to escape directly in this case. The gauze was hung up apart, consequently there was no contact, whatever, with one of the electrodes. The etching being finished, copper proved to have been precipitated on the wires of the gauze, which deposit was almost conform to the shape of the electrodes. This was still more visible at a second etching-experiment with the same copper-alloy: a small cup was placed under the anode, which partly hung im it. Again on the gauze a copper-deposit was perceptible, which showed at the lower side a distinctly designed horizontal margin, nearly as high as the brim of the cup. It was to be expected, that copper should precipitate on the gauze, placed between the electrodes, as the whole apparatus can be con- sidered as two voltameters, connected in series‘). But, why is by this electrolysis not the whole side of the gauze, facing the anode, cop- pered, as is the case with the kathode by any ordinary electrolysis ? To answer this question the experiments were altered somewhat. 1) The anode and the side of the gauze facing it, are the electrodes of one, the other side of it and the kathode, those of the other voltameter. ol Proceedings Royal Acad. Amsterdam, Vol. V. 4660) Instead of water acidulated with sulphurie-acid a saturated solution of copper-sulphate was used as electrolyte; the electrodes were formed in future by two equally large Dutch bronze coins, The back part of these coins and the battery-wires, to which they were sol- dered, were varnished, as far as they were immersed in the electro- lyte, in order to be sure, that, during the electrolysis, the facing- sides only served as pole-plates. The gauze tube was left away and a screen of platinum (4 4¢.m.), hung up isolated, placed just amidst the electrodes, who were 4 c. m. from each other. If a copper- deposit might appear on the platinum, this could be ascribed to electrolytic actions only. Very soon after the circuit was closed (intensity + 0,3 amp; voltage of the battery = 4 volts) there came on the piece of platinum facing the anode a sharply bounded copper- deposit, which, by continuation of the experiment, changed of thick- ness exclusively and not of size. The experiment was continued for 2 days; still the results remained the same. Now I resolved to remove the platinum screen between the electrodes, to do the experiment over again and repeat this several times. The deposits obtained in all these cases were not exactly of the same size. The smallest deposit (diam. 18 mM) was obtained by hanging the screen between the electrodes (diam. 19 mM.), from which we ¢an conclude to a small gradual contraction to the middle. If two electrodes of different shape were used, then, by removing the platinum screen from the anode to the kathode, the copper- deposit passed from the shape of,one electrode into that of the other. This was very clearly visible by using a nut as anode and a square piece of sheet-copper as kathode. The hexagonal copperdeposit gra- dually took a square shape. Superticially one would be inclined to suppose, that the only thing, that has happened is the locally making of sections of the envelope of the two electrodes by means of the screen, but consider- ing, that, if electricity passes from one electrode to the other, the stream-lines divide through the whole fluid — the current-density is it will be ob- vious, that there must have been another cause, which made only larger within the above-mentioned envelope some stream-lines prefer to take the way round the screen to the shorter one through it. Considering, that the resistance of the platinum can be neglected in regard to that of the longer way through the fluid, the explanation of the deviation of these stream-lines can only be found in the polarisation, caused by the screen of platinum. To prove the supposal, that stream-lines are going out from the elee- trodes in all directions, the following experiment may serve: The ( 467 ) anode was hung in a platinum cup, which must replace the platinum diaphragm and was therefore partly filled with the electrolyte. Directly the circuit was closed, the inside of the cup was evenly coppered, as high as the surface of the liquid, while at the outside an intense gas-development took place, which was soon impossible to be observed well, as on account of the polarisation the current- intensity was considerably decreasing. In some cases from 0,9 amp. to 0,02 amp. If on the reverse the kathode was hung in the cup, the development of gas took place at the whole inside. Half of the outside of the cup facing the anode was partly and unevenly covered with a copper-deposit. When making the experiment with a sheet of platinum (5 & 5 cm.), dividing the glass in two equal parts, the results were just the same. Here also the platinum was entirely covered with precipitated copper. At a distance of the electrodes of about 10 m.m., the copper- deposit was pretty evenly spread over the platinum. At a smaller distance of the electrodes (4 m.m.) there came between the electrodes on the platinum a distinct circular deposit, while the copper precipit- ated on the remainder of the screen was very faint. A same deposit perfectly corresponds with the sections of the stream-lines we should expect. The same results were obtained, when using two diaphragms dividing the cup into three parts. At the first experiment two dia- phragms were used, completely shutting off the fluid and connected with a copper-wire. The side of the first diaphragm, facing the anode, counting from the anode to the kathode, was entirely coppered; the side of the other one, facing the kathode, was covered with gas-bubbles. At a second experiment only the connecting wire was taken away. The sides of both diaphragms, facing the positive electrode, were entirely covered with a copper-deposit. On the other sides gas was developing. At a third experiment two platinum screens (44 cm.) were used, thus not shutting off the fluid completely, but connected, however, with a copper-wire. The same circular copper-deposit came on the first screen, facing the anode, but, when breaking the connection the same side of the second screen was, on the contrary, entirely covered with copper. The latter phenomenon can be explained in this manner: The copper-ions, leaving the anode, yielded their charge to the first screen, over which it is entirely distributed and which, over the whole side, facing the kathode, serves in its turn as anode towards the second screen, which is coppered over the whole surface. If the second 31* ( 468 ) screen was larger than the first, then, the side of the former, facing the anode, was coppered for a part about as large as the latter. Then, the experiment was repeated with a screen, dividing the basin into two equal parts, but having a small hole in the middle. Just as a part of the stream-lines in some of the former experiments went round the screen, so here a very great contraction of the stream- lines towards the hole may be expected. Some of them will deviate from their straight way preferring the way through the hole, to the way through the screen. This is confirmed by a cireular part of the screen remaining uncovered. The following data are the results of a series of experiments, taken with holes of different size. Diameter of the hole. Diameter of the uncovered part. 1 mm. 7 mm. 2 on 10 4 4 14 » 5 on 17 4» 5 7] 25, " its) whole screen uncovered. distance between electrodes 3 em., diameter of electrodes 19 mm. If the smaller screen is taken, so that stream-lines can also go round it as well, then the uncovered part is considerably smaller. The diameter of it was 3 mm. at a 1 mm. diameter of the hole. It is worth notice, that, while the electro-motive force remained the same, the current-intensity increased on increasing the diameter of the aperture. If for instance at the experiment with the smallest hole (diam. 1 mm.) the intensity after the beginning of the polari- sation was 0,1 amp., it amounts under the same circumstances to 0,3 amp., when using the screen with the biggest hole. It is curious, that at the first experiment a copper-deposit was seen on the case of brass gauze surrounding the kathode, though properly it is nothing but a sereen with a great number of small holes. According to what is said before, it might have been expected,: that all the stream-lines would pass from tie anode through the holes of the case to the kathode and therefore not form any deposit on the gauze. In connection with this, some more experiments were taken with different sorts of brass gauze, but already by using the next size — stitches of 2 mm? and 0,38 mm. wires — no traces of copper were precipitated. If the way through the fluid was made considerably longer, then, in some cases, the current still seemed to prefer this round- ( 469 ) about way to the undoubtedly shorter one through the screen. This was done in the following way: Again the anode was hung in a platinum cup, over the brim of which hung a bent glass-tube, filled with the copper-sulphate solution, thus forming the connection between the electrolyte at the inner- and outer side of the cup. Even if a capillary tube was used, a deviation was observed in the copper-deposit, namely: a part of the cup near the lower end of the tube was not coppered, this, however, only when the tube was hung over that place on the brim of the cup between the electrodes. A 3 mm. tube, however, caused a deviation of the deposit, even, if the tube was hung over the brim of the cup on the prolongation of the centre-line of the electrodes. Of course, there must be some relation between the coppering of the inner surface of the cup in these cases and the circular deposit on the screen. It must be possible, therefore, to pass gradually from one deposit into the other. Instead of the cup a cylinder of platinum, having a diameter of 4 cm., was used, which at the bottom was melted in a basin with paraffine and projected from the fluid. The anode was hung in it again. The circuit being closed, the inside of the cylinder was of course coppered again as far as it was immersed in the electrolyte (50 mm.). Then a vertical cleft of 1 mm. wide and 1 mm. high was made in the cylinder on the extension-line of the centres of electrodes. A part of the inner wall round the cleft remained again uncovered. When gradually giving the cleft a height of 20mm., the uncovered part took the form of an ellipse, till ata height of 25 mm. a strip of 8 mm. wideness was not covered with copper, along the whole height, i.e. 50 mm., of the electrolyte. When still enlarging the cleft, the deposit gradually receded more from the margins and after unfolding the cylinder into a plane it finally took the already known circular form again. To make the explanation, given of the deviation of the stream-lines on account of the polarisation of the platinum, more acceptible, the experiments were made with different electromotive forces by inserting resistance. By means of a resistance box, connected parallel with the voltameter, the terminal voltage of the latter could be increased. The current-intensity could be read on a milli-amperemeter, joined in cireuit with the voltameter. As long as the potential difference was less than the electro-motive force of the polarisation, nothing was precipitated. After more resistance had been inserted in the resistance box, a current began to pass through the voltameter, but without forming a deposit on the sheet of platinum, although the experiment was carried on some hours. For that reason this current ( 470 could not have chosen its way through the sereen and must have gone therefore round it. If some more resistance was inserted, then a deposit came gradually on the sereen, smaller and more uneven than in the ordinary case, but also taking the normal size and thickness as formerly, when going on inserting more resistance. Different salts were used as electrolyte, in noné however, a deposit was so easily formed as in cupricsulphate. The phenomenon, when using this salt, was so clear, that once a deviation in the shape of the deposit was observed, because the wire which was connected to the anode, was not sufficiently insulated. In saturated solutions of zine-, aluminium-, nickel-, cobalt-, ferrous- and ferricsulphate deposits were formed, one clearer than the other even if in all these cases the constant current-intensity was secured by inserting resistance. Chlorides were also used as electrolytes. In chlorides of zine and cadmium exactly the same circular deposit was formed, but in those metals, which can form more than one chloride (e.g. iron), a secondary phenomenon always appeared. When a solution of cupric-chloride was electrolysed, copper precipitated on the kathode; when, however, a platinum screen was put between the electrodes, again a circular deposit of a white substance was formed on the screen, quickly getting green in the air and being hygroscopic then; probably it might have been cuprous chloride, afterwards becoming cupric chloride again. When using a solution of Hg Cl, as electrolyte a white deposit of Hg Cl came on the platinum. A solution of Au Cl, gave conformable results; a brown red deposit was formed. Using H, Pt Cl, and a screen of gold-leaf, a yellow brown one was formed on the latter. When a solution of ferric chloride was used no deposit was ever formed. The explanation may be found perhaps in the solubility of ferrous chloride which is precipitated on the platinum as copper before. Though in many of the former cases an explanation could be found in the polarisation, yet, however, there is one thing, that cannot be explained, i. e. the curious sharp margins of the deposit. It seems as if the stream-lines keep their original direction within a certain tubular surface also in the presence of the platinum screen, while this screen has a strong influence on the lines outside of it, which change their direction and go round the screen. Perhaps the explanation may be found by calculating the course of the circuit, but I am not able to do it. In the making of all these experiments I have become indebted to professor Aronxsters and professor ScHroeDER VAN DER Kok for their assistance of various kinds and to these I tender my best thanks. Also to Professor H. A. Lorentz, professor at the Leyden University, for his help and information. Mineralogical Laboratory. Polyt. School. Delft, Jan. 1903. (February 25, 19038). KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, PROCEEDINGS OF THE MEETING of Saturday February 28, 1903. (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeecling van Zaterdag 28 Februari 1903, DI. XD. GAS ANF as aD ANP Aste J.P. Kurxen: “Critical phenomena of partially miscible liquids—ethane aud methylaleohol” (Communicated by Prof. I. Kamernixcu Oxnes), p. 473. A. PP. N. Frasenironr: “On the so-called compounds of salts of sulphonearboxy lic acids with sulphuric esters”, p. 482. Jax pe Vairs: “On the spheres of MoycGr belonging to ordinary and tangential peneils or quadratic surfaces”, p. 484. J.D. vax ver Waars Jr: “he variability with the density of the quantity J of the equation of state”. (Communicated by Prof. J. D. vax per Wars), p. 487. J. W. Morr presents the dissertation of Dr. J. C. Scnourn: “Die Steli-Theorie”, p. 497. H. Kamercixcu Oxses: “Methods and apparatus used in the cryogenic laboratory. ILI. Bath of yery wniform and constant low temperatures in the cryostat”. p. 502, (with 6 plates). The following papers were read: Physics. “Chitical phenomena of partially miscible liquids — ethane and imethylaleohol” By J.P. WKeexnx, (Communicated by Prof. H. WKaMurnicGH Onxnus). (Communicated in the Meeting of September 27, 1902). Some years ago Mr. W. G. Rosson and T began a systematic investigation of the phenomena of condensation for mixtures of liquids Which do not mix in all proportions '). Shortly afterwards Prof. vax pyr Wats communicated to this Society an important paper in which he discussed our results?) and again in the second volume of his treatise on the Continuity *) he devotes some pages to the conside- ') Zeitschrift tir Physik. Chemie 28, p. 342-365. Phil. Mag. (5) 48, p. LS0—203. 2) Kon. Ak. van Wet. Amsterdam 25th March 1899, 5) Die Continuitiit ete. I. 1900. p. 184—192. Proceedings Loyal Acad, Amsterdam. Vol. Y. 474 ) ration of the same phenomena, After the publication of Prof, vax ber Waats’s paper L approached him privately with some objections to his views to which he replied in the most courteous manner, Though not) completely satisfied it seemed winecessary at the time fo publish my views until TP should be in a position to add to our knowledge of the phenomena by further experiments. I have recently resumed the investigation and the results obtained, though naturally far from complete, seem of sufficient importance to deserve an immediate publication and to be discussed in connection With previous experiments. For various reasons we had fixed our choice on mixtures of liydro- carbons first of all ethane and alcohols. Briefly our results were as follows: e ra oad) = a WE og CHOK GH SZ a } aC) : ~ a. Fig 1. For mixtures of ethane with ethyl-, propyl-, isopropyl- and butyl alcohol there are two temperatures A and £6 (Pig. 1) between which three phases two liquids and vapour — are possible and the critical (i.e. plaitpoint) curve accordingly consists of two branches, (1A and (LB, C, and C, representing the eritical points of ethane and alcohol respectively and AZ the three-phase curve. For ethyl alcohol A and #4 are comparatively far apart: for the higher terms of the series these points gradually approach each other and with amylalecohol no separation into two liquids could be observed; in this case the critical curve jas a continuous curve joming the two critical points @, and CL in the usual manner. For mixtures of methylalcohol and ethane we found a branch C\A i et? el ee ne » saa Caan) and a three-phase curve ending at 1, as with the higher alcohols, but not a limit B below whieh the liquids mix in all proportions. The character of the other branch of the eritieal curve which begins at (,, the eritieal point of methylalcohol, therefore remained uncertam. Prof. vax per Waats’s remarks concerned firstly the explanation of the behaviour of the first group of mixtures and secondly of the different behaviour of methylaleohol and the prediction of the phe- homena outside the limits of our researches. The experiments com- municated in this paper have reference to the latter problem. First of all Prof. vax per Waats shows how the two branches (1A and (,4 may be made into one continuous curve by producing them in the region of the metastable and unstable conditions, a region which I shall call the “theoretical” region. In our paper we had pointed out that the phenomena were completely explained by the formation of a new subsidiary plait with plaitpoint emerging out of the main plait on the y-surface and the subsequent withdrawal and disappearance of the main plaitpoint’). Having regard to VAN DER Waats’s original investigation and to Korrmwna’s treatise *) on the properties of the y-surface, the simplest interpretation appears to be fo assume that at some temperature higher than 7'¢ a closed plait begins to develop on the spinodal curve, increasing in extent as the temperature falls, until one of its plaitpoints — that of the first kind *) — at wf pierces the connodal curve of the main plait, thus giving rise to the formation of the subsidiary plait and the three-phase triangle. On further fall of temperature the inner plaitpoint exchanges partners, so as to form a closed plait with that branch of the main plait on Which the original plaitpoint lies: at 4 the connodal curve of the main plait begins to enclose this closed plait. We may moreover assume the latter to contract on further cooling and ultimately shrink to nothing *). Transferring the above changes to the p--diagram we obtain the figure deduced from ours by Prof. vax per WAALS. 1) 1. c. p. 3d58—359. 2) Arch. Néerl. 24 p. 295—368 in particular p. 316 ete. 3) Comp. Korrewea p. 67. *) Whether this actually takes place seems at least doubtful. The formation of the plait on cooling is hardly open to doubt, seemg that at Ingh temperatures the surface cannot siiow any abnormalities in the region under consideration : but this condition does not hold at low temperatures and the contraction of a closed plait on cooling is in contradiction with the rule enunciated by Prof. vax per Waats regarding the influence of temperature on the extension of plaits. BEd OL” ( 476 ) The possibility of producing the theoretical curves in the p-(-diagram had’ escaped our notice '), Iu the first place Prof. vax per Waans observes that the completed figure is in contradiction with the luv previously deduced by him?) that a mixture of non associating substances may have a maximum or minimum critical temperature, but not both. To this point one of my objections refers. The law depends entirely on the simple characteristic equation, but apart from that it only refers to the critical point of the homogeneous mixtures and it must be looked upon as a possibility that the curve of the critical points the plaitpoints should have both a maximum and a minimum. Prof. vax per Waais replies to this*) that near a maximum or minimum the two curves in question are so close to each other that no such difference between them can be admitted. This argument does not satisfy me. The two curves touch each other at points where a maximum or minimum rapeurpressure exists and the two phases have the same composition, but points of that kind do not exist in the case under consideration. It is true that a maximum or minimum occurs on the plait when the connodal curve intersects the spinodal curve, but the character of these points is entirely different from that of the points referred to. The three-phase pressure for mixtures of ethane and the aleohol is between the vapourpressures of the components and there is thus no occasion for assuming the existence of another maximum or minimum. That being the case, there is no reason for a close resemblance between the two curves nor any 1) Note added to translation. The above was wrilten by me in the conviction which I then held that Prof, VAN DER WaAALS’s views of the formation of the new plait — although arrived at in a different way — still agreed essentially with my own: indeed I do not even now see, how else the phenomena could be interpreted. From the paper contributed by him in the October-meeling of this society (critical phenomena of partially miscible liquids. Kon. Ak. van Wet. Amst. 25th Oct. 1902) it appears that such was not the case and that I ought to have been more careful in accept- ing the theoretical curve drawn by him as corresponding to the changes on the y-surface as understood by myself. Doubt never arose in my mind on this peint at all and I never considered the question. Still | ought to have noticed that the theoretical curve has no vertical tangent at its extreme points, but ends in cusps, corresponding to the circumstance that the curvature of the connodal curve is the same in both plaitpoints of the closed plait. This is the only respect in which I think my paper requires emendation although some of my arguments would have been presented in a different manner had I realised how completely his views differed from mine, 2) Arch. Néerl. 24 p. 23. 5) Continuitat Il p. 188 1. 17. ( 477 ) ground why the “homogeneous” critical curve should have a loop as well as the plaitpointenrve. 1 am = strengthened in this opinion by the fact, that even in the “symmietrical” case Prof. KorTEWkEG has Come across similar peculiarities in the plait and it follows, that theoretically even those mixtures Which obey vax per Waatrs’s equation may have a critical curve with a loop i it. 1 do not mean to maintain that the homogeneous eurve in our case does not possess a loop or to deny the probability of Prof. VAN prER Waats’s hypothesis according to which the association of the alcohols plays a part in producing the abnormality. What I want to point out is that it has not been proved that with normal mixtures the abnormality cannot occur, although it is very probable that this abnormality and in general the formation of two liquid layers —- while theoretically possible for normal mixtures with special values of the constants — in reality occurs with associating substances only ?), The critical curve in the p,f-diagram having been completed in the way described one feels inclined to say with Prof. van par Waats that the case is one of a modified cross-plait and not of a true liquid- plait. According to VAN per Len’s experiments *) the liquid-plait for mixtures of phenol and water has its plaitpoints turned in the direction of the positive volume-axis and above a certain temperature is entirely independent of the cross-plait. Prof. vax per Waars seems inclined to look upon those properties as characteristic of the liquid-plait and to withhold this name from that part of the plait which in our case is turned towards the w-axis. It will appear presently that this view cannot very well be sustained so that at any rate this ground for drawing ihe distinction in question disappears. Still the peculiarity remains *) that the critical Curve is a continuous curve, at least when no account is taken of the objection urged above against joining the curves beyond B. Even then however it will be observed that on the y-surface two independent plaits exist completely or partly inside each other and thus when the y-surface itself is considered the contrast between our case and one in which a true liquid plait would exist disappears. association Moreover the abnormality is ascribed to the same cause as the formation of the liqnid plait; if both are due to the same cause, one feels even less inclined to maintain a distinetion in the nomenclature. ') Continuitiit IE p. 176. 1 doubt the possibility of deducing a relation between M@. on the one side and a, and dy. on the other. >) Zeitschr. Physik. Chemie, 33, p. 622, 630. 5) Continuitat II p. 188. 478 The following may be added in’ further explanation: there is a well defined contrast, between the two plaits as regards the causes of their existence. “The cross-plait depends for its existenee on the shape of the yecurves for the separate homogeneous mixtures, the liquid-plait) on the other hand is due to the manner ino whieh these curves change with the composition. In the formation of the latter plait association scems to be the principal factor, But notwithstanding this distinet contrast there mast be a number of eases in whieh it will be impossible to say whieh kind of plait one is dealing with and to which sort of plait a given plaitpoint belongs. We shall presently come across a striking instinee of this kind where a eross-plait with its plaitpoint gradually changes info a plait: with its plaitpoint turned towards the w-axis from which it is impossible to withhold the name liquid-plate. Let us now consider the case of methylucohol and ethane. Before communicating the new results T will discuss Prof. vax per Waats’s views of these mixtures. He assumes that the critical curve | is again a continuous one but with a loop turned upwards this time instead of downwards as with the higher terms.") There are some serious objections to this theory. The critical curve, starting at the critical point of ethane C,, disappears from the practical part of the surfaee at of, as in the former case, and the part) bevond can therefore only represent a theoretical plaitpoint which remains hidden, because at higher tem- peratures no three phases coexist. Beyond 1 the curve should there- fore be dotted throughout, and it cannot be interpreted as in part real. In this case as in the other the shape of the curve was deduced by keeping in view the homogeneous critical point and a striking instance is afforded of how this curve does not give us any clue as to the shape of the real critical curve. In the second place T think the bending upwards of the critical curve assumed in’ this case is open to doubt. At somewhat high temperatures there is) probably no abnormality on the surface and no plait except the cross-plait: as the temperature falls a closed curve develops) one of whose plaitpoints pierces the main plait at A and moves from there towards €,. As in the other mixtures the three-phase pressure is lower than the vapour pressure of ethane ; it follows that the subsidiary plaitpoint is turned towards the .-axis and represents a maximum pressure on the closed plait. This being so the simplest) supposition to make is that the other plaitpoint of 1) Comp. his diagram Kon. Ak. vy. Wetensch. Amst. March 25th. 1899 p. 5. ( 479 | this closed plait is one of minimum pressure: starting from this point the pressure on this plait passes through a maximum and a minimum successively and reaches its highest value in the real plait- point. In other words the theoretical part of the bent critical curve in the p,édiagram should lie below the practical part, as with the other alcohols. ‘This supposition seems so much simpler than the Opposite one that TI feel prompted to state the following rule: when the three-phase pressure is betiveen the LU POUL PVeSsuUres of the com- ponents the theoretical critical curve bends downwards, when it is higher than the vapour pressures of the components (as with ether and water?)) the curve bends upicards. In his book on the ‘Continuity’ *) the author discusses the pro- bable behaviour of the mixtures at higher temperatures. Apart from a possible plaitpoint on the side of the small volumes on the liquid- plait, there is no practical plaitpoint left above A. Prof. vax DER Wants assumes that this condition will continue wp to the critical point of anethylalcohol, that the plait will close itself here, gradually contract and ultimately disappear either at the limiting liquid-volume ov by its plaitpoint meeting with a possible liquid plaitpoint. This expectation has not been realised by my experiments and must in itself be looked upon as improbable. The formation of the liquid-plait is ascribed to the association of methylaleohol, Above a certain temperature this abnormality has disappeared and in any case athe ¢ritieal point it is for most substances very small. Considering the great difference between the critical temperatures of the two constituents of the mixture an admixture of ethane to methylalcohol eummot but lower the critical point, even if the mutual attraction of the components were comparatively great. As a matter of fact methylaleohol seems to have some association left at the critical point *). But this association has the effect of making the mutual attraction appear even smaller and thus increases the probability of av lowering of the critical temperature by the addition of ethane. It follows that the cross-plait has to appear on the yesurface in’ the usual manner with fall of temperature, with its plaitpoint turned towards the ethane side. In view of the fact that at low temperatures there is a liquid- 1) KUENEN and Losson |. c. p. 351. 2) Continuitit I, p. 189 verv. ‘) Ramsay & Suetps, Zeitschr. Physik. Chemie 15, p. 115. Nobody seems to have observed as far as I know that the comparatively high value of the critical temp- erature of methylaleohol may be explained by association, as also the deviation from Korr’s law for the boiling points of series of organic substances. 480 plait there ave still two possibilities with regard to the development of this eross-plaits (1) the plaitpoint continues by itself and gradually begins fo form the closing plaitpoint of the liquid-plait) whieh may disappear at the limiting liquid) volume or (2) it disappears by meeting With a second plaitpoint belonging to an independent liquid-plait so that the two plaits then form: one large one, with or without a closing plaitpoint on the liquid: side. The experiments confirm the above view of the effect of an vdmixture of ethane on the critical point of methylalcohol and as far as they go seem to show the first alternative to be the correct one. Tt appears that the general behaviour of mixtures of methyl alcohol and ethane thus disclosed agrees with that of ether and Water as predicted without however any grounds being given — by Kortrwee *) and laid down in some r-r-diagrams. On the grounds set forth above | support this expectation as regards ether and water, Addition of ether to water will lower the critical ten perature, ium at afo 200 CHOH - | HY H C sO ae) | CH ¢ 7} Oo . . * e . . . - 50 (9) so 300 I50 250 250 Vig. 2. The results for methylacohol and ethane are laid down in figure 2. I can give only a short explanation here. Starting from (, — the critical point of methylalcohol the critical curve runs in a per- fectly normal way at first, owing to the influence of the association being as yet insufficient. It ascends, passes through a maximum at 120), and then falls, evidently tending towards the critical point *) Arch. Néerl. 24 p. 338—340, —— -— ( 48° ) of ethane: the association however becomes gradually stronger; the dip in the surface caused by this ') gradually modifies the shape of the cross-plait: the plaitpoint passes through a minimum: pressure between 25° and 30°, and the critical curve then begins to rise rapidly. The end of the cross-plait thus changes without a disconti- unity into a liquid-plait; in the mean time the main plait goes on developing on the approach of the critical point of ethane: as explained a small subsidiary plait is formed which appears at 21 on the pract- ical part of the surface. Probably an exchange of plaitpoints occurs on the theoretical part, of the same nature as with the higher aleo- hols, the result being that at low temperatures the cross-plait is ent through by one self-contained liquid-plait. But as far as the phen- omena are concerned this is entirely immaterial. As far as the experiments could be carried (i.e. up to 275 atmospheres) the critical curve continued to rise towards the left, so that there is no indication of the existence of a different plaitpoint. The rapidity with which the mixing-pressure increases is— truly remarkable. If we compare the figures for methylaleohol and for the higher terms, a certain resemblance will be noticed, especially if we do not assume the contraction of the closed plait to nothing in the latter case. The association tends to produce the same modification in the usual diagram in both cases, but the acting causes appear to be much more effective with methylalcohol —— the stronger association of the alcohol, possibly a smaller mutual attraction or the influence suggested by Prof. vax per Waats of the small molecular volume of the aleohol may contribute to this result. For this substance the plaitpoint remains outside the cross-plait at low temperatures, with the others it succeeds in disappearing inside. Whether inside this plait any changes take place similar to those occurring with methyl- weohol on the practical part of the surface we cannot tell. But in any case IT have assured myself that with ethylaleohol a new plait- point curve does not appear down to —78 : ethylaleohol and ethane remain miscible in all proportions. Methylalcohol and ethane min by pressure. In this respect they contrast. with mixtures phenol and water for whieh the liquid) plait above a certain temperature far below the critical region separates completely from the cross-plait and thus has a plaitpoint on the side of the positive r-axis. In view of the probable disappearance of the association at high temperatures it is possible that in the latter case 1) Continuitét ete. I. p. 191. ( 482 further experiments will disclose a second plaitpoint on the liquid side of the plait, as predicted many years ago by van pee Waars from the value of the volume-constunts. LE expect to be able to throw more light on this subject by the continuation of my investigation with the higher hydrocarbons, Ether and water behave in all probability in A ommatnner similar to methylalcohol and ethane, Chemistry. “On the so-called compotuls of salts of sulphon- curborylic acids with sulphurie esters.” ly Prof. A. Fate IS RANCHIMONT. (Communicated in the meeting of Jannary 31, 1908). The first of this kind of compounds was obtained accidentally by Laver in 1879 in the laboratory of Grerner in Jena. Tle wanted to reduce sodium sulphonacetate with soditua amalgam and water, but afier acidifying with sulphuric acid, evaporating, and extracting with absolute alcohol, he obtained an acid liquid whieh gave with barium carbonate a salt of the empirical composition C, Tl,, Bas, O,,. This salt has, therefore, the composition of one molecule of barium sulphonacetule plus one molecule of ethyl sulphate plus one moleeule of water and may, according to Grurier, be considered as a deriv- alive of a disulphuric acid in whieh two hydrogen atoms have been replaced by ethyl groups and one OH group by the group CH,— COOITL He obtained the same compound by digesting a mixture of sodinm sulphonacetate, soditm-hydrogen sulphate and alcohol. The acid was euled “ Diaethylessiydischive flsiinve”. Acetic acid: itself did not yield a similar compound. In 1888. in’ the same laboratory, SrexGer successfully attempted jo obtain a similar compound with metasulphobenzoie acid; the amuysis gave the composition C,, H,,O0.5, Ba + 3), H,O. The acid was called = Diaethylbenzotdischivefelsiure”. Analogous compounds were also obtained with methyl and propyl aleohol. Benzoie acid, however, did not give a similar compound and it is, therefore, attri- buted to the sulphonic acid group. ENGELCKE obtained similar compounds with isethionic acid but not With benzenesulphonic acid and = Niriack did not obtain it with methylsulphonie acid. Gretier looked upon these compounds as salts of a derivative of e () ) LZ O\ Iz OC, Hy disulphuric acid S,O JH, such as C, H, — Pa Zo ye a) OG, HH; CO.H OH In Berster’s ‘Handbuch’, however, these compounds are deseribed as double compounds of salts of sulphoncarboxylic acid with neutral sulphuric esters. For a lone time, however, | have felt serious objections to this theory. T had already repeated the experiments with sulphonacetic acid and metasulphobenzoic acid but did not obtain pure compounds. T was also unsuecessful in attempting a synthesis by means of the salts of sulphoncarboxylic acids and dimethyl- and diaethylsulphate. The phenomena observed during this research induced me to request Dr. Arrema to try to obtain compounds of the same empirical composition in’ a different manner, namely by bringing together in molecular proportions the barium salts of the acid esters of meta- sulphobenzoic acid with the bari salts of the alkylsulphuric acids. If in this proportion they yield a compound this ought then to have the same empirical composition as the last named compound. Dr. Arrema now observed that on evaporating a solution containing in molecular proportions the baritm salt of the ethyl ester of meta- sulphobenzoic acid and barium ethylsulphate, the greater portion of the ethylbarium salt of metasulphobenzoic acid was deposited first in beautiful crystals; affer this a double compound of the two barium sults made its appearance in the form of large rosettes of tender needle-shaped crystals whilst’ from the motherliquor barium ethyl- sulphate was obtained. Tf an excess of barium: ethylsulphate is taken for instance, 5 erams of the same to 1 gram of the salt of barium ester the double compound separates immediately and from the motherliquor barium ethylsulphate is obtained. The double compound cannot be recrystallised) from water; its aqueous solution presents the same phenomena as one containing in molecular proportion the two salts; on evaporation, the salt of barium ester crystallises first, then the double compound and finally the barivain ethylsulphate. As the double compound cannot be recrystallised from alcohol it was freed from motherliquor by strong pressure and analysed. The results of the analyses of three different preparations were concordant and agreed with the format: COLE alal, , Ba + (C,H, SO,), Ba + 6 H,0. Dr. Artema has afterwards repeated Srmxcue’s method of preparing the compounds, but here he also obtained first the ethyl barium: salt of metasulphobenzoic acid and afterwards, although less readily, ( 454 the double compound. An analogous result was obtained with the methy| compound. We may, therefore, come to the conclusion that there exist no compounds of salts of sulphoncarboxylie acids with neutral sulphurie esters: there exist, however, double compounds of salts of the acid esters of sulphoncarboxylic acids with salts of the acid sulphuric esters. This result’ gives rise to a number of questionst some of which Dr. Arrema intends answering by practical experiments. Both salts ave alkyl-metallic salts of dibasic acids whose acidic functions (at all events in’ the case of metasulphobenzoic acid) have avery different power, whilst salphurie acid as oxysulphonic acid is some- What comparable to isethionic acid which also exhibits the property. Mathematics. —— “On the spheres af Monor belonging to ordinary and tangential pencils of quadratic surfaces.” By Prot. Jax DE VRIES. 1. In Part I of the “Proceedings of the Section of Sciences” pages 305—310, I have developed, making use of Fimpier’s cyelo- graphic representation, some properties with respect to the system of the orthoptical cireles of the conies of a linear system. By extending Fiep.er’s considerations to a four-dimensional space the corresponding case of the three-dimensional space might be treated. In the following essay the indicated extension on quadratic surfaces is arrived at analytically. Given P the point of intersection of three mutually perpendicular tangent planes of the quadratic surface S* represented by the equation 4, ta, ta, 242 a,, cy+2 a,, rze+2 a,, ye4+2a,, 742 a,,4-++ + 2a,,z+a,,= 0. These three tangent planes form with every fourth tangent plane a tetrahedron circumscribed about SS? that may be regarded as polar tetrahedron with respect to the point-sphere (isotropie cone) /* repre- sented by (e—2,)* + (y—y,)? + €—2,)" = 0- So the invariant @ belonging to S* and /? is equal to zero *). Therefore we have: 1) See a.o. Satwon-Fiepier, Anal. Geom. des Raumes, 3d edition, vol. I, p. 253, where S? is represented by an ellipsoid. QM, GN, Gs eased | GM, Ns 0 G4 Gra) (ea as == ify Gig atta i) Gs. fe i Gin) ae pee ce Th Ces | Ge, Oy yy by (a7, TP 2) Cy lay ey Na | | 4 0 Cremer i i} Ge dan ay | Oy, 1 Uy; yy Woq yy My, oe ao == (0). (ys () On Us, () @y3 Oy» On, U4 a a ay Sei yg ey UGG lf we represent the minor: of ay, mm A= > -+ a,, @,,4,,¢,, by Am, it ensues from this relation that the locus of the point 7? is indicated by the following equation (where the indices of the coor- (linates are left out) Abn (seat taa*) 3 (Anal Ae) (A, day = 0, So the locus of the points of intersection of tripiets of mutually perpendicular tangent planes of jS? is a sphere (Moan). , The tangential cone to S* with vertex P possessing three mutually perpendicular tangent planes, the tangent planes form according to a well-known property an infinite mumber of triplets of mutually perpendicular planes. For A,,=0O we find S? to be a paraboloid and the sphere ot Moner degenerates into a plane. The obtained equation can be replaced by Now however 4,,4,,— A’,, is equal to (¢,,«,, — «?,,) 4. ') The radius of the sphere is indicated by the square root out of eS (4,433 — a5) 3 Al? Consequently the sphere of Monen will be reduced to a point- 14 sphere when S? is a cone (4=0) or into an equilateral hyperboloid if namely the equation 1) This ensues inter alia from Wa Chi ie ei 1, AL, Li, Ai, A a, %, 0 (rics ae (ie Uy ls, : Q ] Q) () Q yy (CP ) ee er en (CO Os ft | OEP RT ! “Ot an. ca. 0 Uy, Ugg yy Ugg A Abs AN, ZV Ua, 3, A (See a.o. Batrzer, Determinanten, Sth edition, p. 63). ( 486 ) . 2 (4,143 Oa) (ty 5455 a" 45) + (45,4,, — 4,5) = 0 is satisfied. In the latter case the asymptotic cone possesses as is known x! triplets of mutually perpendicular tangent planes, 2. When in the equation A, (@?--y? +27) — 2(A,, e+, }- Aly, 2) + (4,,4+-4,,4 Acs) sau we substitute ay. + 2b, for ag. the new equation represents the system of the spheres of Monae belonging to the quadratic surfiees of a pencil. The equation is a cubic one in 2; so the indicated spheres form aosystem with index 38, that is, through each point three spheres pass. If for brevity’s sake we represent the formula Coe treba ty by Cy, the cubic equation is I, C, 2 “—F L C, 2 - I, C, 2 a5 I, C, =". The power of a point with respect to the sphere (4) is then equal to LC #41,6, V4LC +L, LPL eS Lae This expression becomes independent of 4 for the centre of the sphere cutting the four spheres C, orthogonally; a// the spheres of the indicated system are intersected at right angles by a jived sphere. On this orthogonal sphere the point-spheres of the system are of course situated; so it-contains in the first place the vertices of the four cones, in the second place the centres of the two equilateral hyperbo- loids*) belonging to the peneil. From this ensues that the locus of the centres of the spheres is a skew cubic. This is moreover confirmed by the observation that in vy witty >» Y= AytAy » % =A, AQ the numerators and the denominators are cubic forms in: 2. The square of the radius being represented by the quotient of two forms of order six in 4, the system contains six spheres with given radius. 3. The quadratic surface indicated by the equation in’ tangential coordinates $, 4. § 1) Their parameters are determined by ze [(4,, +4, 4) a Ay (4,,+4,, 4)*| = 0. dy Se -}- 24,5 $7 | 22> a, 8 Co 3 3 3 has for equation in point coordinates y+ ie Dyas : as = A, 2 Pal A ey 2 > AL Al, = 0. 3 3 3 If now «ey is the minor of the determinant 2 +- 1 pik ale corresponding to ty, the sphere of Mone of the indicated surface 11 is represented by Os, (uw +i 4-2) — = (ee, tt, if + (542) a (Case Gear 53) == Ne But we have!) «@re=anr4>; so this equation can be replaced ly W,, (ey? 2") — 2)(G, ,@ + a, 4-4.) +— (d,, 4,2 4,,) = 0, So for a tangential pencil of quadratic surfaces we find y & = = ” | Dern Ss! =< (be Selene 4) (a +Y are == 2 (4,457 ey A) ie ee (¢,,+4,, 2) ay 3 3 that is, the corresponding spheres of Monee form a pencil. To this belong the point-spheres indicated by = (qa tbs 4)? = (4 +11 4) (4,,+,, 4)] = 9%, 2 o originating from two equilateral hyperboloids, and the plane determined by a,,+6,,4=0 belonging to the paraboloid of the tangential pencil. Physics. — “Zhe variability with the density of the quantity / of the equation of state” By Dr. J. D. vax pur Waats Jr. Com- municated by Prof. J. D. van per Wats. § 1. If we suppose the molecules of a gas’) to be perfectly smooth, elastic spheres, the influence of the fact that their diameter is not infinitely small, on the form of the equation of state may be allowed for in first approximation by diminishing the volume V7) in which the eas is contained, with four times the volume of the mole- cules. If we understand by distance sphere a sphere deseribed con- centric with a molecule and with a radius 2 6 (where o denotes the 1) See inter alia Batrzer, |. c. p. 605. » I say only “gas” not “gas or liquid’, for we must not apply the formula for a liquid without introducing still other approximated terms than those that will be discussed here. ( 488 ) radius of the moleeule), then we may also say, that we must diminish Mowith half the combined volumes of the distance spheres, whieh quantity is usually denoted by 4, or by 4, if we wish to take into accomml the variability of the correction in consequence of variation in density. Various methods have been followed in order to investigate this influence; all these methods vielded a conformable result, so that no reasonable doubt can exist as to the correctness of this statement. We should be inclined to deduce from this, that the influence may he correctly allowed for in’ second approximation by diminishing with half the volume really occupied by the distance spheres, in Which a segment which two distance spheres have in’ common, is counted only once, or what comes to the same, by writing 4, — 2S instead of 6,,, YS representing the sum of all the segments which are covered by two distance spheres at the same time. The correc- tion has been introduced in’ this way by Prof. J.D. vax per WAALS"); and Dr. J. J. van Laar?*) has made a calculation of a second correc- tion term, Which is based on a similar sapposition. T will however confine myself to the discussion of the first correction term, for whieh ig ee ; 30° Che question whether the first correction ferm is correctly found in’ this way has not been ansWered un- we find in this way animously in the affirmative. BoirzMany *) follows quite a different Sy yf method for calculating it and finds : r Though BourzMaxn in his communication in these Proceedings expressed the wish that his publication of this result differing from my father’s would give rise fo a discussion by which this doubtful point might be elucidated, no discussion has followed by which the question has been settled conclusively. Now I think IT can show that there is no reason for 17h. introducing the correction in the way which yields the value 39 na and at the same time I will give a reasoning, by which the term 3) ff * is derived in a shorter way than that followed by Botrzmayy, 8 J The simplest way to show clearly what supposition we must E z ‘ UT Ue : ‘ make in order to vet the correction term 55 a is to start from the 1) Versl. Kon. Akad. vy. Wetensch. V. p. 150. Oct. 1896. 2) These Proceedings Vol. I, p. 273. Jan. L899. 3) These Proceedings Vol. 1, p. 398. March 1899; and ‘Vorlesungen fiber Gastheorie” I, p. lol. ( 489 } virial equation as my father has done for the external pressure and for the pressure of the molecular attraction in Chapter IL of his “De Continuiteit van den Gas- en Vloeistoftoestand” and for the forces eventuating in collisions of two molecules in these Proceedings Vole, p: dss:Ock 39s: First, however, | will point out, that the virial equation need not necessarily be applied for a definite: quantity of matter, which ts contained in a definite volume and enclosed within a solid wall, as is the usual method of applying it. We may as well apply that equation for a part of a homogeneous phase, separated by an Imaginary separating surface from the surrounding substance which is in the same phase. We shall not always find the same molecules within such a surface, but we may assume, that at two different instants 7, and f, we shall find the same momber or at least with very great approximation the same number of molecules within it, du and that the expression Yyiav will also have the same value at dt the instants /, and ¢,. We may therefore put: d 2 da Lm == ||!) lt dt and also the corresponding equations for the 7- and for the 2- coordinate, From this we may deduce : dine diniy dinz : Ss = —— Se + y Baa Pray «eon cAl lt eli dt In the case that we may neglect the volume of the molecules with regard to the volume in which they are contained, and that We aay assume that the molecular forces act in such a way that they yield) on average zero for the force exercised on a molecule Within a homogeneous phase, the righthand member of this equation has only a value at the border of the volume under consideration; it may therefore be reduced to a surface-integral. The lefthand member of this equation is independent of the cireum- stance whether the space under consideration is enclosed within an imaginary separating surface ov within a solid wall, and in’ the latter case it is also quite independent of the properties of this wall. So the righthand member cannot depend upon these ciretumstances dm either. In the case of a solid wall we may write: == (); So) we ; dt get for the righthand member: Proceedings Royal Acad. Amsterdam. Vol, V. ( 490 . = fr r cos (ny r) do = 3 P" V . . . . . . (RB) Here + represents the radius vector drawn from the origin of the system of coordinates to a point of the surface, lo represents an element of that surface, cos (2,7) the cosine of the angle which the ‘adius rector forms with the normal to the surface. 7?’ is the force per unit of surface which prevents the molecules to leave the space and compels them to return towards the inside of it. We may distinguish a in it the molecular pressure : and the pressure p exercised by the a wall. . . Fy ° - “ d de J For the case of an imaginary separating surface, 5 is the ‘ ‘ momentum in the direction of the positive «axis conveyed through the surface to the inside of it. Momentum conveyed to the outside has to be taken into account with the negative sign. In this case also the righthand member may be represented by equation (/3) though here the symbol ?’ does not any longer represent a force which really acts on the molecules. In the case that the volume really occupied by the moleentles is not so small that we may neglect it, also the virial of the forces eventuating in the mutual collisions of the molecules must be taken into account. If we denote this virial by / then we may write equation (1) in the following form: . =ms? = — I —| Pr cos (ny vr) do = — I 4-5 PV. ms? and J being independent of the properties of the bordering surface, /? cannot depend upon them either. /? appears to be greater than P’; for a wall this is because the number of collisions is augmented in consequence of the abbreviation of the mean length of path which a molecule describes between two successive collisions; for an imaginary separating surface this is because the conveyance of momentum through that surface has augmented in consequence of the fact that in collisions between two molecules whose centers lie at opposite sides of the separating surface, the momentum is transplaced instantaneously from the center of one molecule to that of the other; so the momentum has been transported with infinite velocity. But the way in which we have derived the quantity 2? which may be estimated to represent the pressure prevailing in the gaseous or in the liquid) phase, warrants in any case that this quantity is ( 491 ) independent of the shape of the vessel and the properties of the Walls in which the phase is enclosed, but on the other hand it warrants also that we may find the quantity 7? by calculating the pressure which would be exercised against a plane wall if the a molecules did not attract one another, or by adding —— to the pres- ns sure exercised by mutually attracting molecules against a plane wall. The way in which the virial of the forces eventuating in mutual collisions of the molecules has been introduced bij Prof. vax DER Warts is as follows. We assume that in first approximation ? represents also the pressure exercised on the distance spheres of the molecules. This would yield the value 2 Ph, for the virial. We must, however, take only half this value, else all the forces would have been counted twice. The distance spheres, however, cannot be considered as wimoving solid) walls, but as moving and movable walls and therefore it is perhaps not quite superfluous to show expressly that they are indeed subjected to a pressure amounting in first approximation on average to P. 1 will give the proof of this proposition in § 2 of this com- munication. 17h Phe introduction of the correction term a5 = is based on the con- sideration that the value of the virial given above will be too great because some of the distance spheres partly coincide. The parts of the surface of a distance sphere I falling within a distance sphere II are protected from collisions with all other molecules but IL. There- fore the pressure on such parts is assumed to be zero; on the other parts the pressure on the distance spheres is supposed to be 2. This comes {to the same as the assumption that the average pressure during a time rt (and every pressure which we consider, the pressure P also, cannot be anything else but an average value during a certain fime 1) exercised on an element do of a distance sphere would be smaller than ?, because of the fact that the element do is only during a part of the time r exposed to the pressure P, during ano- ther part of that time, however, it would have been subjected to no pressure, because it was protected by the distance sphere of a mole- cule IL from collisions with other molecules. T have two objections to the calculations based on these considerations. In the first place the assumption is made, that a part of a distance sphere would never experience any pressure, when it lies within the distance sphere of another molecule. In fact the reverse is tre: in order that a surface element should experience a pressure, a 33% molecule must collide against it and then it lies in the distance sphere of that molecule; and the considerations in which the pressure inside the distance spheres is assumed to be zero, outside them to be P, are certainly nota correct representation of What really happens. Yet points lying insitle distance spheres are in somewhat different conditions as to the pressure that may be exercised on them, than points outside distance spheres. I is not clear to me how these conditions should be taken into account. Tt is, however, not necessary to know this in order to calculate the correction term, as will appear from my second objection. In the second place the facet has been overlooked that not only some parts of distance spheres lie within other distance spheres but that the same cirenmstance occurs for parts of the bordering surface. It is indifferent whether this is an imaginary surface or a solid wall"), in any case a part of it will lie within the distance spheres of the molecules, and may therefore with as much (or as little) right be estimated to be protected from pressure. Now let 1/2 part of the bordering surface lie within the distance spheres. If we must assume that this part of the surface experiences a pressure zero, and that the free surface experiences a certain pressure, that we will call 7?,, then the quantity /?, which represents — as appears from the way in which it has been introduced — the average pressure, would be 2—1 Let us now investigate what part of the total sur- equal to —— P,,. 4 face of the distance spheres lies within other distance spheres, and let 1/4, represent that fraction, then the average pressure of a distance ° bat . . sphere will amount to P,. If 4, were equal to 4, then the average 4, pressure on the bordering surface and on the distance spheres would be the same, and we should not have to apply any correction to the term by. : 17 We find the correction term Bei = if we make the following assumption, but only in that case: every surface element, — no mat- ter whether it is a part of a solid wall or ofan imaginary separating surface, and whether the surface is plane or curved and no matter whether it lies within or without the distance spheres of molecules — 1) The virial of the forces excercised by the wall must properly not be integrated over the wall itself, but over the surface which contains the centers of the mole- cules colliding against the wall, i.e. over a surface parallel to the wall and lying at a distance « from it. ( 493 ) it will always experience a pressure 7? Only the distance spheres make an exception to this rule, for parts of them, falling within other distance spheres experience a pressure zero. I can find no reason for this exception and therefore [ think the Vb . ms : value = 7 incorrect. The question whether in fact a correction must he applied depends on the fact whether 4, is equal to 4 or not. This may be investigated in the following manner. Let J/ in the figure represent the center of a molecule and let the circle deseribed with J/ as center, represent the section of the distance sphere (1) of that molecule with the paper. Now we are to calculate the average pressure exercised during a time t ona surface element do, the center of which we call the point ?. To this pur- pose we describe a cirele LU with ? as center and with a radius 26 and we also consider the tangent plane in 7? whieh we eall LA. Two cases may be distinguished ; Ist The space within sphere IL but outside sphere IT and at the left of the tangent plane (the section of the space in question with the paper has been hatched in the figure) may contain the center of a molecule; if this is the case P lies within the distance sphere of that molecule, 494 | 264 The space under consideration may net contain the center of any molecule. We will call that) part of the time rv during whieh the former T : ‘ fakes place —; so that part during which the latter takes plice "t wd : ; u— | : ta ee tr. During the time tT the surface element do is quite if te ul the sume circumstances as an element of a plane wall. Therefore it will experience on average a pressure 7? This pressure 7? is a quan- lity whieh we may derive from the virial equation; in order to deter- nine it, it is therefore not required to decide whether the considerations A—1 in Consequence of which we find 7? equal to ~~ 7, are correct or not. But when the former case takes place, so during the time " we are certainly justified in assuming that do does not experience tas A a any pressure. The average pressure on do is therefore Pi; a We may find the value of jw in first approximation by determining the volume + of the hatched space, and by assuming that the chance that a certain definite molecule will lie within that volume is equal 4 to a If w denotes the total mumber of molecules, then the chance ~ that the space contains a molecule will be represented by 1 \" On average the value of '/a will be equal to this chance: therefore in . . . 1 v first approximation 9 46== 7 \" 2 : 1 We find by a simple calculation for r the value hia rr. where y= 26= the radius of a distance sphere. Therefore : l 3 cy yee 4 3b Vesa — = ~ } ot) 3h The internal virial 7 will therefore be 5 1’4, ¢ Da «| and equation (1) assumes the following shape : Sine” 3b? te NS — LO (1. = )=P(r = =o 5 = a ( 495") § 2. In order to introduce the internal virial / [ started from the supposition that the distance spheres of the molecules experience a pressure which is on average equal to 7. As I never found a direct proof of this thesis I will give it here. The pressure /?? namely may i.a. be considered to represent the pressure exercised against a solid wnmovinge wall, disregarding the molecular pressure. The distance spheres, however, are not to be regarded as a solid, unmoving wall. In consequence of their motion the number of collisions against a surface element do of a distance sphere is greater than that on an equal element of the wall; moreover the force in each collision is proportional to the relative velocity of the molecules, which is greater than the velocity of each molecule separately. From these two circumstances we are apt to assume that the average pressure on the distance spheres would be greater than fe On the other hand the impulse of a molecule colliding with a velocity s normally against a solid, unmoving wall is 277s. If, however, the molecule collides with the velocity s centrally against another unmovinge molecule with the same mass, then the first molecule will be stopped and the second will obtain the velocity s; so the impulse is in this case only ns. In consequence of this circumstance we should be inclined to expect the pressure on a distance sphere to be smaller than ?. The following simple caleulation will suffice to show that these influences cancel each other and that the pressure exercised on the distance spheres is really equal to 7, at least in the case that we may neglect the volume of the molecules with regard to the volume in which they are contained. Let us imagine two molecules I and IL with the same mass. The same proposition might be proved without difficulty also for mixtures, so for molecuies with unequal masses, but [| will confine myself here to molecules with the same mass. The velocities of the molecules will be denoted by s ands, and the components of these velocities by wor and a.7,,1,. The chance that molecules occur whose velocities have these components will be represented by /’ (u,v, 1) and 7 (i, @,,70,) and the ae beat by s,. Then we have: 8° = (u—u,)? + @—v,)? + (w—2,)?. If we take the direction of S, as a axis of a system of spherical coordinates, and if we eall the latitude g the longitude y, then a surface element of the distance sphere of molecule I will be repre- sented by 7° sin g dgdy. The number ef collisions per wnit of time of molecules of group IL against such a surface element is: F (u,v, w) F (uy, vy, w,) du dv dw du, dv, dw, 8, 7° sin g cos p dy dys, 406) a Not the total relative velocity s, changes its sign ina collision of this kind, bat only the component normal to the tangent plane in the point in which the moleenles touch one another, “The impulse is therefore as, cos gq. The total impulse of the collisions of the kind under consideration will therefore be equal to: E(u, roi) Fr (4,5 %,. 1,) du de dir du, de, dir, a sin Y cos? f dy dit. The eightfold integral of this expression vields the total pressure exercised on the surface of the distance spheres. We lave: ) | | ry sin & cos? gf dg hy = r Fs dt a if we integrate according to y between the limits O and 2 a and 1 according to g between the limits O and >. The limits for g are not O and a, for the parts of the distance sphere of molecule T for which g > 5 2, cannot come into collision for the given relative velocity s,, We may write s*-+s,*, for s,* for the terms ss, cos (s,s) vield zero on average. Doing this we may integrate the term with s? according to du,, dr, and «dir,; so we get: : \e (0,5 ¥j5 1) dt, dd, dio, == . The term with s,? on the other hand may be integrated according to du, de and dir; so we vet: | F(nvrvaw) dude du = n. This yields for the total pressure on the surface of the distance spheres ; 2 ~ 7 : : aru | | ms? Furie) du de dic 4 | mt ion FE (4.0). uw) du, de, div, = . . Both integrals in this expression are equal to js?, nist represent- ing twice the mean kinetic energy of a molecule. We may there- fore write this expression as follows: i _—-—_. we Dividing this quantity by the total surface of the disiance spheres 4ay?n, we get for the value of the average pressure: noms. le Od ete ln ( 497 j This is the same value as we find for the pressure exercised om a solid, unmoyving wall. In order to ecaleulate the number of collisions we have here neglected the extension of the molecule and the mutual attraction of the molecules. Therefore it is apparent that we cannot have obtained anything else but a first approximation, Botanics. — ‘* Die Stelir-Theorie’. Dissertation of Mr. J.C. Scuourn. (Communieation of Prof. J. W. Mont). According to the idea of vax Tingnenm, given about the tissues of root and siem of the vascular plants, they must be divided into three groups or systems of tissues, namely, epidermis, cortex and central- evlinder. It is such a natural thing to call the epidermis a separate tissue that already a long time before vax TimeHem, it was acknow- ledged and is at present generally accepted. It is a different thing about the theory that the central part of stem and root is taken up by acylinder of tissue, the central-cylinder (or “stele”), which may consist of elements differing greatly, but Which must nevertheless be regarded as a connected whole, forming a certain contrast with respect to the cortex. This consideration which can be called the “Stelar-theory” is accepted by some, rejected by others. It is of the greatest importance for instruction and for the construction of descriptions of the inner structure, and it has undoubtedly for both these reasons such a great practical weight, that for this reason only it deserves our attention in a high degree. The scientific foundations for this theory are not in such a good condition and assuredly its non-acceptance is owing to this. Of course the important question is, whether this distinction between cortex and central-evlinder has made its appearance already at an carly period in’ the phylogeny of plants. With the present state of our knowledge this can perhaps not be proved with certainty; but to be able to answer this question in the atlirmative two conditions must be put: 'st. the central-cylinder must be indicated if not in all, still in the greater;part of stems and roots, 2°¢) it must appear uready at an early period in the development of these organs. As for the root these conditions are amply satisfied, which gives great support to the theory of vax TineHem. But this is not the case fo such an extent for the stem, partly perhaps in connection with the complications formed already at an early period by the develop- 498) ment of the leaves, partly in connection with the splitting up of the central-evlinder in these organs of many plants, Concerning the latter point VAN ‘Tiraue himself and of late a number of American and English investigators: Gwysxe-VAcGHas, Jererey, Boonie, Faun, Worspen., Brerownp Farmer & Hint, Miss Parp, Taxsiry & Lenian, Bresyer have shed much light. In all those cases in which stems show a number of loose strings, regarded by some as parts of a central-eylinder (schizostely), by others as vascular bundles, a single central-eylinder, the monostelie structure, is rule in the youngest internodes of the plant, in hypo- and epicotyl and in the internodes following immediately. But in most cases there is no question about sehizostely and so according to VAN ‘TinGHkmw we must expect monostely. However it is a fact, that whilst in every root the most superticial microscopic investigation easily proves the existence of a central-evlinder, this is not at all the case for many stems. The inner laver of the cortex (endodermis), it is true, is often developed as a bundle-sheath indicating as that of the root does, the boundary of the central- evlinder, or also it contains stareh-grains, so that a distinct stareh- sheath is formed; but in a great many other cases, also in an inves- ligation made for that purpose, as was done by H. Fiscner, it has not been possible to point out a well defined central-evlinder. Fiscner found in 100 investigated plants only in 32 cases a distinet endodermis. It has now been shown by Mr. Scnovrr that this objection to the Stelar-theory does not exist in reality. He collected out of the lite- rate on this subject numbers of cases, in which a distinet endodermis had been observed in) some shape or other. He himself studied a great number of stems of different plants and then it was evident how necessary it is to examine these organs in different and especially in young stages of their development, a thing Fiscner had not done. The result of this method of working was, that of about 400 dicotyledonous plants only in 7 no distinet endodermis was come across and among these 7 there were vet 4 which even showed a sharp boundary of the central-cylinder. Also the greater part of the Monocotyledonous plants possess an endodermis. It is not to be found in Gymnosperms but vet here as is the case in most of the above-mentioned exceptions, a distinet boundary between cortex and central-cylinder is often to he seen. Seo this result is very favourable for the Stelar-theory and is a contribution to its scientific confirmation. But in vet another manner has Mr. Senovrr endeavoured to test the Stelar-theory, a test, which it is true has led toa negative result, but which enables us to draw weighty conclusions with regard to nw ( 499 }j the value of the well known Theory of the hisfogens of Hansrrin. In working out his theory vax ‘Tingumm purposely avoided as much as possible to make use of the history of development, and as has been proved justly. Yet it was quite natural to think that there Was a Connection between the structure of the full-grown stem and root and that of the same organs ata very early period of development, in embryo or growing point. For Haxsrum had established a doctrine about the structure of the meristems, very much like vax ‘Tinaienm’s theory and had gained a number of adherents. He thought, especially on account of the arrangement of the otherwise equivalent cells, to be able to distinguish three tissues in those meristems, called dermatogen, periblem and plerome. The last was a column of cells in the middle part of the stem and root. Of course if was quite natural to think of an identity of dermatogen and epidermis, periblem and cortex, plerome and = central-cylinder, in such a manner that the latter had developed out of the former. Tf it were possible to point out such a correspondence, this would be for the Stelar-theory as well as for the Theory of the histogens of great importance, though not of equal importance for both. If the central-eylinder is already found in’ the meristem as an independent whole, this points to the faet, that the differentiation of this tissue is old and then the Stelar-theory has gained another support. But as [said above, it is fully established in another way and can very well do without this support. The Hansrm-theory of the histogens is a different case. Every one who studies the literature impartially, will have to own that this doctrine rests on a very weak foundation, perhaps not with respect to the dermatogen, but very certainly as faras the plerome is concerned. I is true, there are some roots and a very few stems in whose thin tops the cells are arranged in a remarkably regular order, so that a central- eylinder can be distinguished as plerome. But in many roots and in nearly all stems there is no question about tracing such an arrange- ment up to the growing-poit. It is really to be wondered at that this HAsxsrrm-theory in its generaltty has found so many genuine adherents; this is certainly partly owing to the conviction, expressed by many and silently shared by others, that plerome and central cylinder are one and the same. Yet this had never been accurately examined till it was undertaken by Mr. Scnourn. But it is clear, that a positive result would be of the greatest importance for this theory. For there is no sense in accepting histogens without full-grown tissues corresponding to them. Moreover might be expected of a positive result the possibility of finding an undoubted plerome when following the boundary of SOO) the central-evlinder upwards, also in those eases in which up till now the efforts had not been successful, perhaps on account of the vreat number of cells. The investigation of Mr. Scenourk was an accurate comparative study of connected series of cross and lengthwise sections. It would lead me. too far if T were to speak of this more in particulars. But in general the investigation was conducted in such a way that an attempt was made to pursue in the direction ef the growing point the boundary between the series of cells which could be distinguished as endodermis and central-evlinder in the older parts. The results were in short as follows. Of the root of Hyacinthus orientalis and Linwin usitatissinnm the series of cells of the endodermis and the outer layer of the central- cylinder (perieycle) were successfully and uninterruptedly pursued up to the growing-point. In these cases a evlinder of tissue could be distinguished in the top, which could quite naturally be compared to the plerome of Haxstem and which corresponded exactly to the later central-eylinder. Also in) Helianthus annuus in the main the same was found, though the plerome did not appear here as a complex of cells closed at the top. In the stem of Hippurus vulgaris, one of the few stems in which different investigators have distinguished a plerome, this was not only successfully found back, but also the series of cells of endodermis and pericycle could be pursued uninterrup- tedly to the growing-point. However the cells of the plerome proved to form not only the central-evlinder but also the endodermis and two layers of cells of the cortex, so that the required correspon- dence did not exist here. In the stem of Llodea canadensis an un- certain result’ was obtained, as here a stareh-sheath and a bundle- sheath were found, and it was not possible to make ont which of the two must be regarded as endodermis. But in the root of /Yearia ranunculoides and in the stalks of Aesculus Hippocastanum, Lysi- machia Ephemerum, Lronymus CULO paeiuts and Ajuga reptans an im- portant negative result was obtained. Here it was perfectly evident that the series of cells of endodermis and perieyvele cannot be pursued up to the top, but that they very soon stop short and are replaced by shorter series of cells not exactly in their prolongation and which in their turn soon undergo the same fate. In other words in all these cases the expectation was not only disappointed that in this way in difficult cases a plerome was to be found, but it was also irrefutably established that it does not exist here. After the above-mentioned explanations it need not be demonstrated that these results as a whole must be regarded as fatal to the Theory a a a ( 501 ) of the histogens. That in some selected roots there is some corres- pondence, makes no difference. That in slender tops built up out of relatively few, lengthwise series of cells a regular arrangement of cells may appear as was deseribed above, is the most natural thing in the world. To give a particular explanation of this is unnecessary, and in no case are these single indications sufficient to establish solely on them a theory of histogens as that of Haysrem. And yet this would have to be done if one wished to adhere to this theory, for all other facts plead strongly against it. A//ppirs, almost the only plant showing a plerome in the stem, has a structure altogether opposed to the theory. And the irregularly built tops form without doubt the overpowering majority. It seems fo me that by the investigation of Mr. Scnourn the Histogen theory of Hanxsrrix is proved to be erroneous. A conclusion of somewhat general importance can still be deduced from these investigations. Many botanists think that to the celldivision in meristems a certam phylogenetic importance must be given, somewhat comparable to that of the germinal layers in zoology. But here is forgotten that in zoology in the history of development folds and again folds are spoken of, to a certain extent also histological differentiation is mentioned, but litthe or nothing of directions of cell-division or of arrangements of otherwise entirely equivalent cells. If the zoologist attains at beautiful results by the study of the history of development, it in nowise ensues from this that the study of the arrangement of cells in’ meristems will be able to furnish these. Rather will the hotanist have to expect such explanations from the study of the development of outer forms, and of inner differentiations as a result of differences in the nature of cells. Experience has taught us that this expectation has a right to exist. But the Histogen-theory has certainly contributed to nourish the above mentioned wrong opinion. Now that this has been proved to be incorrect we may expect that the historic and phylogenetic importance which has often been ascribed to the divisions and arrangements of nondifferentiated and perfectly equivalent meristemeells will be reduced to its right and very slight proportion, Groningen, Jan, 29, 1908. ( 502 Physics. * Vethods and Op Prats used in. the eryoqene lahova- tory. IT. Baths of rery uni forin and constant low len peratires m the cryostat” Communication N°. 838) from the physical laboratory at Leiden by Prof. TL Ka wernincit Ones. (Communicated in the meeting of December 27, 1902.) § 1. By means of the cryostat deseribed in § 8, Comm. 14. Dee. 94, and § 3, Comm. Sl. Sept. “99 we can obtain a bath of liquetied gas which is shut) off from the atmosphere and boils at ordinary or diminished pressure. In such a bath the temperature is sufficiently uniform and constant for many experiments and mea- surements. If we use almost pure gases and if the evaporated gas is regularly recondensed by means of a compression apparatus, which as described in Comms. 14. Dee. “94, 53. Sept. “99 and 54. Jan. “OO, does not contaminate the gas, the bath may be maintained as long as we wish. The operations in the bath itself as well as the addition of the liquefied gas can be watched through the observing vlasses. Vacuum glasses are not required so that similar ervostats may be constructed for measuring apparatus of any dimensions. Before long we shall describe a cryostat where the gas apparatus and the bath are more independent. I was led to deseribe the form of the eryostat, as it occurs in Comm. 51, through the communication of the results for the di-electric constants of liquid gases. (Comm. 52 Oct. 99), for which measurements only the temperatures of — 90°C. or — 182°C. were required. For other measurements, however, a measuring apparatus, once immersed in the cryostat, has been used at the whole range of temperatures between, — 23° C. (boiling point of methyl chloride at ordinary pres- sure) and — 210° ©. (nitrogen at reduced pressure), given by methyl- chloride nitrous-oxide, ethylene, methane, oxygen and nitrogen as they were successively admitted into the cryostat. For a long time iunprovements have been made in this cryostat by means of which we ean attain a much greater uniformity and constancy in the temperature, while retaining the afore-mentioned advantages. A description of these alterations has now become neces- sary in order to judge of the accuracy of the temperature readings in the results from various measurements where we have availed ourselves of these improvements. These measurements will be treated in the next communications. Among others I mention here those bearing upon the isothermals of diatomic gases (Comms. 69 March ‘OL ( 503 ) and 78, Mareh 02) and the comparison between the platinum resistance thermometer and the hydrogen thermometer (Comm. 77 Febr. 02) In this deseription, as in Comm. 51. Sept. ‘99. it seems to me desirable to illustrate the use of the crvostat by means of a special example. We will consider the comparison of the hydrogen thermometer with the resistance thermometer where also a thermo-element had been immersed in the bath. Plate 1 shows the cryostat and some of the auxiliary apparatus to scale, the connections are represented schematically. It has been drawn on a smaller seale than plate IT of Comm. 51 Sept. 99, (which should be consulted together with the one now given) but it will suffice fo give a survey of the whole arrangement and to show some of the alterations. While the details of the unmodified parts can be studied on plate 1 of Comm. 51, plate IL of the present Communication shows the details of the parts enclosed by the dot-dash-line of plate I, as far as they are required for consideration of the new arrangements. The connection of the apparatus shown in PI. 1 with the gas cireu- lation can be seen in’ Pl. TY Comm. 51. The comparison of the platinum thermometer p and the hydrogen thermometer 7 and their connections to the other pieces of the apparatus ave given in Comm. 77 Febr. ‘02 §3. For the comparison of the thermo-element @ [ amas yet obliged to refer to the very rough diagram of 1896 (PI. 1 of Comm. 27 Mai and June °96). The communication, however, of some results for which the temperatures have been determined by means of a thermo-element will soon call for a description of the recent considerable improvements in the use of the thermo-elements. On plates 1 and Il a correction thermometer § which is entirely independent of the cryostat, will be seen besides the three measuring apparatus mentioned above. It serves in our case to indicate the mean temperature of the capillary of the hydrogen thermometer, or in general, the mean temperature of similar pieces of measuring apparatus occupying the same part of the cryostat. For this purpose two spirals of platinum wire are wound round a glass rod, the one for that part of the rod, where the temperature varies slowly ©, the other for that part where the temperature varies rapidly ¢ 1 1° By means of the leads §,,, connected to the places of contact §,,, 6,, and soo? $&,, and emerging through the tube §,,, we can determine the resis- tance of these spirals. § 2. First we shall mention some small changes in the cryostat of Comm. 51 which have no relation to the question of keeping the temperature constant and uniform, 504 ) The jet of liquefied gas let in at a (plate J) is directed, by means of the cock A, and the filter 7) against a glass wall from which it streams along the delivery spout /2, into the bath, here a double heaker 4,, B,, (Pls. I and Il), placed in the beakers 4, 4, 2, of Plot Comm. SL. The cock and filter form part of a cover which as deseribed in Comm. 51, may be removed together with S, and S, from the cryostat and may also be replaced by a sy phon or a capillary with a cock ontside the cryostat. The spreading of the jet over the wall may be watched through the windows V,, and the height of the liquid in the bath through the windows IV. The filter / serves principally to prevent opaque dust from the lead (oxide of copper ete.) from depositing just at the place where the jet touches the glass. In many cases, however, it happened in spite of the care taken in purifi- cation, that the liquefied gas itself, while evaporating under reduced pressure in the cryostat, had deposited a substance, formerly dissolved in it but solid at the lower temperature, thus rendering the bath opaque. Therefore, differing from Comm. 51, a glass beaker (, (Pls. | and IH) with numerous openings in the bottom C,, (Pl. ID) and con- laining some glass wool was suspended by the regenerator spiral 4 (Pl. | Comm. 51). This filter may be lifted from the cryostat together with the piece S,. With the arrangement as described in Comm. 51 all the gas, formed afier the liquid leaves the cock, goes in the direction indicated by the arrows on Pl. I Comm. 51. With the arrangement as described here, however, the gas which is formed while the bath is being filled follows in the main a different direction to that which afterwards evaporates from the bath. In fact, differing from Comm. 51, a valve D,,., with aspring D,, has been added, which almost closes the opening of the delivery spout J, for gas, but allows liquid to flow through a very narrow opening ,,, along the gutter D,,. The first consi- derable quantities flowing from the cock, serve to cool all the beakers and the whole cryostat in’ the way indicated in Comm. 51 (the arrows of plate I might be borrowed from plate | of Comm. 51), unless the supply becomes so great that the valve D,,, is opened and the gas also flows out through the opening /,, in the ring /,, plate IL. The gas which later evaporates from the beaker /,,, finds the valve a. indicated by the arrows on plate II, so that it serves only to screen o.? closed and escapes only through the opening /,,, along the way the immediate neighbourhood of the bath from external heat. The difference in form between the rings R, and &, on plate UH and those on plate 1 Comm. 51 is very slight. This follows from the wish to use the parts that served in the experiments, referred to in ( 505 ) Comm. 51, as much as possible in the arrangement of the measuring apparatus considered here. Formerly the bath could be excentrically mounted with reference to the tube /, whereas this time a central mounting was desirable. The existing dimensions of parts of the apparatus have also had the result that in the experiments described here the bath must be placed a little too high with regard to the observing glasses V,, which might easily have been avoided if we had been perfectly free in our construction. The glass ring /,, not occurring in the arrangement of Comm. 51, serves still better to screen the bath from external heat. Like the other beakers and glass cylinders 4,, B,, B,, B,, B,,, B,,, it is silvered inside and outside, leaving open, however, vertical strips nearly corresponding in width with the resistance thermometer p. The conical rim 4,, lies loose on the beaker 4,,. When the liquid boils up, it streams back to 4,, along the wall of the funnel; if, however, £,, is filled to the brim and more liquid is poured in, this superfluous liquid flows over into the beaker B,,, which also is filled before a measurement is made. If an intense cooling of the neighbourhood of the bath is required, the beakers B,, B,, 2B, must also be filled. It should be remembered, however, that if this is done, the evaporation at low pressure, as long as liquid remains in the outer beakers, requires a powerful vacuumpump. The bath itself only evaporates slowly. Instead of the double beakers 6,, 5,, we might take a vacuum glass in order to diminish the evaporation as has sometimes been done (comp. § 3). But it is not always easy to obtain vacuum glasses of the required dimensions and internally finished with the accuracy necessary for the proper working of the stirrmg apparatus. Moreover one will not be inclined to immerse delicate measuring apparatus in the bath before one is suffi- ciently certain that the vacuum glass will not burst as such of greater dimensions sometimes do. § 3. To make clear the purpose of the arrangements to be described in the next sections, it seems to me that the following particularisa- tions will be useful. First of all the temperature gradient in the bath. Even when the liquid boils regularly we find that in the lower layers, as a result of the hydrostatic pressure, the temperature exceeds that of the upper layers. If, as often happens with greatly diminished pressures when boiling is not produced artificially, only evaporation at the surface oceurs instead of boiling, the temperature in the upper layers of the bath may fall considerably below that of the lower, -If then the liquid suddenly boils up, whieh always happens whenever 3 Proceedings Royal Acad. Amsterdam, Vol. V, OO) we do not stir vigorously, an unexpected change takes place in the distribution of the temperature in the bath and hence in the tempe- rature of any measuring apparatus placed in it. In measurements of the kind considered here, we cannot allow such irregularities and fluctuations in the temperature of the bath, either as to time or place. Of the various methods of preventing this sudden ebullition, the simplest is the generation of small bubbles of gas by means of the heat of a short resistance (boiling thread). If, however, there are ignitible gases among those successively introduced into the apparatus and if consequently an explosive mixture with air might be formed, this method is not without danger. To bring about ebullition a current of gas is often led through the liquid, which, however, has the disadvantage of contaminating the evaporated gas. To avoid this diffieulty I have led throngh the bath a current of the gas itself. This means was applied for instance to avoid the retardation in boiling in the vacuum vessel mentioned at the end of § 2, and also in order to cause a strong stirring in the bath by means of the current of gasbubbles. But this means also presents many difficulties, mostly arising from condensation phenomena in the delivery tube, or higher temperature of the gas- bubbles: I therefore, preferred, the arrangement as described in § 4. If the cryostat is used as it was intended to be in Comm. 51, the requirements for very accurate measurements would not be fullfilled, even though a uniform temperature throughout the bath was attained. There still remains a systematic regular rise of the tempe- rature, because the gas used is never perfectly pure and the more permanent part evaporates first. In cases where measuring apparatus require longer to adopt the temperature of the bath than the time in which the temperature changes the amount permitted by the accuracy of the observation, we cannot reach more accurate results without additional means. § 4. We now pass on to the description of the arrangements which form the subject of this Communication. The uniform tempe- rature in the bath is obtained by stirring. The stirring apparatus is placed concentrically to the bath, thus leaving room in the most profitable way for the measuring apparatus. From this space the stirring apparatus (as in Comm. 27 May and June “96 Pl. HD is separated by a protecting cvlinder S, (comp. the figure to the left of plate 1). The upper ring z,, is provided with small valves %, covering openings of the same form. If the stirring apparatus moves in the eylindrical space between §, and 4,, the valves shut up | =". eS ee ed >% during the upward movement and open during the downward movement. The upward movement is brought about by means of the thin wires y,, the downward movement by the weight of the stirring apparatus itself which for this purpose is weighted with the heavy ring %,, by means of the rods %,,. As yet a more rapid motion of the stirring apparatus than this method affords has not been required; if wanted a construction with small rods instead of threads would be necessary. The valves are hinged on bent pins %ou- The complete section of the stirrer to the right of plate II shows the valves shut, the section of y,, at the top shows them open. When the stirring apparatus is moved up and down and the bubbles of vapour escape the movements of the valves resemble those of the fins of fishes. It is very important that the up and down motion of the ring should be perfectly perpendicular and that the protecting cylinder §, and the beaker B,, should have a perfectly vertical position for, to make the valves work properly, only a narrow space can be left between the stirrer and the cylindrical walls. The cylinder §, is enclosed between two rings provided with grooves §, and §,, of which the upper is connected with the ring §, by means of glass tubes. Through the operation of the spring $,, and the arch §,,, this ring is pressed against the ring 6, on to which the beaker B,, with a ground upper rim is fastened by means of cords. To this ring §, the hooks §, are also fastened, against which the upper rim of the beaker B,, is also pressed by means of cords. In this way a cylindrical space is reserved for the pumping motion of the stirrer. In order to admit the measuring apparatus it was advisable to leave free the whole space offered by tube /,, which is equal to that in the bath available for a measuring apparatus. To this end the threads z,, formed of very thin silk cords enclosed in steel wire are led through 3 openings £,, in the cover / of the bath and then over a pulley axis y, with three grooves to a connecting piece ¥y,, Which is moved by a single thread passing over the pulleys x, and y,. The cord must be moved from outside the case and the case must remain perfectly air-tight. This is obtained by passing the cord through an india rubber tube z,,, which at x,, fits hermetically on to the cover of the cryostat and in which the thread ,, is also hermetically fixed. A thin steel wire is wound spirally round the india rubber tube. In this way the walls of the tube offer sufficient resistance to the atmospheric pressure to prevent them from collapsing when low pressure exists in the cryostat, while at the same time 508 ° they remain elastic enough to permit the movements of the cord. A regular up and down motion of the stirring apparatus is secured by the wheel x,. § 5. A constant temperature is attained by continually adjusting the pressure, at which the liquid in the bath evaporates, to the indications of a resistance thermometer p placed concentrically in the bath. A sensitive thermometer forms an inherent part of the eryostat under consideration when it is to be used for very constant tempe- ratures and the dimensions allowing a resistance thermometer to be introduced, the latter has been chosen as the most trustworthy. Its inner diameter controls the greatest cross section of the measuring apparatus which can be immersed in the bath, and therefore, as in our case, it must correspond to that of the tube /’,. The eon- struction of this thermometer has been described in detail by B. Mnink (Comm. 77 Febr. °02) with a view to a comparison between it and the hydrogen thermometer referred to above. The leads pass through the openings F,,, &,, of the ebonite rings R, and R,, and then through the stopper into the tube 7’,. On the plates I and IL they are indicated by the same letters as on the plate of Comm. 77. When the bath has reached the required temperature the galvano- meter in the Wurarstonr’s bridge, which serves to measure the resistance of p, is adjusted to zero by introducing suitable resistances. As soon as the deviations of the galvanometer make it necessary, a sign is given to the assistant, charged with the regulation of the pressure in the cryostat, who then raises or diminishes the pressure, whereby the temperature in the bath rises or falls. The great volume of the eryostat is here very useful in checking oscillations in pressure. The arrangements required for the regulation of pressure are shown in plate I, the separate pieces of apparatus to scale and the connections schema- tically. (Comp. Comm. 51 Sept. °99, pl. IV). The assistant uses the oil manometer X,, which is connected to the cryostat by _N, and YX, (comp. pl. Il Comm. 51) and the cock X,,, the cock X,, being open. If we shut the cock Y,, the motion of the oil enables us to very accurately watch the variations of the pressure in the eryostat by means of the difference between the pressure in it and of the quantity of gas temporarily shut off in the reservoir X,,- If through some cause or other the variations of pressure increase considerably, or if we want to stop the regulation, or to proceed to another pressure, the oil is prevented from running over hy our opening the cock X,,. The pressure in the cryostat is varied by more or less opening the fine cocks )°,, and )’,, of the regulation ( 509 ) \ tube 7,,. Two eases are to be distinguished here. With operations at ordinary pressure it will be sufficient to adjust the cryostat at a pressure a little higher than that of the atmosphere and to either connect the cock ¥,, with a gasholder Gaz. or to disconnect them, as the oceasion demands. As soon as the pressure passes a certain limit settled for the cryostat, the gas escapes from the cryostat through the large safety apparatus. For operations at reduced pres- sure, the eryostat, after the pressure has been sufficiently lowered by means of the exhaustpump of the circulation Hvh. 1, is diseon- nected from the latter and connected by means of the cock Y,, to the exhaustpump eh. 2., and is then reduced to a lower pressure. Obviously we can sometimes avail ourselves for this latter operation of the same exhaustpump as used with Hvh. 1. The evaporation will proceed more gradually when a connection is made to a reservoir at reduced pressure Vac., plate. If a reservoir of large volume is used we can even work without an exhaustpump, which may be valuable when it is necessary to avoid vibration for the measure- ments. Thus with the bath of nitrogen under diminished pressure the auxiliary compressor of Comm. 54 Jan. *O0 plate VII was connected near rh. 1 to the gaslead and the vessel of 5 m* men- tioned above (comp. Comm. 14 Dec. “94 § 10) served as vacuum reservoir, after being exhausted through Y,, and Y,, by means of a BurckHarpT vacuumpump, connected to the gaslead at /ivh. 2. This vacuumpump will be described later. In a few words we shall indicate the method which we usually follow in order to get a wellfilled bath at diminished-pressure. First the double beaker 4,,, 4,,, or several beakers B,, B,, B, are filled at ordinary pressure, then we begin to slowly exhaust through )7,,; all other cocks being shut by means of the pump, generally used for the circulation Heh. 1; while boiling is prevented by rapidly moving the stirring apparatus described in § 4. When the required pressure is reached the cryostat is to be connected to the great reservoir |e. at the same pressure. If this cannot be done we hardly ever succeed in admitting through the cock /, the yet required quantity of liquid slowly enough to keep the pressure in the cryostat free from undesirably large fluctuations or even to avoid with the help of }’,, momentarily returning of it to nearly its ordinary value. Therefore, if a change of temperature for some time is allowed, if is in that case better to shut )’,, before more liquid is added and to connect the cryostat through ,, to the gasholder. As long as the beaker B,, is not full the gas leaving the cryostat is allowed to pass through Y,, into the gasholder. If the beaker /,, is full, which is shown by ( 510) the vise of the level in 2... we onee move begin to diminish the pressure ()%, shut, Vy, open) whieh process generally takes some time. Then more liquid is admitted as before and if necessary this process is repeated several times, If the beaker is sufficiently filled at the desired reduced pressure we begin to regulate the pressure with the duly exhausted vacuum reservoir as deseribed above. Plate IIT shows a couple of graphical representations of the varia- tions of the temperature of the bath. The ordinates show the deflee- tions on the scale of the galvanometer in centimeters. The abscissae represent the time in minutes; fig. 1 relates to a measurement in methane at ordinary pressure; a deflection on the scale of 1 ¢.m. corresponds to about 0.009 deg. (the open space in the figure indi- cates a magnetic disturbance). Fig. 2 refers to oxygen at a diminished pressure; here a deflection on the scale of L ¢.m. corresponds to 0.005 deg. They were borrowed from the measurements of MEILINK mentioned above. The temperature of the measurement is determined by the help of graphical representations, extending over the whole time of measurement, from which the portions reproduced on plate IIL have heen taken. For this determination the readings of the galvano- meter are noted down about twice every minute. By means of the planimeter we derive from the graphical representation obtained, the mean ordinate, which mean is considered as the temperature of the bath during the whole measurement. (March 25, 1903). KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, PROCEEDINGS OF THE MEETING of Saturday March 28, 1903. DEG (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 28 Maart 1903, DI. XI). COENEN n= J. J. van Laan: “The meltingpoint-line of TineAmalgams” (Communicated by Prof. H. W. Baxuuis Roozesoom), p. 511. A. W. Nizuwenuuis: “Influence of changed conditions of life on the physical and psychical development of the population of Central Borneo”, p, 525. P. H. Scnoure: “Relations between diagonals of parallelotopes”, p. 540. E. Conen and Tu. Srrencers: “On the atomic weight of Antimony (Communicated by Prof, W. H. Juriws), p. 548, (with one plate). E. Coven and C. A. Losry pr Bruyn: “The conductive power of hydrazine and of substances dissolved therein” (Communicated by Prof. C. A. Lopry pr Bruyn), p. 551. A. H. J. Berzer: “The velocity of transformation of tribroomphenol bromine into tetrabro- mophenol” (Communicated by Prof. C. A. Losry pr Bruyn), p. 556, J. H. Boynema: “Some new Under-Cambrian Erratic Blocks from the Dutch Diluvium (Com- municated, by Prof. J. W. Mott), p. 564. J. J. van Laan: “On the course of the values of 4 for hydrogen, in connection with a recent formula of Prof. van per Waats.” (Communicated by Prof. J. D. van per Waatrs), p. 573. W. H. Juris: “Peculiarities and changes of Fravnuorer-lines interpreted as consequences of anomalous dispersion of sunlight in the corona’, p. 589. P. Trescu: “On the refractive index of rock-glasses” (Communicated by Prof. J. L. C. ScHRoEDER VAN DER Kok), p. €02, (with one plate). G. B. Hocenraap: “On an “Lisenrose” of the St. Gotthard”. (Communicated by Prof. J. L. C. ScuRroEDER VAN DER Kok), p. 605. Hi. A. Lorentz: “Contributions to the theory of electrons, I. p. 608. H. Kamertincn Onnes: “Methods and apparatus used in the cryogenic Laboratory”. III feontinued) IV, V. p. 628. H. Kameruincu Ones and H. H. Francis Hyxpan: “Isotherms of diatomic gases and their binary mixtures. V. An accurate volumenometer and mixing apparatus”, p. 636, (with 2 plates ) The following papers were read: Chemistry. — “The meltingpoint-line of Tin-Amalgams.’ By Dr. J. J. van Laar. (Communicated by Prof. H. W. Bakuvis Roozusoom). (2"¢ Communication). (Communicated in the meeting of January 31, 1903). 1. In a previous communication (Proc. Dec. 1902) I showed, that when the molecular potential of tin in a liquid tin-amaleam is ex- pressed by the formula 35 Proceedings Royal Acad. Amsterdam. Vol. V. ( 512 a, = f(T) + RT log (1—2) + (a, wv? + 2, a +...), a very good agreement is obtained between the calculated values of the melting-temperatures at various values of «, and the temperatures observed by VAN Heteren (compare his Dissertation), at least up till about 80° C. In a conference, 1 had since with prof. vax per Waats, he called my attention to an expression for the correctionterm in g,, which may be taken as a fairly good approximation’). This expression is: a, 2 (1 + ra)? After he had first shown (p. 193), that the correctionterm is really of the order «*? — this I also showed in my previous com- munication, but in a different manner — and had observed, that (in the case investigated by him) the value of «¢, does not remain constant, but decreases when . increases (p. 198), he afterwards arrived at the said approximate expression (p. 218, 214), in agreement with an empirical relation of THOMSEN. Though Prof. van per Waats has briefly given the deduction ot his formula, it may be useful to state once more how this expression ean be arrived at. The matter is of great importance, because the same Quantity u,—(",),—o0 constantly occurs in a great number of formulae, such as those for the lowering of the freezing-point, elevation of the boiling-point, alteration in vapour pressures, etc. If therefore this quantity is once for all accurately known, we may get a better insight into a great number of problems relating to binary mixtures. 2. As the ‘otal thermodynamic potential is represented by $= — E (nh) T (log T-1) + |= (% ()) — TE, oo | - == | forr—ar | + RT Z (n, logn,), we obtain for the molecular potential of the component 1, : 0s aa = -k, T(logT-1) +[(e,),-T0i,)9 |- | foav-rs +RT+RTloan,. n, With = nN, Ler a eee 1) Zeitschrift fiir Ph. Ch. 8, pg. 188 (1891). Also compare different passages in the second part of his *Continwitat” on p. 43—45; 148; 152. Recently, Prof. van per Waats has returned to this question in his * Ternary Systems” (Proc. March to July 1902). He gives there a more general and accurate expression, wherein occur the crilical temperature and pressure of the mixture (Compare in particular IV, p. 92—96). Gabe we find: a fot —— n, RT log (V—b) ol a and therefore 0 IV — RTI v1 Ft; -RTO(V—b) _ a OV 1 da af al a RU ae V—) On, V? On, Von, Dedueting from this: 0 Koes a. 82 a |0V Pon, V—b V? \0n, CY hee OV. ss : Speed ai pdV —p Ee RT log (V—b)— — vp b+ = a, + n, 4,4) 1 we get: Substituting a= n,?a,+ 2n,n,a,,+ 7,2? a, for a, and the linear relation 6=7n,6,-+x,b, for 6 in the case of two components, the expression for yt, becomes: Bw, = — kT (log T—1) — RT (log (V—6) — 1) 4+ [(e,), — T(m,).] + Sink fel 2 : aa r (a Oe A= sO) SS det Tyg a fo ele oe (A) in agreement with what I wrote down in my first communication. If now we write n, =1—w#,n,— 2, this then becomes: uy = — ky T (log Tl) — RT (log (V—8) — 1) + [le,). — Tiel + BE te 2 V—b For the determination of the complete function of #, which oceurs here outside R7'log(1—-2), we will now determine the value of Jd A ay a — pld—a) a, + © 4,5]. The term with /og (V—S) is supposed to be but very little dependent on « in regard to these two. If in the equation of condition we put p=0, which is certainly permissible in the case of liquid phases, , + &a;,) + RT log (1—a). yy a then Tap may be replaced by Ve and the above expression becomes: (1l—«#)? a4, + 24 (L—2) « a + 2 a,) b, 2 ((L—2) a, + #a,,) v2 V If now we replace V by 6, which will hold for liquids at low temperatures in approximation, we obtain: 30* ( 514 ) ((1-w)* a, + 2 (1-a) a,, + 2* a,)b,—2 ((1-a) a , + © a,,)((1-«) 6, + @b,) b ‘ cer or: — 4a, ((1—.)? b, -t- 2a (1—.) b,) — 2 Ys x b, “fh ay x b, > i (las ee z= y Om . 5? EE . ’ which we may also write as a ? 4 a, b,” = 2 ers a, by - ) ) We therefore finally and approximately obtain : “, = — kT (log T—1) — RT (log (V,—4,) —1)+ [(¢:)o—Z(%,)o] =a Boe OS RT hog (1 i? b, t b, I? + og (L—a), when we call a, 6,7 — 2 a,, 6, b, + a, b,? = « The corresponding expression for pa, evidently becomes : a are k _ TP (log T—}) a RT (log (V,—b,) a 1) ai [(¢.). —Z'(45)o] a a, A _ a As eee p) it follows from the equation of condition, that : RIV? RTb V) = a) a a ; Ribas and that, therefore, log (V,—,) = log + log T. a, general: , =e, —¢,T— (k, + RB) Tlog T+, ae > H, =e, — ¢,T — (k, + R) Tlog T+ @, om ein + RT log « (1--re)* In this equation then 4 a 1 = (4), ——; &, = (es)o . b Rb *, = (m,), — (4, + R) + R log —-; a, whilst ine | and also Rb ¢,—=(7,),>—(#. +2) == R log “ ’ , we may write in + RT log (1 — wx) | (2) —b,+b, — - tr. b, ; ; 5 Remark. The quantity «,—=-—— may also be obtained by the opera- On, : 0g . tion php, =S$ — ez 50° For the term — foavtoy. occurring in §, may e Ov be written |e °T'log (V-0)——,. The required function of 2 may therefore also be found by calculating (V =, oe) for which we then find exactly in the same way as above: rs 2 3 » a, Kingda +445, See b bb? 1 The two methods of calculation are, of course, identical. The last has the advantage, that we see at once that the differentialeoefficient 2Ax 0 fa of the correctionterm of ., 1. e. Fa 18 nothing but « al , so ) ; av that we have: Ie Oe Poet a er By 0? ($) 2A a Ox ae lee ny ex T Oe? Re 6b when §, w, and ww’, represent the quantities & w, and uw, with omission of the terms containing log(1—.) and log. As regards the quantity 05 u, =~, we must remember, that this is also obtained from the relation v 0S i (US) : x 3. It is now the question, whether the expression 2 v a, 2 (1 rx)? represents the melting-points of the tin-amalgams as well as, or better than my semi-empirical expression aw + Ba + ya Let us first observe, that van Der Waats iota found @, negative in the case of electrolytes and other aqueous solutions (I. ¢. p. 195). Now it is evident, that if we may write a,, = Va,a,, the coefficient (d, Va, -b, Va)? ee and ought therefore to be always found a, becomes 516 positive. (L found for instance «, positive With tin-amalgams). — It therefore seems, that when one of the components (water for instance) is wn associating substance, or when the other component is electrolytically dissociated, we must certainly not follow D. BertneLor in writing aa,=e,,, independent of the fact, that in such cases neither a, and a,, nor 4, and 4, are constants. The formule (8) in my previous communication now becomes: i Oe aa a : qo (1+re)? 7 -— Sie ¥ 7h =5 ae RT, if— — log 1—.) do Lee RT. or with — = a, _°§—@: Vo do ax ie, (1-+- re)? ; T= TF : a “i=7 log (1—«) : From observations, where the values of « are less than O,1, the value of @ was found to be exactly 0,396°). If we now further accept for the values of the coefficients @ and r: a= 0,0453; pe ae which are calculated from other observations with higher values of , we obtain (7, = 273,15 + 231,63 = 504,8) the survey on the next page. We notice, that in this table the agreement is an excellent one ; the average deviation is about 0,9°, whilst in the case of the empirical formula with $e? and y«* (see previous communication), if the last value is not counted, it amounted to 0.85°. van DER WAALS’s expression for the correctionterm, therefore, represents at least equally well the course of the meltingpoint-line over the portion, observed from 212° to 65°. But what is still more important, is the fact, that whilst my former empirical formula does not very accurately represent the two last observations (the difference in the last even amounted to 10°), VAN DER WaAats’s expression not only satisfactorily represents these, but also the four observations at still lower temperatures (compare p. 22 of van Hereren’s Dissertation). In this observations the values of # and ¢ were determined by analysis of the liquid phase, which is in equilibrium with the solid phase at a given temperature. 9 1) In the previous communication 0.400 was accepted, but eae = 0,396 is some- what more accurate. } | | Numerat. eee | ; . | 2 Denom. | dpray| | ce ‘ | id. | in | [1—olog ‘1—z) 1 aeepeaico cubated found | 0.4005 'o.01010 4.0420 0.000458, 0.8567 4.0005 | 214.6 2u 6 | 0 0.1716 0.02945 1 0745 0.001433) 0.7621 | 1.0018 | 197.5 |198.6 j—1.4 0:2338 0.0540" 1.1054 0.002475 | 0.6839 1.0036 | 185.2 483.7 1S 0.2969 0.08815 1.13895 0.003993| 0.6089 1.0066 | 4172.8 |173.0 |—9.2 0.3856 |0.1487 | 1.4930 0.00673° | 0.5108 | 4.0132 | 155.6 55 2 |-++0.4 0.5001 0.2501 1.2745 0.01133 | 0.3968 1.0286 | 134.3 133.4 +0 9 0.5973 |0.3568 | 4.3602 (0.01616 | 0.38114 | 1.0519 | U7) eh” THlilsy.o 9.4 0.6467 0.4182 | 4 4419 |0.01894 | 0.9719 1.0697 | 109.3 |107.4 |-1.9 0.6754 |0.4562 | 1.4456 0 02067 | 0.2502 | 4.0896 105.0 103.4 4.6 | | 6813 |0.4642 | 1.4528 0.02103 | 0.2458 | 4.0856 | 104.0 [102.4 |44.6 0. | 0.7104 |0.5047 1.4907 0 02286 | 0.2250 1.1016 99.9 | 99.0 9.9 | | | 0.7155 0.5149 1.4978 0.02319 | 0.92914 1.1048 GON 98.8 0.4 | | 7477 '0.5591 | 4.5454 0.09533 | 0.4995 | 4.4970 95.0 | 95.4 |—0.4 | | 0.7547 '0.5696 | 1.5565 0.09580 | 0.1949 | 1.492% | 94.4 | 940 |40.4 | ‘ | ea | | 0.7963 [0.634 | 4.632 |0.62873 | 0.4687 | 4.4703 89.3 | 90.0 |—0.7 | | | | | | | lee 0.8189 0.6706 | 1.6767 0.03088 | 0.1552 | 1.1957 | 86.8 | 88.4 |—1.6 | | | 0.8921 }0.7958 | 4.8817 0.03605 | 0.4455 | 1.3121 | 78.9 | 79.7 |-0.8 | | | | | | 0.9483 |0.8993 | 9.1731 (0.04074 | 0.c8898! 41.4579 | 65.5 | 65.2 |4-9.3 | | | | | ! | | ae oe ate * | | | T—273.15| id. Ceeie ec ei Wenome ax |(1-+ra)?) Numerat. | | A | | | | calculated) found | | | | | | | ] | 0.9879 0.9759 | 2.7482 (0.04421 | 0.07931) 4.6144 29.9 | 95.0|\—9.4 0.9903 |0.9807 | 2.8357 0.04443 | 0.07140| 1.6293 | 15.7] 45.040.7 | | | | 0.9944 |0.9882 | 3.0396 [0.04477 | 0.0c991| 1.603 |— 0.4] 0.00.4 0.9964 0.9928 | 3.9282 0 04497 | 0.0690!, 1.6516 | — 14.9 |-18.8 43.9 The agreement is even unexpectedly great, when we consider, that the meltingpoint-line runs here almost vertical, and a quite insigni- ficant change in # causes a difference of several degrees in 7. 518 ) 4. Let us examine the formula wv 3 1 + 0,0453 . . i (, —0,74 ) 1 aeeNed hy . 1—0,396 log (A—~*) more closely. With small values of « it passes into ; 1 1 — 0.0458 2? 1 1 ; 4 T=—|T - — T' —0.396 2 O,004 a]. “1+ 0,396 (@ + */, 2*) ol a Because the coefficient of x? is accidentally nearly O, the melting- point-line in this case runs over a fairly large region (from 232° to 120°) as an almost straight line. To ensure this, it is generally necessary, that 0? — 40a is very small or 0. As, for equilibrium between the solid tin and the tin in the amal- gam, @ =f, or —pe+n, =9%, we also have: 0 0 da age 2 Bd eet ed ae : 0 q Now according to a well-known theorem (—' +) Sa or he The molecular potential « for the solid phase is moreover not depen- dent on w. Therefore: q , Om, de — = 0 Tt dx dT : and consequently ar a q Ox We therefore see, that supposing the solid phase (as in this case) - dT uy, contains no mercury, oe cannot become 0, unless = == (I). But ae fia then the liquid phase will be unstable, and we find ourselves on the spinodal line, so that the liquid amalgam would long ago have broken up into two phases of different composition. 7 c . Now, —— and therefore also — may become zero in the case of im Ow da two values for x; there are therefore in this case always two hori- zontal tangents. A limiting case of this is of course a point of inflection with only one horizontal tangent. As ( 519 ) CT L 07m, du, d Lr Fas q Oa? ap Ow da this limiting case will evidently occur este a arid a are 0 at the same time. Now Ou, Rts DART ae ChE RT 2A 1—2n0 ee? um tate uy b,? (1-Ere)? Ov, d= 4 b, 3 (1 rz)' so that for this point of inflection we shall have the relations Hla) Gene! (=a arn) RE (1--re)! mors cia (1+ 72)* Oe ; On dividing, we find : :(1 + rx) = (1—2z) U—2 ra), or —2(1 +- ryau +t 1 === (); When 7 is either negative or positive, we find from this : te Oe ei V ——— , (0) when «, indicates the value of v at the point of inflection. 7, may fun irom ~/5 Gf 70) to 1 @ r——1), when 7 is negahve. V, however, 7 is positwe, x, runs from */, (if r=0) to 0 Gf r=o). The positive sign forV 1+ 7+ 7% would give in both cases impos- sible values for 2... We now further obtain : «(1 —a,) Tice be West at dt OP pT (1-+re,)? 2aq, Gh eae yi Me aol ae 0 Tr that is to say, when for r is substituted its value from (8dzs) : y 6 u(l—a,) — YZ 4 : (L+-ree)* (1+72)? ~ 2a 1—JOlog(1- te)” Ou . . . a 1 . where the lower sign indicates conditions, where —— < 0, and which Ou are consequently stable. From this then follows : Otay (—«#,)) than this value, then 5 becomes 0 on av one or two places on the meltingpoint-line. : ee ; From the expression for 7 jsee above) it follows immediately, Ov Of, that when A, and consequently @, should be negative, a, cam never & become 0, still less positive. The occurrence of unstable conditions on the meltingpoint-line may, therefore, only be expected in the ease of positive a, and only then, as soon as @ reaches or exceeds the value, given by (}). The relations (a) and (4), when united, give therefore the con- dition for stable phases along the entire meltingpoint-line. In our example + = — 0.74, and (a) gives 7, = 0.863. The equa- tion (4) further gives with 0 = 0.396 : 27 0,396 x (0,137)? eZ 0,863 X(1,137)?[2 X1,137(1— 0,396 log 0,137) —3 X 0,396 X 0,863] that is to say = 0,180 — 0,180 Now, in our case @ was 0,0453, so that everywhere we find ourselves in the stable region (as may in fact be seen from the shape of the observed meltingpoint-line). If @ had been 0,059, we should have had a point of inflection with horizontal tangent; and had a been 0,059, we should have noticed the occurrence of a horizontal tangent in two places of the meltingpoint-line. This last case is, of course, not realisable, as the liquid amalgam would break up into two heterogenous liquid phases of different composition. *) 1) It is perhaps not devoid of importance to observe, that when the solid phase forms a solid solution of the two components, the presence in the meltingpoint- line of a point of inflection with a horizontal tangent points as before to unstable conditions. For-in the general relation Ou Another question is, at what values of w and 7’ does FI first ae become 0, or where does the plait commence, independent of the fact whether we find ourselves on the meltingpoint-line or not, which had just been investigated. Ou O7u r . . 1 ¥ We have only to combine the relations ——=0O and —-—0 fa Fi | ee Ce.) —— dl , ; : Oa: ane tx Wa, dT —— always becomes 0 in ove place only in consequence of %,—2a, becoming 0, aa z dT whilst on account of —— becoming 0,—— always becomes 0 in two places, or On? da in the limiting case in f2vo coinciding places in a point of inflection with a hori- zontal tangent. De Visser thinks he has found such a point of inflection with mixtures of stearic and palmitic acids.1) It is, of course, not impossible, that we are dealing here accidentally with a case, in which the quantity 2 possesses the value indicated by (}). That the line of the end-solidifyigpoints also shows in the immediate neighbourhood a similar point of inflection, points to the fact, that the Ate pea Ms 0s conditions a0 AG ~=(Q are fulfilled on both lines at about the same time, Mi which renders it more accidental still, because z would then possess the value required for this also in the solid phase. It should be pointed out, thatas a rule Se US ars the conditions <= = (l} = ==0 for both phases by no means include x, = 2. For : ; S, 0s, : ‘ ; this requires 2. = ate: It is there‘ore a new accident, that both points of Re ee inflection appear to coincide. But for this a reason may be given here. From the equation, from which (@) is found, namely ra? —2(1+7r)a2+1=0, it follows that with r=0, x=1/,. De Visser now found both points of inflection to be at « about 1/3 (= 0.525), so that the quantity 7, both in the solid and liquid phase, is about 0 (b;=b,). And in that case the values of # at both points of inflection must agree, namely both at x= }/. The case, studied by pe Visser, may therefore be an accidental coincidence of 2 2° . ae . TOR : the two points of inflection. But then, on account of —— *— 0, both ue, ane the liquid and solid phases must have broken up te two layers, although of identical composition. The smallest delay in solidification would however imme- diately have carried the system within the plait, and then both phases would have broken up into two layers of a somewhat differing composition. It is however more probable, that both lmes nearly show a point of inflection with a horizontal tangent, and that they approach very near, but not touch each other. 1) Rec. Trav. Chim. (2) T. 2, N?. 2 and 4 (1898), 522 ) to find the values of « and 7’ at the “critical” point. We find as above : 14r—V14r+r tp =- rr whom” be gos ee - 7 fare oe Gv fe Mere _ Of, rhe temperature 7 of this critical point is found from —— A | Or that is to say from w@(1—ac) _ Qe (1+ rt,)* Qa T. ; We consequently find : 2a a(1—a,) iy — fh = — > 0 (1-+-rx,)* 19; or, as l+re,=3 oe ] 2a x(2—2,)? T.=—T,.— ie 2— Hee)" 2 Sa 27 a (1—z,)? i Of, |. a At this, or at lower temperatures, | being then positive, we find Or ourselves therefore in the plait. In the case of tin and mercury we find for x, the value 0,863 (see above), if r= —0,74. For 7, we find: 504.8 0.0906 or Ot0896 The “critical” point is therefore situated at 16° C., that is to say T.= X 67,60 = 2897.2. fully 57° lower than the point of the meltingpoint-line, belonging to xv — 0,863 (13,7 atom-percent tin), namely 83°,2 C. There are of course cases, where that distance is smaller, and where consequently a trifling supercooling already carries us within the region of the plait, which then — in the absence of the solid phase — causes a separation into two layers. I may observe, that the value «, does not correspond as a rule with a point of inflection (with oblique tangent) on the meltingpoint- line, when the critical point is not situated om the meltingpoint-line. Orn 2T —1—(),—* —0 do not lead to — 0, when these differen- Ox Ox? dau? tial-coeffients do not become 0 on the meltingpoint-line. . On, a For 5. The value of g, the heat of fusions of tin in the liquid amal- gam, is evidently: ess pa 2? 7=% sea) When the value of w is small, and assuming, that mercury dissolved in tin is monatomic, we find for qo by calculation 2550 eram-cals. Person found experimentally 1690 gram-cals. Should this figure be confirmed, it would prove, that the associationfactor of mercury is about 1.5. Now, it follows from the above formula, that at 25°, where w is about 1, g ought to be = 2550 & 1,6114 = 4110 eram-cals., whilst van Hwrrren, by electromotive measurements, found about 3000 egram-cals. From this it would follow, that the value, used for q,, is about 1.4 times too large, which would be a confirmation of the fact, that the mercury in the amalgam is not present as single atoms. In order to obtain certainty as regards the molecular condition of the tin in the amalgam, it would be necessary to know the melting- point-lne of the mercury, and to determine the lowering of the melting-point in addition to the heat of fusion in the presence of very small quantities of tin. There are indeed indications, that the tin is also not present as single atoms. Indeed, the quantity 7 = — b, + b,, b, which was found by us to be — 0,74, gives for i the value 0.26, ) y from which it would follow, that the molecular volume of. tin (b,) would be about four times larger than that of mercury (b,). Now, the atomic volume of He is 14,7, that of Sn = 16,1, so if these two Peyibe ; components were monatomic, — ought to be approximately = 1, ) 1 whilst in reality that relation is '/,; this points to the probability, that in the case of tin several (may be six) atoms are united to one molecule. It certainly would be highly desirable if this question were fully investigated. For in all our calculations the values of w are only then valid, when both mercury and tin are assumed to be monatomie. This is also the case with all similar calculations, relating to other amalgams. May I be allowed to point out, that the molecular condition of mercury may be determined from the lowering of the melting-point of tin, if this contains « little dissolved mercury — whilst the molecular condition of tin may be ascertained from the lowering of the melting- point of mercury in the presence of a /ittle tin. For in the case of dilute solutions something is learned only about the condition of the dissolved substance, but never anything as regards that of the solvent. In the limiting formula ( 524 ses ? T= eg Veo where 7’, and q, relate to tin as solvent for example, everything on the right hand side will remain unchanged, although tin siould not be monatomic, but say n-atomie. For 7, the concentration of the dissolved mercury, would then become j-times greater, but q, would also become n-times greater, because the heat of fusion relates to 1 mol. = n-atoms. On the other hand, if the mercury were m-atomic, the value of « alone would change; 2 would then become m-times smaller, and we shall, therefore, observe a m-times smaller lowering of the melting-point than that, calculated on the basis of mono-atomicity. In this way we might attain to the knowledge of the molecular condition at the ends of the curve, « being O (for mercury), and 1 (for tin). But in order to form further conclusions with other values of x, the whole of the meltingpoint-line would have to be accurately examined, and this may in many cases become an exceedingly com- plicated matter. 6. There is, however, another way to get to know something about the molecular condition of the solid tin, and that is the com- position of the so/id phase, which is in equilibrium with the liquid one. If we equate the molecular potentials of mercury in the two phases, we obtain: = a,(1—2)? ; ‘ a’ (1—za')? 0,25 71 a RT log cL a - saad —e@.,—C, T 4- RT log a =F Seema! = (1+ re)? ‘ 7 (1+r'e'y This further gives: Seen a’,d—e')? — a@, (1—«)? (e,—e’.) — (ec, —e'>,) T= RT log— + BAe — Caht aes P 5 ; re (1 + 7a’)? (1+7r.)? or with e,—e,—=4q',, and with introduction of the meltingpoint 7”, of pure mercury : Te av |e id., q 0 ( fT! ) og z + 1 0 therefore ; Feb The x a, (1—)? a’, (1—a')? q 0 => 1 log ' ae ria al \ 3 = az, . T—T', x RT (1+ re) RT (1+ 7' 2")? Now in the liquid condition b, b, a, aq, T, b, a Lote = —— s =— =— —, Oe Ay 8d X75? pr RT, om ee 504,8 50 This quantity is therefore 0.1144 398.9 we 3 Putting «', =e, and 7’ =, as a first approximation, the value of the correction becomes : 0,012 y 0,99 a) (ari < 0,988, C= SOLO 0,745 and, as at 25° the composition of the liquid phase was found « = 0,988, and that of the solid phase #' = 0,01 (perhaps 0,06), the said value becomes : 0,745 (0,0020—0,9950) = — 0,74. A change of 2 from 0,01 to 0,06 can only cause a slizht alteration. iO The value of the chief term log — is: a — >< 3,85 = 8450 eram-cals., whereas Prrson found g' = 2,82 & 200,83 = 565 er. cals. We therefore find a value 15 times too great. And a small error in the correction term 0,74 cannot upset this result. If, however, the tin in the solid amalgam is taken as hexatomic, w' becomes six times greater and q, comes down to about 4400 gram-cals. If, moreover, .7' is origi- nally taken not as 0,01, but as 0,06, so that with a hexa-atomicity wv now becomes 0,32, the value gq’, begins indeed to get more close to the value, obtained experimentally. The above, therefore, contains indications enough of the poly- atomicity of both mercury and tin. To arrive at a decision, however, accurate experiments will have to be made in the direction indicated, together with fresh determinations of the two heats of fusion. Ethnology. — “Influence of changed conditions of life on the physical and psychical development of the population of Central Borneo.” By Dr. A. W. NruweEnatis. (Communicated in the meeting of February 28, 1903). There is great diversity of opinion among competent authorities about the influence exerted by external circumstances of life on the development of a person and on that of the peculiarities of a tribe. If this difference of opinion already gives evidence of the difficulty, of determining this influence for the individual, the difficulty is greatly 526 ) increased, as soon as we try to find, between two groups of men, characteristic differences, which are to be ascribed to their different circumstances of life. Examining the highly cultured nations whieh live in very complicated conditions of life, the difficulties become almost insuperable. We are not a little hampered in this investigation by the faet that among civilized nations mutual intercourse and mixture have a disturbing influence on the eventual effect of special conditions of existence. In Europe some data are furnished by the Israelites, which have preserved themselves as such for centuries in different countries under the circumstances prevailing there and which have absorbed few foreign elements. But here, too, the influencing conditions of life are very complicated, and the Israelites of the different countries have mixed with each other. Chiefly because the relations in the societies of tribes, which have not reached so high a degree of civilization, are simpler and the conditions of life for all their members do not differ so much as elsewhere, it is likely that amongst them eventual changes in those conditions of life will stand out more prominently and that much becomes clear to the investigator, which was difficult to point out under more complicate relationships. It is moreover noteworthy, that among them the influences of nature, of the surroundings in which they live, have a much greater effect than in higher civilized societies, which have learned to shield themselves better against this direct dependence. We also meet with tribes where the great disturbing factor of frequent mutual intercourse and mixture is excluded in examining the modifications which two tribes have suffered by different external causes. A still simpler case presents itself where two large groups of the same race have lived for a long time under different external circumstances and have mixed little, if at all. Before it has been proved that the people forming these tribes, are in their original qualities the same as Europeans, we must not directly apply what has been observed in them, to European society. For the right understanding of the pre-historic course of the development of mankind, however, we may refer to the tribes, which have reached as yet but a lower degree of culture; in my opinion we are equally justified in drawing certain conclusions as to the corre- sponding influences on higher cultured nations from many things, which we have observed in the social matters of the former. During my second journey through Borneo I had the privilege of living among two groups of the same tribe, which have existed for a century and longer under very different circumstances. They were the Bahaus on the Upper-Mahakam, with whom I lived for two years, and the Kenjas on the Upper-Kajan, with whom I spent some months. The tribe-groups of this name occupy together the upper- and middle course of all the rivers, which fall into the sea on the North coast, beginning with the river Batane-Redjang, and as far as the Kast coast, including the river Mahakam. They are called collec- tively the Pari-tribes, and they all consider the region contaiming the sources of the river Kajan as their original country. Mutual quarrels, the result of too dense a population, were the cause, that for centuries again and again tribes moved away to neighbouring rivers, as e.g. if happened no more than 25 years ago with the tribe Oema Timé, which settled on the Tawang, a tributary on the left of the Mahalkam. The Bahau-tribes on the Upper-Mahakam also originate from this native country, which they call Apo Kajan, but they have lived in their new home already for more than a hundred years. This was curiously confirmed on my arrival in Apo Najan with my Bahau- escort. Them chieftain Kwine Irang then received for the first time a full account of the history of his ancestors, which was already forgotten in lis own tribe. How little intercourse the inhabitants of the Upper-Mahakam have with those of the Upper-Kajan may be derived from the fact that among all the younger Bahaus only-one man had ever been in Apo Kajan, and that, when in the company of 60 Bahaus and 20 pseudo- Malays I set out on the expedition thither in August 1900 none of us knew the way. The journey lasted a month, and we had to traverse uninhabitated land. The way was indicated by sticks put up in a special way in the river-mouths by some Kenjas who travelled in boats in front of us, the sticks denoting which rivers we had to take. We may therefore assume as certain that we have to deal with tribes of the same origin, to which moreover their language, dress, morals and customs point, which distinguish them clearly from other tribes, e.g. from those on the Barito- and Lower-Batang Redjang. Them descending from Apo Kajan to the Upper-Mahakam, however, brought the Bahaus in peculiar conditions, which exercised a great influence on them. On the Upper-Mahakam, namely, the Bahaus live at a height of from 250 to 200 metres, the Apo Kajan is 600 metres and higher. That this difference as regards the climate is very considerable especially in Borneo, may be derived from the 36 Proceedings Royal Acad. Amsterdam, Vol. V, ((528>) fact that in Java the region of moss vegetation does not begin lower than at a height of 2500 metres, whereas in) Borneo it) begins aoa height of a thousand metres, This is caused by the following circumstances. The situation of Borneo being under the equator, the middle region is but slightly affected by the influence of the trade-winds, which e.g. in Java make the difference between the wet- and the dry- monsoon so great. Hence it may happen that more rain falls from December to March than from May to October, but particularly in the highlands really dry times are unknown, and we may find low water in the rivers in the rainy period. The regular distribution of moisture through the whole year is greatly furthered by the cireum- stance that the whole island is covered with one large primitive forest, which itself retains large quantities of water, and harbours mouldering rocks which do the same. The annual rainfall amounting from 8000) to 5000 mam. at different places, the climate is very humid all through the year, and the sky is always more or less overcast, so that a cloudless sky is a great rarity in the higher regions. Soon after sunset a low hanging curtain of clouds is formed in the valleys. This does not rise until seven o'clock in the morning or later and envelops the summits of the mountains till pretty late in the evening. In consequence of this the maximum temperature at a height of 250 metres is 30°C. in the shade on the Upper-Mahakam; at six o'clock in the morning however it was never lower than 20° C. Noteworthy is also that strong winds of long duration do not occur there, only some blasts of short duration, which are generally preceded by heavy showers. The climate of Apo Kajan and of the Mahakam differs but little in most of its peculiarities, such as humidity, and a cloudy sky, but the latter is a good deal colder on account of the greater height, and what is particularly striking is the continually prevailing wind. This accounts for the fact that though in two months I never found a lower temperature than 17° C. at six o'clock a.m. and though it hailed but once, the climate is yet much rougher. The red cheeks, specially of the women and children prove this, and also the fact, that the different kinds of rice require a month longer to ripen in Apo Kajan than on the Mahakam. Yet the method of growing rice is the same, and consists in cutting down and drying the wood, after which it is burned and the rice sowed in holes, which are made hy pushing pointed sticks into the soil, which is covered with ashes. The geological formation is the same in Apo Kajan as on the Upper-Mahakam:; we find in both a strongly denuded upland, where ( 529 ) everywhere old slate layers come to the surface. Only here and there younger formations, specially free-stone, cover the older. If we now take into consideration that only in the last 30 years either the Bahaus on the Upper-Mahakam or the Kenjas on the Upper-Kajan have come into such close contact with higher civilized nations that if induced some of their men to undertake commercial enterprises for the purchasing of salt and linen, I think that Tam justified in asserting that the two groups of tribes under consideration belong to the same race, that they have lived for upwards of a hundred years in countries with a different climate, that they have had but little mutual intercourse and have not mixed; that they have not changed them life as cultivators of the soil and have developed without external influences. What effect this difference of climate can have on the popu- lation, may be derived from the fact, that in my opinion the thin- ness of the population in Borneo depends in the first place on the influences of the climate, and much more on the customs of the people than on the infectious diseases, such as cholera, smallpox, which are introdueed from the coast. As both Upper-Kajan and Upper- Mahakam are so difficult to reach that infectious diseases but very seldom extend to them, we have, when trying to determine what the result of those changed conditions of life is for the Bahaus, only to deal with those factors which are sometimes comprised under the name of influences of the climate. What is understood by influences of the climate in the highlands of Borneo became clear to me for the first time in the sultanate of Sambas on the West coast of the island, where I was struck by the difference in the spread of malaria among the population of the marshy coast regions and that of the highlands. In order to get a fuller knowledge of this difference, 1 made an inquiry into the traces of malaria infection on about 8000 children, both in’ the marshy alltvial plain and in the highlands. These children had not heen offered to me on purpose for this investigation, but for an inquiry into the results of the vaccination among the Malay and Dajak population. Among the population of the alluvial plains IT found among 2103 children only 6 with a chronic hard splenic tumor, or 2,8 per L000. Among 420 children of the uplands it occurred in 403° children, or 959.5 per LOOO. The remamneg 396° children originated from regions, whieh in their formation were the transition between the alluvial plains and the uplands. Janus. Deuxieme Année 1898. 36%* This inquiry vielded the result, that in the marshy alluvial plains Which consist entirely of vegetable and animal remains, malaria hardly ever occurs, as opposed to the uplands where nearly all children suffer from chronie mataria-infection. At the same time I saw, that soon affer birth the hardened and enlarged milt makes tts appearance, for it was long before | could: find a Dajak child of three weeks old, whose milt was not to be felt. It is impossible to give the morbidity and the mortality caused by the malaria-infection among the population of the uplands in figures. I only found the death-rate in Sambas extending over 6 normal years, i.e. years without cholera or smallpox, to be for Dajaks 387 per LOOO, for Malays 28 per LOOO, which however does not represent the influence of the malaria, because there are also some Malays who live in the uplands and among those, who have chiefly settled in the lower plains, diseases of the digestive organs are much more frequent than among the hills. In order to appreciate fully the influence of the malaria-infection on the existence of the inhabitants of the higher regions, we must dwell for a moment on the phenomenon, which prof. Kocn says that he observed in New-Guinea, namely, that the native, who went through the malaria-process independently i.e. without any aid except his constitution, became immune against it. Many are the refutations adduced against this statement by physicians, who practised in New- Guinea. They all pointed ont how frequently also adult Papoeas suffered from malaria. Judging by my experiences among the Dajaks, the truth lies between the two. [also have been struck by the fact that not so many hard enlarged milts as symptoms of the malaria-infection are met with among adult Dajaks as among children under the age of ten, which certainly points to a less strong influence of this unfection. Moreover there is a great difference between the action of chinine on Dajaks and on Europeans, who are not immune. Though we must make allowances for other factors than immunity, vet it is remarkable, that we obtained much greater results with at most 1 gram sulphas chinint a day among the Dajaks than with 2 to 3 er. murias chinini among European soldiers, seized by malaria in) Lombok. Among the former if was possible to cure not only the acute cases of malaria, but also cases which had continued from 4 to 6 months and had not been treated before, by administering 1 gram sulphas chinint per day and per dose during 8 days, whereas in the first four months after the war in Lombok in a mixed garrison of 1500 men more thar 500 Europeans had to be removed, most of them by far 531) being malaria patients, whom | myself had treated with from 2 to 3 grams per day and per dose, and who had little chance of being cured in Lombok itself. Among at the least 2000 Dajak malaria patients, whom T treated specially in Central-Borneo and of whom hardly any died, | observed another telling difference between the reaction of their body agaist the malaria-infection and that of the Europeans. Whereas under unfavourable circumstances many of the latter perished under rabid and strong symptoms, sometimes so quickly, that chinine was of no avail, sueh acute cases with strone icterus, uncon- sciousness and collapse were never found among the Dajaks. [ saw, however, many cases where the disease had reached an advanced stage after protracted illness. That this difference was not due to the inferior streneth of the infection in Borneo, was proved by my European and native fellow-travellers, most of whom suffered badly from malaria; to them I had again to administer from 2 to 3 erams of murias chinini a day, and one of them IT had to give a strong hypodermic injection of 3,25 gram chinine within 36° hours. From all this we may assume that the Dajaks become partially immune if in youth they are subjected to repeated attacks of malaria. Yet even then whatever weakens the constitution may give rise to attacks of malaria, so that diseases of the respiratory organs or of the digestive organs, wounds, diseases of infection and specially everything that is comprised under the name of catching cold, get complicated with malaria. As the mountamous regions on the Upper-Mahakam are among those where malaria is of very frequent occurrence, it is clear, that the Bahau-population suffer greatly from it and that the individual experiences its enfeebling influence from early youth till death. Being used for years in my practice amone them to find that the great majority of cases were those of malaria, | was greatly struck by the change after my arrival among the Kenja population of Apo WKajan. TI must add that my reputation as a physician procured me immediately after my arrival a great number of patients, though only few had ever seen a European on the coast before. It first struck me, that so many hydropie old people called in my help, which had seareely ever occurred in lower regions, whereas the malaria-cases retired to the background and during my stay confined themselves to a few acute cases. I found then, that the change in the sick-rate of the population was chiefly due to the prevalence of bronchitis with emphysema and heart-disease, bronchitis ( Daaet being caused by the rough climate and inereased by the smoking of badly prepared tobaceo, whieh even very young children begin and which is held to be a remedy against coughing. Though more acute malaria cases occurred, when the rough, cold weather set in’ with violent showers, there was not any question of a chronic infection of the population, manifesting itself in an enlarged, hardened milt in the children. This agrees with the well- known fact, that in a rougher colder climate malaria generally decreases in violence, As bronchitis and its consequences do not make their enfeebling influence felt on the constitution before a more mature age is reached and are not to be compared in this respeet with strong malaria- infection, | believe to have found the chief factor of the present difference of the two groups of the same tribe as to their consti- tution and their character in the difference of the occurrence of malaria as a consequence of the difference in height of the country of the Bahaus and that of the Kenjas. Moreover IT must take into account that syphilis is found ina less violent degree among the WKenjas than among the Bahaus. Among some Bahan tribes it was so universal, that I thought the facet that only tertiary forms were found could be explained by assuming exclusively hereditary transmission. Among the Kenjas, however, syphilis was also met with only in that form, but the cases were so isolated that we could not possibly ascribe them to hereditary in- fluences. The cases observed seemed to have a less injurious influence on the general condition of the Kenjas than on that of the Bahans. That this endemic form of syphilis is so much less common and that ifs symptoms are so much less dangerous among the Kenjas than among the Bahaus is due to a great extent to their stronger constitution. If we now take into consideration, that among all these tribes every family, even that of the chiefS is dependent for its daily food and sustenance on the continual labour of all its members, which is not the case in more highly civilized societies, we feel, how vreat the influence must be which the more or less frequent occur- rence of these diseases must have on the prosperity of the tribe. A striking example of the better conditions of existence offered by Apo Kajan which is of equal extent to the Upper-Mahakam, com- pared with the lower river-basins, is furnished by the fact that for centuries many tribes have been leaving this country for other parts of the world and that nevertheless the population there is at present much denser than in other Dajak regions, Instead of 800 to S00 inhabitants as on the Upper-Mahakam, the villages count there 1500—2500 inhabitants, though they certainly do not lie farther apart. Moreover the general appearance of the Kénjas makes a much better impression because of their stronger build and the less frequent occurrence of deforming diseases among the scantily dressed figures, which is enhanced by the absence of the cachectic persons so numerous elsewhere. The difference between the Bahaus and the Kenjas is even more marked in their psychical qualities than in their physical indivi- duality. The enfeebling moments which on the Mahakam affect them in a so much larger degree seem to have had a strong degenerating effect on the psyche of the Bahaus. This is proved by their history: in the beginning of the 19% cen- tury they made themselves known not only by head hunting but also by raids undertaken on a larger seale till far into the river-basin of the Kapoewas, the Barito and the Mahakam, mm which regions no tribe could resist them; at present smaller forays rarely occur, larger expe- ditions are quite out of the question and in a fight with other tribes the wounding or death of one man may put his tribe to flight. The greatest difficulties which confronted the European stranger in lis intercourse with the Bahaus, arose in his continual strugele with their timidity, fear and suspicion even after a long intercourse and in the fact that his movements were continually hampered by the pecuhar religious and other convictions of these tribes. The strong contrast i these respects between them and the Kenjas is therefore very striking. After my arrival in Apo Kajan 1 was at once struck by the fact, that the 150 men, who had come under their principal chieftain to assist me by bringing boats and inproving roads, were much freer and noisier in their behaviour than my Bahauw escort, that the chief- tains gave their commands with much greater energy and that they were also better obeyed. During my stay in their villages this impression was greatly strengthened by the want of shyness on the part of the women and children. Remarkable was the contrast between the behaviour of the young Wenjas and the Bahaus when I, as T usually did, distributed small presents, such as beads, finger- rings, needles and pieces of cloth among them. Amone the Bahaus I could quietly keep in my chair, and though occasionally a little hand may have been stretched out too quickly towards the coveted object, yet all the little ones waited patiently for their tum and never became boisterous. When | distributed things amone the Bahaus, the proceedings were quite different: L had to begin with taking a asd firm footing, for boys and girls pressed in’ upon ae with loud shouts and extended hands; every one was afraid to be behind hand and they seuffled among each other, to get nearer, Tt soon proved that they are Jess sensible to the bad smells of their fellow-men than the Bahaus among whom one can sit’ for hours with impunity even in large companies; therefore they also prefer to go a long way round rather than pass a dead body, and who protest to a disagree- able smell by violent gestures and spitting. Remarkable also is the greater perseverance of the Kenjas at labour, which [T specially observed when making long expeditions in rowing-boats on the Mahakam in the great heat to which they were not used. Though they are more used to walking than to rowing in their highlands, where the roads are better and the rivers smaller than in the country of the Bahaus, yet they kept on rowing for days together much more persistently than the latter, and always arrived earlier. These few examples already give evidence of a greater vivacity, less sensibility and also of a greater power of resistance of the ner- yous system; moreover their mental capacities are far superior. When telling the Bahaus about some remarkable features of our society, 1 got accustomed to meet with an absolute ineapacity to imagine these things, which gave rise to disbelief, and induced them, but often afler a long interval, to try and cateh me at an untruth. Among the Kenjas, however, [| soon concluded from their questions, that they at least tried to imagine railroads and similar inventions, and that they really understood other things. A very good criterion is furnished by the explanation of the motion of the sun, the earth and the stars with the origin of night and day, and the causes of a solar- and Innar eclipse. Of course the Kenjas-also did not immedi- ately believe that the earth is round and moves, nor that it is not a monster that eats sun and moon in case of an eclipse, but they understood at least my explanation. Of practical use to us was the greater interest and the more extensive knowledge of their surroundings shown by the Nhenjas. In the course of our topographical survey of the Mahakam and When inquiring into the names of the principal mountains and rivers we met among the Bahaus with such utter ignorance, that we were for a lone time convinced they were mnwilling to tell them to us. It proved however later on, that it was not tnwillingness on their part, but that only few among them knew anything about rivers and moun- tains outside their immediate neighbourhood, and that e.@. high mountains, Which, though they stood at some distance on the territory ( o3o.) of another tribe, but commanded the landscape, had no name among them, and that in order to find out its name, we had to apply to tribes living nearer the mountain. If was, of course, quite out of the question to avail ourselves of their help in determining the different places from such a mountam top. I was therefore greatly struck, when among the Nenjas [ascended a mountain, for the purpose of getting a survey of their country and Boei Djalong, the chief of the country, who accompanied me pointed out all the mountains as far as the horizon with their names, also those we could verify in the Mahakam territory; he also indicated the roads leading to the different adjoining countries as accurately as a European could have done. Not only we, but also the Bahaus who accompanied me, were astonished at the knowledge of the history of times long past, which the Kenjas displayed. It is a wellknown fact that tribes, who cannot write and who possess a low degree of civilization, lose quickly the memory of past events, and the knowledge of the Bahaus about their ances- tors was therefore very imaccurate. Great was therefore the asto- nishment of Kwine Trang, when the Kenjas told him the traditions of his own ancestors during the time of their stay in Apo Kajan. This greater development of their psyche keeps pace with pheno- mena, which evidence a stronger personality as regards their sur roundings. They are braver, which appears clearly from their way of conducting warfare. The tribes in) Borneo are notorious on account of their headhunting, a method of taking revenge and of fighting, which is justly looked wpon as bemg rather cunning and cowardly than brave, as it consists in the laying of ambushes and the sudden attack of superior forces on but a few individuals. An open fight is rare amone the Bahaus, and as has been said before, if two tribes are confronted, the death ov wounding of one man suffices to put his party to flight. Quite different is the warfare among the Kenjas: hand-to-hand fights are frequent, in) which chiefly the sword is used, and in which many are killed before the battle is decided. Though headhunting occurs also among them, yet it recedes more into the background, and when if occurs more personal valour is displayed. A few years ago e.g. a young Keénja chieftain, When performing a war-dance during a visit on the Mahalam, sud- denly cut off the head of one of the spectators, and took it with him in his flight. This was certainly treacherous, but it requires courage to do such a thing in a large gallery with a great many lookers-on. It is irritating to see, how the Bahaus submit to be illtreated by the Malays, who live at their expense by deceit, theft and grave- Nab. ) robbery ete. Only ravily do they take revenge on these unwelcome enesis, who live among them either beeause they gather the forest produets, or beeause they bad to fly from the coasts on account of crimes. The Kenja-tribes ave less long-suffering: two gangs of Malays, one consisting of five members from the Mahakam and one of eight from Serawak, who tried to live upon them in a similar way, were all murdered. As soon as we come in contact with the Kenjas, this bold perso- nality impresses us favourably. Among the Bahaus we could not establish for years the frankness of intercourse between them and ourselves, which was brought about with the Kenjas in as many months. Only incidentally and by indireet means could I get to know wnong the Bahaus what they thought of a plan and what they intended to do. When alone with one of them I occasionally sue- ceeded in getting him to express his thoughts freely, because he had no reason to be afraid of his fellow tribes-men, but they never quite relinquished their fear and distrust. In our intercourse with the Kénjas the last trace of suspicion had soon vanished, and never shall I forget the impression made by their political meetings on us Europeans, used to the uncertain, hesitating and insincere behaviour of the Bahaus, even when discussing affairs of great importance. In the meeting of the Kenjas all the chiefs present freely expressed their opinions with peculiar ceremonies on subjects as e.g. whether it was advisable to adhere to the rajah of Serawak or to the Duteh-Indian government, and the advantages and disadvantages were openly discussed. If on account of these peculiar qualities the behaviour of the Kenjas is noisier, coarser, braver and less sensitive than that of the Bahaus, it is interesting to see what influence this has had on their society. Among the Bahaus on the Mahakam we find a number of perfectly unconnected tribes, in which every individual considers himself quite independent of all the others, and perfectly free to look upon his own interest as of chief importance, which renders the chiefs powerless to exert any influence over their subjects for more general interests and enterprises. Everybody entertains the greatest fear for unexpected sudden attacks from far or near, and while in the day-time the men always go to their rice-fields strongly armed, in the evening they dare not even be under their houses without a naked sword. Of course women and children are still more afraid. Among the Kenjas, on the contrary, we find a somewhat loosely constructed, but yet connected whole of all the tribes under the acknowledged supremacy of the tribe of the Oemo Tow and its chief Boei Djalong. The country is so safe, that the population goes to the fields only armed with a light spear as support, and that women unarmed and unaccompanied dared to come and visit me from neigh- bouring settlements at many hours’ distance through the primitive forest or im boats. In this better regulated society the higher moral qualities of the Kénjas also stood out to advantage. If among the Bahaus the want of interest in the public welfare was strongly felt, among the NKenjas this was different. In the character of the Kenja chiefs a sense of responsibility and disinterestedness came to the front accompanied with more moral courage and influence on their subjects. When questions arose as 10 wages, the payment of which always consisted in goods chosen by the party concerned, the Bahau chiefs always retired for fear of quarrels with their people. Among the Kenjas the chiefs calculated, how much was due to each of their people, took it home and distributed it there. When it had been resolved in the political meetings, that repre- sentatives of several tribes should @o with me to the Mahakam, hundreds of Kenjas prepared to go. Bad omens for the journey, however, caused more than 400 to draw back, and though the principal chiefs might have done so too, they only sent baek their followers and went on themselves, because they felt the great importance of carrying on the negotiations. Among the Bahaus no chief would easily have gone to look after the general interests, and certainly not against bad omens. Also the conduct of their inferiors during the journey was quite different. Eighty Kenjas sueceeded in deriving the required favourable omens from the flight of birds, the cries of does and the appearance of certain snakes, and accompanied us. Though from different villages, they formed one company, having their victuals in common, and when the Bahaus and ourselves had not enough they shared their stock with us, which was then soon exhausted. They had, however, full confidence in my assurance that [ would buy them fresh provisions on the Mahakam. The different groups in’ a Bahau escort never voluntarily share their rice with each other, and when T and my Malays were in want of rice on the journey, we could only get some from them at very high prices. At last a young man had the assurance to ask me three times that exorbitant price for his rice, though as a physician [ had saved his life, and had treated all of them without asking any reward. 538 } In spite of the great advantages, which the Bahaus derived from our stay, TE never met with any direct proofs of gratitude; they only put somewhat greater confidence in me than in other strangers. When however | left a WKénja tribe after a six days’ stay, the family of the chief came personally to thank ime for everything | had given to them either by way of exchange, presents or medicine ; the first expres- sion of gratitude for many years. All this proves that the Kenjas of Apo Kajan are far superior to the Bahaus also as regards those traits of character, which ave considered as higher ones among Europeans. Another striking example of their stronger personality is furnished by the way, in which their religious ideas influence their existence. From their standpoint as agricultural tribes of fairly low deve- lopment, with whom the influence of nature on their prineipal means of subsistence, agriculture, and on their persons in diseases and disasters is strongly felt, these peoples contemplate their surroundings with great fear. Their thoughts about these surroundings and the place they occupy in them, which represent their religious conviction, are not of a very elevated nature. They think that their lives are ruled by one chief god, whom they cul Tamei Tingei, our high father, and who punishes already on earth all crimes with adversity, disaster, disease and death. For the execution of his will he makes use of a host of evil spirits, who people all nature around. All calamities and diseases, therefore, even death on the battlefield or at a confinement, ave to these tribes the manifestations of anger of their chief god with regard to the sufferer, who has incurred this anger by the conscious or unconscious violation of human usages or divine laws. When the attempts, to guard themselves against the manifestations of the anger of their god by observing these laws and usages scrupulously, proved fruitless, they tried to reach their aim by extending the prescribed laws to the minutest details, so that they have definite precepts as to the course to be followed not only in all emergencies of every day life, but also in agriculture, the chase and fishery. All these precepts are called pémali, and they render certain actions in certain cases lali, pantang or taboe. If the observation of the pemali is to shield them from the evil spirits, they enjoy the assistance of a whole multitude of good spirits, indirectly through the mediation of the priests and priestesses or directly by warning omens, which are communicated by certain birds, snakes and does, and also by certain events. These omens are very numerous, and are strictly followed, especially by the Bahaus. ( 539 ) As however these pemali and omens have risen, independent of the true requirements of the existence of these tribes, they have constantly a disturbing influence. To give an example: the Bahaus, when growing rice, do not regulate their work according to dry or wet weather, or to the condition of their fields, but all the families ot a tribe have to conform to what the chieftain does, and he sees that the necessary religious rites before the special successive agricul- {ural proceedings are duly performed. When the preliminary rites for the sowing have commenced, no one is any longer allowed to burn dead wood on his field; if the chief is weeding, every one must cease his sowine, ete. In the same way they begin all important enterprises, such as travelling, the building of a house, ete. not according to the demands of the moment, but according to whether a bird flies up to the right or to the left, and whether a doe is heard or not. Of course, stronger races do not so meekly submit to the galling restraints of these pemali and omens, as more timid natures. Thad an opportunity of observing this as a characteristic difference between Bahaus and Kenjas. It is true that both have the same religion and that their pemali and omens are essentially the same, but the pemali are more developed among the Bahaus and go more into details, than amone the Kenjas. Among the former all the adults in a tribe are obliged to observe the pemali closely; among the Kenjas the priests are specially charged with this, so that the mass of the people have more liberty. Among the Bahaus e.g. nobody eats the flesh of the stag; among the Kenjas the priests only do not take it. The Kenjas have not introduced the above-mentioned very injurious precepts for the growth of rice with the same restrictions. It is true that also among them the chief causes the necessary ceremonies to be performed, but still, every one is free afterwards to (lo in his field, what will prove necessary, and this is of the greatest importance for the success of the harvest. The Bahaus cling much more scrupulously to the existing pemali and omens than the Kenjas. In spite of my having lived for years among the Bahaus, I was forced, to observe their precepts as serupu- lously as they themselves did. Only in case of urgent necessity | dared set out on a journey or receive a patient during the time prohibited by their laws, and I was therefore as much shut out from the outer world as they were. Once they made the inhabitants of their own village on their return from an eight months’ expedition remain in the forest, starving, rather than violate the lali of their village by admitting them or bringing them provisions. ( 540 ) When T arrived with my companions among the Kenjas, the prin- cipal chief and his family happened to be in the condition of Tali, but in order to be able to receive us he quickly had a new house built in another place for the priest family in his house, who were the principal bearers of the pémali. By this means it was permis- sible for him to receive us in his house. Later on we proceeded to another village, where the house of the principal chieftain was also lali, For our reception le divided his house, which was very long, into two parts by means of a gate, so that we strangers could not enter the one part. In the other he received us. The Kenjas watch the omens before every enterprise as earnestly as the Bahans, but as soon as they are in confliet with the require- ments of the moment, they dare take their own course to a much greater extent. I have already mentioned that the Kenja chiefs ventured to accompany me to the Mahakam in spite of the bad omens of their birds. In case of imminent danger, e.g. if an enemy is thought to be hidden in the neighbourhood, the Kenjas disregard omens. So we see among the Bahaus the more scrupulous observance of a more developed system of religious usages keep pace with the deterio- ration of many of their physical and psychical qualities. In these the Bahau is inferior to the Kenja, which can originally not have been the case, but which is owing to the change of abode of the Bahaus more than a hundred years ago, because through this change they were exposed to the more injurious influences of their new surroundings, the principal of which is a greater prevalence of malaria. Mathematics. — Prof. P. H. Scnourr discusses: * Relations betireen diagonals of parallelotopes” with a view to show by a simple example how it is possible that investigations of more-dimensional figures lead to new theorems on figures of our ‘hree-dimensional space. This example relates, as the title indicates, to those figures which continue in the spaces with more than three dimensions the well-known series of line-segment, parallelogram, parallelepipedon .... and can there- fore be called by the name of parallelotopes. Here diagonal always denotes a line connecting across the inner part of the enclosed space — two opposite vertices. /irsf owr attention may be drawn to the faet that the number of diagonals of the parallelotope is doubled line-segmtent, parallelogram, parallelepipedon,... Fig. 1. every time a new dimension is added, whilst the number of constants determining the figure, though at first larger than the number of diagonals, increases less strongly than the latter; this is illustrated by the following little table, where under each other the corresponding values of the number # of the dimensions, the number d of the dia- gonals and the number y of the determining constants are indicated, whilst the meaning of / is explained further on, A Ni) pap es WS hays Cyr he is} 9 LO pees 5079, @ || 2\ 418 116139164) 198 | 256/509)... . Qe @ | 316 (10/15/21/28) 36) 45°] 55 |... . $n med) Pn MALS NG L299 OLOAGeHLe. 2 LO ae eye From this is evident in the second place that when constructing parallelogram and parallelepipedon all diagonals can be used as determining lines, but that this is not possible for the parallelotope P, with five and for the following parallelotopes P,, ?,... with still more dimensions; and from this ensues in the third place, what becomes the principal thine here, that between the 16 diagonals of P, at least one relation must exist and that this number of relations for P,, P,... must increase consecutively to 32—21 or 11, 64—28 or 36,... If in the fourth place we wish to trace those relations and try to do so under the condition that the length of all the edges must figure amongst the determining data, then we find that the sum of the squares of all the diagonals — always equal to the sum of the squares of all the edges is known at the same time, and that the other relations, between the diagonals only, always present them- selves in the form of homogeneous equations, the number / of which is indicated above. This includes that already for the parallelotope P, we come across a relation between the diagonals. This simple relation can be expressed as follows: If we divide (Fig. 2) the eight vertices of one of the eight parallelepipeda forming the boundary of ho} the four-dimensional figure into two groups C4,, .4,, 4,, 4.) and L,. BB, By) of non-adjacent: vertices, the sum of the squares of the diagonals terminuing in the four points of is equal to the sum of the squares of the four remaining ones, terminating in the points 7. And from this ensues, the common centre of the eight diagonals being indicated by QO, the equation OA,? + OA? + OA,? OA? OB? + OB? 4- OB, + OB, or in words: Ifwe divide the eight angular points of a parallelepipedon info two groups of four non-adjacent points, the sium of the squares of the distances from an arbitrary point O to the points of each of He C Fig. 3. the two quadruples is the same. If we now suppose in the /i/th place that this point © lies with the parallelepipedon in the same three- dimensional space, our space | may say, we finally find the following theorem belonging to our solid geometry : “If we connect (Fig. 3) an arbitrary point O of space with the two quadruples of non-adjacent vertices of a parallelepipedon, we obtain two quadruples of line-segments for which the sum of the squares has the same value.” This simple theorem which up till now T never came across in any handbook is of course easily proved; we have but to know the formula for the median line in a triangle. With the help of this formula we find that, disregarding quantities not depending on the place of QO, the sum of O.4,° and OA? can be replaced by two times OC?,, the sum of 0 A,? and A O,* by two times OC, and twice the sum of O€", and OC". by four times O.J/*; from which is evident that for the two sums named in the theorem, disregarding the same quantities not depending on ©, the same value is found, namely four times (.1/*, ete, ( 548 Finally this observation: it is not our purpose to emphasize even in the slightest degree the above-mentioned theorem, up till now acei- dentally remained winoticed. Neither have we in view to point out that for each parallelotope 7, the diagonals and the sides furnish equal sums of squares and that all possible relations between dia- gonals mutually can be represented in the above mentioned form. Whilst referring for this to a paper, to appear shortly in the ‘Archives Teyler’”, we repeat here, that this short communication was given to satisfy the wish to show also to non-professional mathematicians by means of a simple example how the study of polydimensional geo- metry may lead i.a. to the discovery of new theorems of plane or solid geometry. Chemistry. “On the atomic weight of Antimony.” By Prof. Erxsr Conen and Mr. Tu. Srrencers. (Communicated by Prof. W. He Junius). (Communicated in the meeting of February 28, 1903.) 1. In connection with a physico-chemical study on the nature of so-called explosive antimony conducted by one of us (C.) conjointly with Dr. W. E. Riyenr, the question of the exact atomic weight of antimony became a very important one. Notwithstanding a number of investigators * ) have attempted to determine this atomic weight, it is not as yet known with sufficient certainty. CLARKE *) sums up his criticism on the determinations made up to the present with these words: “..... This result, therefore, should be adopted until new determinations of a more conclusive nature, have been made.” ~~ 1) Berzerius, Poceenp. Annalen 8, 1 (1826); Kesster, ibid. 95, 215 (1855); Scuneiwer, ibid. 98, 293 (1856); Rose und Weser, 98, 455 (1856); Dexrer, ibid. 100, 363 (1857); Dumas, Annales de chimie et de physique (3), 55, 175 (1859); Kersster, Pogg. Ann. 118, 145 (1861): Uncer, Archiv der Pharmacie 197, 194 (1871): Cooke, Pree. Amer. Acad. 5, 13 (1877); Kesster, Ber. deutsche chem. Gesellschaft, 12, 1044 (1879): Scanemer, Ueber das Atomgewicht des Antimons, Berlin LS80. Journal f. prakt. Chemie (2) 22, 131 (1880): Cooke, Amer. Journ. Sciences and Arts, May 1880; B. B. 18, 951 (1880); Prerrer, Lice. Ann. 209, 161 (1881); Popper, ibid. 2388, 153 (1886); Bonearrz, B. B. 16, 1942 (1883); G@. Cl. Friend and Epcgarn F. Sarre, Journal Americ. Chemical Soc. 23, 502 (1901). 2) The constants of nature, Smithonian Miscellaneous Collections Part VY, Washington 1897. Proceedings Royal Acad, Amsterdam. Vol, \ 44 2. Popper’), under von Prsats guidance has tried to make a determination of the atomic weight by an electrical method. He connected in the same circuit a silver Coulometer and a cell containing a hydrochloric acid solution of antimony trichloride. A rod of pure antimony (wrapped in linen) suspended in the liquid constituted the positive electrode, whilst the negative electrode con- sisted of a weighed platinum wire. During the electrolysis the electrolyte was kept in continual motion by means of a stirrer so as to exclude local changes in the concen- tration of the liquid. Under these circumstances explosive antimony is deposited on the negative electrode *). Porrnr fused the substance formed in a tube made of hard glass in an atmosphere of nitrogen; in this way the antimony trichloride present in the metallic mass was expelled. As soon as all the chloride had volatilized the antimony regulus was washed first with solution of tartaric acid, then with water, dried at 120° and weighed. Additional experiments had proved that the glass tube did not suffer any alteration in weight on heating and melting the metal contained therein. The silver electrode in the coulometer was wrapped in a piece of linen. After the electrolysis was completed, the silver which had deposited in the platinum dishes employed was boiled and washed with water until this no longer gave a reaction with hydrochloric acid and it was then dried at 120°. Poprrr’s results obtained in the electrolysis of solutions containing respectively 7 and 22 per cent of SbCl, are given in the subjoined table. We have, however, recalculated the data as Popper still uses the atomic weight 107.66 for silver whereas more accurate investiga- tions have shown this to be 107.93. In a second series of experiments in which a few more improve- ments had been made as regards the insulation of the silver coulo- meter, Popper found for 7 per cent solutions as equivalent weight the value 40.53, therefore as atomie weight the value 120.99. As he could not discover any sources of error in his process and still believed in the accuracy of the results obtained by Cooker, who, by purely chemical means, had found the atomic weight of antimony to be 119.9 he concludes his paper with the words: “Sollte nicht die Entdeckung des Elements ‘Germanium’ durch Wiykier den 1) Compare 1. 2) Such was the case with solutions containing 22 per cent of SbCls. In solu- tions containing 7 per cent. Popper obtained crystalline monv-explosive antimony. I will fully refer to this particularity later on in my paper with Dr. Ringer. (Conen.) ( 545 ) Grams of Sb CL, in 100 Grams solution. | Weight of the metal Electrolytic Atomic deposited in the same time — equivalent weight. circuit in the same time. = ; of Antimony (Silver Antimony | — Silver | == 107.93) 7 1.4788 3.9099 4) 25 120.75 7 20074 5.3649 40.39 Alea Z 7 4.1893 44.1847 | AW} 121 29 a 4 ASSD 11.4847 {0.42 121 .26 fi 5.6869 15.1786 40.43 121.29 7 5.6904 15.1786 10.46 124.38 29 1.4856 3.9655 {0.43 121.29 29, 2.0120 5.3649 40.47 121.44 29, 3.8882 10.3740 10.45 (OAV SSS 292 3.8903 10.3740 (OAT 121.41 92 4.2740 11.3868 40.48 121.44 29, | he W752 11.5868 40.52, | 121.56 Wee andeuten, auf welchem die Losung des vorliegenden Ratsels zu suchen sei?” 3. We have not only repeated the research of Popper but also extended the same by using hydrochloric acid solutions of SbCI,, whose concentration varied between 2.5 and 83.3 percents of SbCI, by weight. It was necessary to pay particular attention to the purity of the materials employed. The antimony trichloride was obtained from Merck; 20 erams were dissolved in solution of pure tartaric acid and then digested on the waterbath for some hours with excess of clear sodium sulphide. The liquid remained perfectly clear *). Some kilos of this antimony chloride were precipitated with sodium carbonate free from foreign metals, the precipitated Sb, O, was washed, dried and reduced to metal by fusion with pure potassium cyanide in a Prrror’s furnace. The crucibles used were previously tested to see whether they would yield any foreign metal to potassium cyanide but we could not prove the presence of any impurity in the melt. 1) As commercial antimony generally contains lead whose atomic weight exceeds that of antimony it was absolutely necessary to prevent the possibility of any lead being present in the materials employed, Qo Oil 546 The fused metallic antimony was poured into cylinders of asbestos paper tied round with copper wire: the rods of antimony thus formed were cleansed with hydrochloric acid and washed. By way of control we dissolved a piece weighing 20 grams in pure strong nitrie acid with addition of 75 grams of crystals of tartaric acid. The clear acid solution so obtained was rendered alkaline by adding small lumps of sodium hydroxide prepared from metallic sodium (the lye was free from foreign metals) and digested on the waterbath with a clear solution of sodium sulphide but gave no precipitate. The solutions were prepared by weighing the pure antimony trichloride roughly and dissolving the same in pure hydrochloric acid of 1.12 sp. gr. at 15°. The exact composition of the solutions was determined by electrolysis of the liquid in presence of sodium sul- phide according to NeuMANN’s directions *). 4. In each experiment two silver coulometers were put into the circuit; one in front and one behind the series of antimony solutions which took part in the electrolysis. The coulometers consisted of 200 ce. platinum dishes with rough inner surfaces. We will not omit to point out that such dishes are particularly suited for coulo- metric determinations as it is possible fo precipitate in them a large amount of silver with litthe chance of any traces being detached on washing the precipitates *). The amount of silver deposited in our experiments varied from 25 to 50 grams whilst when using the smooth dishes usually employed it is difficult to handle a few grams without loss. As electrolyte we used a LO or 15 per cent neutral solution of silver nitrate; no difference was noticed with these solutions. The positive silver plates were cast of silver which we received from Dr. Horrsema, Comptroller-general at the local Government Mint. On analysis, we could not trace foreign metals in 100 grams of this silver. The plates were 6.5 ¢.m. in diameter and 4 mm. thick. ’ They were surrounded by a covering of filter paper (SCHLEICHER and ScuuL). Each silver plate was suspended by a thick platinum wire. The coulometer dishes after being filled with the silver solution were covered with a glass plate with a hole in the centre through which a platinum wire was introduced. 2) Analytical Electrolysis of Metals, Halle 1897. S. 145. Here, we provisionally took the atomic weight of antimony to be 120; as will be seen from what follows, the uncertainty of the atomic weight is of no consequence here. 2) Compare Kante. Wien. Ann. 67, N.F. 1 (1899); Ricnarps, Cottrys and Herron, Proc. American Acad. of Arts and Sciences XXXV, 123 (1899). Ricwarps and Heirop, Zeitschr. f. physikalische Chemie 41, 302 (1902), Great care was bestowed on the insulation of all the apparatus. The conducting wires were strongly imsulated and were, as far as possible, in contact with air only. Each platinum dish was placed on a copper plate which stood on a glass plate; the latter was carried by porcelain insulators which acted as feet. For a rough orientation a technical ammeter was included in the circuit; the current was taken from 1 to 3 storage cells. 5. The antimony solutions which were subjected to electrolysis were contained in spacious beakers (1 litre) (6 in fig. 1) in which constant stirring could take place by means of Wirt’s centrifugal stirrers. A Herrict hot-air motor kept all the stirrers in motion. The rods of antimony which served as positive electrodes were sur- rounded by a piece of linen which was fixed to the rod with platinum wire, or by glass tubes closed at the lower end containing a large number of not too small perforations (0, 0, 0...) (8 or 4 m.m.). The object of surrounding the rods was to prevent any loose particles of antimony from getting into the liquid. As negative electrodes we used platinum wires (2) about 10 em. in length and 0.3—0.4 mm. thick; they were provided at the upper end with the capillar glass pieces (C), on which a number was UL), engraved. Both antimony rods and platinum wires were attached to copper binding screws which moved along glass standards (S). In order to prevent contamination of the liquids by contact with copper, a piece of platinum wire (/’) was placed between the binding screws and the rods of antimony or platinum suspended thereby. 6. ‘The experiments were now conducted as follows: After the platinum wires had been weighed they were put in their places; the silver coulometers were connected up and the current closed. At the commencement the strength of the current may only amount to a few hundredths of an ampere; if this is exceeded, evolution of hydrogen instead of separation of antimony takes place. When the precipitate on the platinum wires had reached a certain quantity, When in other words, the surface had become enlarged the strength of the current Was increased and gradually raised to about 0.38 ampere. At the end of the electrolyses the rods were rinsed with a 12 per -cent solution of tartaric acid ?), then washed with water, alcohol and ether and dried over sulphuric acid in a desiccator. 1) By a special experiment we had convinced ourselves that this did not cause any perceplible diminution m weight. 548) To determine the amount of antimony separated by the current the following method was adopted ‘). The rod was placed in a tube of hard Jena glass closed at one end (length of the tube 80 em., diameter 1 em.). This tube had been previously cleaned, strongly heated in a current of dry air (dried over H,SO, and P,©,) and then weighed. The antimony rod was now weighed and by way of control the tube and rod were again weighed together. The air from the tube was now expelled by means of a continual stream of carbon dioxide which had been dried over sulphurie acid and phosphoric anhydride. The tube (ecplosion-tube) was then closed with a properly fitting india-rubber cork and put into a metal cooling vessel made of composition tube in the manner represented in fig. 2. This tube was connected with the water tap. If now the explosion tube is shaken for a moment the explosive anti- mony explodes. The tube is then strongly heated with a triple burner on the spot containing the rod; the Sb Cl, evolved condenses on the cold wall of the tube to a clear white mass. The heating is continued until the antimony is perfectly fused and this is then allowed to cool slowly. The tube is then opened, the SbCl, is removed by rinsing with a mixture of alcohol and ether (8:1) the tube is then rinsed with ether and dried by heating in a current of dry air as described above. The tube with the antimony regulus is now weighed. A previous experiment had proved that the explosion tube suffers no alteration in weight by the heating and subsequent treatment. It was found for instance that an explosion tube weighed 29.6614 gram before the experiment and 29.6610 gram after the experiment the contents having been removed by means of nitric and tartaric acids. By way of illustration one of the experiments is reproduced in detail whilst the results of the other measurements are united in a table. Electrolysis of a 15.6 proc. SbCl, solution. Silver coulometer N°. 1. weight of platinum dish + silver 73.1920 grams " u " 36.7310 weight of silver 36.4610 grams 1) Further particulars about this method will be found in the paper of Coren and Dr. Ringer. ( 549 ) Silver coulometer N°. 2. weight of platinum dish + silver 71.4530 grams x - s 34.9902, weight of silver 36.4628 grams weight of explosiontube +--+ regulus +--+ platinum wire 55.0281 grams " I 41.0780 weight of regulus + platinum wire 13.9501 grams weight of platinum wire 0.2696 — , weight of regulus 13.6805 grams From this result the equivalent weight of the antimony is caleulated as follows: 7 OF BOGS x 13.6805 — 40.49. 36.4625 The results so obtained are collected in the following table. (p. 550). From this table we see that the atomic weight obtained increases with the concentration of the Sb Cl, solutions and varies between 120.87 and 121.89 within the concentrations 2.3 and 83.3 per cent. From this it is quite plain that we cannot arrive at the determination of the atomic weight of antimony by the electrolysis of solutions of antimony trichloride and that the values found by Popper, to which in the calewation of the atomic weight is attached the same value as to those of ScuNemer, Cooke and Boncarrz'), are quite accidental, being dependent on the concentration of the solutions employed. It further appears from the above that unknown electrolytic or chemical changes play a part here which require further investigation and which may be expected to add to our knowledge of the formation and composition of the vemarkable explosive antimony. We hope, shortly, to investigate these changes. 1) Compare Osrwatp. Lehrbuch der allgemeinen Chemie I, 53 (1891). 550°) —_e._ en —— eee eee Grams of grams solution, Weight of SbCl, in 100) the antimony regulus in grams. Weight of the silver in the Coulometer in grams, NO, 4. NO, 2, Kquivalent Atomic weight weight of the of the Antimony. | Antimony, —_—————— ———eeSSSSSSSSSSeSeSeSeSeSeS 83.3 ~Y) This result washing. 1G. 8747 14.5914 18.7961 16.9175 14.6298 18.8627 12.6206 15.0054 13 1219 18.8884 12.6470 95049 13.6805 13.6803 13.5984 13.8618 14.6912 15.0689 13.7122 14.7014 15.6305 14.9494 13.8998 45.2069 30. C805 45.2019 3O_O816 50.3791 50. S860 45.2019 | 45.2069 39 0805 | 39.0816 | ; 3 Tae | 50.8701 | 50.3860 | | 33.790 | 33.7203 | 40.0810 40.0794 | 3.9633 34.9680 | 50.3791 50.3860 33.7224 33.7203 25.346 | 25.3407 | 36.4610 | 36.4628 | 36.4610 | 36.4698 Ss OTS RIB 36.2088 36.2094 36.9531 38 9046 40.0810 36.9566 38.9098 0 0794 40.28 120.87 40 29 36.4610 39.0805 | | | 36.2088 | | 36.9531 ' | 36. 4628 39.0816 36.2094 39.6998 36.9566 is decidedly too low, as a trace of MO 26 | 4120.78 1) 40 38 421.47 40.39 4D AO 40.38 421.20 | WOM 40.49 40.46 124.4 40.47 | 10.48 | MW 49 121.47 WO.49 40.53 424 .59 M53 40.56 121.71 40.58 40.58 bee tay ii 40.59 40.63 40.61 124.89 40.64 antimony got lost during the Chemistry. — “ The conductive power of hydrazine and of substances dissolved therein.’ By Prof. Erxsv Conn and Prof. C. A. Losey pe Bruyx. (Communicated by Prof. C. A. Losry pr Bruyn). (Communicated in the meeting of February 28, 1903). The investigation of the conductive power of non-aqueous solutions has of late years been known to have an increasing significance and particularly so on account of the important result that the laws and rules applying to aqueous solutions do not appear to apply in the case of other solvents. Apart from methyl and ethyl alcohol (the constitution of which does not differ much from the type water) sulphurdioxide, ammonia (NH,), formic acid, hydrocyanic acid, pyri- dine, some nitriles, hydrogen peroxide and others have been studied as such’), The physical properties of free hydrazine *) N,H, although still incompletely known, might lead us to suppose that this liquid would manifest a strong ionising power. In the first place, like water, the lower alcohols and acids, it possesses an abnormally high boiling point. This is obvious if this point (about 113° at 760 m.m.) is compared with of ammonia (— 84°), difference of 147°, and if one considers that the difference between the boiling points of CH, and C,H, is decidedly less (80°); this fact as well as the high critical temperature of (at least) 380° point to an association of the N,H, molecules. The solubility of several alkali salts in hydrazine has also been shown to be very considerable although less than im water. Another existing observation points to the fact that hydrazine may, like ammonic take the place of water of crystallisation *). And finally, the dielectric constant of hydrazine, which Prof. P. Drepr (Giessen) had the kindness to determine at our request, has turned out to be rather high, namely, 53 at 22°. It is now a known fact that there exists a certain although sometimes remote parallelism between the dissociating power of a liquid on the one hand and the association of its molecules, the solvent power and the dielectric constant on the other hand. As according to the experiments of FRANKLIN and Kraus and of Capy liquefied ammonia is an ionising solvent, this might also be expected in the case of hydrazine. From the experiments") presently to be described it will be seen that such is the case. 1) Compare Jones, Am. Ch. J. 25. 232. Kanvenserc, J. Phys. Chem. 5. 339. Watpen and Centyerszwer, Z. phys. Ch. 39. 514, 557 e. by J. Travse, Chem. Zt. 26. 1071. (1902). 2) Lopry ve Bruyy, Recueil des Travaux Chimiques des Pays-Bas. 15. 174. 3) Ibid. 179. 4) Some preliminary determinations were already made in 1896. 1. ¢. 179. 552 ) Let us first observe that the dielectric constant of hydrazine is only surpassed by those of five other liquids and is decidedly larger than that of NH,. We have namely : hydrocyanic acid = 95 acetonitrile 40 hydrogen peroxide 93 nitrobenzene 36.5 water 82 methylaleohol 32.5 formie acid Vf ammonia 22 (at —34°) nitromethane 56.5 pyridin 20 hydrazine 53° The peculiar properties of hydrazine (its very hygroscopic nature and liability to oxidation by atmospheric oxygen) demand great precautions in its preparation. It took place, according to the method already described"), by treatment of the so-called hydrate with barium oxide and distillation in an atmosphere of hydrogen. The heating with barium oxide and subsequent distillation were thrice repeated and the base was finally collected in six different fractions in pipette-shaped tubes in the manner previously described. During the last distillation the base had been only in contaet with purified, dry hydrogen. Apart from the properties of hydrazine mentioned, the high cost of the material was a factor which in our experiments had to be taken into account. A special apparatus (see illustration) was, therefore constructed which admitted of working with a small quantity of the base (about 5.5¢.¢.) and through ‘3 which pure, dry nitrogen *) could be passed, whilst through the exit tube for the gas the weighed portions of the different salts could be introduced. On account of the some- what limited quantity of the base at disposal we could not, as is customary in the determination of the conductive power of solu- tions, start with the largest concentration and succes- sively dilute this by adding the solvent, but the reverse was to be done. 2) IL ec. sp: 175; 2) We take the opportunity to call attention to the fact that platinised electrodes Weighed quantities of a salt were, therefore, successively dissolved; on account of the unavoidable errors in weighing it was difficult to experiment with very dilute solutions of accurately known composition, but by evaporating a measured quantity of a very dilute aqueous solution in a pipette which was then rinsed with the hydrazine we have reached for KCL a concentration of V = + 900. In view of the above we wish to remark generally that our results cannot lay claim to very great accuracy, although they quite suffice even from a quantitative point of view, to prove that free hydrazine has a strong ionising power comparable with that of water. We have worked with solutions of H,O, KCl, KBr, and KJ and made a few experiments with a solution of Na and H,N in N, H,. In the first experiment the six different fractions of the hydrazine had not been kept separate; as we had previously found ') that the meltingpoints of the second and fourth fractions were the same we thought we might conclude that at least the middle fractions were similar. It then appeared, however, that the conductive power of the bases taken from different tubes often showed appreciable differences. For this reason a second preparation was made and the hydrazine of each fraction (each time collected in several tubes) was examined separately as to its conductive power. From the following figures it appears that the conductive power gradually decreases and is smallest for the last fraction. fraction n°. 2 eat 25° 18 4-10n é ADE Sian 4 a 7 5 10.0 , 6 (5), fp We do not know what impurity (in any case very small) is the cause of this; possibly we are dealing here with a minute quantity of ammonia which is present in largest amount in the first fractions The smallest conductive power observed by us in any fraction prepared previously was 4.10—°. Our experiments have been mostly conducted with fraetion N'. 6 of the above-mentioned quantity. dried in the air may occlude such an appreciable amount of oxygen that this must make its influence felt when working with readily oxidisable liquids. Such appeared to be the case when filling our apparatus with hydrogen when a spont- aneous deposit of visible drops of water was formed. *) Prepared from air and phosphorus. NAG ey jon tly ilo 554 ) The apparatus was put into a glass vessel containing paraffin oil Which was placed in an Ostwald thermostat; the temperature was 25°, Hydrazine and water (¢ = 25°) 5¢ fraction. G = 5.185. 6° fraction. G = 4,249, N, x N x 0 10.0 40> 4 0 6.04.10 0.93 9.79 » 41.1 4.71 p 7.94 8.95 -» 49.5 4.5 » ate 7.68 » 58.4 4.36 » 33.8 7.22 » 69.5 455 65.6 6.04 » 81.6 4.9 » $2.4 6.09 » 124.7 To y 101.8 7.85 » 156 10.51 » 955.5 AiR ees | Potassiumchloride. (—2o" x = 6,2.10—5 Noli, G g V K A) 5.369 0,0272 44.7 iQue s 102.9 ; 0,0157 25.4 4.2» 106.7 » 0,0080 49.7 Pe Nes I 109.3 [+5.4 0,00045 + 900 49.40% + 107 2) ] Potassiumbromide. 5 * = 6,5.10—° Nou, G g ¥; % A 5.350 0,0617 10.3 40.05.10 —3 103.8 » 0,0329 19.3 5.66 » 109.2 » 0,0214 29.9 SE7Ti as ADT » 0,0105 60.7 1.965 » 118.9 1) Ay could not be determined, so that the degree of dissociation of the salts is not known. The A’s, however, agree in magnitude with those of the aqueous solutions of the same salts. 2) This value, obtained in the manner described on p. 553, is as a matter of fact uncertain. It proves that a very minnte quantity of a dissolved substance may increase the conductive power considerably. Potassiumiodide. j= 259 2 = HAD AMO) N.H, G g Wi x A 5.600 0,072 12.9 8.149.403 105.6 » 0.0493 18.8 ovis >) 108.8 » 0,0280 Doe 3.40 » 112.8 » 0,0129 72 1.64 » 118 G = weight of hydrazine in grams. A = aequivalent conductive power. g = weight of the salt in grams. V = number of Liters, in which is dis- solved one mol. of the substance. »% = specific conductive power x for the water used = 0,28.10 ~~ ° Without commilting a grave error the sp. gr. of hydrazine at 25° may be taken as 1.00. It is already known that soditm dissolves in’ hydrazine with evolution of hydrogen’). Pure hydrazine (gz=9,1.10~) was introduced into the apparatus and two particles of sodium (weighing about 10 milligrams) were added. The metal slowly dissolved with evolution of hydrogen and after solution was complete the specific conductive power appeared to have increased to 151.10—°. It seemed very peculiar that a powerful evolution of gas still went on after the sodium had dissolved, showing a decomposition of the hydrazine with formation of ammonia. This decomposition ceased as soon as the liquid was poured out of the apparatus; apparently it only takes place by contact with the platinum black present on the electrodes and is, therefore, quite comparable to the spontaneous decomposition of an alkaline solution of hydrogen peroxide exposed to the same influence. Finally a few experiments were made with a solution of ammonia in hydrazine. The solubility of that gas at the ordinary temperature did not seem to be large; about 4.8 per cent of NH, is present in the saturated solution. After a few bubbles of ammonia had been absorbed in the hydrazine (with x = 5.2.10) the conductive power appeared to be but slightly increased (x = 6.9.10—°); this was also still the case after the liquid had been saturated with ammonia (about 1) le. p. 183. Dr. J. W. Drro has found that an atom of hydrogen is replaced here; the NaH, N, formed is a substance which on being exposed to the air causes a yiolent spontaneous explosion, ( 556 220 mer. of H,N in 4.920 gr. of N,H,, » = 0.38, x= 9.10-). It is known that on dissolving ammonia in water the conductive power is but very slightly increased, From the foregoing we may draw the conclusion that, with regard to its ionising power, hydrazine is comparable to water. As regards mixtures of hydrazine and water it may be observed that on addition of water the conductive power at first decreases reaching a minimum with a mixture of 60 mols. of H,O to 100 mols. NH, (about 25 per cent of H,O and 75 per cent of N,H,) then increasing again. This minimum, therefore, does not correspond with the com- position NH, + H,O, or the so-called hydrate. Utrecht— Amsterdam, January 1903. Chemistry. — “The velocity of transformation of tribromophenol- bromine into tetrabromophenol.” By Mr. A. H. J. Benzer *). (4% Communication on intramolecular rearrangement, presented by Prof. C. A. Losry bE Bruyn). (Communicated in the meeting of February 28, 1903). BexepikT 7) found in 1879 that tribromophenol brought into contact with bromine water is capable of exchanging a fourth hydrogen atom for bromine with formation of a tetrabromo-derivative. The study of this substance led him to the conelusion that one Br-atom occupies a peculiar position in the molecule; it is, in fact, the cause of a certain number of reactions in which that Br-atom is readily displaced. As moreover the new substance seemed to have lost the character of a phenol as shown by its insolubility in alkalis, BENEDIKT gave it the formula C,H, Br,.OBr and the name of tribro- mophenolbromine. Beneprkt also noticed that, when melted under sulphuric acid, it passes into the already known isomeric tetrabromo- phenol, a true phenol which no longer contains a loosely bound Br-atom. In his first publication Bexepixr looked upon this transformation into tetrabromophenol not as an intramolecular displacement of atoms but as a process taking place between two mol.s of tribomophenol- bromine; in a later Communication however he does so, without stating any reasons. When a few years ago, Jon. TureLe*) found that BrNnepiKt’s 1) Proc. 31 May, 28 June and 25 Oct. 1902. 2) Annalen 199. 127, Monatshefte 1, 361. 5) Ber. 33, 673 (1900), ( 557 ) tribromophenolbromine by means of leadacetate passed into 2.6 dibromoquinone, with substitution of 2 Br by O, he looked upon it as a dibromoquinone in which one O is replaced by 2 Br | therefore as a tetrabromoketodihydrobenzene|; he is of opinion that its forma- tion from tribromophenol can only be explained by assuming that the latter can react in the tautomeric form of a p-quinoid ketone as follows: ou = Kyo + Br, nko In a paper which appeared a year ago, Kastie') has come to the same conclusion as THIELE, as the result of investigations conducted conjointly with LorvennartT, Rosa Speer and Gitpert. Kastie has also established the fact that it is only sulphuric acid which, even at the ordinary temperature, is capable of causing the transformation into tetrabromophenol; a dozen other reagents gave a negative result. In order to explain this specific action of sulphuric acid, KasTie assumes the intermediate formation of an additive product of this acid with tribromophenolbromine; this at first would lose HBr, which would then again react at once with reformation of sulphuric acid and cause the migration of Br into the benzene nucleus. This inter- pretation of the transformation requires the appearance of two non- isolated and therefore hypothetical intermediate products and of three successive reactions. Mr. Betzer has now studied the velocity of transformation of tri- bromophenolbromine. The circumstance that the first substance readily parts with an atom of bromine would lead to expect that its quantitative estimation would be possible in the presence of tetra- bromophenol. It now appeared that the elimination of free iodine from hydriodic acid, also observed by Kastix, takes place quantita- tively; tribromophenolbromine may therefore be estimated in the presence of tetrabromophenol by titration. At the commencement of the investigation the behaviour of the solid substance towards sulphuric acid was ascertained. If the crystals are covered with the ordinary 96 per cent acid it is noticed that they lose their yellow colour and become opaque and white; of solution in the acid taking place nothing can be perceived even by the aid of the microscope. No formation of striae can be observed; the whole phenomenon seems to be enacted within the solid substance commencing on the surface where the substance is in contact with 1) Amer. Ch. J. 27, 31. (1902), ( 558 ) the acid. If the velocity of transformation is measured under these circumstances it is no matter for surprise firsf/y that no reaction constant is found, second/y that the reaction coeflicient constantly diminishes as the inner parts of the erystals get more and more inaccessible to the acid, As expected beforehand the experiment has shown that very small crystals or the powdered substance are, on account of the larger free surface, move rapidly transformed than the larger erystals. The continuation of the research will show that the transformation is monomolecular and must, therefore, be taken as a real displacement of atoms (perhaps of two displacements one of which takes place with very great velocity). It is a remarkable facet that there should take place inside the molecule of a solid substance a displacement of atoms, an internal change of equilibrium leaving the molecule intact, by mere contact with sulphuric acid, without there being any question of solution. Although we could not expect to get reaction-constants for a heterogenous mixture of a solid substance and sulphuric acid, this should be duly the case when we worked in a solvent. Here however a difficulty occurred which at first threatened to put a stop to the further prosecution of the research. A solvent was wanted which had no action either on tribromophenolbromine or sulphuric acid. Acetic acid scarcely dissolved the first substance and chloroform appeared to dissolve only traces of 96 per cent sulphurie acid. It was finally decided to choose the latter solvent and to thoroughly shake the solution with sulphuric acid *). The experiment proved that on applying the formula of the first order, constant reaction- coefficients made their appearance. A first result was thus obtained ; the transformation does not proceed bimolecularly. Mr. Brizer has now studied the influence of the concentration of the sulphuric acid and the temperature. In most of the experiments, 3 grams of the substance were dissolved in 150 cc. of pure chloroform *), the solution strongly shaken with the acid and after definite times 25 cc. were titrated. Use has been made of: a. H,SO, with about 36°/, SO,, 6. H,SO, with about 1°/, SO, c. equal volumes of 6 and d. d. 96 per cent H,SO,. In the following tables the results obtained are not given in the form of reaction-constants, but to make the matter more plain, the 1) A uniform emulsion is very soon obtained. 2) The chloroform was agitated a few times with water, dried over calcium- chloride, shaken with strong sulphuric acid and redistilled: it was preserved in the dark, ( 559 ) times (T) are mentioned at which the transformation has proceeded halfway. | A. Influence of the Concentration’ of Sulphurie Acid. t = 25°. 0,5 cc. sulphuric acid. | acid a | b | c dd T. | 5 min. 49 sec. | 2 hours 57 m. | 13 h. 40.5 m. very slowly t = 25°. 1 cc. sulphuric acid. | acid a b | c d T. | too rapid | 2m. 445, | 2h: 385 m 7h. 45 m. 4. Intluence of the Quantity of Sulphuric Acid. t = oes acid ar il CE | 0.6 ce. 0.5 ce. 0.3 ce. | ine | too rapid | too rapid | 5m. 49s, | 3h. 8 m. t = 25°) acid \b: eer 2uce, ‘liay (xo, 4) | 1.25 cc. deces 0.5 cc. | 0.23 ce. *) | T. | too rapid | too rapid 95 m. 44 s, | 55 m. 20s, | 2 h. 57 m. | fh == 26) EO 1.5 ce | 1 ce. 0.5 ce. i BG 1h. 16 in. | al, Ot, BRYA Tai 13 h. 40.5 im. | 2. 2h. 38.4 m. Influence of the Temperature. Acid a. | 0.5 ce. | 0.3 ce, | O}2%ce: | | etatate—ooe | ——— 6 m. 12.5s. ) oa 30 | 32 m. 33 s. » 95° | 5 m. 49 «. ee 410 3h. 8 m. ) times — » 450 (58 m. 45 5.) times | ans bin Acid b. ice. | 0.5 ce. —_ <0) ————— + 5 ~ 1S Bhi 1s, == 8) 33 m. 56 s. ) +4 » 25° «125 m. 44 s.} 20) Qehe oi ial times >» 450 [4h 15 m,) Hmes | — 1) Transformation almost completed after 20 minutes. 2) Not yet decomposed to the extent of 15 °/) after 21 hours, OQ 4 05 Proceedings Royal Acad. Amsterdam. Vol, V. ( 560 ) Acid ¢, Acid d. 1 ce. 1 ce. Ty at t == 85° 58 m. 10 s, 4h. 53.6°m, D 25° 2h. 35 m, | 7h. 45 m. ” Ao 3h, 27 m. From the results obtained it appears in the first place that the transformation is a monomolecular one and, taking into consideration the circumstances under which it takes place, must be considered as an intramolecular rearrangement of atoms. To this conclusion the following observations may be added. A. The influence of the concentration of the acid, the other cireum- stances being the same, is very great. The course of the figures leads to the idea that the active agent, the catalyser is not H,SO, but SO,. Experiments were therefore made to ascertain how chloroform behaves towards the four acids employed. Whilst from ordinary 96 °/, acid (d) but very minute traces were dissolved, this amount was perceptibly larger with acid ¢ and still larger with acid 4, whilst acid @ appeared to yield very much SO, to the chloroform *). The idea that SO, is the catalysing substance is consequently confirmed. The rapid decrease of the concentration of the acid is also in agreement with this idea; this velocity is therefore as it 0 were a measure of the concentration of the SO, still present in sulphuric acid of given concentration. Bb. lt is now also very plain that the quantity of the acid must have a great influence. As shown by its behaviour to acid a, chloro- form may dissolve considerable quantities of SO,. On shaking with sulphuric acid of a lesser concentration, the amount of SO, which passes into the chloroform will consequently depend on the quantity of the acid. The equilibrium for the SO, which distributes itself between the chloroform and the sulphuric acid changes, as is known, with the relative quantities of the two liquids and with the temperature. As a consequence of the view taken here, it must be assumed that ordinary 96 °/, sulphuric acid still contains a minute quantity, of free SO,-molecules. This view is admissible *) since it is known ~ 1) The ratio in which different acids yield SOs to chloroform will be further determined. 2) Kwrerscu, in his well-known research on sulphuric acid, has shown that an acid of 97—98 °%) absorbs SO; much more readily than acids of smaller or larger concentration. From the results obtained up to the present it does not appear that, in the transformation of tribromophenolbromine, the 98 °/, acid ¢ behaves in a particular manner; an ex'ension of the research will elucidate this question, 561 ) that 100 °/, sulphuric acid contains a little SO, and consequently free H,O. (. The temperature-coefficient for sulphuric acid @ is particularly large and increases rapidly with the temperature; for acid / it is decidedly smaller and very small for the 96 °/, acid. It will be readily understood that in the case of the acid « the dissociation of H,SO, into SO, and H,O and the distribution of SO, between chloro- form and sulphuric acid are modified in a large degree when a change of temperature takes place. The rearrangement of atoms may now be represented by the following schemes which respectively correspond with Benepik?’s formula (1) and Ture.e’s formula (Il): H Br 3 ar BF Son: —S B Bae Soe <— Br / >. HBr H_ Br sll Against the acceptance of Tuiete’s formule (IT) it may be pointed out that in the displacement a Br atom must first remove an H atom; this then proceeds to the O atom with migration of the double bonds, a rather intricate process practically consisting of three succeeding displacements. As it has been proved that the reaction is one of the first order, two of those displacements must take place with immeasurable velocity. Against Bunepixt’s formula (1) may be remarked that, according to experience, the meta-position is hardly ever selected in the migration of an atom or of groups from the side chain into the nucleus. The hypothesis proposed by Kasrie, which assumes the inter- mediate formation and decomposition of non-isolated products, is not at all supported by the observations communicated here. The investigation as to the transformation of tribromophenolbromine will be completed and also extended to other analogous compounds. Geology. — “Some New Under-Cambrian Evratic-blocks from the Dutch Dilucium?. By J. H. Boxxema. (Communicated by rote Je. VVi. Mont): I. In the Geological-Mineralogic Institute at Groningen is found a piece of sandstone which a few years ago I found at Odoorn, in the province of Drente. With muriatic acid applied to it, there is no effervescence; consequently it does not contain any calcium- carbonate. The grains of sand are small, but with a magnifying glass they may be well distinguished. They are peculiarly lustrous. The colour of this erratie-block is chiefly dark-grey. In some 38* ( 562 ) places it is brownish. Moreover there are light-grey worm-shaped parts, varying in length and having a breadth of about 6 millimetres. This erratic-block is most probably a piece of Under-Cambrian sand- stone, in which is found one of those problematical things that are sometimes called worm-passages. As they are not straight and do not run parallel to each other, they are different from those described as Scolithus linearis Hall. They show more resemblance with those tubes that were described by Torext.") as Scolithus errans of Hardeberga and Andrarum. According to Hotst*), however, there are various kinds of these worm-passages differing from Scolithus linearis Hall, whilst they also occur in different layers. This geologist makes men- tion of them as being found both in many places in the neighbour- hood of Simrishamn and near Kalmar. The Odoorn erratic-block bears no resemblance to the Hardeberga sandstone, in which Scolithus errans Tore. is found. Mopere *) writes that this sandstone shows a greyish-green colour, and that the worm- passages are dark-coloured. Nor does it resemble the Andrarum (For- semolla) sandstone. According to TuLLBerG *) the latter is a white, quartziferous sandstone with yellow worm-passages. The erratic-block also differs from the “Kraksten’, which Ho.st mentions, as being found near Kalmar, and which is greenish grey. From the kinds of sandstone with worm-passages which according to Hoist are met with in the neighbourhood of Simrishamm, differs that which occurs to the West of Raskarum in being whitish ; and that which is found close by Ljunglyckorna is different because its worm-pas- sages possess a dark colour. The sandstone which, according to this geologist, occurs to the North-West of Raskarum, may resemble, in colour, the Odoorn erratic-block : he says that its colour is sometimes a dirty-grey one. Untortunately he does not tell his readers what is the colour of the worm-passages. Consequently we. cannot with certainty conclude whether this kind of sandstone still exists as firm rock, or not. Nor have I been able to find anything whatever concerning the presence of suchlike erratic-blocks in the German and the Duteh diluvium. 1) Torett, Petrificata Suecana formationis cambricae. Lunds Univ. Arsskrift. 1869. Tom. VI. p. 12. 2) Hotsr. Beskrifning till kartbladet Simrishamn-Sveriges geologiska Undersékning. 1892. Ser. Aa. N’. 109, p. 13. Horst. Bidrag till kiinnedomen om lagerféljden inom den kambriska sandstenen. Sveriges geologiska Undersékning, 1893. Ser. C. N°. 130, p. 6, 13, 14. 3) Moser. Geologisk vagvisare inom Fogelsingstrakten. 1896. p. 30. +) Tuttserc. Om Agnostus-arterna i de kambriska aflagringarne vid Andrarum. Sveriges geologiska Undersékning. 1880. Ser. CG. N°. 42, p. 3. ( 563 ) Il. Some years ago I made an excursion in the surroundings of Murmerwoude in company with Mr. Borkr, at the time a teacher at Murmerwoude, now a teacher at a secondary school at Nimeguen. To the West of this village, situated in the north-eastern part of the province of Frisia, we found in the sand that lay by the side of a freshly-dug canal two slab-shaped pieces of sandstone that fit each other exactly and must have formed one whole. The dimensions of the bigger piece are about 20, 10 and 4,5 centimetres. The other piece also possesses the two first-mentioned dimensions, but the third is 3 centimetres. These pieces drew my attention as containing many more or less complete stone-kernels and offprints of pyramidal Hyolithus-shells. The pointed ends of all these lie in the same direction, which must certainly be attributed to the influence of streaming water. These erratic-blocks consist of hard, grey, very fine-grained sand- stone. With muriatic acid applied to them there is no effervescence. Here and there they show small, yellow-brown spots. Some of the stone-kernels and that which lies close around them show the same colour. The stone-kernels are straight and slowly increase in breadth. The dorsal side is flat or somewhat concave; at the mouth it is more or less convex. This side is not lengthened towards the front, so that we have here a specimen of the subgenus Orthotheca. With the exception of the dorsal side the surface of the stone-kernels is regu- larly vaulted. Consequently the transverse section is about circle- shaped, with only one segment cut off. Towards the pointed end they become more or less triangular. In one stone-kernel, which is not exposed to view in its full length, the visible part points to a length of about 35 millimetres and to a breadth, at the mouth, of 7 millimetres. It appears from these properties that these stone-kernels originate from the Hyolithus (Orthotheca)-species, which has been described and pictured by Hotm') as Hyolithus (Orthotheca) de Geeri. Horm tells us already that sandstone with Hyolithus de Geeri is Under-Cambrian. I have, however, not been able to find in his work, on what grounds this assertion is founded. Most problably he came to this conclusion because the nature of the stone points to it. At the time sandstone with Hyolithus de Geeri was not yet known as firm rock. Even now I have not been able to find in the books at my disposal, that sandstone with Hyolithus de Geeri should be known 1) Hot. Sveriges Kambrisk-Siluriska Hyolithidae och Conulariidae. Sveriges geologiska Underséknung. Ser. G. No. 112. p. 54. 564 ) as such. As far as I can see this species of Hyolithus, when Holm described it, had not been discovered in company with a fossil from which its age might be determined. Mopere*) afterward found many specimens in a few big blocks of sandstone, which furnished him the material for the description of the new species of Trilobites called Holmia Lundgreni. The latter lay in the neighbourhood of lake Tun- byholm in the eastern part of the province of Schonen; according to Mopere suchlike stone with remains of Trilobites oceurs as firm rock not far from this place. As Mosere informs us that sandstone with Holmia Lundgreni is older than that with Holmia Kjerulfi Linrs, this was probably also the case with the sandstone-layers of which the Murmerwoude erratic-blocks formerly formed part. It appears from Mosere’s description of the stone of the erratic- blocks with Holmia Lundgreni, that this stone in some respects resembles the material of which the Murmerwoude erratic-blocks consist. Both are very fine-grained and contain no caleium-carbonate. There does not seem to be much difference in colour either, at least as far as some parts of the Swedish erratic-blocks are concerned : MobereG tells us that the sandstone described by him is chiefly of a bright light-grey colour, though sometimes showing small brown spots of ferrihydroxide. My erratic blocks, however, contain no pieces of phosphorite, which those from the neighbourhood of lake Tunby- holm do. desides the erractic-blocks spoken of just now, others of sandstone with Hyolithus de Geeri-remains were also found, as Holm tells us, in the province of Schonen, near Simrishamn and Képinge. The same author makes mention of suchlike stones having been gathered near Riidersdorf not far from Berlin, and near Biitzow in Mecklenburg. It follows from the descriptions he gives of these pieces, that petrographically they bear no resemblance to those found at Murmerwonde. The latter are least different from the erratic-block found by Prof. pe Grrr at Riidersdorf. My pieces, however, contain no particles of glimmer. No more have corresponding erratic-blocks of Hyolithus-sandstone been found in any part of the Netherlands. The first of this kind of stone were made mention of by van CaLKER*). They originate from Steenbergen in the northern part of Drente; they are three stones 1) Mopere. Sveriges alsta kinda Trilobiter. Geol. Foren. in Stockholm fér- handlingar 1899. Bd. 21. Haft 4. p. 324. 2) Van CALKER. Ueber ein Vorkommen von Kantengeschieben und von Hyoli- thus- und Scolithus-Sandstein in Holland. Zeitschr. d. Deutsch. geol. Gesellschaft. Jahrg. 1890. p. 581. resembling each other. From the description van CaLker gives of the stonekernels occurring in them, Houm already drew the conclusion that they originate from Hyolithus de Geeri. These erratic-blocks consist, however, of dark asch-grey sandstone, so that they differ in colour from the Murmerwoude ones. Afterward two more pieces of Hyolithus-sandstone were mentioned by me‘). One was found at Kloosterholt (Heiligerlee), the other at Roden, in the North of the province of Drente. The former is « small piece of fine-grained sand-stone, yellow-grey on the inside and brownish on the outside, in which are found some fragments of stone-kernels of Hyolithus-shells. A few of these fragments are enti- rely dark-brown, others have a light-grey surface. One of the stone- kernels shows the transverse section characteristic of Hyolithus de Geeri. The Roden erratic-block is rather a large slab of sandstone, containing especially offprints of pyramidal Hyolithus-shells. This one is reddish on the imside and light-grey on the outside. Where the sandstone-layers of which the Murmerwoude erratic- blocks in former times formed part, were originally found as firm rock, cannot be said with certainty, as appears from what was written above. Most probably it was near the western coast of the southern part of Sweden. Ill. That the knowledge of our sendimentary erratics still leaves so much to be desired, must certainly be partly attributed to the fact that so few of them have been gathered up to this time. Non- geologists, too, by their researches, may deserve well of this branch of knowledge, as was proved once more by Prof. Dr. J.C. Kapreyy, filling a chair at the Groningen University. This well-known Astronomer, who in summer lives at Vries, in the northern part of Drente, last summer searched the surroundings of this village for sedimentary erratic-blocks. To his researches we owe a piece that is certainly the most interesting of the erratics described here. Just outside this village, by the road leading to Donderen, was found a small, slab-shaped erratic-block three centimetres thick, the largest dimension of which is 14 centimetres. It consists of sandstone coloured yellow-grey by ferrihydroxide. At the surface it is brownish. With muriatic acid there is no effervescence. The grains of sand 1) Bonnema. De sedimentaire zwerfblokken van Kloosterholt (Heiligerlee). Vers}. y. d. Koninkl. Akad. v. Wetenschappen 1898. p. 450. Van CaiKer, Ueber eine Sammlung von Geschieben yon Kloosterholt. Zeitschr. d. Deutsch. geol. Gesellsch. Jahrg. 1898. p. 234. ( 566 ) are for the greater part very small; they are not easily distin- guished. Among them are bigger transparent ones. The diameter of these latter grains is at most ‘/, millimetre; they are mostly arranged in parallel planes, in consequence of which an indistinct layer-like construction becomes visible on the vertical sides. On one of the horizontal sides there are still parts of a few thin layers. In the stone are a great many small cavities, which were formerly evidently filled with organic remains. On both of the horizontal sides we find remains of Tribolites. On one of them the most important are an off-print of a mid-shell about 5 millimetres long, and a stone-kernel 10 millimetres long, part of the shell of which, turned into iron-hydroxide, is still present. On the other horizontal side is found the front part of an off-print of a much larger mid-shell, which once had a length of about 15 millimetres. Undoubtedly these remains, which in many respects resemble each other, have come from the same kind of Tribolites. The two first mentioned are remains of younger individuals; the other belonged to a more or less full-grown specimen. With the younger individuals the glabella was convex, its length surpassed its breadth a little, its breadth diminishing towards the front. On the front side the glabella is somewhat rounded. On the plaster- cast | made of the off-print of the small mid-shell, it is clearly visible that the glabella possessed at least 2 side-furrows on either side. The stone-kernel shows that the neck-ring was broadened in the middle. The cheeks were vaulted, which is very clear in the stone-kernel especially. Very characteristic is a deep furrow enclosing the glabella in front and being continued on either side on the cheeks, where it broadens and becomes less deep. Before this furrow is a vaulted part, which does not turn down. The front-edge of this part is on about the same level with the back-edge, whilst its height is equal to that of the glabella. In the off-print of the little mid-shell the glabella is 4'/, millimetres in length, and the part in front of it nearly 3 milli- metres in breadth. It is apparent from the off-print of the mid-shell of the more or less full-grown animal, which mid-shell is only partly exposed to view, that the glabella and that part of the mid-shell which is in front of it, which does not turn down here either, are less vaulted, and that the furrow separating the two, is less deep. Here are no side-furrows to be distinguished on the glabella. With the assistance of the scientific works I dispose of, I found that these remains are most like those of Arionellus primaevus BrOGGER, of which up to this time only mid-shells have been pictured and described. The first pictures were given by Kysrrunr' , after remains of the “er¢n skifer” from Tomten (T6mten?) in Norway. He informed us already that they came from an Arionellus-species. Later on they were described by BrégcEr*), who by them was induced to assume the new species Arionellus Primaevus. Under this head he also ranged the mid-shell that had been pictured by Kurrunr in fig. 6. Afterward LinNarsson *) pictured and deseribed remaims of this Tribolite. He moreover tells us that the mid-shell pictured by Kserur as fig. 6 rather seems to belong to a new species called Ellipsocephalus Nordens- kidldi, instituted by him in the same essay. His material had been got from the “grivacke-skiffern” of Forsemélla near Andrarum. He dared with certainty to range under the head Arionellus Primaevus a small mid-shell 5 millimetres lone, which had been found in a sandstone-like variety of the stone mentioned above. This was not the case with mid-shells from the ordinary stone, which are about 15 millimetres long. He gives as his reasons for not daring to range these latter among Arionellus Primaevus Broéeerr : first that they are much flatter, secondly that the furrows are much shallower, thirdly that the glabella has no side-furrows, fourthly that the glabella towards the front considerably diminishes in breadth. Why, notwith- standing all this, he at first ranged them under this head, though he had never heard of transition-forms, he explains by saying that Barranpré had found exactly the same difference between the old and the young specimens of the Bohemian species Arionellus Cetice- phalus Barr., of which transition-forms are known. The very same points of difference occur in the Trilobites-remains of the erratic-block found at Vries. Here, however, the glabella of the older specimen does not diminish in breadth more considerably than that of the younger individuals. As I wished to be as certain as possible in my determination, I wrote to Prof. Mosrre, director of the Geological Institute at Tund, to ask whether there was any material for comparison at my disposal there. Remains of this species of Trilobites seem to be very rare at Forsemolla, however, so that my request could not be complied with. I received as a present, however, a mid-shell of the Ellipsocephalus Nordenskiéldi, whieh seem to occur more frequently there, Prof. 1) Kserutr ,Sparagmitfjeldet’. Universitetsprogram Kristiania. 1872. p.81. Fig. *) Bréccer, Om Paradoxidesskifrene ved Krekling. Nyt Magazin for Naturviden- skab. 1878. Bd. 24. p. 58. 5) Linnarsson, De undre Paradoxideslagren vid Andrarum. Sveriges geologiska Undersékning 1882. Ser. C. N°. 54. p. 21. Taf. IV. fig. 3, 4. 965) Monere supposing that my Trilobites-remains would prove to belong to this species, which is not always to be distinguished from Arionellus Primaevus. Indeed, | had been thinking of this species, but as Linnarsson declares that here the vaulted part of the mid-shell before the glabella towards the outside slopes strongly down, [ thought I could not range my remains under this head. The mid-shell I received from Lund con- firmed my opinion. | informed Prof. Mosera of this and sent hima few plaster-casts of the Trilobites-remains occurring in the erratie- block found at Vries. I was answered that Prof. Mopera shared my opinion and considered them as having come from Arionellus Pri- maevus. At the same time he was so kind as to send me a plaster- cast of the best of the mid-shells of this species of Trilobites, found in the collection at Lund. Now T could ascertain that in Arionellus Primaevus the part of the cephalon in front of the glabella does not turn down, which is not specially mentioned by Bréeerr and LINNARSSON. Also in the mid-shell of which Mosera sent me a plaster-cast, the breadth of the glabella diminishes but litthe towards the front, though its length is about 14 millimetres. I think, then, that we now may with certainty conclude, that in the Vries erratic-block we find remains of Arionellus Primaevus Broccrr. As this Trilobite occurs only in layers that contain remains of Holmia (Olenellus) Kjerulfi Liyrs, and as these are taken to be the youngest of the Under-Cambrian ones, the age of the layer of which this erratic-block in former times formed part, may be easily determined. Besides oceurring at Témten in Norway and at Forsemdlla near Andrarum in Schonen, which places I mentioned already, Arionellus Primaevus is probably found in two more places in firm rock, viz. at Kiviks Esperéd to the North and at Gislofs Hammar to the South of Simrishamn in Schonen. The former place was first made mention of by Naruorst'), who told that he had found there an off-print of an Arionellus? That in Gisléfs Hammar remains of an Arionellus occur, Was first communicated to us by Linyarssoy, in his description of the Arionellus-remains of Forsemdélla. According to this writer, many of the mid-shells found there by von ScHMALENSEE much resembled the larger shells of Forsemélla, which he dared not with certainty call Arionellus Primaevus. 1) Natnorst. Om de kambriska och siluriska lagren vid Kiviks Esperéd ete. Geol. Féreningens i Stockholm Férhandlingar. Bd. 3. 1877. p. 264. ( 569 )j As for two kinds occurring in the same place, Horst’) mentions that the “grivackeskiffer” may also contain a species of Arionellus (Arionellus Primaevus Bréaeur °). From communications made by TuLLBerc*) and Hennig *) the conclusion might be drawn that Arionellus Primaevus Broce occurring at Kiviks Esper6éd and Gisl6fs Hammar, had been sufficiently indi- eated. I think, however, that this should not be done. The list of fossils which these two authors have drawn up with regard to the ‘“erivackeskiffer” of the two places mentioned just now and of Andrarum, must refer, in my opinion, to these places taken collec- tively and not to each separately. I am confirmed in this opinion by the fact that remains of Holmia Kjerulfi Linrs (or of a kindred species) are not mentioned by Mopure *) as being found at Kiviks Esperéd, whereas they are mentioned by them. The origin of this erratic-block must most probably be looked for in the eastern part of Schonen or in the Baltic Sea-region bordering on it. That petrographically it differs from the ordinary “gravackes- kiffer’, does not clash with this opinion, several writers informing us that the latter often changes into sandstone. The thin layers on the lower side indicate that something of the kind has been the case here. It is not likely to have come from Norway, for never was a sedimentary erratic-block found in these parts, of which this may be said. As was mentioned above, I take this erratic-block to be the most interesting one of the pieces that are described in this paper. | do this because it is the first piece coming from layers with Holmia Kjerulfi Linvs that has ever been made mention of. Nowhere in literature did [ find anything about an erratic-block of that age. IV. Shortly before the summer-holidays of last year I found, when visiting the loam-pit close by Hemelum, a slab-shaped piece of fine- grained sandstone three centimetres thick, whilst its largest dimension is a litthe more than 20 centimetres. It is layered and contains caleium-carbonate, so that with muriatic acid it gives effervescence of dioxide-carbonate. Owing to the large number of Glauconite-grains it contains, the 1} Horsr. Beskrifning till kartbladet Simrishamn, p. 17. *) TuntBerc, Skanes Graptoliter. I. Allman 6fversigt Gfver de siluriska bildingarne i Skane och jemférelse med éfriga kinda samtidiga aflagrinzar. Sveriges geologiska Undersdkning. 1882. Ser. G No. 50. p. 26. 3) Hennig, Geologischer Fiihrer durch Schonen. 1900. p. 26. +) Mopere, Sveriges alsta kinda Trilobiter. 570 ) stone of which this erratic-block Consists is coloured a strong green. This is the case with some layers especially. Some particles of a light-coloured kind of glimmer are found in it. My attention was drawn to this kind of sandstone, because, when splitting this erratic-block into two parts, | found that it contains Hyolithus-remains, viz. grey-coloured stone-kernels. The lower part of one of them is brown. When visiting the Natural History-Museum at Hamburg last sum- mer, and admiring its collection of sedimentary erratic-blocks, | asked Prof. Gorrscnk whether he knew of suchlike erraties. Prof. Gorrscng thought he remembered such pieces to have been found in the sur- roundings of Hamburg. Owing to want of exposing-room, however, they lay packed up among other pieces, in consequence of which they could not be shown me. He drew my attention to the fact that in this kind of erratic-blocks sometimes occur small conical valves of horn-shelled Brachiopodes. These valves were shown to me in a brown-coloured erratic-block. A short time after I found on the beach at Borgholm in Oeland not only an erratie-block with Hyolithus-rests entirely corresponding with my Hemelum piece, but also a brown piece of sandstone with a valve of a small horn-shelled Brachiopode. I searched my books for anything on the subject of this kind of erratics or stone, but at first without any result. As Prof. Mosere at Lund in the summer of 1901, when I had requested him to be so kind as to give me some information con- cerning Oeland, had noted down on my map of this island that on its coast, to the North of Farjestaden, occur erratic-blocks with Dis- cinella Holsti (then unknown to me), and the valves of Brachiopodes I had found were, like those of Discina, horny and flat-conical, but much smaller, I supposed that Prof. Mosere could give me some information about this stone. For this reason | intended to write to him concerning this subject, and, was going to do so, when acci- dentally I discovered in the essay of Horm’) on the Swedish Hyoli- thidae and Conulariidae, that by Mosrre *) a greenish kind of sand- stone, rich in Glauconites, with Discinella Holsti Mospere and Hyoli- thes, oceurring as erratic-blocks in Oeland, had been described. Having studied Mopere’s essay, I find that the stone of which my 1) Hots. Sveriges Kambrisk-Siluriska Hyolithidae och Conulariidae. Sveriges Geologiska Undersékning. Ser. C. No. 112. 2) Moserc. Om en nyupptickt fauna i block of kambrisk sandsten, insammlade of dr, N. O. Hoist. Geologiska Foéreningens i Stockholm Férhandlingar 1902. No. 142. Bd. 14. Haft 2. p. 103. aiid 9) erratic-blocks with Hyolithus-remains consist, has been described by this author as type a. The piece of brown sandstone with the valve of a small Brachiopode I found at Borgholm, belongs to his type ¢. The fossil occurring in it has been determined by me as a vaulted valve of Discinella Holsti Mosnre. The erratic-block that was shown me by Gorrscnn probably belongs to the same type; the organic remains occurring in it are likely to have come from the same species of Brachiopodes. The Hyolithus-remains in the Hemelum erratic-block have been very imperfectly preserved, which, according to Hotm,*) is usually the ease with this stone. A longitudinal section possesses a leneth of 10 millimetres and at the mouth a breadth of 4 millimetres, so the dimensions of this shell remind of the one pictured and described by Mosere*) under the name of Hyolithus Insularis nov. spec., whereas Hom afterward called it Hyolithus Confusus nov. spec. The relative age of this kind of erratic-blocks does not seem to be with certainty known yet, as up to this time no corresponding stone has been met with as firm rock, and the organic remains found in them have not yet been discovered in company with such as might contribute to the solution of this question. Mosrre, however, thinks he may conclude from the general character of the fossils occur- ring in them, from their petrographical nature and from the way in which they are spread, that they come from Under-Cambrian layers. Houst*) draws the same conclusion, after tracing the manner in which they are spread. I think I may infer from his essay, that in his opinion they come from the youngest Under-Cambrian layers. In accordance with this is the presence of Discinella-remains, this genus of Brachiopodes occurring, according to Mosrre, in North- America, in layers containing Olenellus. As was said just now, a corresponding kind of stone was not yet met with as firm rock. Most probably it formerly occurred west- ward of Oeland; it may be found there even now at the bottom of the sea, because this kind of erratic-blocks is found in large num- bers only on the western coast of this island, between Halltorp and Morbylinga, and on the little isles and cliffs in the neighbourhood. Less numerous they are in the other parts of the eastern and western coasts of the Kalmarsund. 1) Horm loc. cit. p. 74. 2) Mosere. Om en nyupptiickt fauna i block of kambrisk sandsten ete. p. 117. 3) Horst. Bidrag till kinnedomen om lagerféljden inom den kambriska sand stenen, p. 9. 572 } MoserG says that these erratics were found by Dr. Hoist on Bornholm, too. Neither in) German nor in Duteh literature have I been able to find anything concerning suchlike erratic-blocks. It is almost doubtless, however, that they are mentioned by Gorrscne ") as “Cambrische Grauwackeschiefer”. Only those erratic-blocks which, according to him, resemble the Swedish ‘Grivackeskifer’, must be taken into consideration then. The description of the latter entirely corresponds with that of type @ by Mosere. The small, round, horny-lustrous Brachiopodes-valves with a diameter of 2 millimetres, mentioned by Gorrscur, which may come from Discinella Holsti Mosere, also cause us to conclude that we have the same kind of stone here. Gorrscne does not inform us of Hyolithus-remains occurring in suchlike erratic-blocks. No erratics containing them had perhaps been found at the time. It follows from what he orally communi- cated to me, that now they have most probably been found. The same author says that according to Lriynarsson a kind of stone entirely corresponding with the one described by him, has been met with by Hume. near Tereskov (wich Hummen calls Torekoy), on the coast of N. W.-Schonen, as firm rock. Judging from the description Hummer. *) gives of it, it much resembles, petrographically, type a of the Discinella Holsti-sandstone. Hummet does not say, however, that fossils are found in it. Perhaps we have here the same case as with the Glauconitic sandstone from the neigh- bourhood of Simrishamn, of which Housr*) writes that a corre- sponding kind frequently occurs in the ‘sandstone-region” of the Kalmarsund. Here, too, the resemblance seems to be petrographic at best, for Moprrc, in his essay, speaks about this sandstone no more than about that of Torrkovy. Most probably the thin-layered, greenish stone which resembles the ‘“Grauwacken-Schiefer”’ of the Olenellus Kjerulfi-region, and which petrographically keeps the medium between the Olenellus- stone of Hardeberga in Schonen and the equally old “grén skiffer” of Bornholm, with stone-kernels of a Brachiopode probably belonging to Acrothele, and with Hyolithus-remains bearing the greatest resem- blance to Hyolithus Lenticularis Holm, as SToLiey *) writes, — is also Discinella Holsti-sandstone. 1) Gorrscue. Die Sedimentir-Geschiebe der Proving Schleswig-Holstein. 1S83. p. 8. 2) Huser. Beskrifning till kartbladet ,Bistad”. (No. 60). Sveriges geologiska Undersékning. 1877. p. 10. 8) Hotst. Beskrifning till kartbladet Simrishamn. p. 15. §) Srotitey. Die cambrischen und silurischen Geschiebe Schleswig-Holsteins. Archiv fiir Anthropologie und Geologie Schleswig-Holsteins und der benachbarten Gebiete. 1895. Bd. I. Heft. 1. p. 130. Finally I must mention that, on the occasion of a later visit to the loam-pit near Hemelum, I found two more erratic-blocks, which must probably also be counted among pieces of Discinella Holsti- sandstone. Neither contains any fossils. One corresponds petrogra- phieally with what was described; the other is for the @reater part white, but possesses green layers. If I am not mistaken, | sometimes saw suchlike stones on the beach of Boreholn. Physics. — “On the course of the values of b for hydrogen, in connection with a recent ormula of Prof. vAN pur WAAts.” By Dr. J. J. van Laar. (Communicated by Prof. J.D. van per W AALS). 1. Making use of the theory of cyclic motions, Prof. vAN DER Waats has given a new deduction of the equation of state of a simple substance, in which the size of the molecule appeared to be variable, and to be a function of the voluiie *). For a bi-atomic gas the following formula has been found: b- —b, 1 i= b, ) — pg eee ont) Here 4, denotes the smallest value of 6, corresponding to the case that the two atoms of a molecule touch each other; 6, represents the greatest value i.e. the value for very great (infinitely great) volume. The above equation may be easily derived from the so called “equation of state of the molecule” Jp +54 att) | 6-1) = ar ae geese een (2) - when we take v=o, in which case } assumes the value 6, and Be a ; may be neglected with respect to @(J—0,). So we get: x a (6,—4,)° == Jig If we substitute this value into equation (@, paying regard to we get the equation = Hi cee ee pe eae ae) eae which yields immediately equation (1). 1) These Proceedings of the meetings of February, March and April 1901. See also “Livre jubilaire dédié 4 J. Bosscua” of the Arch. Néerl., p. 47, (The first communication and part of the second discuss principally the specific heat for very large volume). 574 ) The quantity @ in the equation of state (7) depends on the forces, which keep the atoms together in the molecule. These forces are supposed to be proportional to the linear deviation from the position of equilibrium 7—7,. The equation of state (7) for a tri-atomie gas, e.g. CO, which in this case is the combination of two similar equations — will con- tain besides 27 still a factor 7, whose value will vary from 1 to 2 according as the different cases occur, which we may distinguish in the motion of the atoms. For CO, a value of nearly 2 is found for //. As, however, this quantity / for a certain substance is, strictly speaking, variable (see the paper in the ‘Livre dédié a Bosscna’’, quoted above) and as the accurate equation is therefore very complicate, I have chosen a bi-atomic gas, namely hydrogen, in order to test the new equation of van DER Waats. In this case f= 1 and the relation between / and v is represented by the simple equation (1). I hope later to test the equations for oxygen and_ nitrogen, in order to examine whether the results found for hydrogen also hold for these gases. Il. An accurate knowledge of a is required for the exact caleu- lation of 4. This is still a great difficulty. Absolute certainty as to this value cannot be obtained as yet, but still it appears to me that the value a=300X10-6*) has a high degree of probability. Assu- ming another value for a, | found namely that the values calculated for 4 decrease much too rapidly, — much more rapidly than agrees with formula (1); this is principally the case in the beginning, i. e. for large values of v. Only the values of 4, calculated for a=300X10~ varied in such a way, that their course was represented by equation (1) with nearly perfect accuracy. ScHALKWIJK *) also calculated from his last experiments 10° @ = 300 (10° 4, = 910). I therefore thought myself justified in assuming 300 for 10° a. In the following table we find the values for / at 0° Centigrade, calculated from the equation ( 7 oS =) (v—b) = (1 — a) (1--0) (1-+-at). For (1-+a) 1—+) we put 0,9994. All values have been multiplied by 10°; the same will be the case with all values of 4 which we give in what follows. At 0° C. we have: 0,9994 a p+ a 1) All values of v, b, etc. have been expressed in the usual practical units. *) These Proceedings, June 1901, p. 124. , bee ( O75: ) OLE: b L p vo) vp o—h calculated | A found. from (1) 100 LOG90 114.3 2.62 9739 | 951 907 | +44 150 | 7353 54 07 5.58 6495 | 998 901 | +97 200 5690 32.38 9.98 M717 913 396 | U7 20 | 4692 2.01 | 413.63 | 3791 901 | soa | +410 300 4030 16.9% | 418.47 | 3138 892 geo | 6 350 3960 12.67 93 68 2675 885 Bap |) eas 400 3207 10.98 29.48 2399 878 S75 f= 3 450 9933 8.602 34.87 2061 Mp | ie | eo 500 2713 7.360 40.8 [S48 865 865 se (0 5b0 9533 6.416 AG.8 1675 858 860 = 9) GOO 9386° 5.695 Da 1531 855 855 ae (0) G0 2959 5.103 58.8 1410 R19 850) =i 700 149° 4.620 64.9 1307 843 | 845 —2 750 | 2053 he QND HAE? 1917 836 840 So 800 L971 3.885 U2 1139 832 835 — 3) 850 1897 3.599 83.4 1071 826 830 = 900 18335 3.362 89 2 JOLO 823) 826 = 3 950 1774 3.447 95.3 956 818 821 —= 3} 1009 17298 9.967 | 101.4 908 815 817 — 9, 1100 1637 2.680 4141.9 825 812 809 J23} 1200 15575 2,426 NRF 757 Sol SOL ae (0) 1300 1491 97993 | 435.0 696 795 793 + 2 1400 1432 2 0d 146.3 GAG 786 785 +4 1500 1380 1.904 | 156.3 603 777 777 +0 1600 1334 1.781 168.4 D0 769 770 a 1700 | = 49945 1 681 178 5 532 762 763 =i 1800 1258 1.583 189.5 502 756 756 se (0) 1900, 1995 1.501 199.9 476 749 749 oe (0) 2000 11945 1.497, | DAO 2 452, 742 743 = 4 2100 11665 1.361 | 990.4 431 736 736 as (0) 2200 141 1.302 | 930.4 414 730 730 ae) 2300, AEST) 1950! | 240.0 393 i255) 724 ,) +4 2400 10975 1.905 | 249.0 377 720 719 +141 2500 1078 41162} 95879 362 716 714 +2 2600 1059% .493'| 9674 349 711 710 + 4 2700 1042 1.086 276.2 336 706 705 +1 2800 10248 17050) | 285.7 324 701 ) )) 4e4l 1) Up to 1000 atmospheres the values of » have been borrowed from the results of the “second method” of Amagar (méthode des regards); from G00 atm. to 39 Proceedings Royal Acad. Amsterdam. Vol. Y, 576 The values of ¢ have been borrowed from the well known expe- riments of AMAGAT *). The too large values of 4 in the beginning here only to about 300 atm. — are still present. This indicates probably that the value a = 800 is still slightly too great. But from 300 atm. upwards the agreement is quite satisfactory. Small inaccuracies in the determina- tion of the value of ¢ have for large volumes a great influence on the values of 4. To this circumstance also it may be aseribed that the values of 4 are in the beginning not reliable. So the value r= LO690 at p= 100 cannot be accurate to a higher degree than to ten units at the utmost. So it might also have been LOGS8O or LO670O and & or vy — (ve—h) might have been 10 or 20 units smaller. The values of 4 ‘caleulated” have been determined with the aid of equation (1) in the assumption by = 917 ; b, = 468. bh, may be determined in the following way. If we substitute into (1) b—h, b—b, ee and pay regard to —b, = “aE (b,—6), then we get for (1): 3 1 b,—b <= ——_— == |— 7’, 1—as v—) and therefore : b,—b — : i, oe ( —— 7) v—h r For an assumed value of 4, this equation enables us to determine the corresponding value of . from ¢ and / at e.g. 500, 1000, 1600, 2200, 2800 atm. The value of 4, may then be calculated from b, = b — (1 —2?) (v—), which follows immediately from (1). So [ found with 4, = 917 at 1000, 1600, 2200, 2800 atm. respectively the values 4,=455, 463, 462, 466. If we put a=400 instead of @=300, then we find with b, = 1000 at p= 2800 atm. in the same way 6, = 463. With 1000 atm. the values of ¢ at 600, 700, 800, 900 and 1000 atm. represent the mean values of the results of the first method (that of the electrical contacts) and those of the second method. From 1100 atm. upwards the values of 7 have been determined by the first method. 1) Mémoires sur lélasticité et Ja dilatabilité des fluides jusqu’aux trés hautes pressions, p. 32—33 and 38, (577 a = 500, ), = 1100 we find at 2800 atm. again >, = 464. So we may assume with perfect certainty 4, to differ very little from 463. With this value of 4, in the first place 4, was again calculated. From (1) follows: 50 bet bt [A Bees tii My = (0—6,) G23) 68,5 In this way I found at p=500, 600, 700, 800, 900, 1000, 1200, 1400, 1600, 1800, 2000 atm. respectively 6, = 918, 917, 914, 912, TI Oise O19e Gio LT oii. Brom these values I concluded that by = 917. After that the values of 4 (ealeulated) were determined as follows. We derive from equation (1): b—b, (b—b,)? (=n) G2). Cae If we put J—b,=—~y, then we get for 6,—b, = 454: a see ——all us ; (ve—b,) — y 454? a y = 454 paw 0) sy 2 (v—b,) == i We know the values of y already in approximation from 4 (found). from which follows: These values, substituted into the second member of the above equation, yield the accurate value of y, and so also of 6. Il. Let us begin with assuming that the values of 6, and 6, are independent of the temperature, which follows from the supposition of Prof. vay per Waats, that the quantity @, which depends on the forces between the atoms, is proportional to the absolute temperature. Then we may calculate the critica’ quantities in the following way. Equation (1) in connection with the following equation : Shy 2 —————— r u-—o, = = yp (1 3 Bm) Uk 1 + 2(2,-+8,) Or Ui k 3 k Py Po where 39* yields after some reductions *): L[—a \?° cect 8 | : Ler 2 a l -)? \2 1+(—a( 14 “A (45 ~ | ‘b—b, \? h, _: Here is a= and “= . We may write for the "9d by rg —b ; second member : 2(1 4 3.2") (1x) (2—a-a?)* Therefore we get also: le 3(L44)(2—w +2") 2—w + 1) a 4. 1432? The value of « may be derived from this equation. As 4,=917=1,984,, | : ‘ ; ’ : a gets the value = 1,02, and we find in approximation for : O98 the value 0,709, Therefore by—b, cs Se fh) eh by—b, from which we may easily derive: by = 0,922 by = 840. Now we have: 3 v—br. 2(1+-3.? PIE Dh amt tages Se eS nD 2 %% (1+«)(2—a-+- 2)? from which we. find: = eo OES 6B, + 8, = 09,0837. The eritical volume is therefore: = 0.9163, a aU lips = ST 1) ON) Se BT At O° C. this volume is (comp. the table) already reached at a pressure of about TOO atm. The values of r+ at O° range in the experiments of AmaGar to 1025; the verification of equation (1) of VAN DER WAALS may therefore be extended over volumes which have the size of liquid volumes; this fact compensates the want of experi- ments below the critical temperature. We may also calculate the quantities 8, and 3, separately. From’) 1) See v. p. Waats, 1. c. Ill, p. 652. 1) van per Waats, l.c. Ill, p. 651. 1 (l1— v) Dae ae See 1 1+a 2—2-+-a a) follows : Boe O004727; 6B, = 0,0365. We find for K 7): ? 8 « (18, —8,)°'0+2(8,+8,))_ ep Js 27 br. | — B, or Sag oe 83961, 1674 8 a a@ hi — : = 1,029 K —— = 0,305 —. 27 bn 0.9528 27 by. by With a = 300, hy, = 845 we find therefore: Ty RT), = 0,9994 — = 0,108, PATIC: which gives: Dewar found — 30) a 3292). The critical pressure is represented by *) 1 « (1—@,—48,)(1+28,+8,))" y= — ; : 27 by? 1—8, or IL < 1,186 = 4,545. 1—p,—4p, 0.8068 Se - ( =) _ 1=8,—8, 0.9168 padT/; Just as VY comes again very close to the normal value 0,875, so V for hydrogen approaches again close to the theoretical value 4. The expressions for 7 and pe (differ only litthe from those, found for these quantities for tri-atomic gases, such as CO,; the expression for ry, on the other hand deviates strongly from it. This is to be aseribed to the fact, that 4, has here not the value of nearly four-times 4,, but amounts to only twice that value. The quantities 3, and 3, are there- fore much smaller than in the case of tri-atomic gases. VAN DER Waats found for CO, eg. 8, = 0,138 and p, = 0,1, the values we found above amounting to only about one third of these values. 4, is also in this case not 0,864, but 0,92 4,, and for re we find 2,57 4, instead of 2,08 4,, or 2,376, instead of 1,75 by. It is certainly of the highest importance to know whether the result for 7, agrees with the experiments. At the same time the value of the critical coéfficient VY will then agree, for the values of 7) and pe agree very well. But with the investigation of this question, and ‘with the verification of J, we will wait till we have investigated the behaviour of 4 at higher temperature, which will be done in the next chapter. IV. In the first place we will repeat the calculations of § 2 at 99°25 C. We derive the following table (p. 5581) from the expe- riments of AMAGAT") at that temperature. r—h has here been calculated from 0.9994 (1 + 99.25 dx 0,0036627) 1.3627 r—) = — - = : a . a P+ 3 Par oa For the ‘calculated’ values of 4 1 determined quite in the same Way as is indicated above for 0° | 917 3 bh, sts 6) Again the initial values of 4 “found” (up to about 400 atm.) are too great. But afterwards the agreement is sufficient, though the verification was only possible up to 1000 atm., as, alas, no further experiments were available. We come to the remarkable result, that the value of 4, has considerably decreased though the limiting value of 4 has remained unchanged. It seems that at higher temperature the atoms in the molecule may approach one another closer than at lower temperature. 1) Le. p. 38 (20d method). LOOAE | 2 l b p cr v | 2 r—bh calculated | A | found from (1) == Nl ] l 150 | 9846 | 96.94 3.09 8902 4 902 +42 | 200 To Oieee ee 1020 5) 6640 927 897 +30 | 250) 6200 38.44 7 80 5286 O14 892 499 300 | 5986 | 27.94 10.78 4385 901 887 14 350 | 4636 | 21.49 13.95 | 3744 C02) a) 88tiees| a4 400 “M47 | 17.20 17.44 | 3965 CS) Mir ety. NAG | 430 | 3766 AS ete 2892 S74 687i | 3 500 | 3462 |) 44.99 | 25.02 2596 866) | 866 |) 410 | | 550 3214 10.33 29.04 9353 861 | gst | +0 | if | 600 3006 9.036 33.29 | 9159 854 Shien ll =n9) 650 | 9831 8.015 | 37.0 1983 848 fal, a} | | | 700 2680 7.482 | 41.8 1837 B13 1) 86a )|| 3 750 | 551 | 6.508 46.41 1712) || 839 841 59) 800 2436 5.934 50.6 1602 | 834 a36. | =9 850 2336 5.457 55.0 1506 | 830 Geil jf eal 900 | 2944 5 036 59.6 1490 =| 894 827 | — 2 950 | (2174) 4.726 63.5 1345 | (829)1)| 899 | | 1000 | 9093 | 4.381 68.5. | ° 4975 | Sige “Cis al meenG | | From equation (@) follows that for great volumes : a (bj—b,)? = RT. Now we find: O° | bj—b, = 404 | (6,—b,)? = 20,61 K 104 OOS WP ey SS ae] = 28000) an (6,—6,)* has therefore increased in the ratio 1:1,868. But 7’ has increased in the ratio 1: 1,364, from which would follow that @ is independent of 7”. In order to investigate whether this also applies to. still higher temperatures, | have also performed the. calculation for 200°,25. v—h may then be calculated from: 0,9994 (1 +-200,25 x 0,0036627) 11,7324 v—_ 0 = a a ae Bislges 1) The value given for ¢ at p=950 atm. appears to be erronious ; probably it must be 2164, 582 ) With the aid of the following table we may survey the results. 200 s 4 L ] C ee 73 v—h A found calculated 150 12820 151.78 | 1.98 11300 921 RO4 +27 200 420 88.74 | 3.38 R518 2 | RRO +13 250 7US0 DR O08 5.09 G791 RAY RR4 +5 300 6520 42.51 7.06 miH42 878 870 — i 350 NOG 32.42 9 I {Q2 872 873 —i1 400 nOTD 25.76 11 65 4208 807 868 —i1 fo0 f593 21.410 14.99 3732 61 863 —2 500 4210 17.72 16.93 3351 R59 858 +1 da0 BRO 15.44 19.82 3040 851 R53 -—2 600 3627 13.16 9980 2782 8 R48 — 3 650 3403 41.58 95.91 2503 840 M3 —3 700 | 3211 10 31 29 40 9376 835 838 — 3 750 | 3045 9.272 32.46 2914 831 833 9 S00 2900 | 8.410 35.67 2073 827 RUS =| Sole ear 2 ot 7.684 39.0 1949 823 823 +0 900 9657 7.060 hD 5 1838 819 R19 ae Only at 150 and 200 atm. the values for 4 “found” are somewhat foo high: furtheron the agreement is satisfactory. The experiments ranged ouly to 900 atm. The values of 4 “caleulated” have been determmed from (1) with the aid of: iO Qe— 0b: 4, appears to be slightly smaller than at O° and 100°, but 4, has again strongly decreased. It is a remarkable fact that the decrease of 4, between O° and 99 amounts to 77, and that between 99° and 200° to SO; so for each degree the same amount namely 0,5. As to 6,—0;; we have now: ae hb, —h, = 454 (b,—h,)° —— Ar 200° O04 = = 36.48 The ratio of the values of (b, -h,)* is 1,77. For 1+ at we find 1,73. Taking for 4,—, at 200° a value which is only 6 units ( 583 ) smaller, namely 598, the ratio of the values of (4,—d,)* would also have been found equal to 1,73. We may therefore safely assume that (b,—6)* is found to be accurately proportional to the tempera- ture within so large an interval of temperature as that between 0° and 200°, in consequence of which the quantity @ must be qeute independent of the temperature. It is not astonishing that @ is independent of the temperature ; the contrary would rather seem to be remarkable. Being induced to make this contrary supposition for the better agreement of the quantity a (3) for CO, with the experiments, Prof. v. p. WAALs') [DNGEE A immediately pointed out its astonishing character. We shall just draw attention to the following consequence of the fact, that b,—O, is proportional to V7. If we put: by—b, == Vy, then equation (1) may be written as follows: b—bg Vi _ he Cbg De oOo Og 8): o—b dl Vy yL With small value of 4,—4 and great value of v, we get approxi- mately : Vil byt ery therefore ¥T papa =) j av sles oa : RT v being in this case approximately equal to ——, we get: : i; y b,—b atc 0 P ; —it or ' — by—y PP; i.e. the value of 4 depends only on p and no more on 7 or 7, the value of 4, being nearly constant. The values of 4, caleulated for the same pressures, have therefore the same difference whether the temperature be O° or 200°. For we have: by, =U = 4 (Ps —P,)- We found this fact affirmed in the above tables?). For the purpose ees es ps 646; *) I pointed this out already before in a paper in the Archives Teyler (,Sur Vinfluence des corrections, ete.” (2) VIL, 3me partic, p. 26—27.) I tested there the b-values for hydrogen to an empivical formula of Kamertivan Oxves. 584. } of a more direet comparison we collect the values of 4 for pressures differing each time LOO atm. in another table. wo WOT i — 11 20) ROU R07 RAY 10 10 10 SOO SAU RX7 870 11 11 11 {00 875 876 SUS 10 10 10 DOO) 865 S66 R58 10 10 10 G00 RDD R56 R48 10 410 10 700 Rd S46 R38 10 40 10 800 835 R36 828 9 9 9 900 R26 827 S19 9 9 1000 S17 S18 = We see that the differences are the same. All the values of 4 at 200° are 8 units less than the corresponding values at 0° and at LOO", because the value of 4, at 200° is 7 units less. But the course is always just the same. And as at a given value of p we always find ‘mereasing vaiues of ¢ at increasing temperature, so the value of 4, must of course always decrease. From the above follows also, that we may determine 4, immediately, eg. adding 52 units to the values of 4 found at 500 atm., or 32 units to that at 400 atm., ete. On the preceding reasoning we may base the following short calculation. At p,—p, = 100 the initial value of 4,—/, amounts to cirea 10 a 11; we have therefore: 7 —— Me =) 105.20 10S 2R 100 Therefore b, — b, =V7T = 10-4 V0.21 RT = 10-3 V 0,21 X 0,9994 (1 + al), bg — b, = 10-6 VOI Sx 10* (1 + et). So we have at 0° 10°%4,—4,) = 458 (found 454). At 100° we find 10%4,—),) = V 21<10°S<1,3627=535 (found 534). At 200° we find 10°4,—4,) =V 21<10'<1,7324—603 (found 604), (5850) VY. A- slight correction must of course be applied to the caleula- tions of § 3 in consequence of the variability of 4,—4, with the tem- perature. For the assumption that 4, remains constant pleads also the circumstance, that according to an observation of D. Brrrignor the experiment yields the value 2,93 a 2,98 for the ratio between the temperature at which a gas in extreme rarefaction follows the law of Borin, and the critical temperature; for which ratio the sup- position that 4, is constant over this large temperature interval *) leads to the value 2,9. If we assume this same supposition, we shall find 4, to be equal to ecirea 920° also for the critical isothermal. But 4, will be found to be considerably higher than at 0°. We saw above that the difference amounts to’: 77 units for 99° difference in temperature. We shall therefore find 4, at — 242° C. from the equation : 249 b, = 463 + ani < 77 = 463 + 188 — 651. If therefore we put 4, = 920 and 4, = 650, then in the first place b, is no longer equal to 2 6,, but to: by = 1,415 8,. The variability of 4 is therefore much smaller than at 0°, and in consequence of this the quantities p, and 2, will also be found to be much smaller, and the critical quantities will approach still more closely to the normal values. Pe Oras 1 : The quantity # = — isebere —-== 2,41, and the value of by—b, 0.415 bp —b, ‘ : E : v={-—_ } of equation 4 ceases accordingly to be 0,709, but becomes bg —byy 3 0,852. In consequence of this we find: by.—b a Osta) = (0). 3}. b,—b, from which follows: i. (OST 399: Kor ry, and for 8, -+ 8, we find (comp. § 3): UE = 2,87 b, 3 Bi + By = 00228. So we- find: De 2,8 by (= 2:80 b, = 3,97 0.) = 2579, Na apr A Bee a volume which is reached at 0° C. at a pressure of + 550 atm. The values of p, and B, taken separately are: 2. = — 00117. (= Be 0,001: o2— LB —S > = ') Zie van per Waats, l.c. Ill, p. 647. 586 Now we return to the experimental verification of 7,. 1 Gr. Hy at OF C. and 1 atm. occupying a space of 11127 eM’, re is expressed in ceM’. equal to 2579 >< 10-6 > 11127, hence the critical density is: l dt. — — 0.0348. According to the theorem of the straight diameter of Marntas we have : to —2—=— (: 7 A ) y. dt Ve which quantity g has been found by Youne and Matnias to differ little from unity for different non-associating substances. Dewar‘) found the density of the liquid phase at the melting point of H, (16°,5) to be 0,086, so we find, neglecting the density d, of the vapour: 0.086 16.5 5 ee d). 31.0 : which yields for dz, : 0,086 F dy. = —— = 0,0348, 2468 — in perfect agreement with the value of d, we have calculated above. We now proceed to the calculation of the other critical quantities Say) ee Ge le We find for 7): Sa 0.9549 x 1,0456 a ep: Z ——_ - = 1,010 Kk —— = 0,299 —. Oo RT. = —— - 27 bz 0.9883 27 be ly With a = 300, 4b, = 899 we find therefore ; Aly 0.9994 — — 0,100, 273 SO Ty = 27°,2. This value is somewhat too low; the experiment has yielded 7.=+ 31°. We find for the critical pressure: 1 Be 0,9439 1,095 Levit SA aT piv pese a8 BOSS 7 9a 0 27 by? 0,9883 27 by? by? 1) 1. c. bl. 477. Dewar finds the melting point to be 16° A 17°; the critical temperature 10 be 30° 4 32° absolute temperature. [The density of the liquid phase at the boilingpoint (20° & 21°) has been estimated to be + 0,07, but then the vapour density may no more be neglected.) ras ( 587 ) With the values found for a and 4; we get: PE = 14.4 atm. Drwar found + 15 atm. The critical coefficient Y becomes : 3 0.9439 3) v= ao a SAU = Ole 8 “*0,9549 : ie so nearly the normal value 0,375. li d ) Or ee (i a we find now another value than before. In the P dT, I general expression ') We aa) rome lad ae Nev pay lb ae ser pili ‘Pilea dTdb\ de db dP, the factor of — is now no longer zero. For as —-= a4 (b—4,), we av ab have: po (4h rae == = —Ta—, ml db oil as we found @ to be independent of 7, 4, on the other hand to db depend upon 7. We find therefore for the factor of ae av (0-2 +77} We have found above: 6,—),=VyT, so 6, =b,—V7T, and as 4, has been found to be nearly independent of 7’) we get piles lpatge: 1 Wie aA y= — 2 (b,—6,)- A _ db The factor of a becomes therefore : (s 1 a (+! —- 5 (b,—b,) - =| i RT (OS |=) and with VES 5) 1 = }) 1) 1 SS ee ——— ) —-- (ys): (6,—6,)? =| a (o b—b, ‘ | b—b, — as according to (1) we have - = =({ il == —— = (by; —b,)? 55 v—b we get: NG Uy _W. Aats, |. c. Il, p. 644. ( 588 ) 4 WY) 9b NS | 1 —8, (v , site ae ( 2 b—b, ). ms ‘ . f dp . op dh his expression for | becomes therefore, if we put — = py: pat), 7 fy dp 1 ‘ s *}. hy : hs i h, == ( r |= (1+ — | 1+ A,(— *_1)(1- ') |. tab dl I ple hy.—b, : y) by—bh, f This vields with the values calculated above (see § 3): 0.9772, 1680 L270: Jd ayek | 14+-0,0117( ~1)(1- ; = 0.9439 249 } 2 2497), = 4 > 1,035 [1 + 0,0117 % 5,747 %K 0,4578}, or y = 4,140 * 1,0308 4,267. T dp Finally we investigate, whether this value of (= 3 may be k Dewar found namely (Le.): T= 20"a2 p= atm. T= 30°A32° | pe=15 ato. The two data vield by means of the integral formula Pk [Lk ep log— = SS ra ( ; ) for 7 the value: _ _neplog 15 - oF, gt) 7 = a ice ii i =e t ae G rial} We Sad £5 “ 20. 21 according as we take 20° and 32° or 21° and 380°. The lowest value is 4,51, so still higher than the caleulated value 4,27. We must further note that 20° differs comparatively very much from 7% (being */, 7) and that therefore at 20° the factor / will certainly be found to be greater than near 7%, hence 4,51 is probably too ereat. From the above we may in any case conclude, that the large extrapolation, by means of which we have caleulated the value of 6b, at — 242° from the values of } at 0°, 100? and 200°, really yields the critical data with a sufficient degree of accuracy al least in so far as we may judge from the few data, that are available. Only )” is probably too low. We have reason to expect a priori that the new equation, derived by van peR Waats for the variability of / with the yolume, does wht ( 589 ) not represent the experimental data with perfect accuracy. For the correction, introduced before for the partial coincidence of the distance spheres has not been taken into account in the deduction of this formula. The quantity 6 in »—% for a monatomic gas, e. e. mercury vapour, argon ete. would according to the new theory of VAN pER WAALS remain invariable; whereas this quantity which according to the former considerations would for very large volumes be equal to four times the molecular volume, for smaller volumes would certainly have a smaller value, and it would approach to about twice the molecular volume — at least if the shape of the molecules does not exercise any influence on this calculation. Physics. — “Peculiarities and changes of Fraunhofer lines interpreted as consequences of anomalous dispersion of sunlight in the corona’ by Prof. W. He JULIUS. (Communicated in the meeting of February 28, 1903). Especially by Jrwe.u’s investigations on the coincidence of solar and metallic lines’) attention has been drawn to several variable peculiarities of Fraunhofer lines. Here we do not mean the irregu- larities occurring in the spectrum of spots or of faculae, which relate to disturbances in comparatively small parts of the sun, but abnor- malities shown by the average sunlight, as observed when the slit is illuminated by a long strip of an imperfectly focused solar image. In that case, according to Doppir’s principle we may, of course, expect displacements of the lines in consequence of the Sun’s rotation, of the rotation of the Earth, and of the change in the distance between Sun and Earth caused by the excentricity of the Earth’s orbit. But even when all these influences have been allowed for, some irre- gularities still remain. Indeed, Jrwrnn has observed that some Fraunhofer lines do, others do not, exactly coincide with the emission lines in the are spectrum of elements, and that the displacements are unequal both for lines of different elements and for the various lines of one and the same element. Moreover, the shifting of certain lines on one set of photo- graphic plates was sometimes found different from that on a set of 1) L. E. Jewett, “The coincidence of solar and metallic lines. A study of the appearance of lines in the spectra of the electric are and the Sun.” Astroph. Journ. Il p. 8S9—113, 1896. The same: “Spectroscopic notes. Absolute wave-lengths, spectroscopic determinations of motions in the line of sight, and other related subjects.” Astroph. Journ. XL p. 234—240, 1900. ( 590 ) plates taken at another time. With several lines the intensity too appeared to be variable. JEWELL explains these phenomena on certain hypotheses on density, pressure and temperature of the absorbing and emitting gases in the different layers of the solar atmosphere, and by variable ascending and descending velocities of matter. Haue’s abnormal solar spectrin, Much greater than the irregularities mentioned are those, found in an “abnormal” solar spectrum, lately described by G. E. Hane. *) This highly remarkable spectrum had accidentally been photographed as long ago as February 1894 in a series of exposures made with the sole intention of investigating the peculiarities of the grating. Only a few months later it was discovered that a very extraordinary phenomenon had been photographed. Ha. hesitated to publish this accidental discovery. Copies ef the plate were sent to several spectro- scopists for examination with the request that an explanation, referring the phenomenon to some origin other than solar, might be supplied, if possible. As no such explanation was forthcoming, the spectra were very carefully measured and described. On one and the same plate 12 exposures had been successively made in the third order spectrum of a plane grating. A solar image of 51 mm. in diameter was so adjusted that the image of a spot fell exactly on the slit. The length of the slit (6.5 m.m.) corresponded to about one eighth of the sun's diameter. The first exposures show the normal spectrum without any con- siderable changes. Then came the disturbance, which culminated in the eighth spectrum and, in the following four, decreased rapidly. HALE gives reproductions of four spectra, each of them extending from 23812 to 24132. N°. 1 has been taken before the disturbance occurred ; N°. 2 is the most abnormal spectrum; N°. 3 is called by Hane the “intermediate” spectrum, it has been obtained a few moments after the abnormal one; N°. 4 shows once more the nor- mal solar spectrum, as it was photographed at another time on another plate. Nos. 1, 2 and 3 show a dark band throughout the whole spectrum, corresponding to the sun-spot) which had been focused on the slit. The most prominent features of the abnormal spectrum are : 1°. The band due to the spot appears much fainter than in the spectra, photographed before and after the disturbance. ') George E. Hae. ‘Solar research at the Yerkes Observatory”. Astroph. Journ. XVI p. 211—233, 1902. Cason 2°. With several Fraunhofer lines the intensity or the width is greatly diminished. This is most conspicuous with the broad, dark calcium bands H and K and with the hydrogen line Hd, these being almost totally absent in the abnormal spectrum. 3°. Other lines, on the contrary, appear uncommonly strengthened. 4°. Many lines are more or less displaced. The same peculiarities are noticed, though generally in a smaller degree, in the intermediate spectrum, so that the latter, in fact, forms a link between the abnormal and the normal spectrum. This marvellously complicated disturbance was not confined to light coming from a comparatively small part of the solar disk, for instance from the immediate surroundings of a spot; on the contrary, it extended almost equally over the whole width of the spectrum and was therefore nearly the same for all the light which came from a very great area of the Sun. The moments of the 12 exposures and the exact date had not been recorded, but there was sufficient evidence that the whole process of the disturbance lasted only a very short time. Hate calls the phenomenon: “a remarkable disturbance of the reversing layer’. But is it not almost impossible to imagine a rather thin layer in the solar atmosphere undergoing suddenly and simul- taneously over a great part of the sun such a thorough change, as to make its absorbing and radiating power in some parts of the spectrum for a while nearly unrecognizable ? It occurred to me, therefore, that the origin of the phenomenon should be looked for somewhere on the path of the light between the Sun and the Earth. If on this path there be media, causing anomalous dispersion, the beam must show an altered composition. As I formerly indicated’), the properties of the chromospheric light may be derived from the supposition, that this light has been scattered out of the photospheric light by anomalous dispersion. According to this hypothesis the spectrum of the chromosphere informs us, which are the kinds of light, that may follow rather stronely eurved paths in the solar atmosphere. So the idea suggested itself, that the same waves might play a striking part in Hanp’s abnormal spectum. In order to investigate the question as impartially as possible, | marked (before consulting Hatn’s table or a table of chromosphere 1) Proce. Roy. Acad. Amst. II, p. 575—588; Ill, p. 195—203; IV, p. 162—171; Physikalische Zeitschrift 4, p. 132—'36. 40 Proceedings Royal Acad. Amsterdam. Vol. V. Lines whose intensity is less 599 TABLE I. in the abnormal than in the normal speectram, Wavelength i H H 3920 | / 3923 3933.82 3944. 3948 . 3950. 3953. 3958 3961 3968 3970. 3977 3986 3998 . 4012.; 4033. at 67 .63 18 .89 .90 4034.64 4045 9} 4063 .7 4071. 4077. 4102 normal (ROWLAND) 20 (700) Intensity inter medints HALY } Wnormal HALE Chromo sphere LOCK YEH £ ' P i 2 (2) 3 3 Remarks. squewie]y t Not mentioned in HALr’s } list, but distinetly weakened e \; ae Jin the abnormal spectrum Fe on the reproduction. Fe, Fel += 3878.15 and 4 = $878.72; W ILALE mentions Fe, Ma. Fe | ae? fe Cr, Si Ke Ti Vi * These intensities are very probably estimated too high when compared with the Fe Jnumbersin the second column, Fe {Ct the Note on p. 593. Ca Al re Ie Fe, ete. Ti Al Ca lines) on the reproductions of the spectra in the Astrophysical Jour- nal a number of lines, which struck me as being weakened in the abnormal spectrum. By means of Grorcn Hices’ photographic atlas of the normal solar spectrum the wave-lengths of the selected lines were easily read; they are to be found in the first column of Table I. The second, third, and fourth columns show the intensities of these lines in the normal, the intermediate, and the abnormal spec- trum as given by Hare (for the normal spectrum from Row ayp’s tables, for the other two from estimations by Mr. Apams). Hain remarks that the intensities of the lines were estimated independently for the two disturbed spectra’). The fifth column indicates the inten- sities of corresponding chromosphere lines as found by Lockyer in TABLE II, Lines whose intensity is greater in the abnormal than in the normal spectrum. — — — — — ———— — — h— Intensity. Wave- iter: sl re ae Chromo- a Remarks. leneth normal | mediate | abnormal] sphere =) (ROWLAND)! (HALE) (HALE) (LOCKYER - 3921 86 i — 20 Zr, Mn 3927.77 — a D5} ? 3930.45 8 15 28 3-4 Ve 3937 .39 — -—— 10 ? 3940 25 — 7 12 ? 3950.50 2 — 1183 } 3962.29 3 — 11 Fe? 3973.77 6 -- 15 2? |N1,4,he,Ca 3981.92 4 13 30 6* Ti, Pe * In Humpureys’ table wen] 3 tw eg 3996.80 — — 9 ? occur. 4013.90 PS) |i peg 15 Ti, Ie 4OL4. 67 5 9 20 Fe 4023 .38 — | —_ 10 ? sain 2 -\) 1 5 ia 4040.79 Bol iG 20 4 Fe n0is.09] 5 | 20 5 | Ie 1) In eee the lines that appeared weakened in the abnormal spectrum I did of course compare the three spectra mutually. That is why in my table some lines occur, whose intensities, as estimated by Mr. Apams, are not comparatively Jow in the abnormal spectrum. : “40 594 the spectrum, secured at Viziadrug during the 1598 eclipse’); the sixth column shows the absorbing substances. In a similar way Table Il has been composed; here we find the lines, which on the reproduction appeared to be strengthened_ in the abnormal spectrum, The result is very striking. Weakened lines correspond to chromosphere lines, almost without exception; most ofthe strengthened lines, onthe other hand, are notto be found inthe spectrum of the chromo- sphere. Lockyer gives the strength of the chromosphere lines on a seale such that 10 indicates the strongest and 1 the faintest lines. If we take into account that in his list the greater part of the lines bear the numbers 1 and 2, our table shows us, that by merely observing the abnormal solar spectrum we have been able to pick out strong chromosphere lines. This cannot be chance. Undoubtedly both phe- nomena — the weakening of Fraunhofer lines in the abnormal spee- trum and the origin of the chromosphere spectrum — are to be explained in close relation with each other. The strengthening of lines in the abnormal spectrum does not, on the contrary, seem to be so directly connected with the com- position of the chromosphere spectrum. If our view be correct that the chromospheric light has been se- parated by strong ray-curving from the “white” light emitted by deeper layers, those special radiations must, as a rule, show reduced intensity in the spectrum of the Sun’s disk *). Fraunhofer lines cor- 1) Lockyer, Curisuorm-Barren and Pepier. “Total Eclipse of the Sun, January 22, 1898. — Observations at Viziadrug,” Phil. Trans., A, vol. 197, p. 151—227, 1901. 2) It might be thought that the rays forming the chromosphere light, need to be absent only from the spectrum of the edge but not from that of the central portions of the Sun’s disk. By a simple consideration, following from a look at Fig. 4 of my paper, read in Febr. 1900 (Proc. Roy. Acad. Amst. II, p. 580) we see, however, that the chromosphere light visible to us may very well, fora part, have its origin even in points of the Sun which lie opposite to the Earth’s direc- tion. The chromosphere light, reaching the Earth, may proceed from any point of Scuaupt’s “critical sphere. For the greater part it is likely to come from the back half of the Sun. But then the half, facing us, furnishes the chromospheric light which travels to other regions of the universe, and this light, of course, is wanting in the spectrum of the disk. (There is some reason for supposing that, on an average, more chromospheric light is sent forth in directions making great angles with the Sun’s equator, than to the equatorial regions, including the Earth’s orbit.) (595%) responding to chromosphere lines will therefore lave a more or less darkened background in the ordinary solar spectrum. The rate of darkening at various distances from the centre of an absorption line is, of course, connecied with the shape of the dispersion curve near that line; whereas the average shading depends 1s' on the quantity of matter causing anomalous dispersion and 2°¢ly on the slopes and the directions of the density gradients in the gases through which the light is transmitted, viz. on the Sun’s “activity” *). We distinguish, therefore, a twofold origin of the dark lines in the solar spectrum: real absorption of those waves, exactly cor- responding to the periods of the media, and dispersion of the strongly deviated neighbouring light °*). The dispersion will be especially evident where extraordinary diffe- rences in the density of the medium occur; in this way the widening of most of the Fraunhofer lines in the spectra of spots may be accounted for. Dispersed light has not, of course, vanished; the absence of certain rays in the spectrum of a spot is counterbalanced by the increased intensity of the same radiations in the light coming from the neigh- bouring faculae. Thus the distribution of the density in the solar gases may locally be such, that a limited part of the disk seems to emit a considerable amount of rays with abnormally high or abnor- mally low refractive indices. In the spectrum of such parts not only will the Fraunhofer lines show narrower and fainter than usually, but here we may even meet with lines contrasting brightly with their surroundings. These bright lines will not coincide with the corre- sponding absorption lines; their average wave-length will in general be greater or smaller than that of the absorbed light, for, according to the accidental distribution of the density, we shall find either the rays with high or those with low refractive indices most prominent in the beam. The above considerations suggest an explanation of HaLn’s abnormal spectrum. In fact, the lines showing especially faint in this spectrum were exactly those, causing strong anomalous dispersion — witness the 1) The possible influence of the general or regular ray-curving (after Scusupr’'s principle) on the feature of the spectral lines has, in the present paper, been left out of consideration. If we were able to observe or to calculate the radii of the “eritical spheres“ for radiations undergoing anomalous refraction, it would be possible to estimate that influence; but as yet sufficient data are wanting. ®) Proc. Roy. Acad, Amst. II. p. 580. 596) chromosphere spectrum. With //, A, // and some iron lines it is conspicuous that the abnormal faintness regards mainly the broad dark shadings of the lines, i.e. those parts, whose darkness in the normal spectrum we attributed not to absorption, but to dispersion, Moreover, the dark band due to the spot has nearly disappeared. This means that waves, which in normal cirenmstances are wanting in the spot spectrum on account of their strong dispersion, at the time of the disturbance had been gathered again into the beam reaching the instrument. How all this may happen will become evident as soon as we shall be able to establish a plausible cause, by which, within an angular space great enough to include a considerable part of the solar disk, the strongly dispersed rays might be gathered again. It is not necessary to introduce a new hy pothesis for the purpose. The same idea about the Sun’s constitution ') which enabled us to explain the properties of the chromosphere and the prominences, furnishes us once more with the required data. Indeed, if (according to Scumipt’s theory) the Sun is an unlimited mass of gas, surfaces of discontinuity must exist similar to those, whose general feature has been determined by Ewpen *) fora sharply outlined radiating and rotating sun. These surfaces must extend unto the remotest parts of the gaseous body a conclusion in excellent harmony with the visible structure of the corona. For along the surfaces of discontinuity waves and whirls are formed; the core-lines of the vortices nearly coincide with the generatrices of these surfaces of revolution, and in these cores the density is a minimum. This may account for the streaky appearance, shown more or less dis- tinctly in all good photographs and drawings of the corona. This particular appearance may have another cause, though ; for what follows, however, this is immaterial. We only assume that the density of the coronal matter varies in such a way, as to correspond to the striped structure visible at the time ofa total eclipse of the Sun. A coronal streamer which, at a given moment, runs exactly in the direction of the Earth may be very roughly compared, then, to a bundle of glass tubes through which we are looking lengthwise. Such a structure will gather and conduct rays of various directions, ente- ring it at one end. This takes place also if the parts with the greater and those with the smaller optical density do not alternate abruptly, like glass and air, but gradually. 1) Proc, Roy. Acad. Amst. IV, p. 162. 2) R. Empey, Beitriige zur Sonnentheorie, Ann. d. Phys. [4], 7, p. 176—197, ( 597 ) In Fig. 1 the optical density of the matter may be represented by the com- pacitness of the streaking. A ray for which the medium has a large positive refractionconstant would for instance follow the path AA’, curving round the denser parts of the structure; aray LB, | for which the medium possesses a large negative refractionconstant, would move (in a similar way through the more rare- || fied regions. On the other hand, the light | CC" for which the constant exactly equals | zero is not influenced by the fluctuations | of the density ; and if for some kind of light the refractionconstant is very nearly zero, the ray would have to travel a long way almost parallel to the structure before its curving would be perceptible. Fig. 1. Now the corona sometimes shows exceedingly long, pointed strea- mers. We only have tosuppose that the Karth was exactly in the direction of such astreamer at the moment the abnormal spectrum was photographed; then aul the irregularities observed in this spectrum become clear. Light, under normal circumstances absent from the solar spectrum through strong dispersion, has been collected by the coronal streamer ; hence the weakening of the Fraunhofer lines, especially also of those in the spectrum of the spot. As the abnormalities were caused by a peculiar distribution of matter in the vast regions of the corona, lying between the source of light and the Earth (and not by disturbances in a relatively thin “reversing layer’) they could appear in the same way over a great part of the Sun’s disk. The rarity of the phenomenon is the result of the slight chance we have to take a photograph at the very moment on which an uncommonly long coronal streamer is projected exactly on the part of Sun’s disk illuminating the slit; the short duration finally is a consequence of the difference between the angular velocity of the corona and that of the Earth in its orbit. As we have mentioned before, #0 chromosphere lines correspond, in general, to those lines showing extraordinarily strony in the abnor- mal spectrum. How are we to account for the strengthening of these lines? 598 ) We might be tempied to think of absorption in the corona; for if it be true that a streamer was turned towards the Earth, the rays had to go an uncommonly long way through an absorbing medium, But on closer examination this idea is less probable. The particles of the extremely rarefied corona gases will hardly influence each other; their periods will, therefore, be almost absolutely constant, so as to cause very sharp, narrow absorption lines. Thus it is difficult to understand, how an absorption line, already present in the normal solar spectrum, might be strengthened by the absorbing power of the corona. Further, in studying Hate’s table, we observe that many lines which are strong in the abnormal spectrum, show a much smaller intensity in the intermediate spectrum (taken only a few moments later); whilst the reverse happens as well, viz. that lines are strong in the intermediate and very weak in the abnormal spectrum. This hardly fits in with the absorption hypothesis. Some lines showing this peculiarity are given in table IIL. TABLE IL. Lines whose intensity is very different in the intermediate and the abnormal speetram. Intensity. eh novel ae epey ere Snes: Elements Remarks. RowLanpb)| (HALE) (HALE) | (LocKYER) ee 3905.66 12 20 — 2 Cr, Si 3905.81 21 — 20 Si 3921.71 9 14 —_ Ti,La,Zr, Min 3921.87 4 =: 20 Zr, Mn 3950.33 — 10 — P 3950.51 ee || _ 13 ve 3972.30 2 42 — Ni 3972.61 | ae 12 ? 4005.86 3 95 Ry : 4057.39 4 _ 15 1-2 Co, Fe 4057 .66 iv 10 = 2 In the chromosphere spectrum corresponding lines seem to be wanting. (At 2 3905.66 and 4 4057.39 the faint chromosphere line may possibly belong to another element than the abnormally streng- thened absorption line). To arrive at a more satisfactory explanation of the strengthening- phenomenon we suppose that these absorption lines do indeed cause anomalous dispersion of neighbouring waves, but in a very slight deerée. Then, the refractive indices of the neighbouring waves differing hardly from unity, the direction of those rays will only be pereep- tibly changed after they have travelled a very long way through the corona and almost parallel to its structure-lines. Whereas the strongly refracted rays, entering the coronal streamer im various directions, were obliged to follow the structure-lines, curving about them, and so in a sense were concentrated on the Earth, it may happen with the extremely slightly curved rays we are now consi- dering, that they have been bent for instance only once over the whole length of the streamer and continue their way in a direction not meeting the observing station. The divergence of a beam con- sisting of these rays will have increased, the intensity diminished. Thus, the resultant spreading of neighbouring light causes the absorption line to appear somewhat widened and therefore strengthened. Sut obviously it must be possible too, that, after a short time, under the influence of another part of the corona, circumstances turn out even favourable for that slightly curved light to reach the observer. In that case the absorption line is weak again. (Similar alternations, of course, also occur with the more strongly refracted rays, and that in quicker succession, but this does not alter the fact of their average intensity appearing increased as long as the structure lines of the coronal streamer are turned towards the spectroscope. For a detailed discussion of this case see the Note at the end of this paper). In both abnormal spectra a number of absorption lines are more or less displaced. Perhaps this is partly due to motion in the line of sight; but after the foregoing it will not be necessary to explain in detail, that also anomalous dispersion can account for this pheno- menon. Dissymmetric form of the dispersion-curve as well as a peculiar distribution of the density of the coronal matter may une- qually affect the intensity of the light on both sides of the absorption line, and thus bring about a seeming displacement of the line. Certain peculiarities of lines in the normal solar spectrum. If we have been right in connecting the uncommonly great abnor- malities in Hatn’s spectrum with a very particular position of the Earth with respect to the corona, it is to be expected that similar irregularities, though to a smaller degree, will ever be found, as the sunlight always reaches us through the corona. According to JnwELu’s above mentioned investiga ions this supposition proves to be well founded. Many solar lines have varying intensities and positions, so that Jnwnri deems them unfit for standards for GOO) very accurate determinations of wavelengths. And these are for the greater part the most prominent lines of the spectrum, especially the shaded ones ' JEWELL emphasizes the fact that all distinctly shaded lines in the solar spectrum show to a greater or less degree the following typical feature *). Within a broad, shaded, moderately dark background a much darker central absorption line contrasts rather sharply (Fig. 2). wee | | Mig. 2 Fig 3. Besides, the absorption curve often shows dippings close to the central line, as in Fig. 3, sometimes symmetrical, sometimes dissymmetrical. JeweLt aflirms that this is not an optical delusion, due to contrast, but a real phenomenon. He assumes, therefore, that the broad absorp- tion band is produced in the lower portions of the solar atmosphere and under a great range of pressure; that in higher levels radiation prevails again, producing a rather wide emission line ; and that finally in the highest parts, where the pressure is very much less, the sharp absorption line is produced. The position of this central absorption line with respect to the emission line is usually unsymmetrical, which is conspicuous in the case of 7 and A. The central line itself also varies somewhat in width upon different plates and its maximum of intensity is not always in the middle of the line. The displacement of this central line in #7 and A varies in magnitude, but, so far as has been observed, always toward the red with respect to the emis- sion line and the corresponding metallic line (in the are). Jewett concludes that the absorbing caleium vapour descends all over the solar surface with a velocity sometimes amounting to about 75 miles per minute. Upon the same plates showing strong dissymmetry in H and K, the shaded lines of other elements (/e, A/, Mg, Si) have been examined. The strongest iron lines and one aluminium line showed displacements of the same character as that observed in the case of 1) Astroph. Journ. XI, p. 236, 1900. 2) Jewett, “Certain peculiarities in the appearance of lines in the solar spectrum and their interpretation”. Astroph. Journ. Il, p. 99, 1896. ( 601 ) H and K, but to a much smaller degree and sometimes toward the violet, sometimes toward the red. Certain shaded lines of Wg and S, on the contrary, showed no evidence of a displacement, nor did the iron lines without considerable shading, the faint calcium line at 2 3949,056 and many other lines. If we admit no other explanation of line-shifting and -widening besides those, based on Doppier’s principle and on the effect of pressure and temperature, we arrive at very strange conclusions relative to the condition of the elements in the solar atmosphere. Not less surprising is, as noticed by Jnwni’), the small amount of the absorption in the shaded parts of the lines, when we consider the enormous depth of the solar atmosphere and the high pressure which must exist in the absorbing layers, for them to produce a broad absorptionband. By making various suppositions concerning the condition of the gases in the solar atmosphere, JeweLL succeeds in finding an inter- pretation of most of these astonishing facts. But it must be granted that his explanations include a greater number of arbitrary and mu- tually independent hypotheses than is the case with our explanations, founded as they are on selective ray-curving and readily deduced from that principle for each separate phenomenon, without intro- ducing new suppositions. Only the dark central lines of the Fraunhofer lines are to be ascribed, in our theory, to real absorption. Their shaded background of varying intensity we consider as an effect of anomalous dispersion of the not absorbed neighbowing waves. This selective scattering will be strongest in those places where the density-gradients are relatively steep, viz. in whirls in the deeper regions of the gaseous body. But some of the widely dispersed rays may be gathered by the corona owing to its “tubular: structure and be conducted along itg greater or smaller streamers. This will especially apply to the most strongly refracted waves, whose position in the spectrum is very close to the real absorption lines; thus pseudo emission lines are produced in about the middle of the pseudo absorption bands. *) 1, Astroph. Journ. Ill, p. 106. *) A most remarkable fact is that the shading of K, H, the iron-line A 3720.086 and of some other strong shaded lines is sometimes partially broken up into a series of faint nebulous lines, symmetrically situated about the central line. In each case the distance apart of the component lines increased as the distance from the center increased (Jewett, Astrophysical Journal 8, p. 51—53). It might have been predicted by our theory that we should meet with this phenomenon now and then. 602 ) Most likely Hane’s abnormal spectrum has shown us a ease, where these seeming emissionbands aequired an uncommon extent, We may therefore expect that a systematical investigation of solar spectra, photographed at different times, will afford all kinds of intermediate cases. It would be desirable, for the moments when the photographs are taken, to know form and position of the coronal streamers ex- tending toward the Earth. At all events the actual phase of the sun- spot period, with which the shape of the corona seems to be con- nected, should) be taken into consideration; and perhaps the simul- faneous observation of the photospheric reticulation, discovered by JANSSEN, May procure some evidence concerning the position of coro- nal streamers, and thus contribute to our knowledge of their influence on the Fraunhofer spectrum, Mineralogy. — * On the refractive index of rock-qlasses,” by P. Tescu : (Communicated by Prof. J. L. C. ScoroepER van DER KOLK). Of the group of the igneous rocks, the origin of which out of tluid red-hot condition we accept, the voleanic rocks constitute that subdivision, which includes the rocks, that as lavas have broken through the surface of the earth. The quick cooling at the atmosphere renders it possible that in these rocks part of the magma congeals amorphously, so that next to the minerals a rockglass appears, which constitutes either an infe- rior part or a prevailing one of the rocks. So in general this glass Let us consider a beam of light of an exactly defined wavelength belonging to the shaded background of an absorption line. This beam leaves the deeper layers of the Sun with a certain divergence. As it passes along a “tube” of the corona, its divergence will alternately diminish and increase, and on reaching the Earth it shows in the spectrum an intensity, depending on the divergence (or perhaps convergence) with which it has left the last traces of the corona. For a beam of light whose wavelength is only slightly nearer to that of the absorption line, the medium will have a considerably greater refraction constant, so that the rays of this beam, on their way through the corona, may make part of a bend more than the former ones. The beam may therefore arrive with a quite different degree of divergence and, consequently, of intensity. Thus, proceeding towards the absorption line from either side, we easily see that we must meet with a periodically changing intensity. Rays, corresponding to the middle of one of the so formed fringes, will have made one full bend more or less than the rays, belonging to the middle of the next fringe. If this interpretation be correct, the width and the number of fringes visible must prove to be variable. As far as I know, the observations made on this point are not numerous. May the proposed views serve to further the investigation of this interesting phenomenon. ( 605 ) consists of silica and metal-oxides. We may suppose that the silica, which is most likely to be the principal part, will also have a pre- valent influence on the physical characters of such natural glass. A determination of the specific gravity of the glass is made more difficult by the presence of many gas-bubbles. If this obstacle did not exist, the specific weight would be a better expedient for a quick temporary orientation than the determination of the refractive index, for which more instruments are necessary. With respect to the specific gravity it could be stated, that with these rocks where the value of the index the use of bromoform as liquid of Comparison neces- sitated and whose exponent proved to be greater than that of bromo- form (1,593), the specific gravity of the glass was still higher than that of bromoform (2,88). The small air-free, not to be isolated erains, still sank in this quid. Now I have tried to find out in how far the refractive index is dependent on the SiO, percentage. For that purpose 16 rocks have been. examined, forming a series of the most acid to the most basic magmas, which occur in nature. The result has been comprised in the following table: Harzburgite Harzburg, Harz MD, 24 1,630 Name | Origin SiO, | Index } Granite | Magurka, Hungary 72,65 | 1,500 Granite : Brocken, Harz Mountains 71,19 | 1,500 Granite Auvergne 70,62 4,500 Granite Korinitsch, Hungary 67,31 10 Quartzdiorite Adamello, Tyrol 66,58 1510 Syenite Plauensche Grund, Dresden 60 26 1,520 Klaeolite-syenite Ditro, 59,88 a5 25 Diorite | Hodritsch, Wungary | 59,57 1,525 Syenite | Ditro, 57,36 1,530 Augite-syenite | Monzoni, Tyrol 53,79 1,550 Chrysolitenorite | Radau Valley, Harz Mountains 53,64 1,550 Diorite | Auvergne 50,86 4970 Quartzdiorite | Dumkuhlen Valley, Harz 48,89 1,585 Basalt | Dyrafjord, Iceland 4850 1,590 Gabbro | Radau Valley, Harz 44,08 1,620 | | | | 6504 ) From this we see that a classification exclusively according to decreasing SiO, percentage, coincides with an increasing value of the refractive index. Apparently the metal oxides present have only little influence on that value, at least this influence falls within the limits of the errors of observation. A chrysolite-norite and an augite syenite with about the same SiO, percentage have also the same index, whereas the oxides, especially MgO are sure to be there in quite another relation, for in the chrysolite-norite the minerals containing Mg come strongly io the foreground. As regards the colour of the glass it will be almost wholly dependent on the iron-percentage. With the examined glasses the colour changed from light green to dark brown. Just as with isomorphous mineral series, as e. g. the enstatite-hypersteneseries, the dark colour most likely points to a greater iron percentage than the light one. The typical amorphous glassfracture can be easily distinguished at the splinters under the microscope. The fusion of the vock-powder took place in a gastlame in which compressed oxygen was blown. As an underlayer a cupel of chalk or bone-ash was used. But care has to be taken that the melted magma of the cupel remains isolated, because there is a chance that oxides of alealic earths will be absorbed by the cupel and in consequence the composition of the magma does not answer any more to that of the rock. This can be obtained by directing the point of the flame towards the middle; the upperlayer then fuses quickly to a little ball, which remains isolated by the underlaying rock-powder of the cupel. To control the regularity found in the independence of the refractive index of the SiO, percentage, two mixtures of the following composition were made: L. IL. SiO, 60°), 60 °/, Fe,0, 10 20 ALO,: 40 5 Cad 10 5 MgO) 5 10 K,0O,Na,O 5 =a Of both the mixtures the fused glass had the index 1.520; here we see again the prevalent influence of SiOQ,. At last some slags and melted minerals were investigated. ( 605 ) Composition. Index. SiO, 45,5 1,600 CaO 19,8 FeO bye SiO, 27,4 1,750 FeO 41,7 CuBi 0,2 Pb 115) Al,O, 0,8 ZO 21,8 MnO In this slag the ZnO plays the part of the MgO. When ZnQ is replaced by MgO, the index remains the same. Finally the index of the following minerals was determined: Quartz SiO; 100>/, 1,475 Chrysolite i A045 1,610 Orthoelase 1 65 1,485 The last mineral, the pure K.Al.silicate consequently does not. fit into the composed series. After mixing with some grains Fe,QO, (5—10 ,/°’ and fusing anew the index was raised to 1,510. The method described above can be of practical use for a quick determination of the SiO, percentage of slags from the refractive index with an accuracy of + 2 °/,. A word of thanks for the aid and advice to the Professors Dr. J. L. C. SCHROEDER VAN DER Kok and $8. J. Vermags Jr. may find a place here. Mineralogy. — “On an “Eisenrose” of the St. Gotthard.”. By G. B. Hocenraap. (Communicated by Prof. J. L. C. ScHRoEDER VAN DER KOoLk). Some time ago I tried to get a Hematite-streak with a so-called “Kisenrose.” I did not succeed however, for to my astonishment the streak was not red but black. Several explanations came to my mind : 1°. that the mineral was somewhat friable, which was the cause that the streak could not consist of the very finest particles. But in rubbing the black colour remained; only the outlines showed a reddish-brown tint. The same was stated with about 25 other pieces of the same finding-place. So that the explanation proved to be not the right one. 606) 2°. that the mineral contained Mn or Ti, since these clements have a great influence on the colour of the streak. But an analysis only produced little Ti and no trace of Mn, so that this explanation did not hold good either. 3°. that the mineral was magnetite. In its favour spoke the very distinct magnetism, stronger than hematite generally shows. I then consulted some literature, to see whether anything had been written before on the streak, the magnetism and the chemical com- position of “Eisenrose.”” DANa says ' St. Gotthard affords beautiful specimens, composed of crystrallised tables grouped in the forms of rosettes (Eisenrosen), and accompany- ing crystals of adularia. Dana calls this occurring Hematite, though he neither speaks of the chemical composition, nor gives any particulars about streak or magnetism. In the “Zeitschrift fiir Krystallographie und Mineralogie von P. GrotH” I found in Number 13 on p. 3801 a report by A. Carurern from StTrtvER’s account on ‘Pseudomorphose von Magnetit nach Eisenglimmer von QOgliastra in Sardinién”’, written in the Atti della Reale Accademia Dei Lincei 1886. Volume II, 2°. Semestre, p. 331. The report in question follows here : Die Hauptmasse der Stufe besteht aus einem grobkérnigen Mine- ral, dessen unregelmiéssigen Individuen von melhreren Centimetern Durchmesser fest mit einander verwachsen erscheinen. Jedes Korn zerfallt nach einer Richtung dusserst leicht in diimnste Lamellen. Harte 6, Pulver schwarz, stark magnetisch, schwer schmelzbar, in Salzsaure leicht léslich. Diese Eigenschaften kommen dem Magnetit zu. Das Gemenge erscheint ganz frisch, unverandert und urspriing- licher Entstehung. Dass es sich hier nicht um nach {111} blatterig abgesonderten Magnetit handelt, folgt aus dem Mangel jeder Spur von Spaltbarkeit nach einer anderen Richtung ausser jener einen. Die Lamellarstructur als Druckwirkung aufzufassen verbietet die Richtungsanderung der Lamellen in jedem einzelnen Korn. Nach des Verfassers Ansicht bleibt nur die Annahme einer Pseudomorphose von Magnetit nach Eisenglimmer.” So this appearance as regards streak and magnetism corresponds with the specimen examined by me. Through the absence of a chemical analysis it cannot be decided in how far the supposition is right, that he had to do here with a pseudomorphosis from Magnetite to Eisen- glimmer. 1) A System of Mineralogy p. 216. B ( 607 ) In the *‘Zeitsehrift der Geologischen Gesellschaft” Bd. 22, 1870 T found on page 719 in an article by G. vom Rarn the following statement *): “Pseudomorphische Massen von Magneteisen nach EKisenglanz. Farbe und Strich sehwarz, schimmernd auf dem Bruch, magnetisch. Das rz ist aber weder dicht, noch k6rmig (wie es sonst dem Magneteisen zukommit), sondern schuppig. Man erkennt sogar in einzelnen Drusen ganz deutlich die hexagonalen Formen des urspriinglichen Eisenglan- zes; doch auch diese letzteren haben einen schwarzen Strich. Ver- mutlich is demnach jene ganze colossale Schichtenmasse bei Vallone urspriinglich Kisenglanz gewesen”. So to this can be applied what has been remarked on Srriver’s article. Finally D. F. Wiser says *): Die Eisen-Rosen vom Pomonetto wirken sehr stark auf die Magnet- Nadel. Das Strich-Pulver is dunkel-réthlichbraun, beimahe schwarz. Die Wirkune auf die Magnet-Nadel is bei den Schweitzerischen Kisenglanzen gar sehr verschieden, sowie die Niianzirungen von Eisen- schwarz bis Stahlerau in ihrer Farbung. Bemerkenswerth scheint es mir, dass die Eisen-Rosen ohne autliegende Rutil-Krystalle immer die schwiirzeste Farbe zeigen, und dass dieselbe hingegend immer heller wird, je mehr Rutil auf den End-Flachen der Hisenglanz- Tafeln, ich méchte sagen, ausgeschieden worden ist. Die Mineralien, welche die Eisen-Rosen vom Pomonetto begleiten, sind: kleine, graulich-weisse Adular-Krystalle, kleine sechsseitige Tafeln von Tombackbraunen Glimmer und eime schmutzig griinlich-gelbe Rindenformige Substanz die vielleicht den Chloriten beigezahlt wer- den darf. Mein Freund, Hr Bererath Srockar hieselbst, hat die Kisen-Rose vom Pomonetto analysirt und wird hoffentlich néachstens das Resultat seiner Untersuchungen ver6ffentlchen.” However I could not find this promised analysis anywhere in literature, so that I decided to do it myself (1). For a good control the same analysis was made by Messrs B. H. van prr Lixpen (I) and G. W. Mauuén (111). The results of our investigations were as follows : ) Geognostischanineralogische Fragmente aus Italién, chapter VIL: Die Insel Elba, Zeitschr. D. G. G. 1870. *) Bericht fiber Mineralién aus der Scloweilz. N. Jahrb. 1854 p. 26. 41 Proceedings Royal Acad. Amsterdam. Vol. V, 608 I. II. IIT. Ke 69,94 69,13 69,50 a) 29,97 29.60 30,46 accompanying mineral 1,2 99,91 99,93 99,96 *) Reckoned for : Hematite Magnetite Fe 70 72,41 O 30 27,09. So that my conclusion is that we have not to do with Magnetite but with Hematite. The results of my researches are in consequence the following: Ist. That IT have had to do with Hematite with very obvious magnetism and a black streak, which in rubbing along the outlines shows a brown tint (which generally every black streak does) and not with a pseudomorphosis from Magnetite to Hematite. 2ed-— That where in literature of this occurrence of Hematite has been spoken, no analysis has been added, though the magnetism and the black streak have been observed more than once. 3. That it is desirable to convince oneself of the chemical com- position with every “Eisenrose”, which shows these characteristics. Physics. — ‘Contributions to the theory of electrons.” 1. By Prof. H. A. Lorentz. Simplification of the fundamental equations by the introduction of new units. § 1. If all quantities are expressed in electromagnetic units, as | have done in former papers, the relations between the volume-density o of the charge of an electron, the velocity v of its points, the 1) | here by have to mention that first the figure for the oxygen was determined by reduction in a hydrogen-current und weighing of the water absorbed by CaCl; that after that the figure for the iron was determined by dissolving the reduced mineral in dilute H,SO, and making a titration ot this solution (after reduction in a H,S-current and after removing the H,S by boiling in a CO, atmosphere) with a KMnO,-solution, of which 1 eM’ corresponded with 8,9 m.G. Fe. The presence of Ti was shown as follows: the mineral was melted together with KHSO,, the fused mass dissolved in co/d water. This solution together with H:0, gave the well-known orange colour of TiO;. Moreover after adding a little HNO, the Ti after having been boiled precipitated as white TO;. The accompanying mineral, which in microscopic examination proved to be adularia, was removed as much as possible, ( 609 ) dielectric displacement 9 in the aether, the current | and the magnetic foree § are as follows '): dir d= 0, ‘ do li ) 0 == -t- aly Hy) = Ot le — =p +e, div h == 0 ’ roth =4al—4a(d+or), Aa crotd = — h F where ¢ is the velocity of light in the aether. To these equations we must add the formula fH—4aec?d4+ [v.b] for the electrie force, i.e. the foree, reckoned per unit charge, which the aether exerts on a charged element of volume. The equations take a somewhat more regular form if we express o, >, ft and f in. electrostatic wnits (preserving the electromagnetic unit for b) and a further simplification is obtained, if, instead of the units for charge and magnetic pole that are usually taken as the basis of the electrostatie and clectromagnetic systems, we choose new ones, 4a times smaller ®). Introducing both modifications, we have to o d N replace 9,3, 1 by , f by «eV 4a.f, because this ~ (V4a’ eV 4a’ eV 4x letter must now represent the foree acting on the new unit of charge, and likewise § by V4ar.b. This leads to the equations VN ea ie es a as ae ae ine ees (8) Reais ie (aoe Mac ib oun eeeie (1) Of (Snowe sen aes oR) GE As cries a bie Gale = eet eh (iV) th : l aye i ro = oe =e ek . . * . ‘ (V) 1) See my Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Kérpern. 1 shall again suppose that all quantities are continuous functions of the coordinates, so that e.g. the density ¢ will be regarded as passing gradually to the value O, which it has outside an electron. With the exception of the letters, the nolations are the same as in the just mentioned treatise. The sealar product of two vectors a and b will be denoted by (a.b), the veclor product by {a.b|]. The axes of coordinates ave supposed to remain at rest, relatively to the aether. *) This change has been warmly advocated by Heaviswe. The umts [ shail now use are those that have been ailopted for the Mathematische Mncyclopddie, 41% rotd - 0), -c- 6 Sia"aoalamer anes (V1) t d+ TOR Ons > Wel ‘awe, tae (VIL) In connexion with the last formula it may be remarked that 0 is the electric force that would act on an immovable charge. The electric energy per unit-volume is given by d ey } | Dasha sy? Waa Cee ” the magnetic energy per unit-volume by ge Ht, hi lo ae Da and Poyntine’s flux of energy by 0 [td ie vig bo ee (X) We shall further write (@’ for the total electric and 7" for the total magnetic energy of a system. The equations (IV) and (V) suffice for the determination of the magnetic force 6, as soon as the current [is given in every point. Wi, is then known by (IX) and 7’ follows by integration. In this sense, every motion of electricity may be said to be accompanied by a definite amount of magnetic energy. Scalar potential and vector-potential. § 2. The equations of § 1 apply to every system in which charged matter moves through the aether, whether the charge be confined. to certain extremely small parts of space (electrons) or otherwise distributed. Moreover, the motions may be of any kind ; the electrons may have a pure translatory motion, or a rotation at the same time, and we may even suppose their form to change in the course of time. For the validity of the formulae it is however required that each element of volume whose points move with the charged ‘matter should preserve its charge, though its form and dimensions may change. This is expressed by the equation (11) and it is on this ground that the electric current !, as defined by (LID, (the resultant of the displacement-current >» and the convection-cur- rent @y) may always be said to be solenoidally distributed, so that diol: If now the motion of the charged matter is given, the electro- magnetic field in the aether, within and without that matter, has (- Galina) to be determined by means of (1)—(VI), a problem that may be reduced to equations of the form 1 o*u Ayn — — —— SS a ew es (1) c? Oe in which @ is a known, and yw an unknown function of x,y, 2, ¢. Let o be any closed surface and 7 the normal to it, drawn out- wards. Then, if the equation (1) holds in the whole space .S, enclosed by 6, we shall have for the value of y in a point P of this space, at the time f, ea 1 mil A 1 o((0{ on ; 0 1 é : ae ae ee -Alicrel pee ee (<) ve: - () Here the first integral extends over the space SS and the second over the boundary surface 6; 7 is the distance to P, and the square brackets serve to indicate the values of the enclosed quantities for the time ¢— —. : Let us now conceive the surface 6 to recede on all sides to infinite distance and let the circumstances be such that the surface-integral in (2) has the limit 0. Then, ultimately: ul ad (PSS { Sale| el sae oy stator at tame ks (3) Am, ise where the integration must be extended over infinite space. § 3. Equations of the form (1) may be deduced from the formulae ()N—(VI) in many different ways; they may e.g. be established for each of the components of 2 and *.*) The solution is however ob- tained in a simpler form *), if one introduces four auxiliary quantities, a scalar potential g and the three components @,, a,, a. of a vector- potential a. These quantities satisfy the equations 1 0p Ag — — aS c? Od? M 1 074, 1 1 074, 1 z ¥ ep ues th seme aaa ca gO ee so that, with the restrictions that are required if (8) is to be true, we may write 1) Lorentz, La théorie électromagnétique de Maxwett et son application aux corps mouvants, Arch. néerl. T. 25, p. 476 1892. 2) See Levi Ctvira, Nuovo Cimento, (4), vol. 6, p. 93, 1897; WiscHERT?, Arch. néerl., (2), T. 5, p. 549, 1900. s/f l ft ! | jov,|dS , a, | Jo v,| dS, ete. r “44 ‘ Axe, bre, After having found g and a, we may determine the dielectric 1 displacement 0 and the magnetie foree ) by means of the relations *) ] — T= Grad: y (Sc ea Te ee b= 70h. be Se a ee (5) It_is to be remarked that the two potentials are not mutually independent; they are connected by the equation Hi ; die VSS = Qi SI ee, hs, Theorems corresponding to the principle of D ALEMBERT and that of least action. § 4. The physicists who have endeavoured, by means of certain hypotheses on the mecanism of electromagnetic phenomena, to deduce the fundamental equations from the principles of dynamies, have encountered considerable difficulties, and it is best, perhaps, to leave this course, and to adopt the equations (I)N—(VII) — or others, equivalent to them — as the simplest expression we may find for the laws of electromagnetism. Nevertheless, even if we prefer this point of view, it deserves notice that the fundamental equations may be transformed in such a way that we arrive at theorems of the same mathematical form as the general principles of dynamics. This has been done especially by ApBRanwaM in his important paper “Principien der) Dynamik des Elektrons’” *). The considerations in this and the two next paragraphs agree with those of ABRanAM, though presented in a form differing from his. We shall consider a system of electrons moving in the infinitely extended aether, and we shall fix our attention on the different states of this system, the aether included, that succeed each other in the course of time in any electromagnetic phenomenon. From every one of these states we shall pass to another, differing infinitely little from it, and which’ we shall call the varied state. The variation or “virtual change” will consist in infinitely small displacements 9 of 1) 1 shall write grad » (,gradient of .”) for the yector whose components dg dp o¢ are — = Oa’ dy ; 02 *) Drupe's Annalen, 10, p. 105, 1903. the points of the electrons, accompanied by infinitesimal changes in the dielectric displacement. We shall write dd for the difference, in a fixed point of the aether, between the dielectric displacement before and after the virtual change, the sign of variation d having>a similar meaning when it precedes other symbols representing the value of some quantity in-a definite point. If it is affixed to a letter representing a quantity belonging to the system as a whole, such as the total electric energy (7, it will simply serve to indicate the difference between these values in the original or real and the varied states. The variations to be considered are not wholly arbitrary. We shall limit our choice by supposing in the first place that each element of volume of an electron preserves its charge during the displacements q; this is expressed by the relation Go. aw (poy Ons ete a Were a 82) which may be compared to (II). In the second place we shall suppose the variations of ) not to violate the condition (1). In virtue of these restrictions the vector dd +04 will present a solenoidal distribution. Indeed, we see from (I) that div d= J 0, and here we may, according to (7), replace the right-hand member by — dw (9 4). Let us now conceive 4 and Jd» to be chosen for every instant 4 so that they vary continuously with the time. Then, in order com- pletely to define the succession of varied states, or what we may call the ,varied motion” of the system, we shall suppose the varied positions of the points of each electron to be reached at the same instants at which these points occupy the corresponding original positions in the real motion; we assume likewise that, in every point of space, the varied dielectric displacement exists at the same moments as the original one in the succession of real states. By this the varied motion of electricity is entirely determined ; indeed, since we know the velocity of matter and the rate at which > changes, we are able to state what has become of the convection- current, the displacement-current, and also of the total current [ The first thing we have to do will be to express dt in q and dd. Of course we may be sure beforehand that the distribution of both the new | and the variation J1 will be solenoidal. This must neces- sarily be the case, because we know 1s'. that, in the states that succeed one another in the varied motion, each volume-element of O14 an electron retains its charge, and 2°¢. that the condition (1) is con- tinnally fultilled. § 5. Let us begin by considering dv,. This is the variation in a fixed point of-space, Therefore, if (d¥,) is the variation for a definite point of an electron, we shall have Ovr , Ov, Ov, CFs) = We 1 qa Ow r ay Oy T 4s Oe As to (dv,), it is easily shown to have the value fo.) djy dv.) = —, (de, lt pn dq, : 5 ss if we understand by the rate at which g, changes for a definite aed st: 0 q point of an electron. Comparing this to “5 or qr, the velocity of t change in a fixed point of space, we get 09, Oqe Oqx : + Dy = Eis Ow “ Oy Oc These equations, combined with (7), lead us to (dy,) = ag -t- Vx dl. = J (®% + 9 Yy) = ddr + O Dd; + ty SO = : ; OJ Ol» Ol = dd; + Oqr + Otzr=- + Oty — + OX =- — On “ Oy 02 0 Wr 0 Yer 0 Ur Vi =~ On See a Oy By =P Seca ee ba ee or, if we add to the second member the first member of (11), multi- plied by q,, after some further transformation, J sg (Sd. + 0 qu) + 9 Ye Of +oy 4: + ov- One — », div (oq) — x Ot x a Bo Sin Ou Fiat y dy s 5 0z fad ‘ Ov, Ov, Ov, 5 Si tuk Mai earn) Li eae = 4 (dx + 9 4x) + - [9 (Gx vy — qy%x)] — 2 19 (4z Be — qe Y=)]- Here we may remark that the two last terms taken together repre- sent the first component of the “rotation” of the vector whose com- ponents are Q (Gy Bz — Jz By): O (Gz Vx — Gr Vz), O (Ax Vy — Ay Vx): and that this veetor is precisely the vector-product, multiplied by e, of 4 and »v. After having calculated dl, and dl. in the same way as dl;, we may combine the results in the formula yy a i (dd | 04) + ret jo [q-wvf} et eek ogee (0) i) What has already been said about the solenoidal distribution of J) is confirmed by this equation. The two vectors represented on the right hand side both have this property, the first by what we know of the vector do + 03, and the second on account of the mathema- tical form in which it appears. § 6. We may next proceed to determine the variation d 7’ of the magnetic energy. In doing so we shall start from the assumption that the varied motion of electricity involves a definite magnetic energy '), to be determined as stated at the end of § 1. The formula leads immediately to éT = | (61 She + by by + §- dh.) dS = | (b - dh) dS, Where the integration covers all space. The same will be the case with the other volume-integrals appearing in the following transform- wions. If an integration is performed, or if the process of inte- gration by parts is applied, one obtains integrals over the infinite surface which we may conceive as the boundary of the field of inte- gration. These surface-integrals however will be supposed to vanish. We begin by writing vof a instead of §, as may be done in virtue of (5); and we shall next integrate by parts, keeping in mind. that, on account of (VY), 1 rot Jf) = — dl. Fi The result is at * 1 . J Jew a.dh)dS= foc . rot Sh) dS = - fo SOM CIS G =o (CQ) e or, if we substitute for dl its value (8), BS arene: IN abelian (6. 1\ 8 i ac Jd + oq) |dS + a. rot} oly. > JdS. (10) (Cy OF | Wy Cm S | Ny Using (4), we may put for the first term ') This assumption only means to define the value of 7 we shall assign to the wholly fictitious varied state. O16.) l d c dt, 1 . fix fa t+ og} ds fia. tao { eq})dS= l d . . =—- fia-far Loq})ds EJ (ta Leg} dS4 { (orate. too-+eqhs: (11) e dt * . Now, it appears from (9) that ore ~flr-tar Liggi) aS; «en e is the change the magnetic energy of the system would undergo, if we gave to the current the change J? + 99. We shall write d’l for this variation of the current, and d'h, d' 7’ for the corresponding variations of § and 7. As to d’l, it may be defined as the current that would exist if the changes represented by 9 and dd were accom- plished in unit of time. On the other hand, {(>- oo) as is the variation of the electric - energy {7 and the last integral in (11) is O, because the vector Jd + 0} is solenoidally distributed. Thus, the first term in (10) becomes dd' T . re - a ae + f(-ea)as C For the last term in that equation we find, integrating by parts, he fe Lt 1 fee a.fo[qy.v]})dS= —few -Lq-0]) a5 = “fe (q.[v.6]) dS, C € € so that finally dd'T % 1 Cl < oo a+ fol : }» - ~tv.5i{ Jas Now, the equation (VII) shows that the last term is precisely the work done, during the displacements 4, by the electric forces exerted by the aether on the electrons. Writing d/) for this work, we have r dd'T gE = 6 (T—U) — ——.... . .. . « (19) dt an equation closely corresponding to D’ALEMBERT’s principle in common dynamics. § 7. The motion of the electrons themselves may be determined by ordinary methods; it will be governed by the electric forces whose work has been denoted by d/, together with forces of any other kind that- may come into play. We shall confine ourselves to those cases in which these latter forces depend on a potential energy (7,; then the total virtual work of all forces acting on the ¢ G1 electrons will be dH dl’,. Moreover we shall ascribe to the electrons a certain kinetic energy 7, which they have by virtue of their mass in the ordinary sense of the word. Should there be no such ‘true’? mass, we have only to put 7) = 0. One of the forms that may be given to the variational equation of motion for a system of material particles is dd'T. JA = —— — dT’, ( J7, being the change of 7), if we pass from the real motion to some varied motion in which the varied positions are reached at the same moments as the original positions in the real motion, dA the virtual work of the forces, and d'7 the increment that would be acquired by the kinetic energy 7), if variations, equal to the virtual changes of the coordinates, were imparted to the corresponding velocities (the coordinates themselves being kept constant). For our system of electrons dA = JE — JU, ; hence, if we use for d/ the formula (13), ds(THT,) d\(7T 4+ 7,)—-—(U+ Uj — == 0) We shall finally multiply this by dé and integrate from ¢, to ¢,. In case both the displacements y and the variations dd vanish at the limits, we find “| (7 4+ 7,) —(U+ U,)i dt = 0 This is analogous to the principle of least action. § 8. In what precedes there has been question of the variations of the energies 7’ and (7, taken for the system of electrons together with the surrounding aether, which extends to infinite distance. Similar though somewhat less simple results are obtained, if one understands by 7’ and Cl” the magnetic and the electric energies, in so far only as they belong to the space within an immovable closed surface 6. In what follows it is to be understood that this surface may have, relatively to the system of electrons, any position we like; for simplicity’s sake however we shall suppose that it cuts none of them, so that, in every point of 6, the density @ =O. As to the virtual variations, determined by q and dd, they need not at all be confined to the part of the system within the surface. We shall denote by 2 the normal to the surface, drawn towards the ( 618 ) outside, and by aoa. re the angles between this normal and the positive axes of coordinates If now we repeat the above calculations, we have to do with volume-integrals confined to the space within 6, and every integration by parts will give rise to a surface-integral. Thus, to the last member of (9) we shall have to add the term ° COS A, COs ie vox Vr } Qe, Ay, Ae HEAR ee | Ja A In dé s dh,, di), dh- and the value of (12) will no longer be d'7’, but 7°. COR rh COs i. ros yr or. — Nzy. gs, hts RC ee — OL fis = Sn da. (14) d' br, diby, nO De The last integral of (11) becomes | (grad Q. prot d'bi) a5=c fore grad y- J'))dS— “| grad & - Sb |, do (15) Here the first term on the right-hand side is 0, since rot grad g=0. The transformation of the last part of (10) remaining as it was, as we have supposed @=O in all points of the surface, we finally find for the second member of (13) the additional term ; 0 | — fa. dh], + y [a. do], + ¢ lorad @ - Wolfs, v ( But. on account of (4), ) - Ja . Syn -}- e [grad yp - S'S |n ——f (Ady | righ te = fas ae \ 4+ fa.d'yJn + ¢ [grad gp. dd], = ay Pas feds Oe ee SG FY |. e[d. Abn. We get therefore, instead of (13), (aides Pte ode } jn=¢(T—U) = i Pie eee heh te ete ei 5 JE = d\ ) tt | if | at 6 |. [>. d'b] \ 6 (16) § 9. The following are some examples of the applications that may be made of the formulae (13) and (16). a. Let the virtual changes in the position of the electrons and in the dielectrie displacement be proportional to the rates of change in the real motion, i.e. let EV Ss—€D, ( 619 & being a constant infinitely small factor. From these assumptions it follows at once that d' (=e, daly al Now the magnetic energy may be considered as a homogeneous quadratic function of the components of the current; it will therefore change in ratio of 1 to | + 2¢, if the current becomes (1 + ¢)'. Thus: Pe — eT We may also infer from our assumptions that the position of the electrons and the values of d are, in the varied motion at the time f, what they are in the real motion at the time ¢—-+ ¢, so that the only difference between the two motions is that the one is in advance of the other by an interval e«. In this way it is seen that dT GNOE Oh adh i R VU. : a) = —- Se) lt dt Ot Of Substituting these values in the equation (16), we get, after division by ¢ and multiplication by 7, denoting by d/ the work done by the electric forces in the real motion, during the time <7, » dB=—d(U-+ U)—ede{ [dba do. eee Ness CLE) This is the equation of energy. The last term represents the flow of energy through the surface. b. Applying (17) to a single electron, whose motion is a translation with variable velocity along a straight line, one may calculate the force with which it is acted on by the aether, and which, under certain simplifying assumptions, is found to be proportional to the acceleration and directed oppositely to it. The quotient of this force, divided by the acceleration, may appropriately be called the e/ectro- magnetic mass of the electron. ce. There will likewise be a force proportional and opposed to the acceleration, if the latter is perpendicular to the direction of motion. In this case however, of which the uniform motion of an electron in a circle furnishes the simplest example, we must recur to the equation (16), in order to determine the force. The surface 6 Waly be supposed to lie at infinite distance and the virtual displacement must be taken in the direction of the acceleration. The ratio of the force and the acceleration may again be called the electromagnetic mass, though, except for small velocities, its value is not equal to that of the corresponding ratio in the case /. In both cases the result agrees with what has been found by ABRAILAM, 620 Ponderomotive action on «a system of electrons. § 10. A’ virtual change of a very simple kind is an infinitely small translation of all the electrons, combined with what we may call an equal translation in the same direction of the whole electric field. Applying to these variations which we give as well to the part of the system outside the surface @ as to the part enclosed by it the equation (16), one may caleulate the resulting force exerted by the aether on the electrons within the surface. This force may be shown to consist of two parts, the first of which is the foree with which we should have to do, if the surface 6 were subjected to the stresses in the aether, whose components have been already determined by Maxwenn, whereas the second part is determined by the rate of change of a certain integral, relating to the space S within o. The latter part will therefore vanish if the state is stationary, and may be left out of account if, for periodic states, we wish only to know the mean value of the resulting force, taken for a full period. I need not here work out the formulae, having formerly deduced the result in a more direct way. The components of MAXWELL’s stress are 1 (02 — d= 02) = [t= fy — 6.9 ete. | ; \ (18) Xy =e b, ES) ‘F. b, . ete. and the just mentioned volume-integral is Bey eS et dS, S, being the flux of energy in the direction 4, for which we seek the resulting force. Thus, the resulting force in the direction of is given by c? dt > | y4—2¥) dS = y%.—2¥,)do— z fwe.—-€) as.) (en) . . iret § 12. Another consequence of the equations (20), analogous to the well known virial-theorem in ordinary kinetic theory, will perhaps be thought of some interest. In order to find it, we have only to add the three equations, multiplied by w,y,2, and to integrate the result over the space |S, within the surface 6. Transforming such BOING: he eae : terms as | es dS by means of partial integration, we find fia | (Se 4 Yy + Zz) dS = . a | Qe Eg ee) an ed 1 oes BS < == ie Be it 23 Re oe crete [Sex + €,y + Ezz) dS. . (22) For stationary states the last term will vanish, so that, if we substitute in the term preceding it the values (18), [ve + Yy + Zz) dS =|% #+YVYny+%4,2do+ 74+ UV. a Particular cases of ponderomotive action. § 13. In a large variety of cases, in which the system of electrons is confined to a space of finite dimensions, the electric and magnetic intensities in the surrounding field become so feeble at great distances that the surface-integrals in 19) and (21) approach the limit O, if the surface 6 moves to infinite distance. Moreover, the volume- integrals will vanish if the state is stationary, We then come to 622 ) the conclusion that the resulting force and the resulting couple are 0 for the whole system. If the system consists of two parts A and 2, Wwe may express the same thing by saying that the total pondero- motive action on one of these is equal and opposite to the total action on the other, ; Of course this will be equally true if, for a system whose state changes periodically, we have only in view the mean ponderomotive action during a full) period. Thest® theorems are useful whenever the phenomena in one of the parts, say in vf, are not well enough known to permit a direct cal- culation of the force acting on this part of the system. Lf the pheno- mena in 2 are less complicated, so that we encounter no difficulty in determining the force or the couple acting on this part, the action on A will be found at the same time. We may apply this in the first place to well-known experiments on electromagnetic rotations. Let us consider a cylindrical magnet, touched in’ two points of its surface by the ends of a conducting wire IW. Let this wire be the seat of an electromotive force, producing’ a current that flows through J and through part of the magnet. The ponderomotive forces acting on the wire are known with certainty and may easily be deduced from the formula (VID; they produce a couple, tending to turn the wire about the axis of the magnet. Without entering into any speculations concerning the motion of the electrons in its interior, we may infer that the magnet will be acted on by an equal couple in the opposite direction. Of course this reasoning must be justified by showing that the surface-integral in (21) is really O, if it is taken for a surface at infinite distance. This is readily seen to be the case, if we keep in mind that, at great distances, the magnetic force produced by the system varies inversely as the third power of the distance, and that the intensity of the electric field, if it exist at all, will certainly contain no terms diminishing more slowly than the square of the distance. § [4.1 shall choose as a second example some experiments, lately made by Wrrrrnkab') for the purpose of testing a consequence of MAXWELL’s theory that has been admitted by many physicists and is unavoidable in the theory of electrons, viz. that a ponderable dielec- tric, which is the seat of a vanable dielectric displacement, and therefore of a displacement-current, when placed in’ a magnetic 1) Wurrengap, Ueber die magnetische Wirkung elektrischer Verschiebung, Physi- kalische Zeitschr., 4, p. 299, 1903, (623 ) field, will be acted on by a similar force as a body carrying a con- duction-current. In| Wuirrunan’s apparatus two cylindric metallic plates, having the same vertical axis PQ, formed a condenser, in which a rapidly alternating electric field was maintained; at the same time alternating currents were passed through the horizontal windings of a circular coil, surrounding the condenser; the axis of the coil, which is at the same time the axis of its magnetic field, coincided with PQ. A sensitive torsion-balance was suspended by a wire passing along the axis of the instrument; the ends of the beam carried each a piece of some solid dielectric, so that these two equal pieces hung, diametrically opposite each other, in the air-space between the condenser-plates. The two fields, the electric and the magnetic, had exactly the same period, being produced by the same alternate current-machine ; besides, the arrangements were such that there was a phase-difference of a quarter period between the two fields. Thus, at the instants at which the magnetic force had its maximum values, the rate of change of the electric field and conse- quently the intensity of the displacement-current was likewise at its maximum. Under these circumstances a sensible couple acting on the dielectric was expected, but no deviation of the beam, attributable to such a couple, could with certainty be observed. We may remark in the first place that in Wuirenrap’s formula for the expected effect, the specific inductive capacity A’ appears in the numerator. If this were right, a couple would act on the aether between the plates itself. According to the theory of electrons, as here presented, ponderomotive force acts only on the electrons contained in ponderable bodies, but in no case on the aether. The theory therefore regards every ponderomotive action as due to the dijference between the properties of the body acted upon and the aether; it can lead to a formula containing in the numerator A—1, but never to one, containing, instead of this factor, the coefficient AC itself. In the second place Wuirrnnap has overlooked a circumstance by which the effect he sought for must have been, at least for the greater part, compensated. The compensation may be shown to be complete if the properties of the dielectric used differ from those of the aether to so small extent, that quantities which are in this respect of the second order of magnitude, i. e. of the order (A—1)?, may be neglected. If this may be done, the ponderomotive action on a ponderable dielectric, placed between the condenser-plates, may be considered not to be altered by the presence in the field of a second or third piece of the same dielectric. Now, the two bodies suspended at the ends of WHiITkEHEAD’s torsion-balance may be taken to have been parts of a 42 Proceedings Royal Acad. Amsterdam. Vol. V. 624 ) complete dielectric ring, bounded by a surface of revolution with the axis PQ. Moreover it will be safe to assume that the action on the two bodies which it was sought to observe, did not depend on their relative positions with respect to the wires leading to the condenser- plates, and remained therefore the same, in whatever position the torsion-balance was turned. If this was the case, the action on a body that is the 7" part of the ring (being cut out of it by two planes passing through the axis) must have been the n> part of the couple, acting on the complete ring. Consequently, it will suffice to show that the effect is 0, if the experiment is made with a complete dielectric ring. § 15. For simplicity’s sake we shall suppose the condenser-plates to be united by a wire W and their alternating electric charges to be produced by a periodic electromotive force in this wire. As to the currents in the coil, they may be regarded as due to electromotive forces of the same period, acting in the windings themselves; indeed, the action on the dielectrics can only depend on the magnetic field and not on the way in which it is produced. For this same reason it is allowable to ascribe to the windings so small a resistance that they do not carry any appreciable charges. Then no other but electromagnetic forces will act on the windings of the coil and these cannot give rise to any couple about the axis PQ, because such forces are perpendicular to the elements of the windings. By the theorem of § 13 the couple acting on the torsion- balance must therefore have been equal and opposite to the moment of rotation, acting on the condenser-plates and the wire HW. It remains to show that this last moment has been 0. I shall denote by I the electromotive forces acting in the connecting wire IV, by IL those existing in the windings of the coil, and I shall distinguish by the suflixes 1 and 2 the states arising from these two causes. Let us indicate by A, the charges of the plates and the currents in these and the wire J], in so far as they are due to I, and let A, have the same meaning with respect to II; also, let F, and F, be the electromagnetic fields excited by the two causes. In each of these fields there will be an electric force } (acting on charges that are in rest), as well as a magnetic force }; in virtue of the first, the field will exert a ponderomotive force on the charges of the plates and in virtue of the second on the currents, one of these actions being determined by the first, and the other by the last term in the general equation (VII). If we denote by the symbol (/, A) the couple acting on the plates and the wire, in so far as it is due ( 625 ) to a field F and a state A of these bodies, the two actions we shall have to consider may be represented by (Pes AS and (Ho, 21): The first of these is readily seen to be 0. Indeed, the magnetic field, produced by the forces II, though modified by the presence of the dieleetrie ring, is symmetrical around the axis ?Q. Therefore, if the periphery of the condenser-plates is nowhere interrupted, the state A, will consist in circular currents in these plates, without any electrie charge. It is impossible that the field /’, should, by its action on these currents, give rise to a couple, since, whatever be the nature of this field, each element of the stream-tubes will only be acted on by a force perpendicular to its length, In reality the case was somewhat different, each condenser-plate being cut by a vertical slit. There must have been equal and opposite charges at the edges of each slit and the field /’, must have acted on these charges, in virtue of the electric force existing in it. These forces may however be supposed to have annulled each other, because the distance between the charges on the two edges was very small. § 16. The action (/,, A,) is therefore the only one that remains to be considered. Now, in the state A,, the plates of the condenser were the seat of charges, whose amount was modified by the influence of the dielectric ring, and whose alternations were accom- panied by currents in the wire WV and in part of the plates them- selves. In so far as they are currents of conduction, i. e. in so far as they consist in a motion of electrons, these currents are evi- dently unclosed. We may decompose the whole system of them into infinitely thin stream-tubes, the tubes being all thronged together in the connecting wire, and widening out in the plates, at whose sur- faces each stream-tube ends in two elements of surface. Let S be one of the stream-tubes, G the end of it on the outer, and #7 that on the inner plate, ¢ the charge in G, — e that in //, de 23 ae 23) dt \ the current in the tube in the direction from H towards G, and let us consider the action (/’,,.A,) only in so far as it depends on this current ¢ and on tbe charges e and — e. In the first place there will be an electromagnetic force on the tube S, owing to the current 7 The couple arising from it depends on the course of the magnetic lines of force im the field /’,; it is most easily found by remarking that its work during a complete 4% 526 ) revolution of S about the axis ?Q is numerically equal to the product of by the number of lines of force that are cut by S. These lines c are precisely those that are intersected by the surface described by S in its revolution, a surface which may have different forms, accor- ding to the form of the wire HW, but has at all events for its boun- daries the circles described by the points G and HH. Let N be the number of these lines, taken positive if the middle one of them passes upwards along PQ, and let us take as positive directions for the rotation and for the couple the direction corresponding to the upward direction. Then, for a full revolution in the positive direction, the kes work of the couple will be —-—7.V, whence we find for the couple c itself te See MEY ERA ti ch 226c If this were all, we should indeed come to an effect such as was expected by Wuireneap. We must however keep in mind that there can never be a variable magnetic field without electric forces. Such forces, represented in direction and intensity by the vector >, will exist in the field /,, the lines of electric force being circles around the axis PQ. We must therefore add to (24) the couple arising from the action of the field on the charges e and e; its moment may again be found by considering the work done in a complete revolution in the positive direction. The force on the charge e being ed, its work is equal to the product of e by the line-integral of > along the circle described by G. Similarly, the work of the force acting on the charge — e in H is the product of — e by the line-integral of > along the circle described by H, or, what amounts to the same thing, the product of + e by the line-integral for this circle, if it is taken in the negative direction. Now, if we follow the circle G in the positive and the circle H in the negative direction, we shall have gone along the whole contour of the surface described by the stream-tube S, in a direction corresponding to the positive direction of the magnetic force. Hence, by a well known theorem, of which the fundamental equation (VI) is the expression, the sum of the two line-integrals by which ¢ must be multiplied, will be and the couple to be added to (24) will be given by avi 2 2 dt” Taking into account (23), we find for the total couple 1 “yy aN 1 d(eN) ey) = rene Since this is the rate of change of a periodic quantity, the mean value will be 0, as above asserted. The above somewhat complicated reasoning has been used in order to avoid the difficulties arising in a closer examination of the phenomena going on in the ponderable dielectrics. The result may however be verified by making suitable assumptions concerning these phenomena. It will suffice for our purpose to replace one of the dielectric bodies by a single pair of electrons A and 4, the first of which is immovable, whereas the second may be displaced over an infinitely small distance, in a radial direction, by the electric forces of the field /’,. We shall denote by e and + e the charges of A and B, by 7 the distance of A to the axis, by s the infinitely small distance A 4, and we shall write §- for the vertical component of the magnetic force in the field #, and D for the value of the delectrie displacement in this field at a distance 7 from the axis. We shall take the positive directions as follows: for s outwards, for §. upwards, and for D along the circular line of electric force im a direction corresponding to the positive direction of §-., i.e. in the direction of a positive rotation about the axis. . as Now, owing to the velocity — of the electron 4, there will be, € according to the formula (VII), a force (7 d. Ss Chest acting on this electron along a circle about the axis, and producing a moment @ ds ee G aca (24') This is the couple of which Wurrennap has sought to prove the existence. It is however annulled by the moment arising from the action of the field #, in virtue of its electric foree D. For the particle A this moment is —erD and for the particle 6 it is obtained if we replace —e by +e, 628 ) iaking at the same time the value of 7D at the distance 7-+-s from the axis. The algebraie sum of the two moments will therefore be 0 es (rD) or and for this we may write e Of - —— 87 _, Fd MG a een 4 ‘ ot ‘ ) since, by the equation (VI) 0 1 ob- DD) = — =r —, ay c Of For the sum of (24’) and (24’’) we may write e d (sh) aaa ’ c dt whenee if is immediately seen that its mean value is 0 for a full period. Physics. — Methods and apparatus used in the cryogenic laboratory. III. Baths of very uniform and constant temperature tn the cryostat (continued). A cryostat of modified form for appa- ratus of small dimensions. IV. A permanent bath of liquid nitrogen at ordinary and at reduced pressure. V. Arrange- ment of a Burcknarpt-WEIss vacuum-pump for use in the circulations for low temperatures. Communication N°. 83 (con- tinued) from the Laboratory at Leiden. By Prof. H. KaMERLINGH Onnes. (Read February 28, 1903). Ill. § 6. A cryostat of modified form for apparatus of small dimensions. If the cross sections of the apparatus that is to be immersed into the bath are small, vacuum glasses may be profitably used in the construction of the cryostat. For, vacuum glasses of comparatively small diameter can then accommodate the stirrer and the temperature indicator in addition to the measuring apparatus. Plate IV shows a cryostat of the kind, viz. the one used in the determinations by HynpMan and myself on the critical state of oxygen. Obviously the arrangement could be much simpler, as it was not necessary to watch the liquefied gas streaming from the jet or to use the generated cold vapour for the cooling and as no particles of dust from the leads had to be feared, a filter was not required. (Comp. Comm. 51, Sept. °99 § 2. Y, p. 12). The principles for obtaining a uniform con- stant temperature, laid down in the previous communication have all been applied in this arrangement, a vigorous stirring with the ring shaped valved-stirrer, the adjustment at the desired temperature to the indication of a sensitive indicator by regulating the pressure at which the liquid boils while reading a differential oil-manometer made for the purpose, and lastly the determination of the temperature of obser- vation as corresponding with the mean obtained graphically of the readings of the thermometer (as in § 5). Plate V shows in detail the differences in the construction between this form and the former plates I and II (and also Plate I Comm. 51), the parts unaltered remaining are indicated by the same letters as before, and the modified parts by letters with accents, while entirely different parts have new letters. The height of the vacuumglass 5’,, is so chosen that the liquefied gas cannot be blown out; and the glass itself has been silvered, leaving open two opposing windows J',. Through these the pheno- mena in the experimental tube may be watched, and from the position of an aluminium wire fastened to a cork float the depth of liquefied gas may be derived. If the insulating power of the vacuumglass is not perfect, condensation of moisture on its outer wall may be avoided by placing it into a beaker filled with alcohol, which if necessary is renewed when cooled. Thus the same principle is followed which was employed when necessary in the case of the cryostat (Comm. 51) when the windows had to be kept clear and where hot dry air was drawn through the outer spaces of the observing glasses (V’,, see Pl. I of this Comm. and for the details pl. I Comm. 51). The vacuum glass and the auxiliary apparatus are supported by a copper cover N',,, with its rim tinned to protect it from the action of the india-rubber ring N',, and which, like the cryostat of § 1, has been coated with polished nickel-paper. To this cover are fastened the exit tube of the gas 7, and the safety tube Y,,, the connection X', with the oil manometer (for details see plate I) and a copper tube V’,,, into which the india rubber stopper is placed holding the apparatus to be immersed in the bath (in our case the piezometer for the critical phenomena X;,, and the correction thermometer §,, with its leads $,, (comp. § 1) while the thermo-element @ may be considered as forming an inherent part of the cryostat). There is also a tube through which the capillary a, admitting the liquefied gas is led and where it is supported by a piece of cork a’,,. It is closed by means of an india-rubber tube @’,, drawn over the tube and a thin cap soldered on to q,. Between the cover and the rim of the vacuum glass a wooden O30) cylindrical jacket VV’, is placed resting against the latter by means of an india-rubber ring N’,. Two eylinders N',, N’, of nickel-paper serve to diminish radiation, especially in the direction of the delivery tube. As mentioned the frame whieh keeps the protecting cylinder in its place is fastened to the cover. For a complete explanation of the letters and parts of both this and the stirrer reference may be made to § 4. Further we may note that §, is fastened with silk cords to §, and this again with silk cords to the cover N’,,, while §, is supported by the glass tube §, fitting onto the pins §,. The three threads 7, on which the stirrer hangs are led directly through the three india-rubber tubes z',,, connected hermetically to tubes soldered onto the cover and fitting hermetically onto the threads at XZ... to the brass dise ',, and rod %',, which is connected by a small chain z,, passing over a pulley 7',, to the motor by means of a steelwire. The arm of the motor may be adjusted to different throws, while velocity of rotation can be regulated by means of a rheostat. The mounting of the apparatus is very simple. The stopper with the measuring apparatus is placed into the tube .V’,, of the cover, to which all the auxiliary apparatus has been connected, then the vacuum glass is slid into the india-rubber ring which is also connected to the cover and is fastened there by means of tightening bands. In order to secure an airtight fit the india-rubber on the metal and on the glass has been coated beforehand with a solution of indiarubber in benzine. With a view to the description given in III the operations for the adjustments at given temperature require amplification only in a few points. In the case considered here, the evaporated gas was led back through the exit tube to the gasholder or to the large exhausted reservoir of the ethylene circulation in the cryogenic laboratory (Comm. 14, Dec. 94) whence the ethylene was further condensed into the condenser immersed in methyl chloride. As described in Comm. 14 the circulations of the cryogenic laboratory have been so arranged that they may be used at any time. Besides the reservoirs that have to be exhausted, a permanent part of the circulation consists in branched tubes with cocks as shown on plates I and IV. The cryostat had only to be connected to the circulation in order to be easily brought to the required pressure. In the case considered here the experiments were not made in the cryogenic laboratory but in an other room and the length of the lead a’,, was 10 m. Although the liquid ethylene had to be conducted over such a distance, yet the adjustment of the bath to the required temperature (say at — 120°) was obtained within one hour after the pumps in the cryogenic laboratory had been set working. Instead of a resistance thermometer, to regulate the temperature, we used the thermoelement ©, the protected junction being placed at the side of the piezometer (comp. comm. 27 June ’96); it is visible through the window J’', (in plate IV). The electro-motive power of the thermoelement is compared by means of the zero method with that of a thermoelectric control element or a Weston-element. For the same difference of temperature the deflections on the scale of the sensitive galvanometer were almost as large as in the measure- ments made with the resistance thermometer (comp. § 5). An example of the determination of the temperature is not necessary in addition to Plate III. IV. A permanent bath of liquid nitrogen at ordinary or reduced pressure. In Comm. 14 (Dec. 94) a short description was given of the temperature steps obtained by means of circulations of methylchloride, ethylene and oxygen. In connection with that description I mentioned my intention of adding more circulations to those already existing and said that I hoped to repiace more and more parts of the existing circulations by greater and to insert such technical apparatus as should be found advisable so that the existing apparatus could be used in the new circulations with pure or costly gases. An example of this is the circulation of nitrogen added to the existing temperature cascade, of which a description is now required by the completion of some of the measurements rendered possible by it. For measure- ments at temperature between — 195° C. and — 210° C. a nitrogen is much to be preferred to an oxygen-circulation as the tension at Which the oxygen boils at — 195° is so small that accurate regulation at constant temperature becomes very difficult. As the preparation of pure nitrogen in such large quantities as a circulation requires presents many difficulties, the compressor and the vacuum pump must be suitable and efficient. These conditions are fulfilled by the mercury and the auxiliary compressors which are generally used for the compression of pure gas and which in the originally tempera- ture cascade served for the oxygen circulation. However when the Brorngrnoopcompressor (comp. Comm. 14 Dec. ’94 and 51 Sept. 99) could be used for the oxygen circulation in the cascade they could be used for the nitrogen circulation. The nitrogen is prepared from sodium nitrite. Besides being passed through ferrous sulphate and sulphuric acid it is led over hot cop- ( 632 ) per and then again through ferrous sulphate and sodium hydroxide, because otherwise traces of nitric oxide might be left and this blocks the cocks *(this gas is recognised at once by a strong smell of higher oxides of nitrogen when it mixes with the air). In order to remove traces of this oxide, | have sometimes added to the gas a quantity of oxygen as nearly as possible equivalent to the NO contained therein aid have then passed it through sodium hydroxide. The gas is col- lected and provisionally kept in galvanised iron vessels holding 1 M?. From these it is driven out later by water heated by a steam jet and after passing through sodium hydroxide and sulphuric acid it is forced into a small gasholder floating on oil and holding 500 L. By means of the auxiliary compressor AC’ lubricated with glycerine (see Pl. VI and for details Comm. 54 Sept. 99) and the mereury compressor HyC (see Pl. VI and for details Comm. 54) the gas is forced over into a metal cylinder of 18 liters capacity after passing through the drying tubes D,, D, filled with caustic soda in the form of sticks. Plate VI shows the scheme of the entire circulation with the cryostat Cr, into which the liquid nitrogen is admitted at a and where it evaporates under ordinary or reduced pressure at the desired tem- perature. The whole arrangement has been used in the comparison of the platinum resistance thermometer with the hydrogen thermo- meter, which has been mentioned in III. The apparatus themselves ave drawn diagrammatically but in their true proportions, while the con- nections are entirely schematic. A detailed representation of the cryostat with the auxiliary apparatus appertaining to it for uniform and constant temperatures will be found on plate I where the same letters have been used. On the other hand plate VI may be considered as a sup- plement to plate I. Nothing is wanting for a complete representation of the circulation except the gasholder and the vacuum vessel of 5 M*. (comp. § 5 for its use) which are too large to be repre- sented on the same drawing as the parts given. There is an insignificant difference in the coupling of the leads between plate I and plate VI, for on plate VI Exh. 1' indicates the connection of the compression side of a BurckHarpt—Weiss vacuumpump Bu Vae., described below into which the exhaust Heh. 2 terminates, to an exhaustpump (which may also be AC of the circulation). Moreover next to the lead from Y, to Y,, we have drawn what must be sub- stituted for it in comparison with the arrangement on plate IV. RN is the cylinder where the nitrogen has been compressed by means of AC and HgC through the drying tubes D, and D,, while Gaz indicates the 500 liter gas holder floating on oil. The nitrogen may ( 633 ) be admitted at the required pressure into the condensation spiral CS from the cylinder RN through a final drying tube D, containing phos- phorie anhydride, as well as directly from the compressor. The spiral is placed in a vacuumglass 6 with a protecting cylinder A. Liquid oxygen is admitted into B through Ox.lig from the oxygen circulation of the cryogenic laboratory, viz. from the condensation spiral which is cooled in the ethythene boiling flask (Comm. 14, Dec. 94). The oxygen escapes through Owrap, a wide safety tube S being connected in the ordinary way, and is compressed into the spiral by a BrorHERHOOD-compressor which is lubricated with glycerine and arranged as described in Comm. 51. It may be remarked that, with a view to the possibility of an explosion of a glycerine mist mixed with oxygen, the pressure in this operation is not raised above 80 atmospheres. (Comp. the explosion described in the Zeitsch. f. Kohlensi&ure Industrie 1903). The nitrogen condenser itself has been drawn in detail on plate VII. In so far as the parts correspond — either with plate V_ for the cover, or with plate I of Comm. 51 for the regulation cock described there — the same letters have been used, but as some of the parts differ a little the letters have an additional accent. As in the case of the small cryostat plate V, the cover is coated internally with nickel-paper, while the upper turns of CS are protected again by a ring of paste board and nickel-paper. The condensation spiral consists in the condenser proper CS, and the regenerator CS,; here the same principle has been applied which has been followed in the eryogenic laboratory from the first (Comp. Comm. 14 Dec. *94); the vapour of the oxygen is forced by the cylinder 6", which is closed at the bottom with the stopper 5",, to pass along the regenerator spiral. As in the ethylene boilingflask (see comm. 14 Dec. °94) the level of the liquid oxygen in the glass tube W' is indicated by a cork float dr, with a steel capillary dr, to which a thin reed (, is fastened ; the steel capillary passes through a glass tube B’,,. Liquid nitrogen flows out through the fine regulatingcock hh, of the same kind as that through which the liquid gas is admitted into the cryostat. For the description of this cock compare Comm. 51 and 54. It may be added that Gaz’ shows the connection with the auxiliary apparatus deseribed in Comm. 54 for operations where HyC is used, which connection make it possible for the gas to stream back to the gasholder Gaz. V. Arrangement of a BurcKknarpt-Wriss vacuumpomp to be used with a-circulation for low temperature. The well-known excellent 634 Vacuumpump patented by BurckHarpt and Weiss has been first used, I think by Otszewski, for removing the large volumes of gas which rise from a bath of liquetied gas at a reduced pressure. We shall how speak of some modifications and auxiliary apparatus by means of which the perfect purity of a gas is secured in a high vacuum. A pump arranged in this way may also be introduced into cireula- lions of costly gases. In our laboratory it has been worked very satisfactorily for many years. A diagrammatic figure of the entire BurckHArDT-pump has been given on plate VI Bu. Vac., the pump evlinder with its slide valve box, the beginning of the suction- and the delivery tubes with the auxiliary apparatus belonging to them are shown on plate VIII, where fig. 1 gives the side elevation, fig. 2 the top elevation and fig. 8 the section. The well-known working of the piston and the valve, the successive communication of the valve ports 5 and 5’, each individually by means of the slide hole 2 with the suction valve port 1 or with the delivery valve port 4 and together by means of the ringshaped opening 3 may be seen without further comment from the section. The pump displaces 360 M* an hour, hence, when exhausting at a pressure of 2 ¢.m., about LO M*® gas, measured normally can cireulate. At Leiden it is used almost exclusively with an additional vacuumpump exhausting at the compression side. It exhausts then till 2 m.M. As a lubricant and for the airtight fittings to be described in the following pages, only bone-oil is used which after having been tested at the exhaustpump has proved to have no perceptible vapour pressure. For the technical work ordinary ring packings are quite sufficient, I have, however, replaced them by folded packings as deseribed in Comm. 54 Jan. ‘OO for the compressor and the auxiliary compressor. The leather ring of the packing is supported there as in Plate IV b,, by the india rubber ring /,, (for an exhausting packing comp. f,, Pl. VII tig. 8 Comm. 54). The packing cylinders have been made long enough to contain two folded packings (one for exhausting and one for compression) and a bronze tightening piece, but as a rule they only hold the packing for exhaust. New additions are the vessels O, and (, see also plate II filled with oil (or with glycerine for those gases which cannot be used with oil); they serve to protect the packing cases of the cylinder and the slide valve box entirely from the atmosphere and also to cool the piston rod. The covers Q,, and Q,, protect the lubricant against dust or moisture. For the oil holders S,S, we have chosen the construction explained in detail in fig 7. S,, is an ordinary oilpot for visible cylinder lubri- ( 635 ) cation in vacuo. The cover S,,, has been tightly screwed on the hollow rod S,,,, and presses the glass S,,, hermetically on to the packings. By means of the winged nut S,,, the point is adjusted so that the oil drops regularly through the openings JS,,,, into the space S,,, Which communicates with S,,, through S,,, and which may be watched through the glass windows inS,,,. For our purpose the oil holder S,, is placed on a_ stout tube S,, onto which by means of india rubber rings and tightening bands the glass cylinder Sa is filled with oil and covered with a lid $,,. By means of |S is fixed on a copper bottom, soldered to S,,. The glass cylinder 123 NEW oil can be admitted from the reserve vessel into the lubrication vessel. In this way the air is sufficiently prevented from entering the lubrication apparatus. Lastly, between the exhaust tube z and the compression tube p a safety valve has been placed, which prevents the pressure on the compression side from rising above a ceriain height (usually */, atmos- phere). Hence it is possible to let the pump work on and to open and shut the cocks as the work requires. The noise of the safety valve gives warning that the cocks have not been properly used. In any case no difficulty is to be feared if the possible output of the pump might diminish in any way in relation to the intake. Fig. 4 shows a diagram of this connection, some of the parts being drawn to proportion ; fig. 6 shows a section of the safety valve case itself, The side tube p, is connected by a joint A’ with the tube ¢, which opens into the space below the safety valve. The space above the safety valve communicates with the exhaust tube through the side tube z,. The broad valve v, is coated at the bottom with an india rubber sheet which presses against the narrow rim v,. The spring v, is stretched with the key v, while the plate v7, with the nut v,, and packing is tightly screwed on to the rim v,,. The packing cylinder v,,, like the packing just mentioned is kept under oil; a cover v,, above it protects it from dust. The connection A’ between the tubes p, and v, could not be brought about with flanges or with screw joints without causing tension in the tubes. Therefore it was made in the following manner as shown by fig. 5. A widened piece 4, is soldered on p,, v, fitting into this piece. The india rubber connection £, is kept in oil; for this purpose a rim #, was used which was soldered on to p, and a rim &, which was soldered on to z,. Over these rims a wide piece of tubing #, is drawn which is fastened to &, and /, by means of india rubber rings /, 4, and tightening bands, and forms together with these an oilreservoir. O36.) Besides being connected through the safety valve case and the above mentioned connection, the compression tube and the exhaust tube are also connected (comp. again the diagrammatic fig. 4, as an explanation of figs. 1, 2, 3) by the cocks 7,,7,,7,,7, and may be connected with an airpump /, an_ indicator 7 and a vacuummano- a? meter m. The use made of this auxiliary apparatus in regular working or in preparing, mounting, testing, drying and exhausting the pump, requires no further explanation. As a matter ef course, the pump is not introduced into a circulation unless it has worked for a long time with the exhaust- and compression sides closed and no change has been found in the vacuum. I further remark that the principle of an oilconnection as illustrated by fig. 5 may be profitably applied when wide tubes have to be connected, which have neither flanges nor nuts and joints or in cases where it is not advisable to make these contrivances. The method then to be followed is illustrated by fig. 8 where A’,, A’, and A’, are loose pieces slid on the tubes 6, and#,. which we want to connect A good fit is obtained by means of the india rubber rings A’,,, K’,,, K’,, K’,, K’,, under brass tightening bands. A’,, and A’,, serve to admit and to run out the oil. In this way one always sue- ceeds in making within a short time an airtight fit. For the connee- tion of the pump tubes to the conduit at 7, and /, (comp fig, 1) this method has been used in a manner which will be clear from the figure. Physics. — Communication n°. 84 from the Physical Laboratory at Leiden “Jsotherms of diatomic gases and thew binary mixtures. V. An accurate volumenometer and mixing apparatus.” (By H. Kamertinen Onnes and H. H. F. HynpMay). § 19. A compression tube of larger dimensions. In § 6 of Comm. n’. 69 March 01 we have explained that the apparatus described in §§ 38 and 4 hardly gave the accuracy required in the determinations of density, if the total quantity of compressed gas was smaller than 5 cc. Since, however, at most 600 cc. of gas under normal condi- tions is available in this apparatus it is not suitable for densities of more than 120 times the normal. On Pl. I a compression tube is shown which has about three liters capacity and hence which is suitable for measurements up to densities of some 500 times the normal and with at least the same accuracy as the above. The drawing is, as usual, schematic in ( 637 ) the connections but the individual parts are drawn to scale, it can be compared with Pl. | of Comm. n°. 69. For those parts which correspond the same letters are retained, where an alteration has been made the letters are accented, while new parts are characte- rised by new letters. A detailed description is hence unnecessary, but it may be noted that the screw head a, is changed, that a closed nut screwed on at c,,, has been added by which the pressure can be suddenly released if necessary, and that a cock c,, has been introduced, to enable the level glass to be shut off if required. The compression tube Dh. ( 655 ) This is the first time that mention is made of such an erratie- block from the Dutch diluvium. Many of the kind, with remains of Ellipsocephalus Polytomus or of other fossils, occurring in Oeland in the layer with Paradoxides Oelandicus, have already been found in the German diluvium. The first of them was mentioned by Dawns?) and comes from Rixdorf near Berlin. A few years after, RemMELs *) described two such erratic-blocks from the neighbourhood of Ebers- walde. Later on, Rormer*) made mention of two erratic-blocks of the same age. One of them comes from Rostock and bears much resemblance, according to the description, to the Groningen piece. This cannot with so much certainty be said of the second block, which was found at Bromberg and does not seem to be greenish. In Sleswick-Holstein, too, corresponding erratic-blocks seem to have been found, as Sronien*) writes about ,griinliche Kalkgeschiebe der Oelandicus-Zone’”’. This erratic-block also confirms my supposition formerly °) men- tioned, that in the Hondsrug occur more sedimentary erratic-bloeks with a West-Baltic character, than was formerly generally supposed. II. For some time already I have had in my collection several pieces of an erratic-block consisting of limestone that has been tinted dark-grey, even almost black, by bitumen. It was found in the loam- pit near Hemelum. Its calcium-carbonate having for the greater part erystallized, this limestone approaches antraconite. Some nests of little pyrite-crystals and a small phosphorite-nodule are found in the stone. For a long time the only fossil that was exposed to sight was (with the exception of a few unimportant remains, probably of a Paradoxides) what I supposed to be the internal cast of the inside of a piece of Trilobite-shell. Its largest dimension amounts to 9 milli- metres. This internal cast is almost oval, and strongly vaulted. The top-part finishes in a bow. On the convex side of this bow it is steeper than on the concave one. In front, on the least steep part, is a frame in relief, soon turning round the most elevated point and then continuing on the steepest part, where it becomes tinier and tinier. Towards either side springs from this frame a net-work of 1) Dames, Zeitschr. d. deutsch. geol. Gesellschaft. Bd. 31. 1879. pag. 795. 2) Remeve, Zeitschr. d. deutsch. geol. Gesellschaft. Bd. 33, 1881. pag. 181, 700. 8) Roemer, Lethaea erratica, pag. 26. *) Srottey, Die Cambrischen und Silurischen Geschiebe Schleswig-Holsteins und der benachbarten Gebiete, 1895. Bd. I, Heft 1, pag. 40. 5) Bonnema. “Cambrian erratic-blocs at Hemetum in. the South-west of Frisia.” These Proc, 1902, p. 142. 656) suchlike ones. This net-work is very distinet on the less steep part, not so distinct on the other, where it is scarcely to be seen with a iInagnifving glass. Moreover there are on this internal cast round elevations, It being quite impossible for me to find what species of Trilobites this off-print came from, the exact age of this erratie-block could not be fixed. The nature of the stone made it likely to be Cambrian, and that, too, Mid-Cambrian, because of the suppositional Paradoxides- remains. When, however, a few weeks ago, my friend dr. Groxwant from Copenhagen, the author of “Bornholms Paradoxideslag og deres Fauna” ‘Danmarks geolowiske Underségelse IL Raekke No. 13.) took a view of my collection of erratic-blocks, he recognized in the said off-print that of a right cheek of Conocoryphe Exsulans Linrs.*) Herewith the age of this erratic-block was already exactly determined, for the occurrence of these Trilobites-remains is characteristic of the lower part of the layers with Paradoxides Tessini Brongn. This division consists, in Schonen, in Bornholm and (according to an oral Communication of prof. Morere) to the South of Mérbylinga in Oeland, of limestone, which after this Trilobite is at present mostly called Exsulans-limestone, whilst it ceased to be called Coro- natus-limestone. GRONWALL’s Opinion was brilliantly confirmed, when, on his breaking the stone further to pieces, remains of the Trilobites Conocoryphe Impressa Linrs,?) Liostracus Aculeatus Ang.*) and Solenopleura Parva Linrs.‘) were exposed to view by him. Moreover a remnant of Acroteta Socialis v. Seebach was found, which, however, also occurs in older and in younger layers, which is not the case with the Trilobites mentioned just now. The only remnant that has been well preserved, is a mid-shell of Conocoryphe Impressa Linrs. It is for the greater part exposed to view. Only on the sides it is still covered by the stone; so the facial sutures are invisible. It must have belonged to a young indi- vidual, its length being only 6 millimetres. It is slightly vaulted, the glabella a little more than the other part. In front it is bounded by a flat border along the edge, which border is broadest in the middle. 1) Liyyarssonx. Om. Faunan i Kalken med Conocoryphe exsulans (Coronatus- Kalken\. Sveriges geologiska Undersékning. 1879. Ser. C. No. 35. pag. 15. tafl. Il, fig) 21, 99. 2) Liynarsson. loc. cit. pag. 20. tafl. IL. fig. 29, 30. 5) Liynarsson. loc. cit. pag. J1. tafl. I. fig. 12—15. 4) Linnarsson. loc. cit. pag. 14. tafl. L. fig. 16—19, 20? The occipital furrow is shallow, especially on the glabella. The neek- ring broadens towards the centre and bears a little tubercle there. The breadth of the glabella is at the back equal to its length, which is half the breadth of the mid-shell. The glabella becomes gradually narrower towards the front; in front if is rounded. On either side there are three very indistinct lateral furrows. The dorsal furrows are little developed. In front of the glabella the cheeks run almost imperceptibly into each other. On either side an oblong elevation is visible on the firm cheek, just behind the place where the dorsal furrow turns down towards the centre. It is scarcely to be observed that starting from this elevation a line-shaped one runs in the direction of the corners of the cephalon, as Lixxarsson tells us. This must certainly be attributed to the circumstance, that this mid-shell belonged to a young individual. The scale possesses no other sculpture than countless very fine impressed points, placed very close to each other. From the properties mentioned above one may easily convince oneself that the mid-shell described comes from Conocory phe impressa Linrs., and that consequently this erratic-block is a piece of Exsulans- limestone. The other Trilobites-remains, all of them pieces of mid-shells, are too incomplete to be described in such a manner, that the species of Trilobites which they come from might be recognized from the description. Moreover, such a description would be more or less superfluous, as the age of this erratic-block has already been suffi- ciently indicated. So I think I'd better leave it and refer to the authority of Dr. Groxwant with regard to the remains of the other Trilobites mentioned. As he was so kind as to send me some mid- shells of these Trilobites for comparison, I could convince myself of the correctness of his determinations. As was mentioned above, Exsulans-lime is found as firm rock in Bornholm, in Schonen, and southward of Morbylinga in Oeland. Morbylinga does not seem to have been mentioned yet in literature in this connection; but Prof. Mosere told me of it. In Sehonen, Exsulans-lime is without any doubt met with as firm rock near Andrarum, Gisl6f and Kwiks Esperéd. Most probably it is also found as such, according to Linnarsson, near Fagelsing in the neighbourhood of Lund. GRONWALL tells me that my erratic-block does not, petrographieally, correspond with the Bornholm Exsulans-lime, more with that in South-East Schonen. | cannot decide whether it also resembles that which is found at Moérbylanga in Oeland. In the Dutch diluvium an erratic-block of this kind was never ( 658 ) before found. They also seem to be very rare in the German diluvium. As far as I have been able to find out, they are made mention of by Srouury ') only. Mathematics. “An analytical expression for the greatest common divisor of two integers.” By Prof. J. C. Kuvyver. In this paper we propose to construct certain functions 2 of two real variables # and y which for positive and integer values of these variables become equal to the greatest common divisor of and 4 A very simple solution of this problem is obtained as follows. Denote by [| the integer part of the number wu and consider the arithmetical discontinuous function 1 JEL YP) = = 1 — [v] ere For any integer n we have 1 1 Put+n=PW, Pe+0=—5, Pa—HW=+-—5. We will take 1 PQ) =Prn—HN=+4+5 - and consequently [xn] = [xn — 0] =n—l. Integer values of ~ excepted the wellknown relation N= sin 2 NU Pia) = — 2 5 =| 2AN holds and from it we deduce the identical equation u=2z—]} p=r—1 a3 = P(nth) = = P(t) = Pe n), p= a p= a where « and 3 are relative prime integers. That the identity is still valid for integer values of ~ may be easily verified. By the equation Ped Ly gee 2 SOP ee Se a 20 we a discontinuous function of the variables « and y is defined. We may regard it as a first solution of the proposed problem. For if 1) Srouey, loc. cit. p. 41. ( 659 ) xv and y become integers, say v=aD), y=), where « and 8 are prime to each other, we have cao) i {Ly - rst : {Ll : 3 Epes IPD Pe oe BY 2 S210) APY) ye — a 0) a In a somewhat different form this result is found in a paper by Srern'). A whole set of functions of the required kind may be deduced in quite the same way. We only have to notice that the function : m= ros 2 wn U Fs (u) = + —— —, (s >1) n=1 ns satisfies the fundamental relation ee ulin eae a ste => Fy{ut—)= J F,| u4+— | =al-s F, (au), p= « y=0 ‘ a, where again «@ and 2 are prime to each other. Hence if we put fuze Pel, (ay i. (0) a5 25 Meal Abs eee) fe, cea l (LL) p= wv me, cetior 2 = «D7 = 68D p=z—l p=2D>1 4 { up ike) Wes 2 SDS eS, ( ) eg) > ral j=. I's (9), =O u—0 « that is Ds ; é : = ty ; : In the funetional relation (11) the term F,{ is not easily “L : evaluated; hence the series /,(~) may be suitably replaced by the latter of the two series (uw) »(— 1 aa sin 2 anu Peo) 2 (1) 8 n=l (2 a n)2*—1 N=2 Cos 2 NU gay (¥) =2(—1)k-1 J SSS nl) (2 Tv n)ek Indeed, if we denote the Bernoullian polynomial of order 1 n+l 1 wn 13% yn -1 B. ywn—3 (m+)! 2 m 2! (m—1)! 4! “(m—3)! by Sm (uw) the series y,, («) is identical with F'n) for all values of u between zero and unity. Therefore, whatever may be w, the series itr) er ae Ym (ut) may be regarded as a polynomial of the mt" degree in ") *Zur Theorie der Function £(«).” Journal f. Math., 102, p. 9. 45 Proceedings Royal Acad. Amsterdam. Vol. V. u fw) so that, if in the equation Il) we replace Fi(u by gal), By. ‘=|s ' (—1)k-1 —* otk — gS mu (“*), of pe kl = the thus defined function 2 is algebraically expressed in wv and y. But as well as in the equations (1) and (Il) = is still discontinuous for integer values of . in equation (IID). By a slight alteration it is possible to make these discontinuities disappear. Without altering the value of 2 for integer values of « and y we may write instead of (III) B,. #=([aJ (yy 1 : (—1)k-1 ek sk — pk i) LY yx (’ : ) + — yop. (0) + goe (y) P(w)t ATV ) 2k! | ; i — wv 2 \ and the function 2 has become continuous everywhere. The same however is not true for the partial derivatives of 2 with respect to wor y; besides there is as in equations (1) and (11) a lack of symmetry. By interchanging « and y the value of 2 alters. To some extent these disadvantages may be eliminated. The process of integration is apt to level finite discontinuities, moreover symmetry may be intro- duced by it. And indeed a suitable expression of 2 in the form of a definite integral can be given. We consider the function z defined by ; 1 By : Sai ak — sok a ak (wu) ae (yn) due. 2 we (VY 0 Now <¢ depends symmetrically on a and y and is continuous throughout. The function has continuous derivatives; we may different- iate z a number of 4—1 times with respect to v and also /;—1 times with respect to y, either separately or subsequently, before the derivatives lose their continuity, so that by making / larger and larger the behaviour of z tends more and more to that of an analytical funetion of two real variables. We now again substitute in (V) «=a«D, y= 8D and as the trigonometrical series gz (vv) and g_ (yw) are absolutely convergent under the supposition 4 >> 1) we may multiply termwise and integrate the partial products. a But after integration a nonvanishing amount is furnished only by those partial products sin sin 2ahaDu 2alpDu, cos Cos in which we have 108 eee kee henee we find 3 2k (=a > Boe Oe Ba, 2k! (Qx)2* 2 ,=1 g2k 2k! and as before ae Had we integrated the product gm (eu) gn (yw), where m—-- n is even, instead of Gm (rt) Jn (yt) the result would have been similar, only symmetry would have been lost. We may remark that the 2 in equation (V) is still an algebraical function. For remembering that d — 9 (") = gk—-1 (), du d, () = Pu), we deduce by repeated partial integration By y= k—2 oh! 2k — — (—1) a yk tl ey (2) Oh ey) te j=l ak + (11 FE, (er) gre (ye) (HD ga (Ws ua “ or finally By. == k—2 a otk — =: (—1)p ak yk HUE (press (CA) Pko+1 (y) + ak + (—1)* — geri (y) + if! (Vlei fa 1 -+- (—1)k wrk) > goK ( ") =F Ok (9) + gor (y) P (w)}- (VI) v— l Lv From this equation we infer that the product 2*%ey is a rational integral function of . and y of degree 4 / + 2, and generally speaking the equation represents an algebraical surface S of that degree. But it should be noticed that this surface S in reality is composed of an infinite number of partial surfaces, having contact more or less close along a system of plane curves C. And in fact the larger the integer kk be chosen the closer will be the contact of the partial surfaces. Equation (VI) contains the equations of all the partial surfaces, but each of them has a distinct equation the coefficients of which are made up from the itegers [v],[y] and Ey 5 (Sh, oS ooo AA) E Hence we pass from one partial surface to an adjacent one in all places, where one at least of these integers increases by unity. Ad5* ( 662 ) Thus the projections on the wy-plane of the eurves C are of two distinct categories. To the first belong the straight lines w=, y=n, regularly dividing the wey-plane in equal squares of side unity. The second category is formed by straight lines issuing from the vertices of these squares and which, if produced, would pass through the origin, The number of these lines, which have their points of issue inside the square, bounded by the ve-axis, the y-axis and by the lines “v=n, y=n is seen to be 224(n)"'), that is on an average equal to 1. Therefore the partial surfaces remote from the origin ultimately a fake the form of infinitely narrow strips, the length of which varies from | to V2. In order to lower as far as possible the degree of the surface |S, we should take = 1 and we have from (V) and (VI) 1 bd v=[2] uy 1 ha O say | Piva) Pyn)du = S) = Ws (' a = 0) FIL = 5 U,(1)- 0 hoe . j A comparison with (IV) makes it evident that for integer values of w and y the quantity 2 still becomes equal to the greatest common divisor. The surface S is of the 6% degree, the partial surfaces still hang together everywhere but in this case they have no contact along the curves C. Physies. — “On maciina and ininima of intensity sometimes obser- red within the shading of strongly widened spectral lines.” *) By Prof. W. H. Juxius. While examining a series of photographs of the solar speetrum, made by Row anxp in 1888 and 1889, JeweL. discovered one plate on which the shading of /7 and A’ was broken up into a system of faint, nebulous lines, symmetrically arranged about the central absorption lines*). The distances apart) of the component lines of the series increased as the distance from the central line increased. On some other photographs of the solar spectrum, taken by RowLanp and by himself, he only found feeble indications of these series; but 1) »(v) denotes the number of integers less than ” and prime to x. 2) Part of the contents of this communication has already been shortly mentioned in a footnote which was added to the English translation of a former paper (Proe. Roy. Acad. Amst. LV, p. 601) but did not occur in the Dutch original of the same. 5) L. E. Jewett, Astrophysical Journal, ILL. p. 108, 1896, and VII, p. 51—d3, 1898. ee in the shading of some of the strongest lines of iron and a few other elements a similar structure was observed, the component lines being faint, nebulous, and close together. The plate which showed the structure of // and A’ most plainly, displayed an additional peculiarity, as on it the general shading of those lines was tnusually weak. In HALn’s abnormal speetrum’), which was characterized by the extreme weakness of the shaded background of many absorption lines, mnaxima and minima of intensity were also distinguishable under a mieroscope, though they did not appear so clear nor so regularly arranged as in the case deseribed by Jnwnn.. If we suppose the principal cause of the shading of the Fraunhofer lines not to be the absorption, but rather the anomalous dispersion of the waves, whieh in the spectrum are situated on either side the cecntral absorption line *), we can easily account for the phenomenon, before mentioned, as well as for the fact, that in very rare cases only it shows distinctly. Let us consider a narrow beam of light of an exactly defined wave-leneth, belonging to the shaded background of a Fraunhofer line. This beam has emerged from the deeper layers of the Sun with a certain divergence; we suppose if to proceed in the approxi- mate direction of the structure lines of the corona (l.¢.p 597). Let its wave-length be somewhat greater than that of the absorption line; for this kind of light, the medium will then possess a positive refraction constant, and the separate rays of the beam will curve about the denser parts of the “tubular” structure. If we had supposed the wave-length to be a little less than that of the absorption line, the refraction constant would have been negative and the rays would have curved about the rarer parts of the coronal structure. In either case the divergence of our monochromatic beam will alter- muely diminish and increase, and this particular kind of light will reach the Earth with an intensity, determined by the degree of divergence (convergence perhaps) with which the beam left the ultimate traces of the corona. With respect to a beam of other light, the wave-leneth of which differs only slightly less from that of the absorption line, the medium will have a considerably greater refraction constant, so that the rays of this particular beam may have made a bend, or part of a bend, more than those, belonging to the former beam, on their way through 1) G. i. Hane, Astvophysieal Journal, XVI, p. 232, 1902. *) W. HL. Justus, Proc. Roy, Acad, Amst. IV, p. 589—602. 664 the corona. This beam may, accordingly, arrive with a quite diflerent, say a greater, divergence and consequently display a smaller intensity in the spectrum, than the neighbouring beam, first considered. Approaching still nearer to the absorption-line we shall come across waves that reach the Earth in beams whose divergence is smaller again, showing increased intensity, ete. It is plain that in this way periodical alternations of light and dark on either side the central absorption line must arise. The waves, corresponding to the middle of one of these fringes, will have achieved exactly one whole bend i.e. the distance between two consecutive points of inflexion of the path) more, or less, than those corresponding to the middle of the adjacent fringes. From the familiar type of the dispersion curve it follows directly, that, in moving away from the absorption line, to equal differences in refraction constant increasing differences in wavelength will answer. The distance between the fringes will accordingly increase from the centre to either side, as has in fact been observed. Our explanation requires besides, that this system of faint lines should be visible only when sunlight reaches us exactly along a coronal streamer of sufficient length. In my last paper (Le.) I showed that, in case this condition is fulfilled, the average shading of the Fraunhofer lines must be abnormally weak. It is therefore not to he wondered at, that on the plate, plainly displaying the peculiar structure of H and A, the shading really was unusually faint. But the formation of a well defined line-system demands a further condition to be fulfilled, viz. that the configuration of that part of the (rotating) corona we are just looking through, offers all but the same aspect as long as the photographie plate is exposed. This, of course, requiring very special circumstances, we see why even in cases, in which the shading of the Fraunhofer lines is weak, the fringes may be missing all the same. In a few cases has a like structure been observed with some strongly widened emission lines of the arc-spectrum. Kayser came across this phenomenon in a line of the lead-spectrum '); Rownanp too seems to have observed it once; and after many vain endeavours JeWELL suceeeded in obtaining a photograph of the are spectrum of calcium, in which at /7 and A’ the series appeared rather distinetly. This plate was obtained by using an extremely powerful direet current and exposing for three or four seconds only. Under these conditions 1) H. Kayser, Handbuch der Spectroscopie, Il, p. 353. » + ( 665 ) the heated calcium vapour formed a much more extended atmosphere around the poles than with a weaker current. Kayser ') asserts, though, that it has hitherto remained unknown, What are the exact conditions upon which the phenomenon depends. In connection with the preceding considerations, 1 hold it possible that in those experiments the metallic vapour has, during the (short) exposures, formed a kind of flame of tubular structure, which happened to be in the exact direction of the spectroscope. This view seems reasonable if we bear in mind the well-known ‘blowing’? which is of frequent occurrence in a powerful are loaded with much vapour. The radiations, proceeding from the core of the are, which caused the wide emission band, underwent anomalous dispersion in the enveloping vapour and traversed the flame-shaped streamer, following sinuous paths. A simple experiment convinced me that the peculiar light-distribution observed in all strongly widened Fraunhofer lines*), may be strikingly imitated in the absorption-spectrum of sodium vapour. The only thing necessary was to force the absorbing vapour into a more or less tubular structure, such as we presumed it to exist in the corona. A’ slightly converging beam of electric light was thrown on to the slit of a grating-spectroscope. At a distance of rather more than 100 ¢.m. from the slit, and about 1,5 em. below the axis of the beam was the opening of a specially constructed bunsen-burner, from which a sodium-flame emerged. This opening was slit-shaped (30 cm. long, 0,2. ¢.m. wide) and adjusted in a position exactly parallel with the axis of the incident beam. The pressure of the gas was somewhat variable, and a good regulator unfortunately not at hand. In order to supply the long flame with sodium, the con- siruction of the burner included a kind of narrow gutter on either side, into which had been poured a solution of a sodium-salt. This ascended into the flame by strips of asbestos paper. When viewing this flame lengthwise, it was as if one were looking through a com- pressed tube, the sides of which consisted of sodium-vapour. The density of the vapour diminished gradually towards the centre as well as towards the outside. The sodium-lines were observed in the spectrum of the third order. In spite of the great length of the flame the real absorption lines were narrow; they stood out from a_ pretty dark ,softly shaded background, the width of which amounted to several ANGsTROM units. The distribution of the light entirely corresponded to JnwrLt’s ) Le. p. 354. *) Jewett, Astroph. Journ. Ill, p. 101; Hare, Astroph. Journ. Ill, p. 156—161, ( 666 ) deseriptfon of the strongly shaded Fraunhofer lines. Close to the central absorption line there was also an unmistakable increase of luminosity (resembling the supposed emission lines in’ the solar spee- trum); but this inerease ought, without doubt, to be attributed to the most strongly curved rays being kept together by the tubular structure of the flame, and not to direct radiation from the flame. For, the electric light) being intercepted, the emission-lines were scarcely visible in the dark field. And besides, as soon as the flame was disturbed by blowing upon it, or when it was partially covered by a diaphragm, the bright band, as well as the shading, became unsymmetrical with respect to the absorption line. Neither DoprLer’s principle, nor the influence of pressure on wave-length can here have played an appreciable part. I moreover observed fringe-like maxima and minima in the shadings, but they showed irregular and so unsteady, that T could not think of measuring their distances. Nor can there be any question of photographing this peculiarity before means have been devised io keep a structure of sodium vapour, as described above, steady for a reasonable time. Such means are however being prepared. Imperfect as our present experiment must be, it still serves to bear out the assertion, that numerous peculiarities of the solar speetrum may be explained from anomalous dispersion. Physics. — “Oy the emission and absorption by metals of rays of heat of great ware-lengths.” By WH. A, Lorenrz. § 1. Hacex and Reprxs have recently shown by their measure- ments of the reflecting power of metals‘) that the behaviour of these bodies towards rays of great wave-lengths (larger than 8 ft) may be accounted for, if one applies to the propagation of electric vibrations the equations that hold for slowly varying currents, and whieh con- tain no other physical constant of the metal but its conductivity. It follows from this result that a theory which can give an adequate idea of the mechanism of a current of conduction will also suflice for the explanation of tlie absorption of the rays that have been used by these experimenters. A theory of this kind has been developed by Rireke *) and Drepr*). According to their views a metal contains an immense number of free electrons moving to and fro in much the same way as the molecules of a gas or as the ions in an electrolytic solution, 1) Hacer and Rvuseys, Berliner Sitzungsberichte, 1903, p. 269; Berichte d. deuat- schen phys. Gesellsch., 1903, p. 145. 2) Riecke, Wied. Ann., Bd. 66, p. 353, 189s. 5) Drupe, Drude’s Ann., Bd. 1, p. 566, 1900. ( 667 ) the velocity of agitation increasing with the temperature. It is to be assumed that, in this “heat-motion”, every electron travels alone a straight line, until it strikes against a particle of the metal; the path will therefore be an irregular zigzag-line and, so lone as there is no cause driving the electrons in a definite direction, an element of surface will be traversed by equal numbers of electrons, travelling to opposite sides. Things will be different if the metal is exposed io an electric force. The motion of the electrons will still be an irregular agitation; yet, motions in a definite direction will predo- minate, and this will show itself in our observations as an “electric current.” Now we may infer from the relation between absorption and emission that is required by Kircunore’s law, that the mechanism by which the emission of a body is produced is the same as that to which it owes its absorbing power. It is therefore natural to expect that, if we confine ourselves to the case of great wave-lengths, we shall be able to explain the emission of a metal by means of the heat-motion of its free electrons, without recurring to the hypothesis of “vibrators” of some kind, producing waves of definite periods. In the following pages this idea has been worked out. After having caleulated the emissive power we shall find that its ratio to the absorbing power does not depend on the value of those quantities by which one metal differs from another. According to the law of Kurcnnorr, the result may be considered as representing the ratio between the emission and the absorption for an arbitrarily chosen body, or as the emissive power of a perfectly black substance; if will be found to contain a certain constant quantity, whose physical meaning will appear from the theory. § 2. The ratio of which [ have just spoken is intimately connected with another important physical quantity, viz. the density of the enerey of radiation in a space enclosed by perfectly black walls, which are kept at a uniform absolute temperature 7. Tf the electromagnetic motions of which the aether in such a space is the seat, are decom- posed into rays travelling in all directions, and each of whieh has a definite wave-leneth, the energy per unit volume, in so far as it belongs to rays with wave-lengths between 2 and 2+ da, may be represented by BAA, Prd); F’ being a function which many physicisis have tried to determine. BotrzMann and Winn have shown by thermodynamical reasoning that the above expression may be written 665 ta fh GA. U,,--. for the mean molecular velocities, /,, /,,... ( 670 ) for the mean lengths of the free paths, V,, Nj... for the number of electrons of the several kinds, contained in unit of volume. We shall finally suppose, as) Drepr has done, that for every kind of electrons, the mean kinetie energy of one of these particles is equal to that of a molecule of a gas at the same temperature; we may represent it by @ 7, if 7 is the absolute temperature, and @ a constant, In these notations Drepr’s value is *) 1 = — (67 Ny lu ee N, la 5) 4al 2 so that (3) becomes A : (e,° N, t. ut, + e.* N, I. uy - Di atater A. san (5) ~ dacT It is to be remarked that the formula (4) has been obtained in the supposition that the electric force remains constant, or at least that it keeps its direction and magnitude during an interval of time in Which an electron has undergone a large mumber of collisions against particles of the metal. The results of HaGeN and Repens are therefore favorable to the view that even the period of vibration of the rays is very large in comparison with the time between two succeeding impacts. Part of the following caleulations are based on this assumption, § 4. We have now to examine the emission by the plate. It follows from the fundamental equations of the theory of electrons, that every change, Whether in direction or in magnitude, of the velocity of an electron produces an electromagnetic disturbance travelling outwards in the surrounding aether. Hence, it will be at the instants of the collisions that the eleetrons become centres of radiation. We shall calenlate the amount of energy, radiated in this way, in so far as it is emitted across a definite part @ of the front surface of the plate; this part of the emission is due to the electrons contained in a volume w& of the metal. Let © be a point within the area w, OP the normal in this point, drawn towards the side of the aether, and P? a point on this line, at a distance 7+ from QO, which is very large in comparison with the dimensions of @. In this point ? we place an element of surface ’, perpendicular to OP; our problem will be to calculate the energy radiated across this element. | choose O as origin of coordinates and OP as the axis of 2. The components of the velocity of an electron will be denoted by w,, uy, Ue. 1) Drvve, Le., p. 576, This formula does not change by the introduction of our new units. ( 672 ) Now, if an electron with charge ec, is in ( at the time f, and has du, duy dus at that instant the accelerations : ,—, it will produce at the dt dt dt . point 7, at the time ¢ + —, a dielectric displacement, whose com- ponents are *) e du, e duy _ (6) Ame*r ct Ase?r dt On account of the great length of OP, these expressions may also he applied to an electron situated, not in QO but in any other point of the part of the plate corresponding to the area w. The whole dielectric displacement in’ P in the direction of . (it is only this component that will be considered in the next paragraphs) at the time ¢ + ae will therefore be ‘ c= > = So io ee A ra) if the sum is extended to all electrons present in the volume w& at the time f¢. There will also be a magnetic force of the same numerical value, and by Poyytine’s theorem a flow of energy across the element o’, in the direction from the plate towards ?. The amount of this flow per unit of time is given by BE GGT wok gens Merc toes is Gmere oh (E53) § 5. It will be necessary for our purpose to decompose the whole emission into rays of different wave-lengths and to examine the part of (8) corresponding to the rays that have their wave-leneths within certain limits. This may be done by means of Foturrmr’s series. Let us consider a rery /ong time, extending from ¢=0 to t= #. During this interval the value of >, at the point /? will continually change in a very irregular way ; it may however in every case be expanded in the series m— @ mort = : SS SH Gin we af Sl os ge So eae 6 alle) i: vo whose coefficients are given by 2 _ mat i, = — sin Dien aaa os, es sey anette (LO) c 1) The proof of this will be found in one of the next parts of my “Contribu- tions to the theory of electrons.” ( 672 ) Now, if the plate is kept at a constant temperature, the radiation will also be stationary and d,? may be replaced by its mean value S 3 l ™ d,? => ai De dt 0 during the time ® Substituting the value (9), we get integrals of two different kinds, some containing the square of a sine, and others the product of two sines. The integrals of the second kind will disappear, and 5 = mat 1 si? — dt = -—> a, 0 so that a 1] “= = > ty’ of! hv eT es :) ee = n= As to the frequency of the terms in (9), it is given by ma — pee ore n rN ( ) : Lees : * it will therefore increase by equal differences 3 if we give to mits snecessive values. By choosing for % a value sufficiently large, we may make this a4 2 : step aoe small as we like, so that ultimately, even between two values of the frequency x and x + dn, which are in a physical sense infinitely near each other, there will be a certain number of values of (12) and of corresponding terms in the series (11). The number ; o mm of these terms will be — dn, hence, if we suppose @,, or Ki ¢ wea : 3 a = = fe nb De Ube — Se eos ok 0 to have the same value for each term of this group, the corresponding part of (11) will be pe —— Cy ts ae 2x P=. ‘a Substituting this for .,? in (8), we get for the radiation across w’, due to the rays with frequencies between n and n-+ dn, cd ET at | pe Riri a se ck eel (18) 2x ( 673 ) § 6. We have now to calculate the coefficient @,, by means of (13). After having substituted in the integral the value (7), we may still take for its limits 0 and %, provided we reckon the time from r . . an instant, preceding by the interval — the moment from which it ' has been reckoned till now. Thus: i! = ~ 7 diy tii — => aa a: e Sim nt - — dt |, 2a? Ir : oan 0 or, after integration by parts, since s/n vanishes at the limits, a . n = » On ear ee PN | (CAR 05 BOs C1 |b = pee tek be 1B a oD) 2x0 Or Sra 0 The sum in these expressions relates to all the electrons in the part w& of the plate and it is by reason of the immense number of these particles that a definite value may be assigned to @,. We shall begin by determining «*,, and the amount of the radiation in the supposition that there are only free electrons of one kind (§ 3). We shall write ¢y= Vw for their number, e for the charge of each of them, and we shall further simplify the problem by supposing that the molecular velocity w, the same for all the electrons, is not altered by the collisions and that all the paths between two successive impacts have exactly the same length /. Then, the time l a u will also have a definite length. §. 7. Let ¢,,¢,,¢,,... be a series of instants, between O and 9, at intervals + from each other. Then it is clear that, if we fix our attention on the positions of a single electron at these instants, we shall have one point on each of the sides of the zigzag-line described by this particle. Now we may in the first place determine the integral in (15) for the lapse of time during which an electron travels over the side of the zigzag-line on which it is found at the time ¢,. As the length trae 2 t of this interval is much shorter than the period — of the factor n cosnt, we may write for the integral CdiniMine Pie, Ud ch 0, ee Selo ee tay It is clear that we shall obtain the sum in (15), for the q electrons, ( 674 ) if, after having multiplied (16) by e, we perform the two summations, indicated in the formula neTt “ = [cos nity & Url, << oe eee 27 or , We have in the first place to take the sum of all the values of w, for the system of electrons, at a particular instant /, and then to add together all the results obtained in this way for the instants /,,4,, ete. § 8. If we wish to find Sw, for a given time, we must keep in mind that the velocities « of the electrons have at that instant very different directions. We may represent all these velocities by vectors drawn from a fixed point (. The ends JD of all these vectors will lie on a sphere with radius #, and if we let fall from each of these points a perpendicular DD’ on the diameter of this sphere that is parallel to ON, the distances of the projections from C will give the values of «w,. The sum of all these values may therefore be represented by Si. q5: if $ is the positive or negative distance at which the centre of gravity of the points D’, considered as equal to each other, is situated from the centre C. Of course, on account of the large number of the points, this tistance will be very much smaller than the radius uv, and, if we repeat the construction of the diagram of velocities for each of the instants f,, f, . the small value that is found for § will be positive in one case and negative in another. It is to be remarked in this respect. that there is no connexion at all between the values of &, which we shall find for two succeeding instants in the series f,, t,... Indeed, between any two such instants, every electron will have undergone a collision, and it may safely be assumed that, whatever he the direction of motion of an electron before the impact, all directions will be equally probable after the impact ‘). Now, in order to determine a’, , we have to take the square of the sum denoted by Y in the formula (17). This square consists of k terms of two kinds, some having the form “087 >> a = cos" nt [= oi = q° cos* n t. Pe tn A: (18) 1) This is easily shown, as has been done by Maxwett in his first paper on the kinetic theory of gases, if both the electrons and the particles of the metal are sup- posed to be perfectly elastic spheres. aoe el bie el Od —° "ty and others the form ee (9) ee 1S, S) Dinne a6 SI SS iG yes ae Z2cosnt, cosnt, | u a U =2q° cosnt, cosnt KS Kt | le Ar l k k ~ As has already been said, the time contains a very large number 2 x of periods ae A certain value of cos nt, once occurring in the series cosnt,, cosnt,, cosnt,,... may therefore be supposed to repeat itself many times. Also, one and the same value of the product cos nt, cos n ty may be said to occur for many different values of % and &’. Such a product will therefore have to be multiplied by very different expressions of the form &j §,, and, since the different values of § are mutually independent, the number of cases in which §, and sy have opposite signs will be equal to that in which they have the same sign. It appears in this way that the terms (19) will cancel each other in the sum. It is only the terms of the form (18) that remain, and we shall have n?e*t?q? > 2 = = |cos’ nt m 4701972" [ kowKk Sus — 5 ot (20) § 9. Here we may begin by taking together those terms in which cosnt, has one and the same value. Let the number of these be Q. Then, we have to repeat @ times the construction of the diagram of velocities, and it may be asked in how many of these Q cases § will lie between given limits § and $+ d6, or, what amounts to the same thing, what is the probability for § falling between these limits. This question may be reduced to a simpler problem. A series of planes, perpendicular to ( X and at equal distances from one another, will divide the spherical surface into equal parts. Therefore, instead of distributing the points D on the surface in an irregular, arbitrarily chosen manner, we may as well immediately distribute the points D' at random over the diameter, without giving any preference to one part of the line over another. The probability in question is thus found to be *) | Ly) 78g 38 Ba q : Pag= — [a ema rst Let BN Hence, among the Q terms in the sum, occurring in (20), for which the factor cos* nf, has equal values, there will be QPdé& terms, which may be said to have the same &;. Together, they will contribute to the sum the amount 1) See §§ 18—15. 46 Proceedings Royal Acad. Amsterdam. Vol. V. ( 676 ) cos” nt . Q P& d § and the total sum of all the @Q terms is got from this by an inte- gration which we may extend from § = » to §=-+o0. Conse- quently, the sum of those Q terms will not be altered, if, in each of them, we replace §*; by a B= | Pra Ja ee (22) This expression being the same whatever be the particular value of cos? ntp, the sum in (20) at once becomes §* > cos" nts 3. i. Ge Se ier ct ee Again, since the instants ¢,, 4,,.... are uniformly distributed at 2 distances that are very small parts of the period — , the sum will nu remain the same, if in every term we write 4 instead of cos? nég. o , we find for (23) The number of terms bemg — 4 and for (20) <2 820701 Or? he We have by (21) and (22) Ss =, 3q l : hence, replacing t by —, we find u ne? glu ne? NluA On = = = —— = wm 24276497? 242074 Or? and for the emission (14), in so far as it is due to the one kind of electrons that has been considered ve Nuh , ——— ww dn. 48a%¢*7? This value must still be multiplied by 2 because we may apply to the second of the components (6) the same reasoning as to the first component, and the total radiation from the plate may obviously be considered as the sum of all the values corresponding to the (Ohi) different kinds of electrons. The final result is therefore *) Bee (eo? N,l,u,+e,27N,lu,+.--.)Awo'drn. . (24) 2473037? 1 MA TLS 2 2°22 § 10. If now we divide (24) by (5), all quantities Nye, and /, by which one metal differs from another, disappear. This is what might be expected according to KircuHorr’s law and the result an T ——— ww dn 6a0°¢?r? may be taken to express the emission by a perfectly black body under the circumstances we have supposed. It represents the amount of energy which, in the case of such a body, is transmitted per unit of time across an element w’, in the rays whose frequency lies between m and n+ dn and whose directions deviate infinitely little from the normal to the element, being contained within a solid angle 2 @ eee 4am i fdes —. Multiplying by -, we are led to the following expression for r CLOG: % the density of energy of which I have spoken in § 2: 2an7T A TN eg oe ws mys at oe 3h ete (0) Taking for the group of rays those whose wave-lengths are cluded between 42 and 2+ da, we get for the corresponding energy per unit volume 1) It is easy to free ourselves frora the hypothesis that for all electrons of ene kind there is a single length of path 7 and a single molecular velocity w. Indeed, the motion of an electron along one of the small straight lines 7, which it describes between the instants O and J, will furnish for the sum in (15) a quantity € COs Nt. Uy Ty if w is the velocity for the particular line 7 we wish to consider, and 7 the time required for the motion along it. Now, among all these rectilinear motions between two successive encounters, of one kind of electrons, we may select those for which wand/ have certain definite values and we may begin by calculating the coefficient @ and the emission, in so far as they depend on the part of (15) which corresponds to these particular motions; in doing so, we may use the method shown in §§ 7—9%. The total emission may be regarded as the sum of all the partial values (with different /’s and dif- ferent w’s) thus obtained, and alter all the expression (24) will still hold, provided we understand by 4), 4,... cerlain mear lengths 0. path and by i, #)... certain _ mean molecular velocities. We need not however enter into these details, because the conductivity and the coefficient of absorption have not been calculated with a corresponding degree of accuracy. 46% ( 678 ) 9 BF te. A ee ; 2a This is found from (25) by using the relation n= § 11. The result of the preceding caleulations not only conforms to the law of Kircnnorr; it has also a form agreeing with those of BourzMann and Wien. Indeed, the expression (26) follows from (1), if we put 16 f(a) = — xa. AT. : 3 Our last task will be to evainate the constant @ by applying the formula (26) to experimental determinations of the radiation of black bodies, and to compare the result with what has been inferred about the same constant from pther classes of phenomena. Combining the measurements of Lumver and Princsuem'), who have gone far into the infra-red, with the absolute amount of the radiation as determined by Kurveavm *), I find erg C—O - degree On the other hand, we get, starting from VAN DER WAALS’ evalua- tion of the mass of an atom of hydrogen, e120 25: A comparison of my formula with that of PLANCK is also interesting. For very large values of the product 47, the denominator in Tp ch PM he : : (2) becomes ae and the expression itself = This agrees with (26), Ne — = Kk. Now the mean kinetic energy of a molecule of a gas would be Ye 5 &T according to PLayck and has been represented in what pre- cedes by @7. There appears therefore to be a full agreement between the two theories in the case of long waves, certainly a remarkable conclusion, as the fundamental assumptions are widely different. On the absorption by a thin metallic plate. § 12. Take the origin of coordinates in the front surface, the axis of 2 towards the metal, and let there be free aether on both sides. Writing € for the electric force, J for the current of conduction, 1) Lummer and PrinesHem, Verhandl. d. deutschen phys. Gesellsch., 1900, p. 163. *) Kurtpaum, Wied. Ann., Bd. 65, p. 754, 1898. ( 679 ) § for the magnetic force and putting the magnetic permeability = 1, we have for the metal ie fe a d rot ) = — FJ, rot © = — — f, Oe 5 - It is found by these equations that in electromagnetic waves travel- ling in the direction of the positive 2, € and can have the direc- tions of OX and O Y, and values equal to the real parts of the complex quantities int —x«(1+i)z int—4(1+i)= i ee ee ara ae ot) oe 7) a being the amplitude of the electric force, and the constants @ and x being given by 1 se Oo a= — —n0, 3" (1 —— 2) — c 2 2n Similarly, waves travelling in the opposite direction may be repre- sented by Ca gmt a(1-+-2) = int+2(1+2)z (28) Dy SS ee te For the aether the corresponding formulae are somewhat simpler ; in the first case aepaesh te. apes C= ae oo. Hy = ae “ sclcnestcn ware (9) and in the second int + i— z fee eee z G. == "ae Fa Hy, =—ae i ee aan (330) Now, if rays fall perpendicularly on the front surface of the plate, we may unite all the systems of waves arising from the repeated reflexions into the following parts: 1st. a reflected system in the aether, 2°4. transmitted waves in the aether behind the plate, 3"¢. waves in the plate, travelling towards the back surface and 4". rays in the metal, going in the opposite direction. Representing the incident rays and the motions mentioned under these four heads by the equations (29), (30), (29), (27), (28), with the values a,, a,, a, a,, a; of the amplitude, we have, in virtue of the conditions at the two surfaces (continuity of €, and J,) a, + a,=a, + a,, a, — a, =%(a, — 4G,), n s +s a Un a,e =a CO Ce Lee n s +s == ( 680 ) In these formulae, 4 is the thickness of the plate, and a(l 454) Ast 25 a yO oe The solution, in so far as it is necessary to our purpose, is (x*—1) (e-* — ets) = Gtl)eh— (ely 4x i—A Aerie Gee In these expressions 4 and consequently s are now to be supposed infinitely small. Replacing e—* and ets by 1—s and 1-++s, one finds Lift, 1 ef A Ces 8, ; 1 r\ 7 izA ay =|1 Fae (« - \ a, a x The first of these equations shows that the amplitude of the rays retlected by the thin plate is infinitely small, so that we may neglect their enérgy as a quantity of the second order. As to the transmitted rays, the amount of energy propagated in them will be equal to the product of the incident energy by the square of the modulus of the complex expression paces}! This square is whence we deduce for the coeflicient of absorption 0 A SSL. c On the probability with which one may expect that the centre of gravity of a large number of points distributed at random on a limited straight line will lie within given limits. § 18. Divide the line into a large number p of equal parts, and call these, beginning at the end A of the line, the 1s, the 2*4, the 3 part, etc. Denote by g the number of points and let q be very much larger than p. We shall imagine the points to be placed on the line one after another, in such a way that, whatever be the position of the points already distributed, a new point may as well fall on one part of ( 681 ) the line as on the other. The result will be a certain distribution of the whole number, entirely determined by chance. Let us conceive this operation to be very often repeated, say @ times, and let us calculate in how many of these Q cases, a desired distribution of the points over the p parts will occur. Dividing by Q we shall have the probability of the distribution. The probability that there will be a,6,... m points on the 1s*, 2nd, ....p™ part of the line (a+6-+...+m=q), is given by pe LONG: q! jog) Cid (OH Sa omiaY q : ae In the case of a very large value =, this probability becomes P extremely small, as soon as one of the numbers a,6,...m is far We : mG . below —. Neglecting these small probabilities, we shall confine our- P selves to those cases, in which each of the numbers a,/,....7 1s very large. Then, by the well known formula of Stiriine, y A ane a! =[V2azv | —) , ete. e@ and, if we put a b m ! ' ! SS a Ne enn q q q we shall find log P = — 4 (p—1) log (22%q) — g log p — : 2 f rf TO IEE — [(aq +3) log a’ +... -+- (m'g+ 3)logm']. . . . (82) It is to be remarked that the numbers a, 4, ...7 can only inerease or diminish by whole units. The numbers a',%'... m’ can change 1 by steps equal to —; this may be made so small that they may be q considered as continuously variable. § 14. We shall in the first place determine the values of a’, 6’, . . . in’ for which the probability P becomes a maximum. We have 1 1 d log P= — | (4 + — + qlog w )aal Sec +(1 + — + qlog nt Ja 2a 7 2m with the condition da +...+dm=0, which is a consequence of (HAE c.g A= Cog “Soe er hee Seema (353) The maximum will therefore be reached if ( 682 ) dU =... ams ’ so that the uniform distribution will be the most probable. We shall next consider the probability for a distribution differing a little from the most probable one. Let us put »* 1 1 . 1 a=—+a , V=—+4+4 8 , ....m=—-+p . (84) P P P and let us suppose the numbers «, @.... gu, to be so small in com- ; 1 parison with —, that in the expansion of the quantities in (82) in ’ ascending powers of @,3....u, we may neglect all powers surpassing the second. We have for instance haar gee Meateth 1 Lo al Say oga == oe og P+ are eae ate 1-5P a’ s 1 : where, in the last term, we may omit the term oP: because it is much smaller than g. If we put 1 1 = (p—1) log (2 aq) + a log p = log Py and keep in mind that, in virtue of (33), a-t p+... w=0, . 3 2 3 See the equation (82) becomes 1 log P = log Pn — > Pqe +pP+t.... +), P= Pm e- : Lge (38 Pp eos A) It is seen from this that P,, is the maximum of the probability, with which we shall have to do, if e=f=....=u=0. The equation shows also that, conformly to what has been said above, the probability will only be comparable to P,, so long as@,8....u : 1 . é are far below —. Indeed, if one of these numbers had this last value, z) P,, would be multiplied by RUE e 2p’ which, by our assumptions, is extremely small. § 15. Let 2% be the length of the line, « the distance along the u line, reckoned from the end A, and let us take — for the value or : P ( 683 ) this coordinate for all points situated on the first part of the line, 3 P for all points of the second part, and soon. Then, in the distribution that is characterized by a’, 0',....im’', the coordinate of the centre of gravity of the g points will be fae hcl Op —1)m'] / ‘ y M22 utfea4t3B--5y4+.. .+2p—1) pu) P The positive or negative value of HU Sep ea Ba A ated ae 5 5 (aS) is thus seen to represent the distance between the middle point of the line and the centre of gravity. We have to calculate the proba- bility for this distance lying between § and § + d3. The problem is easily solved by means of a change of variables. .a, Which serve to define a mode Instead of the quantities @, By... .4 of distribution, we shall introduce new ones @, ?',....u, the substi- tution being linear and orthogonal. Let us take for the first of the new variables 1 1 Cease iy B+...+-—w,... . (87) Vor VP and for the second 7] Na j= Pe gp TR a Ow a (57) x x x Where the numerators form an arithmetical progression, whereas x means the positive square root of the sum of the squares of the nume- rators. These expressions (87) and (38) may really be adopted, because the peculiar conditions for an orthogonal substitution are satisfied : in both expressions the sum of the squares of the coefficients is 1, and we get 0 if we add together the coefficients of (87) after having multiplied them by the corresponding coefficients in (88). As to the coefficients im the expressions for y',... 4, we may choose them as we like, provided the whole substitution remain orthogonal. The reason for the above choice of e@ and ~ will be clear; the condition (85) simplifies to (iO te) eee seo) and, in virtue of (35), the value (86) will be equal to S “au P in all cases with which we are concerned. 684) Now, the modes of distribution for which the value of & lies between § and § + d6§ are those for which #' lies between ?' and i+ dB’, if PP g.30 nu Since a = 0, every mode of distribution may be defined by the values of 3'...m’, these quantities being, like a, B,...m, capable of very small variations. We can therefore select, among all the modes of distribution, those for which p'...”’ lie between ? and p +d, y' and y + dy, ete. The number of these may be represented by hap... dp). o , oe. Soe where / is a coeflicient whose value need not be specified. It suffices to know that it is independent of the values chosen for ~...q’. This is a consequence of the linear form of the relations between these variables and a, 4,...m. As the just mentioned modes of distribution, whose number is given by (42), differ infinitely littke from one another, the probability P may be taken to be the same for each of them. Hence, the proba- bility for the occurrence of one of these modes, no matter which, must be hPdps: dp... fee From this we may pass to the probability for @’ lying between 8 and + d3', whatever be the values of 7'...u'; we have only to integrate with respect to these last variables. Now using the funda- mental property of an orthogonal substitution e+ pt... 4 wa? t+ ptt... tw, and attending to (39), we write for (43) ——Pq(#°---..4+ 2) Pre dp’... du’. If we integrate this expression from —o to + 0, as may be done for obvious reasons, denoting by / a coefficient that does not depend on »', we find for the probability in question pa ke ? d3’. On account of (40) and (41) this is equal to pg, a Be Pr od Be eae ee eee k’ being a new constant. ( 685 ) It remains to introduce the value of z*. According to the defini- ve : alata tion of this quantity, it is 3 P(p*—)), instead of which we may take 1 ; : Se ; 5 p’, because p is a very large number. In this way (44) changes into 37 5 te See ies oo or ALLS) We may finally determine the coefficient 4’ by remarking that (45), integrated from —o to + 2, must necessarily give 1. This requires that 1 39 I! SS pal u an z= iR bo} oo] als | | 12) o9 aes a Ser Microbiology. — “The decomposition of cellulose by aérobie micro- organisins.” By G. VAN Irerson Jr. (Communicated by Prof. M. W. Brirrtincr). (Communicated at the meeting March 28, 1903). When we introduce into the soil or into natural waters substances consisting of cellulose, such as linen, cotton or paper, it will be seen, that the greater part comparatively soon disappears, whilst the cellulose derived from the continually falling dead leaves and other parts of plants is also soon destroyed under natural conditions either totally or partly. It is also a known fact that the layer of humus in the primeval forests has a limited thickness, the decrease being just compensated by the increase caused by the falling of the leaves. Investigation shows that the cellulose, although chemi- cally so stable, is decomposed by micro-organisms. The observations by Mirscuuriich '), Pororr*), vAN TircHEmM *), TAPPEINER *), VAN 1) Ueber die Zusammensetzung der Wand der Pflanzenzelle, Monatsber. d. Berl. Akad., 1850, p. 102. 2) Ueber Sumpfgasgihrung, Arciiv. f. ges. Physiol., 1875, Bd. 10, 8. 113. 3) Sur le bacillus amylobacter et son role dans la putréfaction des tissus végétaux, Cc. R. t. 88, 1879, p. 88. — Identité du bacillus amylobacter et du vibrion buty- rique de M. Pasteur, C. R. t. 89, 1879, p. 5. 4) Ueber Celluloseverdauung, Ber. d. d. ch. G. Bd. 15, 1882, S. 999. — Ueber Cellulosegihrungen, Ber. d. d. ch. G. Bd. 16, 1883, S. 1734. — Ueber die Sumpf- gasegihrung im Schlamme der Teiche, Stimpfe u. Kloaken, Ber. d. d. ch, G. Bd. 16, 1883, S. 1740. ( 686 ) Sexus') and particularly those of Hoppe Seyter*) and of OMELIANSKI*) proved, that cellulose may be broken up by anaérobic bacteria, with production of methane and carbon dioxide, or hydrogen and carbon dioxide and simultaneous formation of acetic and butyric acids. In this communication it will be shown that cellulose may also be rendered soluble by aérobie bacteria. In the first place it was proved, that this substance may serve as a source of carbon for denitrifying bacteria and may, therefore, be made to disappear with great rapidity in the presence of nitrates. But it could also be shown that cellulose is fit as a carbonfood for common aérobie bacteria and although the solution then takes place slowly, there can be no doubt about the decomposition. The products derived from the cellulose play an important role in the nutrition of other microbes particularly the spirillae, so that an elegant accumulation experiment may be based on the use of cellulose as a source of carbon. Although the destruction of cellulose by anaérobic or aérobice bacteria requires a faintly alkaline medium, it may, with sufficient aération, also be acted on in a faintly acid surrounding by various moulds and mycelia of higher fungi. This was first demonstrated in 1886 by pe Bary for the genus Peziza and the same was shown by later observers for other moulds, whilst the destruction always appeared to be due to the action of an enzyme. Here we will prove that the power possessed by moulds to attack cellulose is not confined to certain species only, as one might imagine from the existing literature, but that a great number of the species of this group share that property. Finally, I wish to observe that I will occupy myself exclusively with the destruction of pure cellulose and not with that of lignified and corky cell-walls, where in the first place higher fungi are at work, as is shown by the researches of R. Hartie ‘). 1. The decomposition of cellulose by denitrifying bacteria. Mrvset *) states in 1871 that in the presence of cellulose bacteria 1) Biyjdrage tot de kennis der cellulosegisting. Dissertation, Leonards, at Leiden, 1890, (this contains a very complete literary review). 2) Ueber die Gihrung der Cellulose mit Bildung von Methan u. Kohlensiure, Zeitschr. f. Phys. Ch. Bd. 10, 1886, S. 401. 3) Sur la fermentation de la cellulose, C. R. t. 121, 1895, p. 653. — Sur un ferment de la cellulose, C. R. t. 125, 1897, p. 970. — Sur la fermentation cellu- losique, C. R. t. 125, 1897, p. 1131. — Ueber die Gahrung der Cellulose, Centrbl. f. Bakt. Abt. Il, Bd. 8, 1902, S. 193. ‘) Die Zersetzungserscheinungen des Holzes, Berlin 1878. ») De la putréfaction produite par les bactéries en présence des nitrates alcalins C. R. t. 81, 1876, p. 533. Nitritbildung durch Bacterien, Ber. d. d. cb. G. Bd. 8, 1875, S. 1214, a me Ses? ee i iba Cable 6 ieee a Le) 687 ) reduce nitrates to nitrites; he has, therefore, proved denitrification, in the largest sense of the word, as being possible with cellulose, but from his short notes we do not understand his modus operandi or the nature of the cellulose used in the experiments. Drnérain') positively states in 1897 that he has not been able to observe denitrification with flax fibres and the attention of Ome iAnskt (1.c.) has also not been attracted to this process when engaged in the study of the fermentations of cellulose. This investigator induces the methane or hydrogen fermen- tation by means of a nitrogenous food composed of ammonium sul- phate or phosphate and sometimes he also adds asparagine, peptone, extract of meat or of manure. Strange to say, he has not worked with nitrates; had he done so, he would have noticed that the nature of the process is completely modified, for instead of the methane or hydrogen fermentation denitrification sets in which is characterised by the production of free nitrogen and carbon dioxide. In a previous research *) on accumulation experiments with deni- trifying bacteria, I have shown that these aérobic organisms can oxidise many different organic substances out of contaet with air with the aid of nitrates or nitrites, according to the formulae: 5C+4K NO, + 2H,O =4K HCO, +2 N, + CO, 3C+ 4K NO, + H,0 =2K HCO, + K, CO, + 2N,. Denitrification was noticed with lactates, tartrates, citrates, malates, acetates, glucose, starch, asparagine, gelatin, broth, methyl and ethyl alcohol and it was, therefore, thought worth while to try Whether cellulose might also be used as a source of carbon supply in the denitrificationprocess, which indeed proved to be the case. Before describing my experiments in detail, I will first make some remarks as to the nature of the cellulose employed. As a rule Swedish filterpaper was taken. Although this paper gives a faint blue colour with a dilute solution of iodine it was found to be very difficult to remove the impurity with boiling water; the so-called starch-free paper from ScHLEICHHR and ScHtLL, which has been purified with hydrofluoric acid, showed the same reaction. Sometimes linen tissues and cottonwool were used, from which the first also gives a blue coloration with dilute solutions of iodine, whilst the latter does not show this reaction. The little impurities, present in the cellulose employed, were however, of no moment in my experiments, as the effect on the cell walls was judged by the changes observed by a microscopical investigation. 1) Recherches sur Ja réduction des nitrates, Ann. agron. t. 23, 1897. 2) Van Iverson, Accumulation experiments with denitrifying bacteria. Proc. Acad. of Science, Amsterdam July 1902. OSS I] obtained the best results with a paper pulp prepared by triturating Swedish filterpaper in water, care being taken that this pulp contained 2°), of cellulose. In order to obtain a thorough denitrification with cellulose, a bottle holding about 200 ce. is filled with the following mixture ; Tapwater ') 100, paper 2, KNO, 0,25, K,HPO, 0,05, and the mixture is then inoculated with a few ce. of mud (from a ditch). The bottle is then quite filled up in the manner deseribed in my former Communication (Le), to prevent access of air, and the cultivation takes place at 35°. After the lapse of about 8 days the action is perceptible, but only after 12 days a brisk fermentation sets in. The cellulose is carried to the top by the generated gasbubbles and a quantity of liquid is forced out of the bottle by the slimy froth, while the paper-pulp is kept back by the stopper. In the beginning of the process a strong formation of nitrite may be observed, but the nitrates and nitrites soon decrease and after the lapse of about 15 days, these compounds have disappeared. The liquid is now carefully decanted from the pulp, which may be done without appreciable loss of paper fibres, as these readily agglo- merate. The bottle is then refilled with the following liquid : Tapwater LOO, KNO, 0,25, K,HPO, 0,05. The process now starts much quicker than in the first cultivation, the nitrate disappears in + or 5 days and by repeating the operation a few times more, cultures may be obtained of an increasingly active denitrifying power, with which it is possible to completely reduce in one or two days 0.5 gram of KNQO, dissolved in 200 ce. of water. This method of working is preferable to adding a fresh quantity of KNO, to the original culture, as it is then not possible to reduce on the whole more than about */,°/, of KNO, (calculated in regard to the quantity of the liquid used, or 25 °/, in regard to the cellulose) because the process then comes to a standstill by the alkaline potas- sium carbonate formed from the nitrate. If now a sterilised liquid is inoculated with the strongly denitrifying rough culture and the cultivation allowed to take place under the same circumstances as described above, the action commences much more rapidiy than in the first preliminary experiment, whilst the same phenomena occur. Even after repeating the inoculation ten times, no change in the intensity of the process could be observed. Not only paper, but raw flax fibres, cottonwool and linen appeared 1) From the Downs at Loosduinen. ( 689 ) capable of inducing denitrification, the cottonwool, however, being attacked with great difficulty. No denitrification could be observed with sawdust or turf, whilst Vax Spnus (Lc. pg. 104) has also been unable to observe decomposition of wood-cellulose by real anaerobic bacteria. This extraordinary difficult decomposition of wood-cellulose out of contact with the air, is, according to this investigator, perhaps the key to the explanation of the formation of humine substances, peat, browneoal and coal. The distribution of the microbes, engaged in the denitrification of cellulose, in the mud from canals, seems to be a very general one, as each sample employed contained these germs. Although they are also very generally distributed in the earth, their number per cc. appears therein to be less, for, on using earth as infecting material, the action was delayed. Even in sea water, taken from the port of den Helder, were always microbes found, which in the presence ot cellulose could induce denitrification ; in how far these forms are similar to the terrestrial ones has not yet been ascertained, but I wish to call particular attention to the fact, that, at least near the shore, cellulose may disappear by denitrification. The changes, which cellulose undergoes during this process, are visible to some extent with the naked eye: the white fibres soon turn orange and the pulp acquires a_ viscous consistency. Microscopically, it appears, that already very soon after inoculation some of the fibres are inclosed in a_ bacterial mucus and after a prolonged culture this is the case with nearly all the fibres. At first, the whole of the fibre is still very plainly visible within this mueus, but gradually, on account of the decomposition, it completely disintegrates into loose fibrillae and at last we only find a few particles of cellulose left, or the fibre disappears altogether (fig. 1). This destruction of the cellulose becomes very pronounced, when instead of paper-pulp strips of filterpaper are used. By repeatedly adding fresh nitrate we then finally obtain bacteria-mem- branes, which still have the exact shape of the strips of paper but in which we only meet isolated fibres disintegrated into fibrillae or even still more decomposed. As is already stated, the woody substance is not attacked by denitrifying bacteria, the few annulated, spiral and pitted vessels, which are contained as impurities in the filterpaper, are found unaltered in this mucus. Fig. 2 shows the form of two very strongly dissolved paperfibres (@) and some non-attacked woody elements (3, y and d), which are still found in such preparations. The eases, liberated during the denitrification of cellulose and of ( 690 which some litres were collected, consist exclusively of free nitrogen and carbon dioxide; no trace of hydrogen, methane or nitrous oxide (N,O) was found. As regards the micro-organisms which take part in this process, a microscopical examination of the said bacterial mucus, which consists of a finely granulated substance, shows the presence of very small rod-like bacteria (fig. 1) and further there are found in the cultures infusoria, ameebae, monads, spirillae, other small bacteria and vibrionae; larger rod-bacteria or spore-forming organisms were not detected. That the bacteria, involved in the process, are no spore forming organisms, was also shown by the fact, that no pasteurised material of whatever origin (mud from a ditch or from the soil) can cause denitrification in the presence of cellulose. Many experiments have been made with the object of isolating the bacteria taking part in the denitrification, but always with a negative result. By inoculation on meat-gelatin and cultivating at 24°, I several times obtained pure cultures of Bacillus stutzeri New. and Leum., which bacterium was also found in large numbers in those cases where other denitrifying bacteria were present, so that denitrification with cellulose is a new accumulation experiment for this important species, which, however, does not attack the cellulose itself. On using meat-agar or one of the following culture liquids: Tapwater LOO, agar 2, sodium lactate 2, KNO, 0,05, K,HPO, 0,05, Tapwater 100, agar 2, glucose 2, KNO, 0,05, K,HPO, 0,05, and cultivating at 35°, other bacteria besides B. stutzeri were found and these were nearly always denitrifying ones. Very often a mucous colony of a motionless, non-spore forming denitrifying bacterium became conspicuous, while in other cases a small, slightly denitrifying spirillum may be isolated. No permanent denitrification with paper could, however, be obtained with any of these forms or with any combination thereof, even the crude mixture as it is formed on the plates was not capable to do this. The fact, that these bacteria may cause a temporary faint evolution of gas (which, at first, made me suspect, that the destruction of cellulose could be accomplished by ordinary denitrifying bacteria) must be attributed to the presence of small quantities of impurities in the cellulose. Still, I think we may take it for granted, that we are dealing here not with an anaérobie but with an aérobic bacterium, first of all, because all known denitri- fying bacteria are aérobic and only behave anaérobically in the presence of saltpetre, secondly because methylene-blue is not reduced, when added to a medium in which cellulose is denitrifying, whilst in ( 694 ) cultures of the know anaérobic bacteria this compound is always decolorised. We therefore come to the conclusion, that the bacterium, which causes the denitrification of cellulose, does not grow on the used nutrient media, or else, growing there, loses immediately its denitrifving properties. If now we compare the hydrogen and methane fermentations with the denitrifving process we find the following points of difference. Ist. In the hydrogen or methane fermentation the liberated gaseous products are carbon dioxide and hydrogen, or carbon dioxide and methane. 2nd. To those fermentations chalk must be added to neutralise the formed butyric and acetic acids, whilst in our case the saltpetre yields potassium carbonate and no volatile acids can be detected. 3d. Those processes take place ina medium wherein sulphates can be reduced to H,S and therefore methylene-blue is decolorised. In my experiments such a reduction of sulphates is quite out of the question as long as traces of nitrates and nitrites are still present. 4th. The methane and hydrogen fermentation are caused by comparatively large, well characterised spore forming organisms, our denitrification by very small bacteria, forming no spores. The velocity with which cellulose disappears during the denitri- fication is about the same as in the methane or hydrogen fermenta- tion of this substance. In a volume of 500 c.c., I sueceeded in completely dissolving 8 grams of cellulose all. but a few fibres, by means of 36 grams of KNO,, in a month’s time. The quantity of KNO, theoretically required amounts to only 24 grams, but in my experiments a portion of the nitrate was lost in the expelled liquid and, therefore, more nitrate was required. By means of the hydrogen fermentation, OMELIANSKI succeeded in dissolving 41.6 grams of cellulose contained in a volume of 3 litres in 3'/, months, and about 12 grams in a volume of 1 litre in 5 months, which velocities agree with the values found by me for the denitrification. Notwithstanding the possibility of denitrification of saltpetre under the influence of cellulose, in the presence of this substance nitrification of ammonium salts and nitrites can proceed without interruption. This has already been shown by Omenianski'), who cultivated the nitrite ferment on paper. We also observed nitrification of ammonium sults and nitrites, when a very small quantity of cellulose (about *) Kleinere Mitteilungen: tiber Nitrifikationsmikroben [, Centrbl. f. Bakt. Abt. I, Bd. 8, 1902, S. 785. 47 Proceedings Royal Acad. Amsterdam. Vol V. ( 692 ) 0.05 ° was introduced into a thin layer of one of the following cntitine liquids, which were inoculated with earth: Tapwater LOO, NH, CL 0,05, K,HPO, 0,05, or " " KNO, O05, ” O05, In my previous communication [| have already pointed out, that nitrification and denitrification may take place together in garden soil and that the aération decides, which of these processes will be the predominant one; the same conclusion may, therefore, now be drawn for cellulose as a nutrient material. A closer examination however shows, that the two processes cannot occur simulta- neously in the same particle, but that a localisation must take place, in this way, that strong aération is necessary in the particles where nitrification sets in, whilst the exelusion of air is necessary for the denitrification process. As has already been previously observed formation of nitrite takes place in the first stage of the denitrification process in the presence of cellulose and as this substance by no means prevents the oxidation of the nitrite to nitrate, these two processes, occurring simul- taneously, may cause the steady disappearance of cellulose. We therefore see, that these same processes may cause the disap- pearance of cellulose in soil and in waters, which plainly shows their reat importance in the “self-purification”, as also in the biological purification of sewage. Di The aerobic decomposition of cellulose hy hacteria. In order to demonstrate denitrification in the presence of cellulose in the manner described above, a very small quantity of this sub- stance (about 0,05°/,) only must be present, for on using more say, 2°/, the nature of the process is completely changed.” This must be attributed to a strong decomposition of the cellulose by aérobie bacteria, which then takes place and which produces a large quantity of soluble organic matter, rendering the nitrification impossible. This last phenomenon may be best observed when use is made of the following culture medium : Tapwater 100, paper 2, NH,CLO,1, K,HPO, 0,05, chalk 2. Instead of NH,Cl we may also add KNQ, (0,1), KNO, (0,1), peptone 0,1) or an unlimited quantity of MgNH,PO,. The cultivation takes place at 28—35° in Eriexmever flasks in a layer from 0,5—J em. in thickness, thus, under very aérobic. conditions, so that on using KNO, or KNOQO,, no denitrification can be expected, at least not at the commencement. ( 698 ) If mud from a ditch is used as infecting material a decided growth is already noticed after 5or6 days, the cellulose turns to an orange colour and may even disintegrate to a thin paste after 3 or 4 weeks. Microscopically, we see, that we obtain besides the cellulose-dissol- ving bacteria a very rich accumulation of spirillae, which however do not themselves attack cellulose. I have often repeated these experiments and always with the same result: the cultures become extremely rich in’ spirillae and these consist of many varieties. As a rule different species were found in a same culture, large spirillae with several windings in company with small, very mobile ones, but- sometimes if also happened, that it looked under the microscope, as if we were dealing with pure cultures of special spirillae. These different results being no doubt connected with the nature of the germs in the infecting materials employed. Often however, we meet besides the spirillae, infusoria, monads, amoebae and small forms of bacteria, sometimes also rod bacteria and spore forming organisms, but the spirillae are always in the majority. If such cultures are transported into the same sterile medium, the chief character remains the same, but the growth takes place more rapidly and as a rule the number of species of spirillae is much reduced, so that frequently but a single one remains. Here it is perhaps the proper place to state, that an accumulation of spirillae may also be obtained in using a nutrient liquid composed as follows : Tapwater LOO, calcium lactate 2, peptone 0,05, K,HPO, 0,05, which is infected with a small quantity of ditch-mud. At temperatures from 28—37° exceedingly rich spirillae cultures are formed in this liquid. It would, however, be too rash thence to conclude, that lactate is formed as a transient decomposition product of the cellulose. The destruction of the cellulose is not only apparent from the strong erowth of microbes, but also from a microscopical examination of the fibres. As in the case of the denitrification process, these are here also found to be enveloped with a bacterial mucus in which is always found a very small rod-bacterium, and occasionally a large micrococeus, which itself does not attack cellulose, but much accelerates its dissolution by the small bacterium. The destruction is no doubt caused by the latter, for sometimes, we have obtained cultures, which exclusively contained this species only. That the decomposition is here an aérobic one, is shown by the fact, that it commences at the surface of the culture and also takes place equally well when we cultivate in a very thin layer. 47% ( 694 ) Owing to the dissolution of the cellulose the absorption of oxygen in the cultures may become so. strong, particularly when working With thiek layers of cellulose paste, that anaérobie processes become possible. Tf now, nitrates or nitrites are still present in’ the culture denitrification will set in, but if these compounds are already decom- posed, or if origimally another source of nitrogen had been added, methane or hydrogen fermentation becomes possible. In the last case We microscopically observe the very characteristic rods with spores, accumulating on the fibres. [na this anaérobic stadium the spirillae are for the greater part expelled but the destruction is now much more intense than when it took place exclusively under aérobic conditions so that in a short time the paper pulp gets for the greater part dissolved and leaves behind a bacterial mucus. When using as infecting material soil, instead of mud from a ditch, we observe on the whole the same phenomena, only we do not find then that variety in’ species of spirillae noticed with ditch-water. As a rule a short, thick, granulated spirillum with one half winding is then conspicuous and | have succeeded in preparing pure cultures of this species, already observed previously *). An experiment with sea water showed, that this also causes the aerobic decomposition of cellulose and an accumulation of different species of spirillae was obtained at the same time. In this case the decom- position in the anaérobic stadium may also be caused by an anaérobic spore forming organism, which much resembles the bacteria of the methane and hydrogen fermentations but still presents a different shape. I have tried to isolate the bacteria connected with the aérobie destruction but was not more successful than in the denitrification experiment. On sowing on broth-gelatin or broth-agar a number of bacteria species were found: fluorescents, B. coli commune, B. sub- tilis, B. meseutericus and several others unknown to me, but none of these species or none combination thereof was capable of attacking cellulose. ‘ Our result that cellulose may be attacked by aérobie bacteria widely occurring in nature, is confirmed in a particularly convineing manner by the following experiment : In a glass box are placed two discs of Swedish filterpaper between which has been sprinkled a little quantity of powdered MgNH,PO, ; the paper is imbibed with a solution of 0.05 gram of K,HPO, in 100 ce. of fapwater. If now we introduce upon the plate thus prepared a little ') Beverinck. Ueber oligonitrophile Microben. Centrbl. f. Bakt. Abt. Il, 1901 Bd. 7, S. 574. ( 695 ) quantity of water containing in suspension humus, garden soil or, still better, diteh-mud, and if we cultivate at 24—28", the paper gets covered atter 4 or 5 days with yellowish-brown spots which, microscopically, are found to consist of bacteria. These spots spread with great rapidity, and it is highly interesting to observe how in a short time the white filterpaper is covered with the rusty cultte. This is accompanied by a decided decomposition of the paper fibre, which is shown in. the first place by the fact that the paper becomes quite soft and pulpy just on the spots exposed to the action of the brown bacterium, losing there all coherence and sinking down along the edges of the phos- phate. The phenomenon becomes still more pronounced, when instead of filterpaper, linen or cotton is used; after about 10 days, the affec- ted spots of the originally strong material have lost all power of resistance and after 15 days large holes will be formed when care- fully pouring water on them. Microscopically, it appears that a powerful destruction of the fibre is taking place (tig. 3) due to the action of a brown, very mobile, little rod bacterium (Bacillus ferrugineus fig. 4). The fibre is again enveloped by a mucus in which is found, in many cases, the sume micrococcus as mentioned above (fig. 5 and 6). Owing to the combined action of these two bacteria the fibre may disappear com- pletely and leave behind a mueus containing only micrococci; we then obtain an image as shown in fig. 7. In addition to amoebae and monads other small bacteria are found, but there is no question of the presence of anaérobies, which occur in the hydrogen or methane fermentations, the action being a purely aérobic one and taking place very well in filterpaper both sides of which are exposed to the air. On transferring the brown spots to previously sterilised paper dises, between which MeNH,PO, has been sprinkled and which have been saturated with a sterile 0,05"), solution of K,HPO,, the phenomenon remains constant. On inocculatine them into the above described cel- lulose pulp a culture is obtained resembling that which arises by the direct action of ditch-mud or earth, but no spirallae are found this time, for these being microaerophilous cannot grow in- the aérobic culture on the paper discs. On the other hand the cultures from paper pulp were occasionally capable of producing brown spots on paper dises, showing that im both cases the destruction of the cellulose may be caused by the same microbe. IT also noticed a few times that the dises were covered with colorless spots caused by a larger mucus-secreting rod, and as moreover the paper pulp cultures often are only little colored, it must be assumed, that the aérobic ONG decomposition of cellalose may be caused by two microbes at least, but among these the beown pigment bacterium is the most conspicuous. On using sea water as infecting material, similar brown spots were observed. When these were transferred to paper without addition of 3°, NaCl they caused no destruction, which shows that we are dealing here with a sperifie sea bacterium, | have made several experiments with various culture materials in order to isolate this very interesting cellulose-destroying brown pigment bacterium, which T was particularly anxious to accomplish after having observed, that the crude bacteria-mixture as grown on different culture media often again produces spots when spread over paper, which shows that on these media the said bacterium had kept alive. But IT was again unsuccessful in isolating a species whieh either alone or in combination with other bacteria was capable of causing the brown spots on paper. Though I sueceeded in isolating from these spots a brown and a yellow bacterium, which as a rule, Were present in large numbers, yet, as in the case of the denitrifiea- tion process, no destruction of cellulose could be induced by their pure cultures. The explanation of this circumstance has not yet been found, The aérobic destruction of pure cellulose and also the more difficult destruction of the lignified cell walls, ') on which we cannot enter in this investigation, must, like the denitrification (which is only possible with non lignified cellulose and takes place out of contact with air) play an important part in the disappearance of vegetable substances in nature. The well known fact that wooden piles, when partly immersed in water are attacked exactly at the place of contact between the water and the air, the breaking of ropes, when suspended in water, exactly at its surface and also the aérobic decay of wood must be attributed mainly to the action of aérobic destroyers. VAN Sexus (le. 108) who was acquainted with these facts, did not deny the possibility of a decomposition by aérobic bacteria but thought it very unlikely “as no phenomenon ever pointed to such a fact.” That the above-described yellowish-brown pigment bacterium plays indeed an important part in the disappearance of the cellulose, is shown by the following experiment. On October 14, 1902 were buried in the garden of the bacteriolo- gical laboratory at about 15 ¢.m. below the surface a linen cloth with a red colored border, and in two other places four sheets of filterpaper, all in a horizontal position. Left in the soil untouched during the recent winter and on exhuming them March 22, 1903 !) The great stability of wood-cellulose towards microbie life is directly opposed to the ready decomposition of wood paper under chemice! influences. —as not a trace could be found of the filterpaper, whilst the linen cloth had become soft and pulpy, had lost all coherence and could only be removed from the soil in pieces; the red border, however, had retained its original structure. The originally white tissue had assumed the same yellowish-brown colour so familiar to me from the cultures on the paper dises, while on microscopical investi- vation the fibres appeared to be much decomposed and disinte- vrated into fibvillae and besides moulds and amoebae only small bae- feria were observed. On putting some of the well-cleaned fibres on the paper dises prepared as described above, | obtained after three days the rapidly spreading, yellowish-brown spots of the destructive, small, rod-shaped pigment bacterium. A cellulose-destroying mould, Mycogone puccnuordes, also could be isolated from the linen, but the faet that the yellowish-brown pigment bacterium was here predominant, could not be doubted. 3. The decomposition of cellulose by moulds. The fact that cellulose may be attacked by certain fungi has been first stated by pe Bary') for Peziza selerotinm, and the same was found by Kissninc *) and by Marswant Warp *) fora kind of Botrytis, by Brnrens*) for Pseudodematophora, Botrytis vulgaris, Cladosporinn herbarum and Aspergillis glaucus. This last investigator did not notice any decomposition by Mucor stolonifer, Penicillium glaucum and Penicillium luteum. KouNstaM™ *) prepared a cellulose-destroying enzyme from Verulins lacrymans the common wood fungus. Wet") has shown, that Monilia sitophila, the “ontjom” mould from Java, is capa- ble of digesting cellulose and Koning *) has found that one of the ') Ueber einige Sklerotien u. Sklerotienkrankheiten, Bot. Zeit. 1886, S. 377. 2) Zur Biologie der Botrytis cinerea, Diss. Dresden, 1889. 5) A lily disease, Annals of Botany, Vol. [, 1888/89, p. 346. 4) Trockene u. nasse Faiule des Tabaks. Der ,Dachbrand”’, Zeitschr. f. Planzenkr. Bd. Uf, 1893, p. St. — Untersuch. ther den Wiirzelschimmel der Reben, Gentr.bl. f. Bakt., Abt. Il, Bd. 3, 1897, S. 584. — Beitrage zur Kenntniss der Obstfiiulnis, Centrbl. f. Bakt. Abt. Il, Bd. 4, 1898, S. 514. Unters. liber die Gewinn. der Hanffaser durch natiirl. Rostmethoden, Centrbl. f Bakt. Abt. 11, Bd. 8, 1902.8. 114. ») Amylolytiscke, glucosidspaltende, proteolytische u. cellulose lésende Fermente in holebewohnenden Pilzen. Bethefte z. Bot. Centrbl. Bd. 10, Heft 2, 1901., S. 90. ®) The influence of feeding on the secretion of enzymae by Monilia sitophila. Brocy Jan. 190: Ueber den Einflus der Nahrung auf die Enzymbildune durch Monilia sitophila (Moxy) Sace Jahrb. f wiss. Bot. Bd. 36, Heft 4, S. 643. 7) Genoolschap ter Bey. y. Natuur- en Heelkunde Amsterdam, 2 series, dl. DV, Afd. 5, Zitting 7 Dec, 1901, ‘ OOS most common houmus-inhabitants from the forest of Spanderswoude, Trichoderma koninga, possesses the same property. We have succeeded in finding an experiment by means of which the vellulose-destroving moulds may be isolated from nature in a direct and certain manner. Two sterile dises of Swedish filterpaper are placed in a glass box and moistened with the following liquid: Tapwater 100, NH,NO, 0,05, KH PO, 0,05, As infecting material earth or humus may be used, but the best results ave obtained by simply exposing the opened box for about 12 hours to the open air. Ifthen we cultivate at 24° and take care to keep the paper moist, colonies of moulds already become visible after 5 or 6G days, but it is only after 14 days or three weeks, that we notice the enormous richness of these cultures, and then we are surprised at the great number of mould species, which make their appearance. Many kinds which we seldom or never notice on malt-gelatin are found in large numbers on these paper discs. These species certainly are also capable of growing on malt-gelatin, but their germs, as ihey occur in nature, apparently find thereon an unfavorable soil. Another advantage of the cultivation on paper is that it is particu- larly favorable to the formation of perithecia and pienidia, which do not readily develop on rich soils *). From these culture experiments it appears that a continuous rain of spores from cellulose-destroying moulds falls in the garden as well as in the rooms of the bacteriological laboratory. For instance on March 11, when the weather was dry whilst the earth was moist, 152 cellulose-destroying moulds were colleeted on a plate of 275 ¢.m. square, after this had been exposed for 12 hours to the open air, and among these moulds about 35 species were recognised. As these germs must con- tinually drop on the soil, it might be expected that the latter would be remarkably rich in living moulds and it appeared from experi- ments. that this is really the case at the surface of the garden. soil, but in a much less degree than might have been expected, while lower down in the soil the number of moulds seems to be still less. From this it follows that most of the spores, which fall on the earth rapidly die off. In order to prepare a pure culture of the fungi isolated by the “paper-experiment™ some material from the raw cultures was trans- ferred to malt-gelatin, where it appeared that the moulds were generally much contaminated with bacteria, from which however, 1) Compare Motuarp, Role des bactéries dans la production des périthéces des Ascobolus, CG. R. t. 136, 1903, p. 899. (699 ) they could be freed by another inoculation. These bacteria are sapro- phytes which do not attack cellulose but grow at the expense of the products generated by the action of the moulds on cellulose. This result was not unexpected for, as stated in the preceding paragraph, the cellulose-destroying bacteria live in a faintly alkaline medium, whilst in the case of moulds the reaction is acid, owing to the presence of KH, PO,. In order to be perfectly certain of the pureness of the moulds, cultures from the spores were finally made on malt-gelatin. The following species, which were detected in’ these cultures, have been submitted to a closer examination : 1. Sordaria humicola Ovp. 2. Pyronema conjluens Ten. 3. Chaetomno hiunzeanin Zorr. 4. Pyrenochaeta Iumicola Ovn. 5. Chaetomella horrida Orn. 6. Trichocladium asperum Harz. 1. Stachybotrys alternans Ovn. 8. Sporotrichum bombycinum (Corps) Ras, 9, rf roseolun Ovp. en Briser. 10. " griseolunm Ovn. 11. Botrytis vulgaris Fr. 12. Mycogone puceinioides (PRrevss) Sacc, 13. Stemphylium macrosporoideum (B. en Br.) Sacc. 14. Cladosporium herbarum (Prrs.) Linn. 15. Epicoccum purpurascens. EMRUNB. In the determination of these species, of which Nes. 9°) and 4, are new, we have been kindly assisted by Prof. Dr. C. A. J. A. OupEMANs, to whom we have to express our thanks. In order to form an opinion on the destruction of cellulose by the isolated species, and also to study their fructification, pure cultures were inoculated on paper dises, which after sterilisation, were drenched with the above-named solution. Instead of merely placing the spores on the paper, it was found desirable to push them in it by means of a platinum wire and then to reduce the spots there to pulp. The culti- vation is made at 24°, care being taken to keep the paper moist, for which it was found advantageous not to use water only but the said liquid, as the nitrogen in particular is rapidly used up. The above-named moulds all grow over the paper dises, form their fructification-organs in avery characteristic manner and often produce intensively colored, brown, black and ved pigments, which are absorbed by the paper 1) Nederl. Kruidkundig Archief, Januari, 1903, TM ) libre. Interesting are the cultures obtained in’ this way of Chaetomium hunzeanmm, Which sometimes produces a carmine-red pigment and Whieh forms dark red peritheciae, the asei of which contain eight grey spores; those of Chaetomella horrida, which forms delicate black hairy pyenidiae, and particularly those of Pyrenochacta humicola, whieh produces an intense black pigment, stable towards acids and alkalis, and which communicates a dark colour to the fibres, quite resembling the humus coloring matters. This latter species however, grew more reudily on an alkaline medium, so that we prefered in this case the said drenched paper dises, between which Mg NH, PO, had been sprin- kled. An interesting culture is also that of Serdaria humicola, as this ascomycete is only then capable of forming perithecia on paper dises, when these give no longer any reaction on ammonia or nitrates. sesides the above-named species, a luxurious growth was obtained of Trichocladium asperum, Mycogone puccinioides and Stemphylinm macrosporoideun, Which three species exhibit great: similarity both in theiv morphological and physiological properties. Lpicoceum pau- purascens also grew strongly on the paper and formed a purple- red pigment. This species 1 met several times in the air and also in company with Cladosporiin herbarum) on half decayed leaves of Populus halsimifera. Cultures of these moulds were not only made on paper dises, but also on cellulose in Ernenmeyer flasks, into whieh was introduced a thin layer of the following culture liquid: Tapwater 100, paper-pulp 2, NH, NO, 0,05, KH, PO, 0,05. In this case a repeated addition of NH, NO, proved very advant- aveous. On the pulp the cellulose-destroyers grow still better than on the paper discs and in 3 or 4 days the cellulose is converted by the mycelium into a coherent mass. Afterwards, the fruetification organs appear, and with Botrytis culgaris even formation of sclerotia was observed. The destruction of the cellulose may be regarded as certain when strong growth on the paper dises and on the paper pulp are being observed. The impurities contained in the paper may also cause a slight growth of moulds which do not attack cellulose, but these soon cease to develop. The decomposition may be seen very clearly by a microscopic examination of the cultures on filter- paper, when these have stood a long time. It will then strike us how a large number of fibres have suffered a process of dissolution; sometimes pores are formed perpendicularly to the direction of the fibre, sometimes the fibres have disintegrated into fibrillae. Fig. 9 . ' 4 ao = ae a ee | eee ee Tear wes "7 ( TOL ) of our illustration shows the image of the destruction by IJycogon puccinioides, in which the structure of the fibrillae and the said pores are visible. The degree of destruction also may be ascertained by direct weighing. A culture with Mycogone puecinioides was made on a double disc of filterpaper, two equally heavy filters serving as control. After a culture, lasting 40 days, the dises, from which the strongly developed mycelium was not removed, weighed 1.00 gram, whilst the controlling dises weighed 1.16 gram, showing that about 14°/, of the cellulose had disappeared. A similar experiment with 7iicho- cladium asperun gave a loss of 9°/,. These great losses only can be explained by the oxidation of the products derived from the cellulose under the influence of the respiration process. The oxidation of cellulose also was studied with filferpaper pulp, namely by weighing the amount of carbon dioxide, liberated during a culture of Chaetomium kunzeanum. In this experiment an oxidation of about 4° a quantity large enough to remove all doubt about the destruction , of the cellulose could be noticed after a 28 days culture, of the cellulose. No, growth or only a very small one, was observed when eulti- vating the moulds on: Tapwater 100, agar 2, NH,NO, 0,05, KH,PO, 0,05, but as soon as cellulose was added a strong development set in, showing in a surprising manner, that agar is a less nutrient food for these moulds than cellulose. The cellulose used in these experiments must be very finely divided and was prepared by treating cottonwool With concentrated hydrochloric acid, which causes the cotton fibres to break up into very small fragments. A preparation, which appeared to be still more suitable was prepared as follows: Paper which has been converted into soda-cellulose by the action of strong soda-lye, is readily soluble in sodium xanthogenate to a light yellow liquid : the “viscose” of Cross and Brvan'), which is purified by precipitation with alcohol; on adding hydrochloric acid to its aqueous solution cellulose is precipitated in a very pure condition. I have to thank Mr. pe JonGH Scuerrer, for a specimen of this preparation, which he prepared in the chemical laboratory of the Polytechnic School at Deltt. I found that, when cultivating on this agarcellulose, the erowth entirely depends on the quantity of the cellulose added: with mueh cellulose a strone growth was observed. 1) Cross and Bryan, Celli/ose, 1895, p. 25. London, Longman Green and Co, 702 As in the ease of the moulds investigated by the above-named observers, also the species employed by me showed the presence of an enzyme, which dissolves cellulose and to which the name of “eollulase” may be given’). If cultures on cellulose pulp were treated with chloroform, the liquid, after being freed from chloroform by evaporation, appeared capable of reducing Fratine’s copper solution, If the culture had been boiled before being treated with chloroform, no reduction took place. From these last experiments, which were conducted similarly to those of Brnrexs (1c¢.), it appears that the moulds only produce the quantity of reducing matter necessary for their growth and no more. That the quantity or the nature of the enzyme secreted by the moulds differs considerably, is shown by the great difference in destructive power, as may be readily observed from the growth on the paper dises and from the dissolution of the cellulose in the paper-pulp cultures. ‘To the powerful destroyers belong: Trichocladium asperumn, Mycoqone puceinioides, Stemphyliam macro- sporoideum, Chactomella horvida, Botrytis rulyaris, Epicoccum pur- perascens. "To the moderately strong ones: Chactominm kunzeanum, Stachybotrys alternans, Cladosporium herbarum, Pyrenochaeta lame- cola, Pyronema conjluens. To the weak ones: Sordaria humicola, Sporotrichum bombycimm, Sp. roseolim, Sp. griseolum and Aspergillus niger. No destruction was noticed with IJycor stolonifer, Mucor mucedo, Demation pulilans and Rizopis eryzea. Summary of results. 1. Cellulose may be made to dissolve by the action of denitrifying, non-sporeforming aérobie bacteria provided there be an /iin/ted supply of aur. 2. Although nitrification cannot take place in the presence of a somewhat large quantity of soluble organic matter, cellulose does not afect this process in case of suflicient aération. 3. The combined action of nitrification and denitrification must play am important part in the disappearance of cellulose in nature, for instance in the self purification of waters and of the soil, as also in the biological purification of sewage. ') This name, already used by Konstam (1.c.) is preferable to the name cy/ase which has been used bij Browy and Morris (Journal of Chem. Soe. 57, 1890, p. 498) for the cellulose-dissolving enzyme in germinating seeds and should accord- ing to Merscunixorr (Ann. Inst. Pasteur, 1899, t. 12, p. 737) be given to an alexin occurring in normal serum. ( 703 ) 4. Cellulose may also be attacked, when there is a full supply of air by widely distributed, aérobic, nou-sporeforming bacteria, among which a brown pigment bacterium (4. fermmginens) is predominant, The destruction is particularly strong in symbiosis with a yellow micrococcus, which itself is inert. >. Extraordinarily rich spirillae cultures are formed in nutrient liquids in which cellulose is being attacked by aérobie bacteria after infection with ditch-mud or garden soil. Probably the distribution of the spirillae in nature is mainly governed by cellulose. 6. The property of moulds to attack cellulose is a very common one. The dissolution is due to a specific enzyme to which the name of “cellulase” may be given. 7. One of the causes of the origin of humus coloring matters is the formation of pigments from cellulose by bacteria and moulds. This investigation has been made in the bacteriological laboratory of the Polytechnic School under the guidance of Prof. Brterinck. Delft, March 1903. EXPLANATION OF THE FIGURES. Fig. L. Fibre of filterpaper with denitrifying bacteria, disintegrated into fibrillae, enclosed in mucus. Enlargement 550. lig. 2. Debris of filterpaper at the end of the denitrification process, most of the fibres are dissolved. z the last debris of cellulose fibres, 6, y and 3 nonattacked elements of *woodcellulose”. Enl. 100. Fig. 3. Fibre of filterpaper with aérobic bacteria disintegrated into fibrillae, ecclosed in mucus. Enl, 550, Fig. 4. VPactertum from the preceding ligure more strongly enlarged; arrows represent motion. Ent. 1500. Fig. 5. Fibre of filterpaper attacked by an aérobic bacterium with saprophytic micrococcus, commencing to disintegrate into fibrillae. Ent. 550. Mig. 6. Two fibrillae of the preceding fibre more strongly enlarged, with z aérobic destructive bacteria and § saprophytic micrococcus. Eni. 1500. Fig. 7. End of the destruction in fig. 5 the fibrillae having become invisible; micrococct only visible. Eni. 550. Fig. 8. Fibre attacked by aérobic bacteria, disintegrating into fibrillae and enclosed in a thin mucous layer as medium for a spirillae culture in which 3 species are recognisable. Enl, 550. Mig. 9. Destruction of a fibre of fillerpaper by Mycogone puccinioides, besides the fibrillary structure, cross pores lave been formed in the fibrillae owing to the action of the cellulase. Enl. 550. (May 27, 1903). ClhOEN, TEN ES: ABSORPTION (On the emission and) by metals of rays of heat of great wavelengths. 666. ABSORPTIONBAND (Observations on the magnetic rotation of the plane of polarisation in the interior of an). 41. — (The calculation “ from the magnetie rotation of the plane of polarisation for substances without an) in the visible spectrum. 413. ACCUMULATION experiments with denitrifying bacteria. 148. ACETALDEHYDE -+ paraldehyde (Equilibria of phases in the system :) with and without molecular transformation. 283. Acip (On the prussic) in the opening buds of Prunus. 31. acips (On the so-called compounds of sulphoncarboxylic) with sulphuric esters. 482. ABROBIC micro-organisms (The decomposition of cellulose by). 685. ALBERDA VAN EKENSTEIN (w.) and ©. A. Lopry pr Bruyn: “Formaldehyde (methylene)- derivatives of sugars and glucosides.” 175. ALLoys (The course of the meltingpoint-line of solid) or amalgams. (1). 424. (ID). 511. AMALGAMS (The course of the meltingpoint-line of solid alloys or). (1), 424. ([).511. AMPHIOXUS LANCEOLATUS (On the structure of the light-percepting cells in the spinal cord, on the neurofibrillae in the ganglioncells and on the innervation of the striped muscles in). 350. Anatomy. J. W. van Wisun: “A new method for demonstrating cartilaginous mikro- skeletons.” 47. ANGLES (On the connection of the planes of position of the) formed by two spaces 8; passing through a point and incident spacial systems. 53. ANTIMONY (On the atomic weight of), 543. are (The influence of variation of the constant current on the pitch of the singing). 311. ARONSTEIN (L.) and A. 8. van Nierop. On the action of sulphur on toluene and xylene. 288. Astronomy. [. I’. van pe Sanpe Bakuuyzen: “On the yearly periodicity of the rates of the standardelsck of the Observatory at Leyden, Hohwii No. 17.” (1). 68. (IL). 193. —- —. I. van pe Sanpp Baknuyzen: “Preliminary inyestigation of the rate of the standardelock of the Observatory at Leyden, Hohwit N°. 17 after it was mounted in the niche of the great pier.” 267. — J. Wreper: “On interpolation based on a supposed condition of minimum.” 364. ATMOSPHERIC PRESSURE (Measurements on the maguetie rotation of the plane of pola- risation in liquefied gases under), 243. 48 if CONTENTS. atomic weicut (On the) of Antimony. 543. atoms (Intramolecular rearrangement of) in azoxybenzene and its derivatives, 51. — (The intramolecular rearrangement of) in halogenacetanilides and its velocity. (1). 178. (IL), 359. auricLe of the mammalian heart (On the duration of the compensatory pause after stimulation of the). 378. AZOXYBENZENE (Intramolecular rearrangement of atoms in) and its derivatives, 51, BAcTERIA (Accumulation experiments with denitrifying). 148. Bacteriology. M. W. Bryerinck and A. vax Detpen: “On a colourless bacterium, whose carbon food comes from the atmosphere.” 398. BACTERIUM (On a colourless), whose carbon food comes from the atmosphere. 39S. BAKHUIS ROOZEBOOM (tH. W.) presents a paper of Prof. Kuc. Dusors: “Geolo- sical structure of the Hondsrug in Drenthe and the origin of that ridge.” (11). 101. — presents a paper of Dr. W. Retspers: Galvanic cells and the phase rule.” 182. — A representation in space of the regions in which the solid phases, which oceur, are the components, when not forming compounds. 279. — Equilibria of phases in the system : acetaldehyde 4- paraldehyde with and without molecular transformation. 283. — Tinamalgams. 373. — presents a paper of Dr. A. Smits and L. kK. Wore: “The velocity of trans- formation of carbon monoxide.” 417. — presents a paper of Mr. J. J. van Laar: “The course of the melting-point-line of soiid alloys or amalgams.” (D. 424. (ID. 511. — presents a paper of Mr. J. J. van Laar‘: ‘On the potential difference, which occurs at the surface of contact of two different non-miscible liquids, in which a dissolved electrolyte has distributed itseif.” 431. BAKHUYZEN (Ff. F. VAN DE SANDE). See SanvE Baknuyzen (E. F. van DR). — (i. G VAN DE SANDE). See Sanpe Bakuuyzen (H. G, VAN De). Bate of very uniform and constant low temperature in the cryostat. 502. 628. — (A permanent) of liquid nitrogen at ordinary and at reduced pressure. 631. REKMAN (E. H. M.). On the behaviour of disthene and of sillimanite at high temperature. 240. BRLZER (a. nH. J.). The velocity of transformation of tribroomphenol bromine into tetrabromophenol. 556. BEMMELEN (J. M. VAN) presents a paper of Mrs. L. Aronsrern and A. S. Van Nrerop: “On the action of sulphur on toluene and xylene.” 288. BENZIDINE transformation. 377. BEYERINCK (M. W.) presents a paper of Mr. G. van Iversoy Jr: “Accumulation experiments with denitrifying bacteria.” 148. — presents a paper of Mr. G. van Iverson Jr: “The decomposition of cellulose by aérobic micro-organisms.” 685. — and A. van DeLpeN. On a colourless bacterium, whose carbon food comes from the atmosphere. 398. w CONTENTS. Itt BLANKSMA (J, J.). The intramolecular rearrangement in halogenacetanilides and its velocity. {[). 178. (II). 359. — Nitration of symmetrical dinitroanisol. 650. BOEKE (J.). On the structure of the light-percepting cells in the spinal cord, on the neurofibrillae in the ganglioncells and on the innervation of the striped muscles in Amphioxus lanceolatus, 350. BOILINGPOINT-cURVE (The) of the system: hydrazine ++ water. 171. BONNEMA (J, H.). Cambrian erratic-blocks at Hemelum in the South-West of Irisia. 140. — Some new under-cambrian erratic-bloeks from the Dutch diluvium. 561." — Two new mid-cambrian erratie-blocks from the Dutch diluvium. 652. BORNEO (Influence of changed conditions of life on the physical and psychical develop- ment of the population of Central-). 525. Botany. £. Verscuarrent: “On the prussic acid in the opening buds of Prunus”, 31. — J. ©. Scuoure: “Die Steliir-Theorie”. 497. BRUIJN (Cc. A. LOBRY DBE). See Lopry pe Bruun (C. A.). BUCHNER (8. H.). The transformation of diphenyliodonium iodide and chloride and its velocity. 646. Bubs (On the prussie acid in the opening) of Prunus. 31. é ony 7 . 5 5 . e ‘ CALCULATION — (The) from the magnetic rotation of the plane of polarisation for sub- mM stances without an absorptionband in the visible spectrum. 413. CARBON Koop (On a colourless bacterium, whose) comes from the atmosphere, 398. CARBON MONOXIDE (The velocity of transformation of). 417. CARDINAAL (J,). On the geometrical representation of the motion of variable systems. 386. €aRTILAGINOUS Mikroskeletons (A new method for demonstrating). 47. cents (On the structure of the light percepting) in the spinal cord, on the neurofi- brillae in the gangtioncells and on the innervation of the striped muscles in Amphi- oxus lanceolatus. 350. CELLULOSE (The decomposition of) by aérobic micro-organisms. 685, Chemistry. H. M. Kyipscueer: “Intramolecular rearrangement of atoms in azoxybenzene and its derivatives”. 51. — ©. A. Losry ve Bruyn and J, W. Drro: “The boilingpoint-curve of the system : hydrazine -- water”. 171. — OC. A. Lospry pr Bruyn and W. Arperpa van Exkensrern: “lormaldehyde (methylene)-derivatives of sugars and glucosides”. 175. — J. J. Buanxsma: “The intramolecular rearrangement in halogenacetanilides and its velocity”. ({). 178. (IL). 359. — W. Rernpers: “Galvanic cells and the phase rule”. 182. — H. W. Bakuuis Roozrnoom: “A representation in space of the regions in which the solid phases which oceur, are the components, when not forming compounds”. 279. 48* lv CON f ON EO Chemistry. I. W. Bakituts Roozesoom: “Equilibria of phases in the system : acetaldehyde -+- paraldehyde with and without molecular transformation”, 283. — L. Aronstetn and A. 8. van Nrerop: “On the action of sulphur on tolnene and xylene”. 288, — H. W. Bakuuis Roozenoom: “Tinamalgams”, 373. — J. Porrer van Loon: “Benzidine transformation”. 377. — A, Smits and L. K. Worrr: “The velocity of transformation of carbon monoxide”. 417. — J. J. van Laar: “The course of the melting-point-line of solid alluys or amal- gams”. (L), 424. (ID). 511. — J. J. van Laan: “On the potential-diflerence, which occurs at the surface of contact of two different non-miscible liquids, in which a dissolved electrolyte has distributed itself”. 431. — A. P. N. Fraxcurmont: “On the so-called compounds of salts of sulphonear- boxylie acids with sulphuric esters’. 482. — KE. Conen and Tu. Srrencers: “On the atomic weight of antimony”. 543. — Ff. Comey and C. A. Losey pe Bruyn: “The conductive power of hydrazine and of substances dissolved therein’. 551. — A. H. J. Benzer: “The velocity of transformation of tribroomphenol bromine into tetrabromophenol”. 556. — ©. A. Lospry pe Bruyn and C. L. Juncius: “Dissociation in and erystallisation from a solid solution’. 643. — E. H. Bicuner: “The transformation of diphenyliodonium iodide and chloride and its velocity”. 646. — J. J. Buaxxsma: “Nitration of symmetrical dinitroanisol”. 650. cuLoripe (The transformation of diphenyliodonium iodide and) and its velocity. 646. COUEN (£.) and Tu. Strexcers. On the atomic weight of Antimony. 543. — and ©. A. Losry bE Bavuyy. The conductive power of hydrazine and of substances dissolved therein. 551. COMMON DiIvIsoR (An analytical expression for the greatest) of two integers, 658. COMPENSATORY PAUSE (On the duration of the) after stimulation of the auricle of the mammalian heart. 378. COMPONENTS (A representation in space of the regions in which the solid phases which occur, are the), when not forming compounds. 279. compounps (On the so-called) of salts of salphonearboxylic acids with sulplurie esters. 482. CONDITION of minimum (On interpolation based on a supposed). 364. CONDUCTIVE POWER (The) of hydrazine and of substances dissolved therein. 55). constants (The value of some magneto-optie). 438. corona (Peculiarities and changes of Fraunnorer-lines interpreted as anomalous dispersion of sunlight in the). 589. cRITICAL STATE (The equation of state and the J-surface in the immediate neighbour- hood of the) for binary mixtures with a small proportion of one of the compo- nents, 321. 336. CONTENTS W eryoceNte Laboratory (Methods and apparatus used in the). ILL, Bath of very uniform and constant low temperatures in the cryostat. 502. 628. A cryostat of modified form for apparatus of small dimensions. 628. LV. A permanent bath of liquid nitrogen at ordinary and at reduced pressure. 631. V. Arrangement of a BurcktiarDt-WEIss vacuumpump for use in the circulations for low temperatures. 633. cryostat (Bath of very uniform and constant low temperatures in the), 502. 628. — (A) of modified form for apparatus of small dimensions. 628. CRYSTALLISATION (Dissociation in and) from a solid solution. 643, cuRRENT (The influence of variation of the constant) on the pitch of the singing are. 311. DELDEN (A, vAN) and M. W. Beyertyck. On a colourless bacterium, whose carbon food comes from the atmosphere. 398. DIAGONALS of parallelotopes (Relations between). 540. DIFFRACTION of Réntgen-rays. 247. DILUVIUM (Some new under-cambrian erratic-blocks from the Dutch). 561. — (Iwo new mid-cambrian erratic-blocks from the Dutel). 652. DINITROANISOL (Nitration of symmetrical). 650. DISPERSION of sunlight (Peculiarities and changes of FrauNnuorpr-lines interpreted as anomalous) in the corona, 589. DISSOCIATION in and crystallisation from a solid solution. 643. DISTHENE (On the behaviour of) and of sillimanite at high temperature. 240. pivo (3. w.) and CG. A. Losry pe Bruyy. The boilingpoint-curve of the system: hydrazine ++ water. 171. DUBOTS (NUG.). The geological structure of the Ilondsrug in Drenthe and the origin of that ridge. (I). 93. (II). 101. Errect (A new law concerning the relation between stimulus and). 392. 441. EISENROSE (On an) of the St. Gotthard. 605. ELECTRIC ciRcuUIT (Some remarkable phenomena, concerning the) in electrolytes. 465, ELECTRIC CURRENT (On the advantage of metal-etching by means of the). 219. ELECTROLYTE (On the potential-difference, which occurs at the surface of contact of two different non-miscible liquids, in which a dissolved) has distributed itself. 431. ELECTROLYTES (Some remarkable phenomena, concerning the electric circuit in). 465. ELEGTROMAGNETIC PHENOMENA (The fundamental equations for) in ponderable bodies, deduced from the theory of electrons. 254. ELECTRO-MECHANICcS (Statistical). (1). 22. (II. 114. ELECTRONS (Contributions to the theory of. (I). 608. — (The fundamental equations for electromagnetic phenomena in ponderable bodies, deduced from the theory of). 254. EMIssIoN (On the) and absorption by metals of rays of heat of great wavelengths. 666. uNtRovY (Lhe prinziple of) in physiology. (Il). 57. EQUATION or stare (The) and the y-surface in the immediate neighbourhood of the critical state for binary mixtures with a small proportion of one of the components. 32]. 336. — (The variability with the density of the quantity 4 of the). 487. vi CONTENTS. FouaTIONs (Reduction of observation) containing more than one measured quantity, 236. — (The fundamental) for electromagnetic phenomena in ponderable bodies, deduced from the theory of electrons, 254. EQUILIBRIA of phases in the system: acetaldehyde + puraldehyde with and without molecular transformation, 283. ernaric-BLocks (Cambrian) at Hemelum in the South-West of Frisia. 140, — (Some new under-cambrian) from the Duteh diluvium, 561, — (Iwo new mid cambrian) from the Dutch diluvium. 652. ERRATUM. 217. esters (On the so-called compounds of salts of sulphoncarboxylic acids with sulphuric). 482- ernane and Methylalcohol (Critical phenomena of partially miscible liquids). 473. Ethnology. A. W. Nieuwenuuis: “Influence of changed conditions of life on the physical and psyehical development of the population of Central-Borneo.” 525. FORMALDEUYDE (Methylene-) derivatives of sngars and glucosides. 175. PRANCHIMONT (a. P. N.). On the so-called compounds of salts of sulphonearboxylie acids with sulphuric esters. 482. FRAUNHOFER-LINES (Peculiarities and changes of) interpreted as anomalous dispersion of sunlight in the corona. 539. GALVANIC CELLS and the phase rule. 182. GANGLIONCELLS (On the structure of the light-percepting cells in the spinal cord, on the neurofibrillae in the) and on the innervation of the striped muscles in Am- phioxus lanceolatus. 350.. Gases (Isotherms of diatemic) and their binary mixtures. V. Anu accurate volumeno- meter and mixing apparatus. 636, — (Measurements on the magnetic rotation of the plane of polarisation in liquefied) under atmospheric pressure. 243. Geology. Eve. Dusors: “The geological structure of the Hondsrug in Drenthe and the origin of that ridge”. (I). 93. (If). 101. — J. H. Bonnema: “Cambrian erratic-blocks at IHemelum in the South-West of Frisia”. 140. - — J. H. Boxnema: “Some new under-cambrian erratic-blocks from the Dutch dilu- vium’’. 561. — J. H. Boxnema: “Two new rid-cambrian erratic-blocks from the Dutch dilu- vium”. 652. GEOMETRICAL representation (On the) of the motion of variable systems. 386. GLucostpEs (Forma!dehyde (methylene)- derivatives of sugars and). 175. — (Investigations of) in connection with the internal mutation of plants. 295. uaGa (H.) and C. H. Wrxp. Diffraction of Rontgen-rays 247. WALLO (3. J.). The value of some magneto-optic constants. 438. HALOGENACETANILIDES (The intramolecular rearrangement in) and its velocity. (1). 178. (II). 359. ueart (On the duration of the compensatory pause after stimulation of the auricle of the mammalian). 37S. HEMELUM (Cambrian erratic-blocks at) in the South-West of Frisia. 140. CONTENTS. VII HOGENRAAD (G. &.). On an /Bisenrose” of the St. Gotthard. 605, woNbskuG in Drenthe (Lhe geological structure of the) aud the origin of that ridge. (1). 93. (LL). 101. HYDRAZINE (Lhe conductive power of) and of substances dissolved therein. 551. — + water (The boilingpoint-curve of the system :). 171. wypRoGEN (Lhe course of the values of 4 for), in connection with a recent formula of Prof. van per Waats, 573. HYNDMAN (H. Hw. FR.) and H. Kamertinau Ones, Lsotherms of diatomic gases and their binary mixtures. V. An accurate voltwnenometer and mixing apparatus. 636. HypotuEsts (An) on the nature of solar prominences. 162. inpdeEx (On the refractive) of rock-glasses. 602. rxervatTion (On the structure of the light-percepting cells in the spinal cord, on the neurofibrillae in the ganglioncells aud on the) of the striped muscles im Amphioxus lanceolatus. 350. rvreGeRs (An analytical expression for the greatest common divisor of two). 658. rNteNsttY (On maxima and minima of) sometimes observed within the shading of strongly widened spectral lines. 662. INTERPOLATION (On) based on a supposed condition of minimum, 364. INPRAMOLECULAR rearrangement of atoms in azoxybenzene and its derivatives, 51. — rearrangement (The) in halogenacetanilides and its velocity. (I). 178. (II). 359. ropipy (Lhe transformation of diphenyliodonium) and chloride and its velocity. 646. ISOTHERMS of diatomic gases and their mixtures. V. An accurate volumenometer and mixing apparatus. 636. ITERSON JR. (G. VAN). Accumulation experiments with denitrifying bacteria. 148. — The decomposition of cellulose by aérobic micro-organisms. 685. JuLivs (w. H.). An hypothesis on the nature of solar prominences, 162. — presents a paper of Prof. fi. Conen and Tu. Srrencers: “On the atomic weight of antimony”. 543. — Peculiarities and changes of F'ravunuorer-lines interpreted as anomalous disper- sion of sunlight in the corona. 589. — On maxima and minima of intensity sometimes observed witbin the shading of strongly widened spectral lines. 662. JUNGIUs (c, L.) and C. A. Losey be Bruyy. Dissociation in and crystallisation from _a solid solution. 643. KAMERLINGH ONNES (H.) presents a paper of W. H, Kersom: “Reduction ol observation equations containing more than one measured quantity”. 236. — presents a paper of Dr. L. H. Srertsema: ‘Measurements on the magnetic rotation of the plane of polarisation in liquefied gases under atmospheric pressure. IL. Measurements with methylchloride”. 243. — presents a paper of Dr. J. E. Verscuarreny: “Contributions to the knowledve of VAN DER WAALS y-surface. VIL. The equation of state and the p-surface in the immediate neighbourhood of the critical state for binary mixtures with a small proportion of one of the components”. 321. 336. vir CO wT. eT 2. KAMERLINGH ONNES (Ht) presents a paper of Dr. L, U.Sientsema;: “The calculation : from the magnetic rotation of the plane of polarisation, for eub- u stances without an absorptionband in the visible spectrum”. 415. — presents a paper of Prof. J. P. Kuenen; “Criticnl phenomena of partially mis- cible liquids- Ethane and Methylalcohol”, 473. - Methods and apparatus used in the Cryogenic Laboratory. III. Bath of very uniform and constant low temperatures in the cryostat. 502, 628. A cryostat of modified form for apparatus of small dimensions. 628. LV. A permanent bath of liquid nitrogen at ordinary and at reduced pressure. 63i, V. Arrangement of a BURCKHARDT-WEISS vacuumpump for use in the circulations for low temperatures, 633. — and H. H. Fr. Hynxpman. Isotherms of diatomic gases and their binary mix- tures. V. An accurate volumenometer and mixing apparatus. 636. KEESOM (wW. UL). Reduction of observation equations containing more than one measured quantity. 236, KLUYVER (J. c.). An analytical expression for the greatest common divisor of two integers. 658. KNIPSCHEER (H. M.). Intramolecular rearrangement of atoms in azoxybenzene and its derivatives. 51. KOLK (J. L. CG. SCHROEDER VAN DER). See SCHROEDER VAN DER KoLk (J. L. C.). KORTEWEG (ov. J.). Plaitpoints and corresponding plaits in the neighbourhood of the sides of the P-surface of VAN DER Waats. 445. KUENEN (J. P.). Critical phenomena of partially miscible liquids-Ethane and Methyl- alcohol. 473. LAAR (J. J. VAN). The course of the melting-point-line of solid alloys or amal- gams. (I), 424. ({L). 411. — On the potential-difference, which occurs at the surface of contact of two different non-miscible liquids, in which a dissolved electrolyte has distributed itself. 431. — On the course of the values of 4 for hydrogen, in connection with a receut formula of Prof. vaN DER Waats. 573. LANGELAAN (J. w.). The principle of entropy in physiology. (LI). 57. Law (A new) concerning the relation between stimulus and effect. 392. 441. Lire (Influence of changed conditions of) on the physical and psychical development of the population of Central-Borneo. 525. Liquips (Critical phenomena in partially miscible). 307. — (Critical phenomena of partially miscible)-Ethane and Methylalcohol. 473. — (On the potential-difference, which occurs at the surface of contact of two dilfe- rent non-miscible), in which a dissolved electrolyte has distributed itself. 431. LOBRY DE BRUYN (C. A.) presents a paper of Dr. H. M. Knipscueer: “Intra- molecular rearrangement of atoms in azoxybenzene and its derivatives.” 51. — presents a paper of Dr. J. J. Buanksma: “The intramolecular rearrangement in halogenacetanilides and its velocity.” (1). 178. (ID. 359. — presents a paper of Dr. ‘lu. Wrevers: “Investigations of glucosides in connec- tion with the internal mutation of plants,” 295. COUN) 2 EN TS: Ix LOBRY DE BRUYN CC. A.) presents a paper of Dr. J. Porrer van Loon: “Benzi- dine transformation.’ 377. — presents a paper of Mr. A. H. J. Beuzer: “The velocity of transformation of tribroomphenol bromine into tetrabromophenol.’’ 556. — presents a paper of Mr. E. H. Bicuner: ‘The transformation of diphenylio- donium iodide and chloride and its velocity”. 646. — presents a paper of Dr. J. J. Buanxsma: “Nitration of symmetrical dinitro- anisol”’. 650. — and W. Aperpa vaN Exensrern. Formaldehyde (methylene)- derivatives of sugars and glucosides. 175. — and E. Coney. The conductive power of hydrazine and of substances dissolved therein. 551. — and J. W. Divo. The boilingpoint-eurve of the system: hydrazine + water. 171, —and C. L. Junetus. Dissociation in and crystallisation from a solid solu- tion. 643. LOON (J. POTTER VAN). See PorreR van Loon (J.). LORENTZ (H. a.). The fundamental equations for electromagnetic phenomena in ponderable bodies, deduced from the theory of electrons. 254. — presents a paper of Mr. A. H. Sirks: “Some remarkable phenomena, concerning the electric circuit in electrolytes”. 465. — Contributions to the theory of electrons. ([). 608. — On the emission and absorption by metals of rays of heat of great wave- lengths, 666. MAGNETO-oPpTIC Constants (The value of some). 438. MARTIN (K.) presents a paper of Prof. Euc. Dusois: “Geological structure of the Hondsrug in Drenthe and the origin of that ridge.” (1). 93. Mathematics. P. H. Scnoure: “On the connection of the planes of position of the angles formed by two spaces Sz passing through a point and incident spacial systems.” 53. — 8. L. van Oss: “Five rotations in S, in equilibrium.” 362. — J. Carptnaat: “On the geometrical representation of the motion of variable systems.” 386. — Jan pe Vrigs: “On the spheres of Monee belonging to ordinary and tangential pencils of quadratic surfaces.” 484. — P. H. Scuoute: ‘Relations between diagonals of parallelotopes.” 540. — J. GC. Kivyver: “An analytical expression for the greatest common divisor of two integers.” 658. MEASUREMENTS on the magnetic rotation of the plane of polarisation in liquefied gases under atmospheric pressure. IT. Measurements with methylchloride. 243. MELTING-POINT-LINE (The course of the) of solid alloys or amalgams. (I). 424. (il). 511. METAL-ETCHING (On the advantage of) by means of the electric current. 219. METALS (On the emission and absorption by) of rays of heat of great wave-lengths. 666. METHOD (A new) for demonstrating cartilaginous mikroskeletons. 47. x CONTEBUT 6. METHODS and apparatus used in the Cryogenic Laboratory, ILI. Bath of very uniform and constant low temperatures in the eryostat. 502. 628, A cryostat of modified form for apparatus of small dimensions. 628. LV. A permanent bath of liquid nitrogen at ordinary and at reduced pressure, 63). V. Arrangement of a BouckHarpt- Weiss vacuumpump for use in the circulations for low temperatures. 633. MeTHYLALCOHOL (Critical phenomena of partially miscible liquids-Ethane and). 473. METHYLCHULORIDE (Measurements with). 243, METHYLENE-derivatives, See FoaMALDEnYDE (methylene)-derivatives. Microbiology. G. van Lrerson Jr.: “Accumulation experiments with denitrifying bae- teria”. 148. — G van Iverson Jr.: “The decomposition of cellulose by aérobic micro-orga- nisms.” 685. MIKROSKELETONS (A new method for demonstrating cartilaginous). 47. Mineralogy. E. H. M. Beekman: ‘On the behaviour of disthene and of sillimanite at high temperature.” 240. — P. Tescu: “On the refractive index of rockglasses.’’ 602. — G. B. Hocenraap: “On an /Eisenrose” of the St. Gotthard.” 695. MIXING apparatus (An accurate volumenometer and). 636. mixrurEs (The equation of state and the J-surface in the immediate neighbourhood of the critical state for binary) with a small proportion of one of the components, 321. 336. — ([sotherms of diatomic gases and their binary). 636. MOLECULAR transformation (Some observations on the course of the). 303. MOLL (3. W.) presents a paper of Mr. J. H. Bonnema: “Cambrian erratic-blocks at Hemelum in the South-West of Frisia.” 140. — presents the dissertation of Dr. J. C. Scuoure : “Die Stelir-Theorie.” 497. — presents a paper of Mr, J. H. Bonnema: “Some new under-cambrian erratic- blocks from the Dutch diluvium”. 561. — presents a paper of Mr. J. H. Bonnema: “Two new mid-cambrian erratic-blocks from the Dutch diluvium.” 652. MONGE (On the spheres of) belonging to ordinary and tangential pencils of qua- dratie surfaces. 484. MOTION of variable systems (On the geometrical representation of the}. 386. MUSCLES in Amphioxus lanceolatus (On the structure of the light-percepting cells in the spinal cord, on the neurofibrillae in the ganglioncells and on the innervation of the striped) in Amphioxus lanceolatus. 350. MUTATION of plants ({nvestigations of glucosides in connection with the internal). 295. NEUROFIBRILLAE (On the structure of the lightpercepting cells in the spinal cord, on the) in the ganglioncells and on the innervation of the striped muscles in Amphioxus lanceolatus. 350. NIEROP (a. S. VAN) and L. Agonstern. On the action of sulphur on Toluene and Xylene. 288. NIEUWENHUIS (a. w.). Influence of changed conditions of life on the physical and psychical development of the population of Central-Borneo. 525. i. CONTENTS. XI NITRATION of symmetrical dinitroanisol. 650. NITROGEN (A bath of liquid) at ordinary and at reduced pressure. 631. OBSERVATORY AT LEYDEN (On the yearly periodicity of the rates of the standardclock of the), Hohwii n°. 17. (1). 68. (ID. 193. — (Preliminary investigation of the rate of the standardclock of the) Hohwii n°. 17, after it was mounted in the niche of the great pier. 267. Oss (8. L. VAN). Five rotations in S, in equilibrium. 362. PARALDEHYDE (Equilibria of phases in the system: acetaldehyde +-) with and without molecular transformation. 283. PARALLELOTOPES (Relations between diagonals of), 540. PEKELHARING (c. A.) presents a paper of Prof. K. F. Wenckrepacn: “On the duration of the compensatory pause after stimulation of the auricle of the mam- malian heart”. 378. PENCILS (On the spheres of Monce belonging to ordinary and tangential) of qua- dratic surfaces. 484. PERIODICITY (On the yearly) of the rates of the standardelock of the Observatory at Leyden, Hohwii No 17. (1). 68. (II). 193. PHASE RULE (Galvanic cells and the). 182. PHASES (A representation in space of the regions in which the solid) which oceur, are the components, when not forming compounds. 279. — (Equilibria of} in the system: acetaldehyde + paraldehyde with and without molecular transformation. 283. PHENOMENA (Critical) in partially miscible liquids. 307. — (Critical) of partially miscible liquids-Ethane and Methylalcohol. 473. — (Some remarkable), concerning the electric circuit in electrolytes. 465. Physics. J. D. van per Waaus: ‘Ternary Systems”. (IV). 1. (V). 121. — J. D. van per Waats Jr.: “Statistical electromechanics”. (Ll). 22. (II). 114. — P. Zeeman: “Observations on the magnetic rotation of the plane of polarisation in the interior of an absorption band”. 41. — W. H. Junius: “An hypothesis on the nature of solar prominence”. 162. — A. H. Siexs: “On the advantage of metal-etching by means of the electric current’. 219. — J. D. van per Waats: “On the conditions for the occurrence of a minimum critical temperature for a ternary system”. 225. — W. H. Kzrsom: “Reduction of observation equations containing more than one measured quantity”. 236. — L. H. Stertsema: “Measurements on the magnetic rotation of the plane of pola- risation in liquefied gases under atmospheric pressure. II. Measurements with Methylehloride”, 243. — H. Haca and C. H. Winp: “Diffraction of Réntgen-rays” (2nd communication). 247. — H. A. Lorentz: “The fundamental equations for electromagnetic phenomena in ponderable bodies, deduced from the theory of electrons”, 254. XII CONTENTS. Physics. J. D. vax pen Waats: “Some observations on the course of the molecular transformation”, 303. — J. D, van per Waats; “Critical phenomena in partially miscible liquids”. 397, — J. kK. A. WertHem: Saromonson: “The influence of variation of the constant current on the pitch of the singing arc”. 311. — J. EB. Verscuarre.t: “Contributions to the knowledge of VAN DER WAALS )-sur- face. VII. The equation of state and the y-surface in the immediate neighbour- hood of the critical state for binary mixtures with a small proportion of one of the components.” 321, 336. . . e . . — L. H. Srertsema: “The calculation — from the magnetie rotation of the plane m of polarisation, for substances without an absorptionband in the visible spectrum”. 413. — J. J. Hauio: “The value of some magneto-optic constants”. 4338. — D. J. horrewee: “Plaitpoints and corresponding plaits in the neighbourhood of the sides of the y-surface of VAN DER WAALS”. 445. — A. H. Smks: “Some remarkable phenomena, concerning the electric circuit in electrolytes”. 465. — J. P. Kuenen: “Critical phenomena of partially miscible liquids-Ethane and Me- thylaleohol”. 473. — J. D. van ver Wasts Jr.: ‘The variability with the density of the quantity 4 of the equation of state”. 487. — H. Kameriincu Onnes: “Methods and apparatus used in the Cryogenic Laboratory: IIT. Baths of very uniform and constant low temperatures in the cryostat. 502. 628, A cryostat of modified form for apparatus of small dimensions. 628. IV. A permanent bath of liquid nitrogen at ordinary and at reduced pressure. 631. V. Arrangement of a BurckuarpT-WeIss vacuumpump for use in the circulations for low tem- peratures. 633. — J. J. van Laar: “On the course of the values of 4 for hydrogen, in con- nection with a recent formula of Prof. vax per Waats”. 573. — W. H. Jouxivs: “Peeuliarities and changes of Fraunnorer-lines interpreted as consequences of anomalous dispersion of sunlight in the corona.” 589. — H. A. Lorentz: ‘Contributions to the theory of electrons.” (I). 608. — H. Kamersinen Onnes and H. H. Francis Hynpman: “Isotherms of diatomic gases and their binary mixtures. V. An accurate volumenometer and mixing apparatus.” 636. — W. H. Juirus: “On maxima and minima of intensity sometimes observed within the shading of strongly widened spectral lines.” 662. — H. A, Lorentz: “On the emission and absorption by metals of rays of heat of great wave-lengths.” 666. Physiology. J. W. Lancrtaan: “The principle of entropy in physiology.” If). 57. CONTENTS XIII Physiology. J. Porke: “On the structure of the light-percepting cells in the spinal cord, on the neurofibrillae in the ganglioncells and on the innervation of the striped muscles in Amphioxus lanceolatus.” 350. — Kk. I. Wenckusacu : “On the duration of the compensatory pause after stimulation of the auricle of the mammalian heart.” 378. — J. k. A. Werruer Satomonson: “A new law concerning the relation between stimulus and effect.” 392. 441. Physiology of plants. Tu. Wrevers: “Investigations of glucosides in connection with the internal mutation of plants.’ 295. PLACE (%.) presents a paper of Dr. J. W. Lancunaan: “The principle of entropy in physiology.” (IL). 57. — presents a paper of Dr. J. Borke: “On the structure of the light-percepting cells in the spinal cord, on the neurofibrillae in the eangtioncells and on the inner- vation of the striped muscles in Amphioxus lanceolatus.” 250. PLAITPOIN’S and corresponding plaits in the neighbourhood of the sides of the p-surface of VAN DER Waats. 445. PLANE OF POLARISATION (Observations on the magnetic rotation of the) in the interior of an absorptionband. 41. — (Measurements on the magnetic rotation of the) in liquefied eases under atmos- pheric pressure, 243. . é re . . . . . — (The calculation — from the magnetic rotation of the) for substances without an absorptionband in the visible spectrum. 413. PLANES OF posiTioN (On the connection of the) of the angles formed by two spaces Sp passing through a point and incident spacial systems. 53. pLANts (Investigations of glucosides in connection with the internal mutation of), 295. PONDERABLE Bobtes (The fundamental equations for electromagnetic phenomena in), deduced from the theory of electrons, 254. poruLaTION of Central-Borneo (Influence of changed conditions of life on the physical and psychical development of the). 525. POTENTIAL-DIFFERENCE (On the), which occurs at the surface of contact of two difte- rent non-miscible liquids, in which a dissolved electrolyte has distributed itself, 431. POTTER VAN LOON (J.). Benzidine transformation. 377. PRINCIPLE (The) of entropy in physiology. (I1). 57. prunus (On the prussic acid in the opening buds of). 31. quantity (Reduction of observation equations containing more than one measured), 236. — # (The variability with the density of the) of the equation of state. 487. RAYS OF HEAT (On the emission and absorption by metals of) of great wave-lengths. 666. REINDERS (w.). Galvanic cells and the phase rule. 182. ROCK-GLASSES (On the refractive index of). 602. RONTGEN-RAYS (Diffraction of). 247, ROOZEBOOM (H. W. BAKHUIS). See Bakuurs Roozesoom (H. W.). = xIV CONTENTS. ¥ f a roTaTION (Observations on the magnetic) of the plane of polarisation in the interior A of an absorptionband, 41, et — (Measurements on the magnetic) of the plane of polarisation in liquefied gases ; under atmospheric pressure, 245. i: a rd . pe tg — (The calculation — from the magnetic) of the plane of polarisation for substances E u“ without an absorptionband in the visible spectrum, 413. gta xoraTions (Five) in S, in equilibrium. 362. a SA\LOMONSON (. K. A. WERTHEIM). See Wertnem Savomonson (J. K. A,). SANDE BAKHUYZEN (B ¥. VAN De). On the yearly periodicity of the rates : of the standardelock of the Observatory at Leyden, Hohwii n°. 17. (B. 68. (10). 193. — Preliminary investigation of the rate of the standardclock of the Observatory at Leyden, Hohwii n°. 17 after it was mounted in the niche of the great pier, 267. SANDE BAKHUYZEN (H. G. VAN DE) presents a paper of Mr. J. Weeper: a “On interpolation based on a supposed condition of minimum”. 364. scuoure (J. Cc). Die Steliir-Theorie. 497. scu OUTE (P. H.). On the connection of the planes of position of the angles formed by two spaces Sq passing through a point and incident spacial systems. 53. — presents a paper of Dr. S. L. van Oss: “Five rotations in S; in equilibrium.” 362. — Relations between diagonals of parallelotopes. 540. SCHROEDER VAN DER KOLK (J, L. ¢.) presents a paper of Mr. A. IL. Sieks: “On the advantage of metal-etebing by means of the electric current.” 219. — presents a paper of Mr. E. H. M. Beekman: “On the behaviour of disthene and } of sillimanite at high temperature”. 240. — presents a paper of Mr. P. Trsca: “On the refractiveindex of rock-glasses”. 602. — presents a paper of Mr. G. B. Hoceyrasp: “On an #Kisenrose” of the St. Gotthard.” 605. suapinc (On maxima and minima of intensity sometimes observed within the) of strongly widened spectral lines. 662. sLERTSEMA (L. H.). Measurements on the magnetic rotation of the plane of pola- risation in liquefied gases under atmospheric pressure. LI. Measurements with Methylehloride. 243. € — The calculation — from the magnetic rotation of the plane of polarisation for Vit substances without an absorptionband in the visible spectrum. 413. sILIcEOUS sPIcuULES (On the shape of some) of sponges. 104. [ sintimanrze (On the behaviour of disthene and of) at high temperature. 250. sinks (A. H.). On the advantage of metal-etching by means of the electric current. 219. f — Some remarkable phenomena, concerning the electric circuit in electrolytes. 465. sMiTs (a.) and L. K. Wourr. The velocity of transformation of carbon monoxide. 417. SOLAR prominences (An hypothesis on the nature of). 162. ‘es ; SOLUTION (Dissociation in and crystallisation from a solid). 643. space (A representation in) of the regions in which the solid phases which oceur, — are the components, when not forming compounds. 279. CONTENTS. XV spaces S, (On the connection of the planes of position of the angles formed by two) passing through a point and incident spacial systems. 55, SPECTRAL LINES (On maxima and minima of intensity sometimes observed within the shading of strongly widened), 662. srecrruM (The calculation < from the magnetic rotation of the plane of polarisation 1 for substances without an absorptionband in the visible). £13. spugres of Monge (On the) belonging to ordinary and tangential pencils of quadratic surfaces. 454. sPonGEs (On the shape of some siliceous spicules of). 104. STANDARDCLOcK (On the yearly periodicity of the rates of the) of the Observatory at Leyden, Hohwii no. 17. (D. 68. (ID. 193. — (Preliminary investigation of the rate of the) of the Observatory at Leyden, Hohwii no. 17, after it was mounted in the niche of the great pier. 267. STATISTICAL electro-mechanics. (I). 22. (IL. 114. STELAR-THEORIE (Die). 497. STIMULUS and Effect (A new law concerning the relation between). 392. 441. STRENGERS (tH.) and E. Cowen. On the atomic weight of antimony. 543. srructore (The geological) of the Hondsrug in Drenthe and the origin of that ridge. (1). 93. (1. 101. suGars and Glueosides (Formaldehyde (methylene)-derivatives of). 175. suLeHuR (On the action of) on toluene and xylene. 288. Y-survacE (Contributions to the knowledge of van per Waaus’). VIL. ‘The equation of state and the y-surface in the immediate neighbourhood of the critical state for binary mixtures with a small proportion of one of the components. 321. 336. — (Plaitpoints and corresponding piaits in the neighbourhood of the sides of the) of VAN DER WAALS. 445. SURFACE OF conracr (On the potential-dillerence, which occurs at the) of two different non-miscible liquids, in which a dissolved electrolyte has distributed itself. 431. surraces (On the spheres of Monee belonging to ordinary and tangential pencils of quadratic). 484. . system (On the conditions for the occurrence of a minimum critical temperature for a ternary). 225, — Acetaldehyde + Paraldehyde (Kquilibria of phases in the) with and without molecular transformation. 283. — Hydrazine + Water (The boilingpoint-curve of the). 171. SYSTEMS (On the connection of the planes of position of the angles formed by two spaces Sv passing through a point and incident spacial). 53. — (On the geometrical representation of the motion of variable). 386. — (Ternary). (IV). 1. (V). 121. TEMPERATURE (Bath of very uniform and constant low) in the cryostat. 502. 628, — (On the conditions for the occurrence of a minimum critical) for a ternary system, 225. TEMPERATURES (Arrangement of a BuRcKHARDT-WEIss vacuumpump for use in the circulations for low). 633. xYI CONTENTS. TERNARY system (On the conditions for the occurrence of a minimum critical tem- perature for a). 225, TeRNARY systEMs. (LV). 1. (V). 121. resceu (p.). On the refractive index of rock-ylusses. 602. TETRABROMOPHENOL (The velocity of transformation of tibroomphenol bromine into). 556, rugkory of electrons (Contributions to the). (1). 608. — of electrons (The fundamental equations for electromagnetic phenomena in pon- derable bodies, deduced from the), 254. TINAMALGAMS, 973. — (The meltingpoint-line of). 511. TOLUENE and Xylene (On the action of sulphur on). 258. TRIBROOMPHENOL bromine (The velocity of transformation of) into tetrabromophenol, 556. vacuumpume (A Burckuarpt- Weiss) for use in the circulations for low temperatures, 633. vanurs of 4 (The course of the) for hydrogen, in connection with a recent formula of Prof. van pek Waats. 573. VARIATION (The influence of) of the constant current on the pitch of the singing are, 311. vELocity of transformation (The) of carbon monoxide. 417. — of transformation (The) of tribroomphenol bromine into tetrabromophenol. 556. VERSCHAFFELT (E.). On the prussic acid in the opening buds of Prunus. 31. VERSCHAFFELT (J. £.). Contributions to the knowledge of VAN DER WAALS’ y-surface. VII. The equation of state and the Q-surface in the immediate neigh- bourhood of the critical state for binary mixtures with a small proportion of one the components. 321. 336. VOLUMENOMETER (An accurate) and mixing apparatus. 636. VOSMAER (G. c. J.). On the shape of some siliceous spicules of sponges. 104. VRIES (HUGO DE) presents.a paper of Prof. E. Verscuarrenr: “On the prussie acid in the opening buds of Prunus.” 31. VRIES (J4N De). On the spheres of Monce belonging to ordinary and tangential pencils or quadratic surfaces. 484. WAALS (VAN. DER) dg-surface (Contributions to the knowledge of). VII. The equation of state and the y-surface in the immediate neighbourhood of the critical state for binary mixtures with a small proportion of one of the components. 321. 336. — (Plaitpoints and corresponding plaits in the neighbourhood of the sides of the W-surface of). 445. WAALS (J. D. VAN DER). Ternary systems. ([V). 1. (V). 121. — presents a paper of Dr. J. D. van DER Waats Jr.: “Statistical electro-mecha- nies”. (lj. 22. ([[). 114. — On the conditions for the occurrence of a minimum critical temperature for a ternary system. 225, — Some observations on the course of the molecular transformation, 303. — Critical phenomena in partially miscible liquids. 307. GON NE ND Si XVII WAALS (J. D. VAN DER) presents a paper of Dr. J. D. vAN ber Wadts Jr. : “The variability with the density of the quantity 4 of the equation of state.” 487. — presents a paper of Mr. J. J. van Laar: “On the course of the values of 4 for hydrogen, in connection with a recent formula of Prof. vAN DER Waats”. 573. WAALS JR. (J. D. VAN DER). Statistical electromechanies. (I). 22. (II). 114. — The variability with the density of the quantity > of the equation of state. 487. warer (The boilingpoint-curve of the system: Hydrazine ++). 171. WEEDER (J.). On interpolation based on a supposed condition of minimum, 364. WEEVERs (TH.). Investigations of glucosides in connection with the internal muta- tion of plants. 295. WENCKEBACH (kK. F.). On the duration of the compensatory pause after stimula- tion of the auricle of the mammalian heart. 378. WERTHEIM SALOMONSON (J. K. A.). The influence of variation of the con- stant current on the pitch of the singing are. 311. — A new law concerning the relation betweer stimulus and effect. 392. 441. ys. 247. WINKLER (c.) presents a paper of Prof. J. K. A. Werturim SaLomoyson: “A new WIND (c. u.) and H. Haga. Diffraction of Rontgen-r: law concerning the relation between stimulus and ellect”. 392. 441. WOLFF (1. K.) and A. Smits. The velocity of transformation of carbon monoxide. 417. WYHE (J. w. V A N). A new method for demonstrating cartilaginous mikroskeletons. 47. XYLENE (On the action of sulphur on toluene and). 288. ZEEMAN (e.). Observations on the magnetic rotation of the plane of polarisation in the interior of an absorption band. 41. — presents a paper of Prof. I. K. A. Werrarim SaLomonson: ‘The influence of yariation of the constant current on the pitch of the singing are”. 311. — presents a paper of Dr. J. J. Hatno: “The value of some magneto-optic con- stants”. 438. Zoology. G. C. J. Vosmarr: “On the shape cf some siliceous spicules of sponges”. 104, cr “ i. 5 — 5 i” “39 ate ae” ~ ; eye 4 ‘ ‘ 4 ‘ ® F é f fi ) i ob PN! ‘ 5 ‘ i » j a. - : « *% 4 . < ‘ ry ’ . Be 4 - PA. ws oe : sh oy - he A ar il —_ * ee ee —v oe _ — : ary O28) (=a ee 7 ‘ ~ _ % 7 i, Y@e “< a. . r - — eh ae a 2s me ¢ ° ¥ : - i =? ‘ = 7 ; : ® 7 -“d . . ‘ : v : = "a y uy “ - , = hoe aoe a ee et 4 ae +8) —Q Akademie van Wetenschappen, 57 Amsterdam. Afdeeling voor ALS de Wis- en Natuurkundilge v5 Wetenschappen Physical & Proceedings of the Section Applied Sci, of Sciences Cc Serials PLEASE DO NOT REMOVE CARDS OR SLIPS FROM THIS POCKET UNIVERSITY OF TORONTO LIBRARY S\ ORAGE wou SF PVP? ut 1 nag + tt Vs Se ope i ctgy tg eet ST eras Si toe hia