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(fA f a ee cso ia “3 " A pompeeray =” a Se aiacetdiate laaptaptcla’s grt Tag Y > - @, § PALL TTT TT abet re TA wee bwe’ oy rap acl HT | Ht BUDA bbb hob dit btep aad ob ba St@aue ae | > Oo < Qe ea ml O SCIENTIF OVERNMENT PRENTING OFFICE cxucsa 0 : . eVeeurry | a Te) te 4 Rite AX faw®t eeese AeUces embR RR ine \ ig od pita & onan bd = aN ‘ FL | ae, Vk fist Pete _ane s oa \ , Homes wh ae “i ww Tbe SRS Bie Mwy Ur va yens ma pW Jt ex re oe f ht ~ if Sigma OUare: 1 } oan | ye" wd Oe ae vr re | restive, me Ni ‘ Yee el + Wo ert TLL TIM yt H+ rant Seey ESS wy, me ' Wey. pe. : | ; ; 441) a i at = (ty, bo ce Samenttel ester No wg BP ; nem, bs | a y we eraee i wiv ge yo aa ail ce aD ureel aeyituee | 5 a ee de Ww won a a anon my ea eat & oe tee acme Nae Nil [Me Le bed tel tt el A dh beh bel —| 1 | a eae ' ; | ems i Ay ~ “~ -2 #25. Dr. F. G. Donnan on a Theory of Colloidal Solution ...... Mr. C. G. Barkla on the Velocity of Electric Waves along WAKES TS. eee ee aw ole eee ve See Proceedings of the Geological Society.............-..008. On the Normal Curve of Errors, by Prof. Karl Pearson .... An Error in Dr. Willows’s Paper ‘‘On the Absorption of Gas in a Crookes Tube,” by Walliam Rollins: 22.12) See Page . 539 548 593 PLATES, 1. & II. Illustrative of Mr. W. Barlow’s Paper on Crystal Symmetry. Ill. & IV. Illustrative of Prof. R. W. Wood and Mr. C. E. Magnusson’s: Paper on the Anomalous Dispersion of Cyanin. Y. Illustrative of Dr. Morris W. Travers’s Paper on the Liquefaction _of Hydrogen. ,VI. Illustrative of Dr. S. W. Richardson and Mr. Louis Lownds’s Paper on the Magnetic Properties of the Alloys of Cast-Iron and Alu- minium. ERRATA. P. 69, in the heading to the last column of Table IIL, 320 3330 for Oa read = Pp P. 70, in the heading to the last column but one of Table IV., 41:0 1410 for a read ¢= Fy P. 145, line 5 from bottom, for 6 read ‘6. P. 584, line 2 from bottom, for (—4; °169) read (—4; -219). : 4\? 8 P. 587, line 4 from bottom, for (5 6 read ( =) 6. P, 587, line 2 from bottom, fe Su 6 — 6 for tan 7 a igen } read tan See : 2 P. 588, lines 2 and 4 from top, for ( =) 6 read (=)2 THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES.]- Cd JANUARY 1901\ . Kr « I. Crystal Symmetry. The Actual Basis of the Thitty-two Classes. By WitLIAM BaRLow*. Se OR [Plates I. & IL] i the study of crystals a large part of the evidence as to the nature of the symmetry displayed is not derived from their external form, but from properties of the crystal sub- stance, such as its action on polarized light, its different degrees of vulnerability in different directions when attacked by solvents, &c. 7: it may indeed be said that no investigation of the symmetry of one of these bodies which fails to take into account the tests of internal symmetry is now regarded as complete. The additional evidence referred to often seems contradictory to, or difficult to reconcile with, the symmetry of the external form ; in many cases it indicates that what had previously been regarded as single crystals are in fact groups of crystal individuals symmetrically arranged with respect to one another. The difficulty arises from the fact that the grouping of crystals is commonly of a highly sym- metrical character, and such that the face-directions of * Communicated by the Author. Published also in Groth’s Zeitschrift fiir Krystaliographie. + Comp. Sohncke in Entwickelung einer Theorie der Krystallstruktur , pp. 3 and 4. This writer gives the following definition of a crystal :—- “Kin Krystall ist ein homogener fester Korper, dessen geometrisches und physikalisches Gesammtverhalten nach den verschiedenen in ihm gezo- genen Richtungen hin im Allgemeinen verschieden ist, und der bei ungestorter Aushildung von ebenen Flachen begrenzt ist.” Phil. Mag. 8. 6. Vol. 1. No. 1. Jan. 1901. B 2 Mr. W. Barlow on Crystal Symmetry. different individuals possessing some lower type of sym- metry, which are found interlocked or intercalated, are so related that their arrangement more or less closely resembles that proper to a single crystal of a higher type. The tendency to persist in regarding external form as the one proper index to the symmetry is meanwhile evidenced by the common use of the term optical anomalies to designate some of the discrepancies alluded to; the use of this term seeming to imply that the classification of crystals has to be determined by the external form, and that.any incongruity of the internal structure with the result is to be regarded as exceptional. If, however, it is asked whether it has ever been the practice to admit that the symmetry of the arrange- ment of individual crystals in a group, and not the symmetry of each individual considered alone, is to be taken into account in a systematic classification of crystals, the reply is in the negative—the grouping of crystal individuals has always been treated separately, and no notice has ostensibly been taken of it for the purposes of classification ; it 1s only in cases where ignorance of the nature of the internal struc- ture has led to a group of differently-orientated crystal individuals being for a time regarded as a single individual, that the torm of the group instead of the form of the individual has been made the basis of the classification ; e.g. crystals of leucite, formerly regarded as belonging to the regular system, are now known to be rhombic twins. Having regard to the facts just alluded to, it is somewhat remarkable that the important work of deducing the existence of 32 classes of crystal symmetry from first principles hus been based on crystal form and not on internal structure. Thus Gadolin, in his classical work on the subject, defines likeness of two directions in a crystal as depending on the similarity of their disposition with respect to the faces of the erystal*. And Hessel, the original discoverer of the 32 classes T, treats crystal symmetry ‘purely as a matter of simi- larity of position with respect to one another of lines and planes which obey Haiiy’s law of rational indices f. : Clearly it is a valid objection to this reference of the * Gadolin, “ Mémoire sur la déduction d’un seul principe de tous les systémes cristallographiques avec leurs subdivisions,” Acta Soc. Scient. Fennica, ix. 1867; and separate, Helsingfors, 1871. Translated by Groth, Ostwald’s Klassiker d. exrakt. Wiss. No. 75, 1896. + See L. Sohncke: “Die Entdeckung des Eintheilungsprincips der Krystalle durch J. F. C. Hessel,” Zeitschrift fiir Kryst. xviii. p. 486. {t Hessel’s ‘‘ Krystallometrie,” in Ostwald’s Klasstker der exakten Wassenschaften, Nr. 88 & 89. Mr. W. Barlow on Crystal Symmetry. 5) symmetry solely to the face-directions, that groupings of dis- tinct crystals exist in which a mere consideration of the: faces does not reveal the composite structure *; but, apart from this, a case is conceivable in which the effect of the employment of Gadolin’s definition is to place an individual crystal in a class of a symmetry higher than can be attributed to the actual internal structure. The case referred to is the one mentioned by Gadolin in which what, according to his definition of like directions, is a trigonal axis, is not a crystal axisf: it may be described as follows :— Suppose that three axes, to which Haiiy’s law of rational indices can be applied, are so situated in a certain crystal as. to form the edges of a regular right triangular pyramid, while the minimum intercepts on the three axes respectively, Fig.. L. AGS O OA, OB, OC (fig. 1), measured from the vertex O of the pyramid for the purposes of the law, are a ; /n.as Vn. a, n being an integer, but Vnand nr? irrational. It can then _ be easily proved that, judged solely by the directions of its __ * For example :—a group of crystal individuals of boracite in the doubly-refracting state. + Gadolin: Mémoire &c. pp. 49 & 50. The assumption made by this writer in his introduction, that two directions which are similarly related to the external form of a crystal display identical physical relations, is not universally true; the case described by Gadolin himself, which is referred to in the text, furnishes an exception to it. B 2 A Mr. W. Barlow on Crystal Symmetry. faces, as in Gadolin’s definition, such a crystal will possess trigonal symmetry, every face having corresponding to it in other. possible faces similarly related, as to direction, to the system of axes. Sucha relation between the faces dom not, however, involve actual trigonal symmetry, and indeed, if Haiiy’s conception of the existence of parallelepipedal ultimate units*, or any other conception of molecular struc- ture, as a cause ‘of the law of rational indices, be adopted, it is easy to see that, with such relations between the intercepts as have just been ‘postulated, the dimensions of the ultimate units of the mass cannot be the same in the three different, directions of the three axes f. Consequently, what trigonal symmetry there is in such a case must be expected to subsist only at a eritical point of temperature and other physical conditions, and when it is present to reveal itself merely by equality of angles, not by any of the properties which, by producing obvious similarity of different directions, ordinarily indicate symmetry: viz., such properties as crystal habit, directional effects on light or temperature, or on chemical solvents. A ease such as that just described suffices to show that Gadolin’s definition is too superficial ; that it does not go deep enough to coincide in all cases with the actual phe- nomena ; what is wanted is a definition of the symmetry of erystals which will zn all respects harmonize with the variation of property with direction which characterizes these bodies t. * Haiiy was led to the discovery of the law of rational indices by the hypothesis that crystals have an ultimate atomic structure of such a nature that they are always geometricuily divisible by three systems of parallel planes into similarly orientated parallelepipedal ideal units of identical shape and composition, and the further conception that crystal faces always have the direction of planes so drawn as to pass through the centres of neighbouring units and be very thickly set with these centres. + For the purposes of Haiiy’s law a great latitude in the choice of units of length for the different axes is admissible in any given case ; indeed, any set of appropriate units having been selected, it is allowable to substitute for any one of them a unit which is an integral part or an integral multiple of it, without altering the others, and this may be dene more than once. A substituted unit will, howevez, it is evident, always be commensurable with the unit from which it was derived. t There are bodies which probably owe their existence to the mani- festations of the same physical qualities and changes as those which. determine the formation of ordinary crystals, but whose forms indicate that they are not strictly homogeneous; e. g., microscopic crystals whose surfaces are highly curved, and ‘what have been called by Lehmann liquid crystals. It is, perhaps, needless to remark that such’ bodies, which do not obey Haiiy’s law, are outside the scope of this inquiry, which is limited to homogenvous structure. - ~ Mr. W. Barlow on Crystal Symmetry. 3D ‘Gadolin’s method, because it dispenses with hypothesis, has commended itself to all students of crystals alike—both to those who adopt some hypothetical basis for the theory of these bodies, and also to those who prefer to exclude all hypothetical considerations whatever. The question is: Can the weak point in the basis of his argument be obviated by laying down a more precise definition of like directions in a erystal, without employing some merely hypothetical concept? The answer is that if it be admitted that the state of scientific research allows us to regard the existence of mole- cular structure of some kind or other as proved *, a definition of the requisite accuracy is attainable ; indeed, that such a definition was, in substance, suggested by Camille Jordan more than thirty years agof. For if molecules are present, an ultimate discontinuity of matter exists, and the following quite general definition of homogeneity of a rigid molecular aggregate can be given :— FunpamentaL Derrinirion.— Homogeneity of structure con- sists in a likeness of the ultimate parts or molecules of a body, both as to their nature and their relative arrangement, of the jollowing kind :—Corresponding to every mathematical point in the mass are found evenly distributed at finite intervals a number of points whose relation to the ultimate structure, regarded as of unlimited extent, 2s the same as that of the point selected; so that the aspect of this structure viewed suc- cessively from all such corresponding points is identically .the same, although the actual orientations of the similar aspects may be different t. Now when in such a homogeneous mass two or more directions are found alike, their likeness may be defined by saying that they are similarly disposed with respect to the molecular struc- ture, or, more precisely, that they are the directions of right Jines not parallel to one another, which cut this structure similarly. * Most persons will regard the law of rational indices as evidence of the existence of some kind of molecular structure, and it is scarcely conceivable that Haiiy’s discovery of this law would have been made without the aid ef some such conception of crystal structure as the one suggested by him. + See below, p. 9. t An example of different orientations of the same aspect observable from different points of view is presented by a partitioning of space into identical regular triangular prisms; the structure of the mass viewed from the centre of any prism presents the same appearance, but from the standpoints at the centres of prisms of the one orientation an opposite orientation of the aspect is found to that presented from the centres of those of the other orientation. 6 Mr. W. Barlow on Crystal Symmetry. For the purpose of classification, homogeneous structures thus defined can, like Gadolin’s systems of crystal faces, be placed in the same class when the number and arrangement of like directions is the same in them*. The similarity of the relation of two directions to ane homogeneous structure may either amount to identity, or, in certain cases, it may be such that the aspect of the ultimate structure viewed from one of them is the mirror -image ft of its aspect viewed from the other direction. As an illustration ot what is meant:—In a system of transparent cubic cells filling space, a cell when viewed in a certain direction pre- sents the aspect shown in fig. 2, and when looked at in a direction enantiomorphously similar to this, the aspect shown in fig. 8. In the following argument identical similarity will Fig. 2. Fig. 8. | be dealt with first, leaving mirror-image or enantiomorphous similarity for treatment later. TIpenticaLtLy Reiarep Directions—Possible Variety of Axes of Symmetry. Two important properties are involved by the identical repetition of the same formation which has just been defined. I. A mass thus constituted can be geometrically partitioned t into identical space units the number of different orientations * Comp. Gadolin, Mémozre, &c., p. 25. + The use of the ‘term mirror image does not imply the existence of a plane of symmetry, or, indeed, in any way express the relative orienta- tion of thé two like directions—it merely conveys that the aspect of the system of crystal properties viewed in the one direction, bears to its aspect regarded in the other direction the kind of resemblance that a right hand pears to a left, The system of crystal properties taken by itself, without reference to the position of an observer, is, in such cases, identical w rith its own mirror-image (comp. below, p. 31). t This partitioning may be merely an ideal one not possible actually, and not corresponding to any conceivable physical subdivision. Mr. W. Barlow on Crystal Symmetry. 7 presented by which will be that of the different orientations of an identical aspect of the structure as viewed successively from some set of homologous standpoints within tt. Proor. For let the positions of some such set of identi- cally repeated geometrical points be noted, the set selected being one which is as numerous as any other such set, and let every one of these points be similarly enclosed by a cell of arbitrary, but identical shape, the relative orientations and positions of the cells being such that the aspect of every cell and of the ultimate structure viewed from the enclosed point is the same ; and provided that the cells are small enough to avoid interpenetration. Next let all these cells expand uniformly and similarly in every direction’, but only till neighbouring cells are encount- ered, two moving cell-boundaries which approach one another coming instantaneously to a standstill directly they touch. As the conditions about all the corresponding points are pre- cisely the same, the result evidently is to completely fill space with enlarged cells which, like the original cells, are all identical, and the mass displays the property that the aspect of the enclosing cell and of the ultimate structure is the same from each of the corresponding points, although the identical aspects, like the cells, may be variously orientated. The partitioning achieved is therefore that required. Fie. 4. * As this is only a geometrical operation, the fact of space being occupied with the matter of the homozeneous structure is, of course, no barrier to it. 8 Mr. W. Barlow on Crystal Symmetry. The cells obtained in this way may be called space-units*. A plane example of units of this nature is given by fig. 4 ; a symmetrical pattern, which is a plane homogeneous struc- ture of the nature defined, being shown divided up into such units by dotted lines. Before stating the other important property of homogene- ous structures, two propositions, based on the one just put forward, may be given. Proposition 1.—Lach of the cells, or space-units, comprises one of each of the differently-placed mathematical points of the structure and only one; except, however, the points formin~ the boundary which are common to two or more cells, and all, or nearly all of which, occur twice in each cell F. Proor. For, by hypothesis, the cells are as numerous as any set of identical mathematical points in the structure, and therefore any kind of position cannot occur more than once within any particular cell; since, if there were two points within one cell identical, there would be two such points in every cell, making twice as many as the number of cells. PROPOSITION 2.— The maximum number of different direc- tions which can be identical with one another in any given structure, is that of the different orientations of its space-units ; in other words, that of the different orientations of the mass which can be made without altering the aspect of its structure as viewed in any fixed direction. Proor. Let a line in some given direction, selected at random, ke drawn to intersect a certain space-unit. Then, since according to proposition 1, no two points within this unit are alike, no other line can be drawn to cut the unit in the same manner. But if any different directions in the mass are identically alike, every right line drawn in one of them must have corresponding to it as many ditferently-directed right lines cutting the ultimate structure in identically the same manner as there are other directions identical to the given direction. And therefore, if one of these similarly situated lines cuts one of the space-units in a certain manner, every other of * Schonflies calls them “ einfache Fundamentalbereiche,” and regards their properties as attaching to the molecules of which the structure consists. (See Krystallsysteme und Krystallstructur, von Dr. Arthur Schonflies, Leipzig, 1891, pp. 572 & 616.) They are not, however, in any sense actual or physical molecules. Their shape, as appears from the method of obtaining them just given, is generally more or less arbitrary. +t See Arystallsysteme und Krystallstructur, p. 572. ‘The points in the boundaries which do not occur twice are what the writer has called in another place senyudar points. (See Zeitschr. fiir Kryst. xxiii. p. 60.) Such points are marked P, Q, R in fig. 4. Mr. W. Barlow on Crystal Symmetry. ) them will cut some other space-unit in the same manner. Thus, in the plane example just given, differently directed lines A B, C D, EF cut three different space-units, K, L, M, and indeed the ultimate structur e, identically. Now, as the space-units are all alike, and bear the same relation to the structure, every one of them can have a line drawn to intersect it in the same manner ; those of such lines whose similarly-traversed space-units are similarly orientated will be parallel to one another, but in differently- orientated space-units the corresponding lines will, it is evident, be differently directed, unless indeed the direction of the latter is exceptional so as to be similarly related to two or more differently-orientated space-units. Therefore the pro- position is established. It has been said that homogeneous structures are of the same class when the number and arrangement of like direc- tions is the same in them. It is evident from the foregoing that where the likeness of the directions amounts to identity, this is equivalent to saying that structures will be of the same class when the various orientations of their space-units display the same kind of relative arrangement. Consequently to tind what variety of classes is possible, the task which hes immediately before us is to ascertain what various kinds of relative arrangement of the different orientations of the space- units are presented when all possible types of homogeneous structures, which are so constituted that their space-units are of finite dimensions, are examined. The second important property of such homogeneous structures furnishes the next step towards this; it is as follows :— Il. Lor every homogeneous structure a group of coincidence- movements exists which comprises every movement of the entire mass requisite to carry every space-unit to the identical place occupied originally by any other space-unit, and every right line drawn to intersect the mass to the place of some identically related right line ; the ultimate structure viewed from any fixed point presenting precisely the same aspect after as before each of these movements *. This property is an evident consequence of the similar nature and situation of the identical space-units. Now, according to a theorem of Chasles, any rigid system can, by means of some screw-spiral movement, be carried from any initial position to any other given final position. * See “Mémoire sur les groupes de mouvements,” par C. Jordan: Annalt di matematica pura ed applicata, Serie 2, Tomo 11. 1868 al 1869, Milano, p. 167. 10 Mr. W. Barlow on Crystal Symmetry. Therefore, if any two space-units A, B be selected, some screw-spiral movement can be made of the entire mass which will transfer the unit A to the exact spot initially occupied by B and leave the aspect of the ultimate structure as viewed from any fixed point precisely the same after as before the change. The screw-spiral movement may be resolved into two components, a rotation and a translation: the former only is concerned in effecting any change of orientation requisite in bringing A to the place of B, and any right line drawn to intersect A to the direction of an identically corre- sponding line passing through B. If the aspect of the structure regarded from the centre of A has the same orientation as its aspect viewed from the centre of B, the rotation component of the movement will be zero, and this movement will then be a translation. A very simple illustration may make matters clearer :— Suppose space to be divided symmetrically into cells which are identical triangular prisms ; half of the prisms then have the opposite orientation to that of the other half. If it is desired to bring a cell to the precise place of some other cell, a movement which is a translation will suffice when the two cells are sameways orientated, but a screw movement or a rotation will be requisite when the two cells have not the same orientation. Any two of the identicaily placed space- units of a homogeneous structure can be selected for the application of a coincidence-movement of the nature de- scribed, and this movement may take place in either direction, 2.e. from A to B or from Bto A. All such coincidence-move- ments as are possible for the given structure, when they are taken collectively, constitute, where the structure is supposed of infinite extent, the infinite group of related movements referred to. The change of orientation effected by the rota- tion component of any one of these movements is adequately defined if the direction of its axis and the amount and direction of the rotation are given. PROPOSITION 3.—In order to locate in any given homogeneous structure the various directions which are identical to a given direction, it suffices to apply to the latter in succession one of each of the different rotations which enter as components inio those movements of the group of movements referred to which are applicable to some single space-unit. Thus in the trigonal symmetrical pattern of fig. 4, there are two directions identical to the direction of A B, viz. those of C D and EF, derived by rotation through 120° and 240° respectively. Proor. As already shown, if two directions bear a similar relation to the structure, any line drawn in one of them to Mr. W. Barlow on Crystal Copan OL intersect some space-unit, has corresponding to it some line drawn in the other corresponding direction which similarly intersects some other space-unit ; therefore some one ot those screw-spiral movements of the group which are applic- able to the selected unit will carry the one line to the initial place of the other line. Now the translation component of this movement does not affect direction, and therefore it is only the rotation com- ponent which is concerned in bringing the direction of the one line to that of the other. But any screw-spiral movements which have the same rotation component, 7. e. whose axes are parallel and rotate through the same angle in the same direction, produce identical changes of orientation. Consequently it is only those with different rotations that, from a given unit, locate differently orientated units and the corresponding differently- directed lines which intersect these units. All directions which have identically the same relation to the structure as some given direction, will therefore be located by successively applying to the latter the different coincidence rotations applicable to some single space-unit. Propostr1on 4.—The symmetry of arrangement of the various directions found identically related to the homogeneous structure of a mass is that of identically placed lines drawn through the centre of some body so formed as to possess axes passing through its centre whose directions and rotations are identical to those referred to in the last proposition, and no others. Thus for every homogeneous structure in which two or more directions are identical, a sphere of reference can be constructed with axes through its centre, so that the repetition of identical directions on this sphere corresponds exactly to that prevailing in the homogeneous structure. Proor. By hypothesis the axes of tke centred body have the same directions and rotations as those of the structure. Therefore every direction in the structure has corresponding to it a line in the centred body which makes the same series of angles with the axes of the latter as the direction in question makes with the axial directions of the structure. Apply to a selected direction, 7. e. to some line drawn in this direction, the various movements of the structure so as to locate other lines or directions identically related to the structure, and apply to the corresponding line in the centred figure the rotations of this figure. As the changes of orientation produced by the latter rotations are the same changes of orientation as those brought about by the movements of the structure and no others, the 12 Mr. W. Barlow on Crystal Symmetry. Imes located in this way in the centred figure must have, when the latter is appropriately orientated, precisely the directions of those located in the homogeneous structure, and will therefore display the same arrangement of like directions. In the case of anorthic symmetry, the rotation components of the coincidence movements are all zero and so no two directions are identically alike, all the coincidence move- ments being mere translations. As the experimental methods at the disposal of the crystal- lographer are not at present refined enough to discover in a direct manner any discontinuity of substance in crystals, variation of property with direction, not variation from point to point, is all that can be discriminated in these bodies, and therefore the only parts of the coincidence movements referred to which are immediately traceable in actual crystals are the rotation components, which, as just stated, determine the nature of the symmetrical repetition of identically related directions. Consequently, for the purpose of ordinary erystal classification, these rotation components, not the translation components, are of significance, and the tracing of merely directional symmetry is all that is necessary. While it is an arduous and extended work to go further than this, and to ascertain all the varieties of type which can exist of the groups of coincidence movements of homogeneous structures, it is a much simpler and shorter task to investigate merely the different rotation components of these movements and their relative arrangement. The former, more extended inquiry, which has had thus far rather a theoretical than a practical utility, has been carried out very fully by various investigators *. The latter, more limited one, taken in con- junction with the principle of mirror-image repetition f, leads to the derivation of the 32 classes of erystal symmetry from first principles, and it alone is the object of the present investigation. To arrive at the 32 classes a method is here adopted which combines some of the arguments employed by Schncke with some of those used by Gadolin and others. The following ten propositions lead up to the solution of the question what varieties of axes are possible in homo- geneous structures ; several of these propositions are taken with some slight modifications from Sohncke f. * See Entwickelung einer Theorie der Krystallstructur von Dr. Leonhard — Sohncke, Leipzig, 1879; Schontlies’ Krystallsysteme u. Krystallstructur ; ‘‘'Theorie der Krystallstructur,” ”’ von EK. von Fedorow, in Zevtschrift frir Ky ystallographe, xxiv. p. 209; and also see Zeit. f. Kryst. xxii. p. 1, and xxv. p. 86. + See below p. 51. { Entwickelung emer Theorie der Krystallstruktur, p. 37. Mr. W. Barlow on Crystal Symmetry. — 13 Proposition 5.—If in the group of coincidence-movements of a homogeneous structure a screw-spiral movement or a rotation is found, the existence of the axis of this movement evolves the existence, evenly distributed in some manner throughout the mass, of axes identical with this axis. This is obviously a direct consequence of the postulated homogeneity. Proposition 6.—Among the identical axes of the last proposition are comprised either parallel axes or such as have their directions inclined to one another at infinitesimal angles (the latter are however presently, by Prop. 9, shown to be impossible) . Proor. The different directions taken by the identical axes are either finite or infiniteinnumber. If the number is finite, some out of the infinitude of similar axes found in the infinitely extended structure, must take the same direction : z. e., be parallel. If, on the other hand, the number is infinite, some directions must be but infinitesimally removed from others ; 7.e., they must be mutually inclined at infini- tesimal angles. Proposition 7.—Two identical axes which are either parallel, or whose directions are inclined at an infinitesimal angle (see Prop. 6) cannot be at a distance from one another which is infinitesimal as compared with molecular dimensions, and this, of course, involves that they cannot cut one another. Proor. Let A, A! (fig. 5) be the points of intersection of the two axes witha plane drawn perpendicular to one of them through the centre P of some space-unit, and let @ be the rota- tion component of the minimum coincidence-movements about these axes. Then, if the coincidence-movements about A, A! are carried out so that the point P is carried in the one case to P,, in the other to P,, these points P, P,, which each locate a space-unit of the system, will, in the case of parallel axes, lie precisely, in the case of slightly inclined axes, very 14 Mr. W. Barlow on Crystal Symmetry. approximately in a plane drawn parallel to the plane A A! P, and distant from it /, where / is the translation component ot the two movements. Let the projections of the points P,; P, on to the plane A A'P be P'P". We have then either precisely or very approximately, as the case may be, the two triangles A P P!, A'P P” similar, and therefore the triangles A P A’, P’ P P! also similar. : _ Now P P’ are two points on the same circle, and therefore the distance P P’ cannot be greater than the diameter 2 A P. Therefore A P cannot be infinitesimal as compared with P’P, and so neither can A A’ be infinitesimal as compared with P’P”, and the latter is either equal, or very approxi- mately equal to P, P,, which is the distance apart of the centres of some two space-units. Proposition 8.—Admuitting that the molecular dimensions are finite, it 1s impossible for any rotation of the structure to have an infinitesimal value, or for any screw-spiral coincidence movement tu have as component an infinitesimal rotation. Proor. Among the identical axes of proposition 5 note such as are either parallel or whose directions are inclined to one another at infinitesimal angles, and of these let A A’ be two which are at the least distance apart; this distance must, by prop. 7, be finite. ~ By carrying out the movement proper to A, from A’ locate a third axis A”, which will also form one of the selected flock. Then the distance A’ A” measured in a plane per- pendicular to one of the axes A’, cannot be sensibly less than the distance A A’, similarly measured, becanse the axes A A! are at minimum distance apart, and this minimum distance can, exactly in the case of parallel axes, very approximately in the other case, be measured in the plane referred to. Therefore the angle A’ A A”, which is the angle of rotation of A, must have a sensible value (2. e. not less than 60°, or thereabouts). PROPOSITION 9.—An injinitesemal value for the mutual enclination of the directions of two identical axes 1s impossible. Proor. The presence of two identical axes in a structure involves the existence not only of the coincidence-movements proper to these axes, but also the existence of a coincidence- movement, screw-spiral or merely rotational, capable of carrying the structure from an initial position to the ultimate position reached by successively carrying out the two moye- aments proper to the two axes *, * See page 9. Mr. W. Barlow on Crystal Symmetry. 15 Let A O A’ B O B’ (fig. 6) be lines drawn parallel to the two ‘axes through some point O to meeta sphere described about O as centre, and let a be the angle of the rotation-component of the two identical screw-spiral movements about the two axes. HiewG: Draw a great circle through A B A’ B’ and two other great circles through A A’, BB’ respectively to make angles = with A B A’ B! oppositely, the two latter circles fiienieecicn in C, and let angle ACB be S Then, as shown by the familiar demonstration employed by Huler +, the change of orientation effected by first carrying out the rotation a about BB’ and then the same rotation about A A’, in the directions indicated in the figure by the arrows, is that which is pro- duced by a single rotation y about CO in the direction also there indicated. But, the change of orientation of a body which is effected hy a screw-spiral movement is that which would be brought about by the component rotation acting alone without the translation component. Therefore, since the rotations (a) _ are the component rotations of the screw-spiral movements about the two identical axes of the structure, the equivalent rotation y about C O is the rotation-component of the screw- spiral movement which is the equivalent of the latter, and which, as stated, is a coincidence-movement of the structure in question. Tt See Entwickelung einer Theorie der Krystallstruktur, p. 31, iii. 16 Mr. W. Barlow on Crystal Symmetry. Now if the mutual inclination of the two axes is infinit- esimal, the lengih AB on the sphere which is intercepted by the lines drawn parallel to them will be infinitesimal as com- pared with the dimensions of the sphere ; consequently the angle 5 and therefore also the angle y, will be infinitesimal. But by proposition 8 the latter is impossible, therefore so also is an infinitesimal value for the mutual inclination of the two axes. ; Proposition 10.—Among identical axes present in a homo- geneous structure, parallel ones are always found. Proor. It has been shown by proposition 6 that either parallel axes, or such as have their directions inclined to one another at infinitesimal angles, are present, and since by proposition 9 the latter are impossible, the existence of the former is established. Proposition 11.—The minimum rotation-angle of an axis of coincidence of a homogeneous structure must be an aliquot part of 360°; z.e. if it be designated ay. nm must be an integer. a Proor. The existence of an axis, whether screw-spiral or rotational, whose minimum coincidence-movement produces rotation through an angle a, involves the possibility of co- incidence-movements whose rotation components have angles 2a, 3a, &e. ; and if a coincidence-movement can be effected in one direction, it can also be effected in the opposite direction. This is evident when it is considered that the asvect of the system from any fixed point, and its relations as a whole to fixed directions, remain altogether unchanged by a coinci- dence-movement, and that an opposite movement can always be regarded as a ‘return to a former position. he pa be the angle of the series 2a, 3a, &c., which is not less than 360° and nearest to this value, p being an integer. Then any other value for pe than exactly 360° would give a possible movement witha rotation-component pa—360° 6, and from proposition 13 itcannot be 5. Therefore since the value 1 gives no rotational repetition, it can only be 2, 3, 4, or 6. Before proceeding to the consideration of what types of combination can exist of the varieties of axes thus not impossible, reference must be made to an important property of the homogeneous structures above defined which identifies them with the assemblages of sameway-orientated units pos- tulated by Haiiy, Bravais, and others, and generally regarded as necessarily existing in crystals. PROPOSITION 15.—Among the coincidence-movements of a homogeneous structure whose ultimate paris are of finite dimen- sions various translations not confined to any one plane are always found, the mass possessing the property that it is Phil. Mag. 8. 6. Vol. 1. No. 1. Jan. 1901. C a 18 Mr. W. Barlow on Crystal Symmetry. divisible geometrically into identical finite portions which are similarly-orientated *. Proor. If the structure has no axis its coincidence-move- ments are all translations. If, on the other hand, axes are present, its possession of tr anslations at right angles to these axes and in other directions may be established as follows :— Among the axes present, some are, by proposition 10, identical and parallel. Let A, A’ be two such axes. Then, if a certain screw-movement, or rotation, proper to A, carries a point P to Pj, a similar movement will characterize A’ and will carry the same point P toa third point P, ; and the points P,, P. thus located from P will le in a plane perpendicular to ihe axes and will be identically related to the structure ; and, further, the aspect of the structure viewed from P, will, since both coincidence-movements have the same rotation component, present hee same orientation as the identical aspect viewed from P,; in other words, the structure will be capable of a eet: translation from P, to P,. The employment of other pairs of the parallel axes will lead in the same way to the discovery of various other coincidence translations perpendicular to these axes. If the system possesses in addition axes having other directions, these also involve the existence of various transla- tions perpendicular to them. If, on the other hand, it does not, identical points not lying in the same plane perpendicular to the axes must be capable of being brought to coincidence either by screw-spiral movements about the axes which are present, or by translations ; and as the former have translation components along the axes, there must, in all cases, be other translations present besides those perpendicular to the one set of axes. Therefore all homogenecus structures, both those wholl destitute of axes, and those possessing them, are capable of coincidence translations in various directions not lying ina single plane direction. The fundamental definition on which this inquiry is based requires these translations to be all finite f. * Unless the symmetry is anorthic these are not the space-units of page 7. They will each, when as smal! as possible, consist of as many contiguous space-units of a certain pattern as are found differently orien- tated. They need not have the same degree of symmetry as that of the structure, although in the majority of cases the partitioning for obtaining them can be so carried out as to give them this symmetry. + See p.5. There are cases of homogeneous repetition in which the translations are not all finite. The structure of columnar basalt, if regarded as quite uniform, is a case in point—the translations in one direction become infinitely small and, although such a structure possesses an infinite group of ccincidence-movements it is not available, not being divisible into finite physical units; it does not follow Hatiy’s law. Mr. W. Barlow on Crystal Symmetry. 19 That the existence of these translations involves the pro- perty that the mass is geometrically divisible into identical portions which are similarly orientated may be shown in the following way :— Select some three directions. in the structure, not in the same plane, in which translations occur, and corresponding to any point taken at random, locate by means of a continual repetition of these translations a set of points identically resembling the selected point ; the points thus formed will, it is evident, form a parallelepipedal network. Surround each of the points of the network in a similar manner with an identical cell, sameway orientated, the cells being small enough to avoid interpenetration, but otherwise of an arbitrary form. ‘Then let all the cells expand simultane- ously and uniformly in every direction but only till the moving walls of contiguous cells meet, as in the partitioning of space previously described * ; the result is to fillspace with the cells, and since, in the present case, the similarity of the conditions of formation of eachcellincludes sameway-orientation these cells will, besides being all identical and containing identical portions of the structure, be all sameway-orientated. The above proposition is therefore established. If a straight line be drawn through any two of the points of a parallelepipedal network of identical points, it is easily shown that this line passes through an endless succession of the points, and that if no other such point lies directly between the two points, the distance between succeeding points on the line is that separating the points referred to. Lines and planes thus encountering a succession of equally spaced similar points may, from this property, be called homogeneous lines or homogeneous planes of points. The dotted lines ST and V W in figure 4 page 7 are homogeneous lines. The Law of Rational Indices Deduced. PROPOSITION 16.—The identical sameway-orientated por- tions of structure of the last proposition correspond to the molécules soustractives of Haty and are available for the use to which he put the latter, which are indeed a speciahzed form of the cells just described. The presence of the sameway- orientated portions of proposition 15 involves the existence of the law of rational indices which connects the directions of homogeneous planes and homogeneous lines of points. Proor. It has just been pointed out that points from which the aspect of the structure is not only identically the * See p. 7. C2 20 Mr. W. Barlow on Crystal Symmetry. same, but presents the same orientation, always form some parallelepipedal network of points. It was by postulating such networks that Haiiy deduced the law of rational indices, the experimental truth of which he afterwards established by observation ; and his work shows that if any three homogene- ous lines of points of any such network, which intersect in a single point, be chosen as axes, the intercepts on each of these axes made by the homogeneous planes of points of the net- work bear rational relations *. The Possible Variety of Relative Arrangement of Directions found Identically related to Ultimate Structure. Tt has been stated above t that homogeneous structures, when their directional symmetry alone is considered, are of the same class when the number and arrangement of like direc- tions is the same in them, and it has been shown that for every homogeneous sumone | in which two or more directions are identical, a sphere of reference can be constructed, with an axis or axes through its centre, so that the repetition of identical linear or plane directions in the sphere corresponds exactly to that prevailing 1 in the homogeneous structure f. It is therefore immaterial to the present inquiry to ascer- tain what, in any given instance, the relative arrangement of parallel axes may tye; ; all the axes in any given direction will be represented on the sphere of reference by a single axis which will have the direction of the axes which it represents and display coincidence-rotations capable of producing all the different changes of orientution effected about these axes, Both in the homogeneous structure and in its sphere of reference, the minimum coincidence-rotation about the given direction will involve the occurrence of all the changes of orientation taking place about this direction : in other words, this rotation will produce a change of orientation which is an aliquot part of every one of these changes of orientation. This becomes evident when it is considered that the existence of a minimum coincidence-rotation a involves that of rotations 2a, 3a, &.§, and that no other rotation than one of these is possible, since, if such existed, a rotation whose amount is the difference between that of the latter and the nearest of the values referred to, p «, would also be possible, z.e. some less * Hatiy’s Traité de Minéralogie, 1891, tom. 1. p. 283. +t See page 6. t See page 11. § See pace 13. Mr. W. Barlow on Crystal Symmetry. zat rotation than a; and this is inconsistent with « being the minimum rotation. Thus in the simplest possible class of cases—those in which ‘the axes present in a structure have but one single direction, the nature of the directional symmetry of the structure is not affected by the relative arrangement of these axes, and will be fully expressed by a sphere of reference which has a single axis whose minimum rotation is the least rotation-component ot any of the coincidence-movements of the structure ; @.9., a structure whose axes are hexagonal, trigonal, and digonal all parallel to one another, will have its identically related direc- tions arranged just as they are found in a sphere of reference which has a single hexagonal axis *. These conclusions may be summed up in the following proposition regarding the symmetrical arrangment of direc- tions which are identically related to the structure where the homogeneity is of the nature above defined :— Proposition 17.—All the different types of symmetrical arrangement of corresponding directions are comprised in the series of types of centred symmetry which present every con- cewvable kind of identical repetition about a centre consistent with the presence of only such axes as are possible for the structures in question 372. e., no other axes than digonal, trigonal, tetragonal, or hexagonal +. So far as zdentical repetition of parts and directions is con- cerned, the task remaining to be done consists therefore first in, obtaining the complete series of types of centred symmetry having the axes referred to, and then in making sure that some homogeneous structure or other is conceivable corresponding to each of them: in other words, in ascertaining that none of these types is impossible for homogeneous structures, Cases where the Axes all have the same Direction. The least complicated types of repetition of identical directions are those in which the coincidence axes present all have the same direction, and, before passing to cases in which there is a plurality of axial directions, the following simple * Similar reasoning to that given above, shows that if a structure possesses axes of more 3 than one sort parallel to one another it also possesses axes with a rotation which is the difference between the rotations of such axes; é. g.a structure with digonal and trigonal axes parallel to one another must also possess hexagonal axes. T See prop. 14, p. 17. 22 Mr. W. Barlow on Crystal Symmetry. classes of centred symmetry of identically related parts may he noted :— Asymmetric (no Tne, i shown in (PI. I.) ve If, (G adolin fig. 58). A single digonal axis 5 Ty Gees 41) A single trigonal axis ee “UL Ge: 53). A single tetragonal axis __,, co 5 3d). A single hexagonal axis ,, 50). All these types of symmetry are Dect: represented in homogeneous structures, since, corresponding to each of them, al type of structure exists which repeats through space the order of symmetry of the centred type*. To obtain such a type of structure proceed as follows :— Construct a space-network of points (Raumgitter) whose symmetry is or includes that of one of the types of centred symmetry. ‘Then place at the points the centres of a number of identical bodies whose symmetry is of the type in question, taking care that these bodies are similarly and appropriately orientated. Thus—to give a simple instance—let a space network be formed whose points lie at all the angles of a number of identical regular triangular prisms fitted together symmetrically to fill space. Then place sameway-orientated, with their centres at the points, and their axes perpendicular to the triangular Jayers of the network, a number of identical bodies having a trigonal axis and no other, e. g. coins of the Isle of Man with the threefold Manx emblem on them. The system obtained by using the latter presents, if the obverses of the coin be neglected, a case ef trigonal symmetry with a single axial direction. The combination of each of the above five kinds of repeti- tion of identically related directions with mirror-image repetition will be considered later. Cases where there is a Plurality of Directions of Coincidence- Axes. Proposition 18.— Where axes in more than one direction are present, axes in at least two directions, have the same rotation-angle. For if some two of the mutually-inclined axes are of different rotation-angles one of these angles must be less than 180°, and when the coration proper to sucht an axis is made at lene: two directions for the other description of axis will be discovered. Proposition 19.— Where there is a plurality of directions * This kind of structure is presented by Bravais’s assemblages. Mr. W. Barlow on Crystal Symmetry. 23 of the coincidence-axes the points of intersection of some set of similar axes in the sphere of reference with the spherical sur- face will mark the angular points of one or other of the regular polyhedra inscribable in the sphere ; including, however, in this category the extreme cases of polyhedra of zero contents whose faces are two coincident regular polygons inscribed in a great circle, For suppose A, A, (fig. 8) are the positions on the sphere of some two axes of the same rotation-angle @ so selected as to be at a minimum distance apart measured by achord a. Then the carrying out of Fig. 8 the rotation about A, will discover A5 a third axis Ag, identical with A,, and chord A,A,=A,A;=a, and the sphe- Ay rical angle A,A,A;=0@. Similarly other axes A, A;...A, of the same rotation-angle can be discovered all lying on the circle drawn thr ough Az A, A, As, the alternate axes being ence identical. One or other of the axes thus located in will coincide with A,. For suppose the A, e process be continued till we reach an axis A,, whose distance from A;, measured along a chord as before, is not >a; then, since a is the minimum distance apart of two axes of the same sort, the distance A,A, must =a@ and An+1 be coincident with A,. Thus the set of axes A, A, A3...A, map out the angles of a regular polygon of n ice on the surface of the sphere *. A second polygon identical with the first, but which will be distinct from it except when 6=180°, is located by a similar series of rotations in the opposite direction. The angles of this second polygon will also lie on the surface of the sphere. Again:—As the rotation-an gle 6 is an aliquot part of 360° (Prop. 11), let d= onus ; there are then p identical polygons of the nature just Le grouped around the axis A, without overlapping ; and as the same will be true with regard to each of the axes which has been located, each polygon will be completely surrounded by polygons identical with it which do not overlap it or one another. Therefore in all cases, where more axes than one of the same rotation-angle are present i in the sphere of reference, a regular polyhedron can be inscribed * Comp. Sohncke, Entwickelung einer Theorie der Krystallstruktur, Satz. xi. p. 42. 24 Mr. W. Bariow on Crystal Symmetry. in this sphere the angular points of which are points of intersection of these axes with the surface of the sphere. Proposition 20.—The existence of coincidence-axes of the same rotation-angle intersecting the sphere of reference at the angular points of a regular polyhedron * involves the existence of axes centrally perpendicular to the polygonal faces and which have as one of their rotation-anglest the angle 6=2. a where n is the number of sides of a polygonal face. Tor suppose, as before, that A, A, A;...A, are the angular points of a polygonal face of n sides, and that @is the minimum angle of rotation of the axes which pass through these points. Then a coincidence-rotation @ about A, which carries A, to A; earries the polygonal face A,A,A;...A, tothe place of anad- joining similar face, and a similar rotation @ about A; (the new position of Ay) which carries A; to A, leaves Az unmoved and brings back the displaced polygon A,A,A;... A, to its original position, but with A, moved to A;, A, to A,; in other words, the resultant of the two movements Is a coincidence-rotation 2(\O e through an angle 2. the polygon. When 0=180°, and the angles of the polygon consequently lie on a great circle, the rotation which brings A; to Ag, simply inverts the polygon so that, as a whole, it again covers the same space ; the second rotation, that about the axis through A3, annuls the inversion, leaving its plane as 12) before, but rotated through the angle 2. about an axis through the centre of about an axis iv perpendicular to the polygon at its centre. PROPOSITION 21.— The only regular polyhedra whose angular points depict the arrangement of a set of axes of one of the possible kinds = in the way just explained are the cube, the octahedron, and such of the limiting cases above referred to as have for their two coincident faces regular polygons of 4, 6, 8, or 12 sides. ; Yor the other regular polyhedra, which are, as is well known, the tetrahedron, the regular-pentagonal dodecahedron, the icosahedron, and such of the limiting cases as have not just been enumerated, are inadmissible for the following reasons. (a) The tetrahedron because each of its four axes cuts the * As stated above, polyhedra of zero contents, having two coincident polygonal faces lying in a great circle, are included under this definition. / + This is not necessarily a minimum rotation-angle ; but if it is not, it must be an integral multiple of a minimum rotation-angle. 7 See p. 17. Mr. W. Barlow on Crystal Symmetry. 25 circle of reference in two points, and consequently the edge of the cube outlined by the eight points of intersection thus obtained, and not the edge of the tetrahedron, is the minimum chord a between two axes*, and forms an edge of the polyhedron. (0) The pentagonal dodecahedron because it gives n=), and therefore 6=2. eee 144°, n For the angles 26=288° and 360°—2¢=72° would, if } has this value, also be rotation-angles of the axes in question, and the value of 72° for the minimum rotation-angle is not compatible with either of the minimum rotation-angles of proposition 14, which are alone possible for coincidence- axes. (c) The icosahedron because it gives 0=72°, which, as just stated, is an inadmissible value for a rotation-angle. (d) In the limiting cases—those in which there are but two polygonal faces which coincide with one another— the value n=3 is inadmissible because each of the three digonal axes through the angles of the equilateral triangle forming the two faces cuts the sphere in two points, and a, the minimum chord between the axes, is therefore the side of a regular hexagon and not the side of a triangle, 2. e. when there are three axes inclined at 120° the polygon which they locate is a hexagon, nota triangle. Of other values for 7 all, except n=4, 6, 8, or 12, give an inadmissible value for the angle of rotation @ of the principal axis of the system, since € 6 2 =2. a! - and 60°, 90°, 120°, and 180° are the only values possible for minimum angles of rotation (Proposition 14). PROPOSITION 22.—In a system of axes :— (a) Not more than one hexagonal axis can be presené. - (b) Lf there is a plurality of tetragonal axes the points of intersection with the sphere of a set of them will lie at the six angles of an octahedron. (c) If there ts a plurality of trigonal axes, the angles of a cube will mark the positions of a set of them. As to digonal axes, a much greater variety is possible. That there is no plurality of hexagonal axes is proved by the fact that the axes of this order are not found among those which locate the angles of the possible polyhedra in the way explained in proposition 19, Tetragonal axes locate the angles of but one type of poly- hedron—the octahedron; and therefore where more tetragonal * See above, p. 23. 26 Mr. W. Barlow on Crystal Symmetry. axes of rotation than one are present, this kind of polyhedral arrangement must be the one displayed. With regard to trigonal axes, the only case in which a set of these axes will mark out the angular points of a polyhedron is the one in which the polyhedron is a cube (Proposition 21). Enumeration of the Cases of Plurality of Axes in which there is no Mirror-Image Repetition. Since one at least of the polyhedra named in proposition 21 must be traceable in every centred system having a plurality of axes, all such systems will be exhaustively traced if every possible case in which one of these polyhedra is formed is discovered. In making this exhaustive examination all cases which are without mirror-image repetition are described first. Taking the cases in the order given in proposition 21:— 1. Where the polyhedron traced by a set of axes of the same 6 O a = 130°: The axes necessarily involved in the existence of this form of polyhedral arrangement of some of them, are tnerefore four trigonal axes in ‘the four cube diagonals and three digonal axes thre ough the centres of opposite faces of the cube. “And as all the axes of each of these sets are brought to coincidence by coincidence-rotations of the system, the axes of each set are identical. The type in which no other coincidence-axis than these exists Is given in (PI. 1.) fig. VI. (Gadolin, fig. 29). As to whether any type in which any other coincidence-axis together with these occurs is possible :— ‘Since the cube- edge a is the minimum distance between two trigonal axes, and there is no point on the sphere of reference whose distance from one or other of the cube- corners is not less than this, it is evident that no additional trigonal axis can exist. And it follows that the axis of any additional coincidence- rotation must be so placed that its movements bring the cube referred to to coincidence with itself. Consequently any such additional axis must either pass through the centre point of a face or the centre point of an edge of the cube. If one of the digonal axes already occupying the face-centres is converted to a tetragonal axis, or if a digonal axis is added which passes through the points of bisection of two opposite cube-edges, the requisite condition referred to is fulfilled and it can be fulfilled in no other way. rotation-angle isa cube: n=4; O=120°; Mr. W. Barlow on Crystal Symmetry. 2M But if one digonal axis be made tetragonal, the existence of the remaining axes involves the necessity of all the three digonal axes being so converted; and if one digonal axis be drawn to bisect opposite cube-edges, the presence of five other digonal axes bisecting the remaining ten edges of the cube is similarly established. Further, one of the tetragonal and one of the trigonal rotations, when combined, have for resultant one of the added digonal rotations which bisect cube-edges*. Consequently the introduction of the tetragonal rotations involves that of the six digonal rotations—they are not independent of each other. Therefore, finally, where the polyhedron traced is a cube there is but one type which has additional coincidence- movements besides those of the type last given, viz. the type given in (PI. IT.) fig. VII. (Gadolin, fig. 27), in which the three digonal axes have become tetragonal and new digonal axes have appeared which bisect all the cube-edges. In this case too, for the reason stated in the last example, the axes of each set are all identical. 2. As to the octahedral arrangement : — Where the polyhedron traced by a set of axes of the same 360° rotation-angle is an octahedron: n=3; 0=90°; d=2 ay =240°. And a rotation-angle of 240° involves one of 360°—240°=120°. The axes necessarily involved by the existence of this form of polyhedral arrangement are there- fore three tetragonal axes which intersect opposite vertices of the octahedron and four trigonal axes which pass through the centres of opposite faces. This type is identical with that last traced; digonal axes bisecting the 12 octahedron-edges are identical with those bisecting the cube-edges in the last example, and are, as stated, involved by the presence of the other axes. A similar argument to that above employed shows that no other axes are possible where a polyhedron traced by the axes in the way described is an octahedron. _ Next come the limiting cases of polyhedra of zero contents with two coincident polygons as faces. In all these 6=180°, 7. e. the axes which contain the angular points of the poly- hedron are always digonal; they lie in the plane of the polygonal faces. . _” For the proof of a very similar proposition see p. 24. Comp. Sohncke’s Entwickelung einer Theorie der Krystallstruktur, p. 31. 28 Mr. W. Barlow on Crystal Symmetry. 3. As to cases where the polygon is a square :— 0 O Here n=4; b=2 — == 180°. In the simplest form there are therefore three digonal axes at right angles to one another and no other axis, the digonal axes being therefore all diverse—the type shown in (PI. II.) fig. VIII. (Gadolin, fig. 88). Every two of the three axes in question intersect the sphere of reference at the four corners of a square inscribed in a great circle. With reference to the existence of any system possessing the axes referred to and other axes in addition :— As the only point on the sphere whose distance from the angles of the square is as great as a the side of the square, is the point of intersection of the third axis (@) there can be no additional digonal axes besides the three. Consequently the only additional rotations possible are such as will bring the system of three digonal axes to coincidence with itself. The axis of any additional rotation cannot coincide with either of these three axes. For the only additional rotation about one of these axes which would bring them to coin- cidence is the conversion of a digonal into a tetragonal! rota- tion, and the existence of the latter is precluded in the case in question because it would involve the existence of addi- tional digonal axes. For the resultant of such a tetragonal rotation and one of the existing digonal rotations is a digonal rotation about an axis inclined at 45° to the existing digonal axes™, | The only other additional rotations which would bring the system of digonal axes to coincidence are, it is evident, those about axes equidistant from two or three of these axes respectively. Axes equidistant from two are inadmissible because they would be additional digonal axes. ‘There re- mains the case of additional trigonal axes equidistant from three digonal axes. This case, which is therefore the only additional one compatible with the presence of two digonal axes so situated as to intersect the four angles of a square in whose plane they lie, has been already deduced by another method f. 860° 4. Where the polygon is a hexagon: n=6; d=2. ae =i120%, In the simplest case there are therefore three digonal axes in the same plane subtending angles of 60°, and a trigonal * The proof of this is substantially that given on page 24 of the value of d. T See above, p. 26 and (PI. 1.) fig. VI. - Mr. W. Barlow on Crystal Symmetry. 29 axis at right angles to them and no other axis, as shown in (Pl. II.) fig. [X. (Gadolin, fig. 47). As to the possibility of the existence of any case of this polyhedral arrangement in which other axes are present in addition to those found in the case just described :— The existence of the trigonal axis perpendicular to the plane of the three digonal axes requires that if an additional axis is found, there shall be at least two other additional axes identical with it. Now in the system described on p. 26and (PI. IT.) fig. VII. there are six digonal axes, and the twelve points in which they intersect the sphere of reference are, it is evident, the twelve bisecting points of the edges of a cube so drawn that these edges touch the sphere; and these twelve points may be regarded as lying on three parallel planes drawn perpendicular _ to one of the trigonal axes of the system, six points being found on the middle plane and three in each of the others. This is the only possible way in which digonal axes can be added in the case of the polygonal arrangement under consideration. For if the axes lying in the centre plane be the three essential digonal axes, and so their distance apart, measured by the side of the hexagon indicated by their points of inter- section with the sphere, has the minimum value a, it is evident that each of the three added digonal axes is at. the same minimum distance from the remaining two and also from two of the three essential axes, and that any departure from this relative situation for three additional axes would bring one at least of the four distances referred to below the minimum. Thus positions for the added axes further from the centre plane would bring the distance apart of the three added axes below the minimum, and positions nearer to the centre plane would shorten some at least of their distances from the essential axes. The question remains, can the system be enlarged in any other way while a continues to be a minimum ? Now any position for an additional axis of a higher type except the positions occupied by such axes in the enlarged system referred to is precluded by proposition 22; the only point left to consider is, therefore, the possibility of converting the trigonal axis into a higher order of axis—an hexagonal one. ‘his is impossible because the resultant of the rotation abont such an axis and the rotation about one of the three essential digonal axes, would be a digonal axis bisecting one of the angles of 60° subtended by these axes; and this would prevent a from being a minimum. * See proof of general proposition 20, p. 24. 30 Mr. W. Barlow on Crystal Symmetry. Therefore the two types described are the only ones com- patible with the polygonal arrangement of digonal axes in question. 3. Where the polygon traced is an octagon: n=8; p=2.~~ =90°. In the le: case there are therefore four digonal axes lying in the same plane and a tetragonal axis at right angles to these; the arrangement being shown in (Pl. II.) fig. X. (Gadolin, fig. 32). To prove ‘that no other case of this polygonal arrangement of digonal axes is possible, ¢. e. that no additional axis or additional rotation about an existing axis can be present :— First, 1 may be observed that the addition of a digonal axis in the plane of the four digonal axes of the simplest case is precluded because the chords a, which are the sides of the octagon, are minima. Next, that the addition of any other axis than this would involve ‘a plur ality of tetragonal axes. Now if more than one tetragonal axis is pr esent, there must be three altogether which are placed at right angles to one another, as shown by proposition 22*. ‘Two of these would therefore lie in the plane of the four cigonal axes. But a tetragonal axis placed anywhere in this plane is sufficiently near to some digonal axis to involve the presence of four digonal axes whose distance apart is under the minimum a. Consequently there can be no tetragonal axis or any other axis in any position not previously occupied. As the essential tetragonal axis does not admit of con- version because an axis whose order is a multiple of it is inadmissible, no axis whatever can*be added. 6. Where the polygon traced has twelve sides: n=12; ie Oi i. In the simplest case there are therefore six digonal axes lying in the same plane and a hexagonal axis at right angles to these; the arrangement being shown in (Pl. II.) fig. XI. (Gadolin, fig. 44). Since no additional digonal axis in the plane of the six essential digonal axes is admissible, and the presence of any other additional axis anywhere else would involve the exist- ence of a plurality of hexagonal axes, which according to proposition 22 is impossible, there can be no other case of this polygonal arrangement. “STS JO, 255 Mr. W. Barlow on Crystal Symmetry. 31 This completes the list of types of identical repetition about a centre presented when there is a plurality of axes. A similar method to that employed on page 22 leads to the dis- covery of a homogeneous structure corresponding to each of them. The types are, as stated above, the six shown by figs. VI.-XI., in which no mirror-image similarity is re- presented. Adding the five cases previously described, there are in all eleven types when mirror-image repetition of directions similarly related to the structure is excluded; viz.: one anorthic and ten which exhibit different directions ‘identically related to the structure. Mirror-Image * Similarity of Parts. As already stated} the similarity of corresponding parts may amount to identity, or it may be mirror-image resem- blance. ‘fo complete the survey it is therefore necessary to turn to the cases in which a similarity of parts exists which is a mirror-image one, the corresponding parts present, whether points similarly placed or directions similarly situated, being divisible into two sets so connected that the relation of the entire system to the individual points or directions of the one set is the mirror-image of its relation to the individual points or directions of the other set. As the aspect of such a system when viewed from one standpoint within it is the mirror-image of its aspect a viewed from some other standpoint, it is evident that corre- sponding to every set of linear directions and parts which bear an identical relation to the structure there is an equally numerous set of directions and parts whose relation to the structure is semilar but not identical to that of the members of the first-named set, and which, like the latter, are identical among themselves. And it follows also that the figure of the entire. system of repetition is, in a case of this ‘kind, irre- spective of orientation, identical with the figure of its mirror- image. Let some complete set of identically related directions be located in a system possessing the property described, care being taken not to select those occupying any specially symmetrical position. It will then be possible also to indicate a corresponding equally-numerous set of directions whose relation to the system is similar, but not identical, to that ot the directions of the first set; and it follows from the fore- going that the arrangement of the one set of directions is * See note 2, p. 6. T See p. 6. d2 Mr. W. Barlow on Crystal Symmetry. the mirror-image of that of the other set. This is true of enantiomorphously corresponding directions, whether occur- ring in homogeneous structures or in their spheres of reference*, As an example of the latter :—the set of similar normals, whose situation is shown in (PI. I.) fig. XIV., may be regarded as made up of the set indicated in (Pl. I.) fig. I1L., and a set which is the mirror-image of the latter. Now whether a system of symmetrical repetition about a centre, which is not a centre of inversion, is identical with its own mirror-image or not, it is always possible to find a system of a higher order of symmetry which presents all the symmetry of the given system and whose centre zs a centre of inversion; and the presence of such a centre produces an additional symmetrical, but not identical duplication of all the repetitions of the system taken. Tor the invert of this system with respect to its centre has the same axes, and the elements of symmetry of the two systems thus related can therefore exist together in a more complex type of repetition having the same coincidence-axes as the two simpler systems, and with the centre of inversion added. If the original system is not identical with its mirror-image, the additional repetitions found in the corresponding system which has a centre of inversion will be all identical and will be the mirror- image of all those of the simpler system. If, on the other hand, the simpler system is already identical with its own mirror-image, though not possessed of a centre of inversion, the additional repetitions, like those of the simple system, will be separable into two sets, one of which is the mirror-image of the other. As an example of the former case the type shown in fig. XIV., which has a centre of inversion, duplicates the tvpe shown in fig. III.; and, as an example of the latter case, the type shown in fig. XXII. duplicates that of fig. XXXIT., the latter being identical with its own mirror-image. But although some centred types which contain a centre of inversion may, in this way, be derived from types that are identical with their own mirror-image, they, as well as the rest of the types possessing such centres, can also always be re- garded as derived by the duplication of a system of repetitions which has not this property. For, in every case where a centre of inversion is present, just half the similarly related directions or parts are identically and not merely similarly placed with reterence to the entire structure; and therefore these, taken alone, possess all the coincidence-movements of the structure and exhibit one of the types of symmetry not * See p: 11. Mr. W. Barlow on Crystal Symmetry. 33: identical with its own mirror-image which has already been described. Therefore a complete list of all centred types which contain a centre of inversion is furnished if, for every system which is not identical with tts own mirror-image, a corresponding system is found having all the coincidence-movements of this system, and also in addition the set of similar repetitions involved by its possession of a centre of inversion. To obtain the diagram of these types let each of the identical normals drawn through corresponding points in the — types already traced be produced through the centre to meet the sphere a second time in a set of points which are there- fore the inverts of the points of the first set. The references to the resulting figures are given in the following table :— TaBLe of the derivation of Types which have Centres of Inversion. The type identical with its own Is derived from the type not mirror-image and possessed of identical with its own a centre of inversion which is mirror-image traced above: shown by and represented by Corton) XI, (Gadolin fig. 07) .22...5. 2. (Ble yties oe DOS G5, ADE Ss ehctacr 1a BOR. (© 55 DG) me dues een Til. EN (ae 59 DO ieee en teee are Ty; D8 i iene ONL) aateye eee V. D0 0 Re OHO) cds nak ie VAL. (PEIE) fie. XVII ( ,, he) cancer Se AE CRE este. Va. ».4 B.C an er 32) eee oe VIII. 2. hs LS) en eer Xe DONG 5, 315) | RS Segre 2G ROX (ss ADI) o aie oe at XI Instances of elementary homogeneous structures which present the same symmetrical arrangement of similarly re- lated directions as is respectively presented by the types ‘possessed of centres of inversion just enumerated, can be arrived at by the method already described *. Tor if the identical bodies placed at the points of a network possessed of adequate symmetry have individually the symmetry of the type intended to be illustrated, z.e. a centre of inversion as. * See p. 22. Phil. Mag. 8. 6. Vol. 1. No. 1. Jan. 1901. D 34 Mr. W. Barlow on Crystal Symmetry. well as the appropriate axes, it is evident that since every parallelepipedal network of mere points has centres of in- version at all of these points, the structure formed with the bodies referred to will, taken as a whole, possess centres of inversion at all the points of the network. The employment of any one of these centres of inversion will locate the set of enantiomorphously-similar directions corresponding to the set of identically related directions previously located, thus performing exactly the same function as a centre of inversion in a centred type*. Finally, as to centred types displaying a mirror-image similarity of parts, but which do not possess a centre of inversion :— It is evident from the foregoing that every system thus characterized contains half the repetitions of some one of the types above enumerated which have centres of inversion. And also that half of its similar directions and parts, 2. e. one fourth of those of the corresponding type possessed of a centre of inversion, bear a mirror-image resemblance to the remain- ing half. Further, that any system of zdentical directions found in it, the number of which, as just stated, is one fourth the total number of similar repetitions in the type possessed of a centre of symmetry, is of one of the eleven types which are not identical with their own mirror-image. To obtain the types in question :— For each of the eleven inversion types of the foregoing table, ascertain which of the eleven types of merely identical symmetry has just one fourth of its repetitions ; the result is shown in the 2nd and 38rd columns of the following table, from which it is seen that in some cases none of the latter are found to fulfil this condition, in others two, in most a single type. ) Rejecting the set of repetitions in the inversion type (the quarter of the points) which are the inverts of those of the system of lower symmetry just arrived at, ascertain which other quarter of the repetitions of the system of higher symmetry can be added to those of the simpler system to produce a system identical with its own mirror-image, and which the addition of a centre of inversion will convert to the inversion type selected. To take an example :— The only quarter system corresponding to that of fig. XVI. is given by fig. IIT. Rejecting the additional repetitions which would convert * See p. 32. Mr. W. Barlow on Crystal Symmetry. 30 the latter system to that given by fig. XIV., and which result from the addition of a centre of inversion, it is evident that fig. XXV. gives the only selection from the repetitions of fig. XVI. which will fulfil the required conditions ; the selection shown by fig. V.is precluded because the added repetitions are ¢dentical and not merely similar to those of the quarter system shown in fig. ILI. The following table gives the results arrived at :— Taste of the Derivation of Types which display Mirror- Image Similarity of Parts but do not contain Centres of Inversion. Type zot identical with its own mirror image which has half ‘Type identical with its own ane the repetitions of the derived A : : : inversion mirror-image which dis- type from ee wre OP ate no centre of inversion. the ccrresponding inversion None derived from ...... ioe) XLT: a Fig. XXIII. (Gadolin fig. 46) XII, ioe None derived from ........ XIV. rf, Fig, XXIV. (Gadolin fig. 34) XV. ios i: IROXEY 5° ( Fs 54) XVI. IO None derived from .....-.. XVII. an Fig.. XXVI. (Gadolin fig. 31) XVIII. Fig, VI. PRET (1), 55 43) XIX, JE Ree O43 59) XX. Til. OE: (| 55 37) XXI, LIM 10.0.8 Siar 40) 9 VIII. 3.00.6 ery 49) OX ISS OOH Wg, 82) EP V. As before, an instance of an elementary form of homo- geneous structure which presents the same symmetrical arrangement of similarly related directions as is found in the corresponding centred type can be obtained for each of the ten types enumerated in the first column; the method of accomplishing this is precisely that previously adopted *. The complete list of types of symmetrical arrangement of the similarly related dzrecteons found in homogeneous 36 . Prof. Wood and Mr. Magnusson on structures of the nature defined, and available for crystals, is therefore made up as follows :— No. of Types.. Anorthic symmetry, destitute of coincidence-rotations or screw-spiral movement, furnishes . . . . . I Identical repetition of parts without mirror-image similarity furnishes . sb he 10 Mirror-image similarity superadded. With centres of inversion furnishes . 11 a1 Without centres of inversion furnishes 10 Total ~.. | -s° sees Il. The Anomalous Dispersion of Cyanin. By Prof. R. W. Woop and Mr. C. EH. Maenusson *, [Plates IIL. & IV. | TTENTION has been already drawn by one of the present writers t, to the very perfect prisms for the exhibition of anomalous dispersion, that canbe prepared by pressing fused cyanin between plates of glass. It was shown to be possible to prepare in this way prisms of any angle desired, with perfect optical surfaces, a thing which it is quite impossible to do by the evaporation method employed by Wernicke and Pfltiger. In the same article was given a table of refractive indices for different wave-lengths, and the dispersion-curve in so far as it was studied. At the time of the publication of this paper no satisfactory readings within the absorption-band had been made, owing to the difficulty of pressing prisms of small enough angle to transmit the strongly absorbed rays. Readings within the absorption- band have been made by Pfliiger with prisms obtained by the evaporation of an alcoholic solution of cyanin, and the dis- persion-curve found to be continuous, but the surfaces of his prisms were necessarily so imperfect, that it seemed important to repeat the work under better conditions. Since the publication of the paper alluded to above, the work has been continued by the present writers, with still more perfect prisms, very satisfactory readings having been obtained not only in the region of the absorption-band, but also in the ultra-violet. * Communicated by the Physical Society. t Wood, Phil. Mag. xlvi. pp. 380-386. the Anomalous Dispersion of Cyanin. 37 All previous workers haye credited cyanin with but a single -absorption-band, the maximum of which is located not far from the sodium lines, but we have found a second band in the ultra-violet beginning at wave-length ‘00037. Two methods have been employed, namely, spectrometer- readings with cyanin prisms, and readings of the displace- ments of the fringes in a Michelson interferometer produced by thin films of the dye. A large amount of preliminary work was done on the preparation of prisms. Many dyes were tried, but cyanin seemed to be the only one suitable, consequently the work has been limited thus far to this single substance. ‘The difficulty of squeezing thin enough prisms to transmit yellow light has been already alluded to. Outside of the absorption- band it is possible to work with prisms of angles as large as 15 or 20 minutes. Within the absorption-band a prism of 1 minute angle transmits practically nothing. By using a small serew press arranged to work within an air-bath kept at the temperature at which cyanin was found to be most fluid, we finally secured some fairly good prisms of the requisite thinness, which was found to be about 30 seconds. It was exceedingly difficult to split off one of the glass plates without shattering the prism, but even this was successfully accom- plished, for parts of some of the prisms. The method employed in the determinations of the refractive indices in the visible part of the spectrum was the same as that described in, the previous paper, the slit of the instrument being illuminated with monochromatic light obtained from a large direct-vision spectrometer. A portion of this hght, made paral- lel by the collimating lens, passed through the prism, another portion passed through a strip of ene glass immediately adjoining the prism. Two images thus appear ed in the tele- scope, an undeviated, due to the light coming through the clear glass, and a deviated formed by the prism. In this way the effect of any slight prismatic form of the plate-glass was eliminated. ‘The “strongly absorbed rays only pass through a very narrow strip bordering the refracting edge of the prism, consequently the image is much broadened by diffraction, and accurate measurements are obtained with great difficulty. Tn the following table are given the values of the refractive indices for various wave-lengths obtained with prisms of angles varying from 24 seconds to 17 minutes, something over 80 observations in’ all. Hach one of these observa- tions is the mean calculated from several settings of the spectrometer. 38 Prof. Wood and Mr. Magnusson on TaBLe I. Prism No. 1, Angle 17’ 3”. r r : p. ; rN ph r 7650 1920 | 4798 p. : : 5 : 1:387 | 4610 1-449 | 4295 1595 7590 1:970 | 4792 1:387 | 4568 1-460 | 4270 1:533 7350 1:985 | 4756 1:416 | 4518 1-479 | 4191 1544 7035 2-050 | 4753 1-401 | 4442 1:496 | 4108 1547 6887 2131 | 4727 1:408 | 4380 1523 | 4065 1°557 6856 2150 | 4700 1418 | 4342 1524 | 4867 1:380 | 4637 1-434 Prism No. 2, Angle 4’ 52”. | Prism No. 3, Angle 23' 59", Xr. ie | d. pL. 6680 2°232 7320 2-027 658 1 2'343 | 6880 2170 5248 1:122 at, ae Mie Prism No.4, Angle 117". 5048 1194 5018 1:266 . 2 4958 1:280 ae aay 4596 1-350 hee een) Prism No. 5, Angle 24”. r. pe r. pe Xr. pl. Xr. p. 6675 2:26 6100 2°14 5890 1°59 5505 1-22 6465 2°35 6070 2:06 5800 1 y/ 5400 1:12 6335 2°30 6070 1-93 5800 1:59 5182 1:14 6330 2°35 5995 1:86 5680 1:45 5065 1:22 6245 2°33 5970 ies) 5640 1:30 6100 2°10 5890 1-65 Prism No. 6, Angle 32". r. pL. d. es 6062 1-88 5610 1:27 5992 1‘8] 5895 1:58 5180 Hel 53810 113 4865 1:33 51838 113 Prism No. 7, Angle 51’. | Prism No.8, Angle 21’ 3". Xr. pl. Xr. ie 6228 2°25 7236 2-014 5895 1-67 7236 2:020 4230 1:E07 Prism No. 9, Angle 2’ 10". r Xr. LL | : ie 7930 9-005 | 5020 1-240 6830 2:190 | A865 1:375 6720 2-250 4690 1-40 6570 2/320 | 4510 151 | 1:50 6555 2°320 | 4410 the Anomalous Dispersion of Cyanin. 39 These results are shown graphically in fig. 1 (p.40), and show conclusively that the dispersion-curve is continuous through the absorption-band. Measurements in the ultra-violet were made by photo- graphy. A Rowland concave grating was used, the slit, grating, and photographic plate being on the circumference of a circle in the customary manner. The slit was illumi- nated with sunlight in some of the experiments, and by the light of an are formed between an iron rod and a revolving iron disk in others. A cyanin prism, formed on a quartz plate, with an angle of 2’51'"5 was placed between the grating and the plate at a distance of 177°6 centim. from the latter. This method was employed by Pfliiger, and though there are some objections to it, it gave fairly concordant results. A portion of the light from the grating passed through the prism, and a portion through a clear place in the quartz plate. There were thus formed two spectra slightly displaced with reference to one another, and by measuring the distance between corresponding lines, the deviation due to the cyanin prism could be calculated. The lateral displacement was very slight, but by using great care in measuring the shift, fairly accurate values for the refractive indices were obtained. The photographic work was extended into the blue and violet portions of the spectrum, in order that a comparison with the more accurate spectrometer determinations could be made, and close agreement was found. The results are given in the following table :— Prism No. 10, Angle 2’ 515. A. ph. 423 1°530 410 1565 404 1573 als, 1°606 380 1°600 302 1610 These values, though not shown on the curve, will be found to fit very well. Beyond wave-length 372 nothing appeared to be trans- mitted through the cyanin, even with a five-hour exposure, though a strong image of the spectrum transmitted by the uncovered quartz was obtained. Hvidently cyanin has a second absorption-band at this point, for the same thing was found in subsequent work with the interferometer, the absorp- tion of glass not beginning until somewhat further along in the spectrum (about ‘00033). Whether this absorption _ Prof. Wood and Mr. Magnusson o the Anomalous Dispersion of Cyanin. Al extends to the extreme limits of the spectrum has not yet been determined. Pfliiger found no traces of this band, and gives values for the refractive index within its limits. It seemed at first that the reason of this might be found in the difference in the optical properties of fused eyanin and that obtained by the evaporation of an alcoholic solution, but we have found that films prepared in the same way as those used by Pfliiger show the band also. By dispersing white light into a horizontal spectrum by means of a glass prism, and then dispersing this spectrum vertically by 1 means of a cyanin prism, the dispersion-curve ean be shown objectively. This method of crossed prisms, originally due to Newton, and used by Kundt in his study of anomalous dispersion, is decidedly the best for illustrating the matter to students. Unfortunately it cannot be pro- jected ona large scale, but we have succeeded in photographing it by mounting the prisms in front of a telescope lens of about 2 metres focus. By using the small angle prism the entire spectrum is secured, though the very slight deviation obtained in this case lees ine, picture unsatisfactory. A number of these curved spectra are shown in Plate III. The Michelson interferometer furnishes an easy means of determining the retardation of light in thin films of trans- parent substances, and a somewhat extended study of the dispersion of cyanin has been made with this instrument. It is far easier to obtain thin uniform films of the dye by evaporating the alcoholic solution, than it is to make good prisms in this way, consequently better results were looked for than those obtained by Pfliiger with his prisms. The cyanin was deposited from a hot alcoholic solution on selected plate-glass. To secure uniform films in this way, it is necessary to use absolute alcohol and keep the temperature between 35° and 40°, the operation of coating being per- formed in an air-bath "by dipping the plates in the solution and setting them on edge to dry. A uniform film was selected, and one half of the plate was freed from the cyanin, that which remained being bounded by a perfectly straight edge. The interferometer was adjusted for horizontal fringes, which are most convenient for measuring smal} displace- ments, and the plate placed upright before one of the mirrors, with the straight edge bounding the cyanin film perpendicular to the fringes. The central fringe was brought into view by using white light, since it is the only one which can be identified, and furnishes us the only means of telling whether the displacement is half a fringe or a fringe and a half. 42 . Prof. Wood and Mr. Magnusson on The interferometer was then illuminated with monochromatic light from the large direct-vision spectroscope, and the double-fringe system photographed for various wave-lengths. “Hrythro” plates were used, enabling us to secure records from the extreme red to the ultra- violet, a series of about thirty exposures being made on a single plate. These photo- graphs show the continuity of the dispersion-curve through the absorption-band most beautifully. Beginning in the red we find a large displacement, which increases progressively as we near the region of the absorption-band in the yellow. As soon as we are in this portion of the spectrum, the dis- placement rapidly grows less, the fringes getting almost into line in the middle of the yellow. Then. the displacement. begins to increase again as we leave the absorption-band on the blue side, the rate of increase growing less as we near the ultra-violet. The displacements were measured on the plates by means of a filar micrometer, and were recorded in terms of fringe width. Since the light passes through the film twice, the total displacement is that which corresponds to a retardation of a film of twice the thickness. To calculate the refractive index from the retardation we require the thickness of the film. In order to avoid the many sources of error involved in any attempt to measure the film’s thickness directly, we made use of the values already determined for the refractive index for those wave e-lengths most freely transmitted by the eyanin. The prism method is the more accurate when reason- | ably large angles can be used, and the investigations with | the interferometer were made with a view of corroborating i our results in the absorption-band. Professor Ames has drawn our attention to the fact that in using a prism of a | strongly absorbing medium the amplitude of the transmitted | wave falls off very rapidly from the refracting edge, and that. this might have some effect on the propagation ot the wave, for in treating wave propagation we always assume the amplitude to be the same at every point on the wave front. This is a most pertinent suggestion, for if a rapid decrease of amplitude on a wave front changes the position of the effective point to which we can reduce the whole wave (by Huygens’s principle) it should certainly modify to some degree the apparent refractive index as determined by a prism.. So far as known no one has ever worked out Huygens’s | principle for a wave of variable amplitude. There seems to Nh be no way of making the usual geometrical treatment cover | the case, although it seems at fir st sight as if the method of ) strip-division might be used. the Anomalous Dispersion of Cyanin. 43, The interferometer method is not open to this objection however, and the very close agreement between the curves obtained by the two methods indicates that any possible effect of the variable amplitude is too small to materially | influence the results obtained by the prism. Two of the interferometer series photographs (Plate IV.) are reproduced, one obtained with a thin film, showing the displacement throughout the region of the absorption-band, and the other made with a thick film, giving much greater displacements, but yielding no fringes in the yellow part of the spectrum. The wave-length of the light used appears below each picture in the series. The two white marks indicate which fringes belong together, and may be taken as giving a rough measure of the displacement. The thickness of the thin film was about 0°00013 millim., that of the thick one 000071. One difficulty experienced in measuring the retardation produced by a strongly absorbing film by means of the interferometer is very troublesome, namely, that due to the weakening of one of the interfering beams without a cor- responding weakening of the other. This causes a strong and uniformly illuminated field to be superposed on the fringes, and may obliterate all traces of them. It is necessary on this: account to use films considerably thinner than would be neces- sary under other conditions. This difficulty can probably be obviated by a compensation device, and work in this direction is now in progress, with every promise of success. The dis- placement of the fringes can be doubled by the introduction | of a second cyanin film in the other interferometer path, in such a position that the two films are seen side by side in the half-silvered mirror, with their straight edges in contact. This method was not used in the work on cyanin, but has been used successfully by one of the writers in some subse- quent work on the retardation caused by thin films of carbon. The introduction of the compensation device will make the method much more accurate, since films several times as thick as those at present used will then be suitable. The results obtained with the interferometer are shown graphically in fig. 2 (p. 44), forty observations being recorded. The curve obtained with the spectrometer is shown by the dotted line. In general the two curves agree very well, slight discrep- ancies being possibly due to a difference in the optical properties of fused cyanin and that obtained by evaporation. There is decided evidence of a rise towards the ultra- violet absorption band, as there should be theoretically, though we do not regard the values obtained in this part of Cyanin. On the Anomalous Dispersion of 44. 5 17) 10 69 Tors SURE 496 7a 1A 1,0 On the Concentration at the Electrodes in a- Solution. . 45 the spectrum as sufficiently accurate to make this point certain. The work in this region will have to be repeated under more: favourable conditions. It was our intention to apply the results of the work to a proof of the Ketteler-Helmholtz dispersion formula, but the: discovery of the second absorption-band makes this impossi- ble until the extent of the band has been determined, and the: extinction coefficient measured, a matter of considerable difficulty. Some of the discrepancies found by Pfliiger between his calculated and observed curves, he thought might be explained by the possible presence of an absorption- band in the remote ultra-violet. University of Wisconsin, Madison. IIL. On the Concentration at the Electrodes in a Solution, with special reference to the Liberation of Hydrogen by Electro- lysis of a Mixture of Copper Sulphate and Sulphuric Acid. By Henry J. 8. Sann, PA.D., Bowen Research Scholar at Mason University College, Birmingham*., ConTENts :—Historical introduction.—Theoretical consideration of the Liberation of Two Constituents at an Electrode.—Calculation of the- Concentration in a Solution contained in a cylindrical vessel, across one end of which a constant flow of salt is taking place.—Application of results to obtain Values for the Concentration at the Electrode of the Solution of a single Salt and of a Mixture.—Experimental determination of the Time required till Hydrogen appears during Electrolysis of ani Acid solution of Copper Sulphate——A new method for determining the Diffusion-Coefficient of Copper Sulphate-—Experiments to show the great influence of Convection-Currents on the quantity of Hydrogen. given. off in the Electrolysis of an Acid Solution of Copper Sulphate —- Summary of results. INCE the electrolysis of mixtures first attracted the attention of scientists, three distinct views have been held about the processes which take place at the electrodes. In 1857 Magnus+ put forward the theory that in the solution of a mixture of two salts, only one is decomposed if a current of small density be employed ; if, however, the current-density exceeds a certain definite value, the second. salt also suffers from decomposition. He attempted to find. this definite value in the case of a mixture of copper sulphate and sulphuric acid, ascribing it to a current-density which. produced a visible amount of hydrogen at a vertical cathode within fifteen seconds. The result obtained was, that the- * Communicated by the Physical Society: read Oct. 26, 1900. + Pogg. Ann, ci. p. 17. A6 Dr. H. J. S. Sand on the Concentration value was roughly independent of size, distance, &c. of the electrodes, and only a function of the composition of the electrolyte. About the same time Hittorf was engaged in his funda- mental researches on the processes which take place within the electrolyte. His experiments, as is well known, proved that in the interior of the solution of a mixture of two salts, both take part in the conduction of the current at all current- densities. Regarding the process which takes place at the electrode, he at that time assumed that the ions of both salts were primarily deposited in the same proportion in which they had taken part in the conduction of the current within the liquid. In most cases, however, one of the components would act chemically upen the solution with a definite reaction- velocity; and it was only when this velocity was exceeded by the rate at which it was being primarily deposited at the electrode that its liberation would become perceptible *. Thus in a mixture of copper sulphate and sulphuric acid, hydrogen would be primarily liberated at all current-den- sities; but it would only become visible when the velocity with which it was supposed to decompose copper sulphate in the nascent state was exceeded by the rate at which it was being primarily set free. It appears that it was Le Blane who first insisted sufficiently on the fact that the mode of conduction of the current within any part of the interior of the electrolyte does not necessitate the same mode at the electrodes. His investigations having proved that the same minimum electromotive force must be applied to various acids and bases in order to cause the con- tinuous passage of a current of appreciable magnitude through them, Le Blane framed his well-known theory, that whereas conduction through the interior of an acid or a base is due in almost exclusive preponderance to its own ions, the trans- mission from the solution to the electrolyte must be ascribed primarily to the ions of water. Generalizing this statement, he expressed the view + that in a mixture of ions at an elec- trode those exclusively are set free which require the smallest E.M.F. for their liberation; and it is only when their con- centration at the electrode has gone down to zero, that those requiring a higher E.M.F. for their liberation also appear. Thus in a mixture of copper sulphate and sulphuric acid, copper only should be deposited till its concentration at the electrode has gone down to zero, after which hydrogen also would be liberated. * Poge. Ann. cili. p. 46. + Zeitschr. phys. Chem. xiii. p. 172. at the Electrodes in a Solution. AZ The decomposition of mixtures has recently been examined theoretically by Nernst*. We shall consider the same subject from a slightly different point of view. For this purpose we adopt the view, probably best adapted for the treatment of chemical problems, that the energy ex- pended by the current in passing through the drop of potential at either electrode is the equivalent of the free energy required to effect the change from ionic to free state, or vice versa, taking place there, plus the energy expended on any other processes which may accompany the passage of the current, and which finally result in an irreversible heating-effect. For our purposes we are justified in considering each electrode separately, as we can always suppose the electrode not under consideration so large that the nature of the processes taking place there and the energy expended there per g.-ion do not vary appreciably with the current-strength. We shall sup- pose a mixture of two salts given, and consider the depo- sition of mn, g.-equivalents of the cation most easily deposited. For the present we shall assume that if processes occur which irreversibly cause the production of heat, this quantity of heat shall be proportional to the number of g.-equivalents liberated, so that it can be represented by hn, h being a constant. Under these conditions, if w, be the quantity of free energy required to liberate one g.-equivalent, the amount of work done in the deposition of the n, g.-equivalents will be independent of the current-density and equal to n,(w,+h). Now the quantity of electricity which causes this will, according to Faraday’s law, have the value fn, f being Faraday’s constant of 96540 pee Therefore, if the drop of potential from the electrode to the liquid be E, the work done by the current in passing through it will be Hin, f, and this according to our assumptions is equal to m (wy +h), or Hf=w, +h. This means that the difference of potential between the electrode and the liquid is independent of the current-density employed, and is always the same as the minimum H.M.F. necessary to deposit those ions which are most easily set free. If therefore there be ions of a second substance present, which require for their liberation a minimum §.M.F., E,>E, none of them will be liberated so long as any of the ions first con- sidered are left in contact with the electrode. It is only when K,=E that simultaneous deposition of both occurs. Our suppositions have thus proved equivalent to Le Blanc’s view. * Zettschr. phys. Chem. xxii. p. 541, 48 Dr. H. J. 8S. Sand on the Concentration It should be noted that our assumption that any heating effect which may take place is proportional to the number of ions deposited, excludes the liberation of heat owing to anything in the nature of electrolytic resistance in the vicinity of the electrode, being bound up with the deposition of the ions—electrolytic heating in a given electrolyte being, as is well known, proportional to the square of the current. In arriving at our result, we also excluded the supposition that at high current-densities ions of the two salts should enter into chemical combination, forming complex ions. As is well known, the 4.M.F. necessary to deposit an ion from a solution on a given electrode varies within certain limits with its concentration in the solution. In the case of reversible processes it can be calculated in volts by Nernst’s formula: H=0°860 x 10-4 Tln > T being the absolute tem- perature, n the valency of the ion, p its osmotic pressure in the solution, and P its so-called solution-tension. When two monovalent metals of solution-tension P, and P, are being simultaneously deposited as a mechanical mixture, this equa- tion in connexion with H, =H, leads to 0:860Tin =! =0'860Tint? or Pia PL P1 Pa yooy lets oa a formula which is given by Nernst in the paper quoted *. * Note.—In his paper Nernst also gives a formula for the ratio y of the quantity of the metal (1) deposited in g.-equivalents to the total number of equivalents liberated, the conditions being as above. This formula is based on the consideration which follows from the results just obtained,. that if we have a solution containing the salts of two metals in a pro- portion in which they are not simultaneously deposited, the metal which is in excess of this proportion will at first be deposited alone until the proportion for simultaneous deposition be again attained. If we there- fore start with a solution which contains the salts of two monovalent 1 ti ‘] by tl ti i ae or, assuming” metals in the proportion given by the equation pee S 2 complete dissociation and indicating concentrations by c, C, rime ae then if we stir in such a manner as to keep the concentration uniform as nearly as possible, the ratio of concentrations which before stirring varied throughout the electrolyte, will have the tendency to become again uniformly CUA aay ai P. ° ° e ) e e ° © ° e (B). C2 2 at the Electrodes in a Solution. ; 49 According to Neumann *, when copper is deposited from the normal solution of its sulphate on a copper electrode, it produces an H.M.F. aiding the current of 0°515 volt hydrogen; on the other hand, when it is reversibly deposited on a platinized platinum hydrogen electrode an E.M.F. of only 0°238 volt, 7. e.a voltage higher by 0°277, is required to liberate hydrogen reversibly from a normal solution of its sulphate than is required to liberate copper under the same conditions. | Now according to Caspari’s experiments Tf, a 0°23 volt higher electromotive force is required to set hydrogen free on a copper than on a platinized platinum electrode; i.e., in order to deposit hydrogen on a copper electrode from a normal solution of sulphuric acid 0°507 volt more is required than to deposit copper on the same electrode from the normal solution of its sulphate. If we employ Nernst’s formula to. calculate the concentration of a copper solution, to deposit It is easy to see that from the two equations (A) and (B) the ratio y men- : 1 . . tioned above can be calculated to be y= PLP, This is the formula given without explanation by Nernst. It should, however, be parti- cularly noted that this ratio y is not the result of simultaneous, but of successive deposition of the two metals, depending on the rate of stirring, and that, as will be seen later (note, p. 60), the ratio of simultaneous deposition, e. g. at the beginning of the experiment, has a ditterent value, irrespective of the fact whether the current employed be large or small. , In order to obtain formule referring to simultaneous deposition, when no stirring takes place we assume the electrolysis to take place in a cylindrical vessel bounded by its cathode, and indicate distances from it by x, times by ¢, and name the quantity of each ion crossing any section in the differential of time in the directicn towards the electrode, 7. e. from greater values of x to less, Fd and F’,d¢ respectively; then, assuming complete dissociation, we have for simultaneous deposition of the two (monovalent) metals as above, P = Ce 10le —O, Soa from which follows: oc P.O 2 OR MOGR i: and as in every cross section ar. Of this gives :— oF, Eg ole ee Soe Ear fOr) C0, (See also note on p. 60.) * Zeitschr. phys. Chem. xiv. p. 222. i, Lied. xxx.p. 93. Phil. Mag. 8. 6. Vol. 1. No. 1. Jan. 1901. I} 50 Dr. H. J. S. Sand ox the Concentration copper from which would require the same voltage as to liberate hydrogen from a normal solution of sulphuric acid at 15°, we find a value of about 2x 107!§ normal. This means, according to the theoretical considerations advanced, that hydrogen will not be given off from an acid solution of copper sulphate till the concentration of the copper has practically gone down to zero at the electrode. In apparent opposition to this, the experimental liberation of hydrogen from a not too concentrated acid solution of copper sulphate is a matter which can be accomplished by comparatively low current-densities, and doubt might well arise, whether the suppositions on which our deductions are based were not at fault. It might be supposed that diffusion of the copper sulphate in the liquid would effectually hinder its concentration from going down to zero at the electrode with the rapidity which the experiments require in order to justify the theory. Indeed, as far as I can see, the idea that the concentration of the copper is zero at parts of an electrode from which hydrogen is being given off has not been entertained by any of the experimenters who have published work on a mixture of copper sulphate and sulphuric acid. It must be remarked here that changes of concentration in a liquid are in most cases no doubt effaced to a much greater extent by convection-currents than by diffusion. But in order to test the theory, it is possible experimentally to do away with convection-currents almost entirely by the methods described in the experimental part; besides from its very nature convection must be an erratic phenomenon, not amenable to calculation and which could not be depended on, continuously and uniformly, to neutralize changes of con- centration arising on the total surface of an electrode. In order to test the theory experimentally, it would be necessary to calculate the concentration of the copper ions at the electrode of an acid solution of copper sulphate from which copper alone was being deposited, under the supposition that only diffusion, and no convection, neutralized differences of concentration brought about by the current. Unfortunately neither the laws of conduction of the current nor those of diffusion in amixture are completely known, and if they were, their application would probably involve extremely great mathematical difficulties. It is therefore not possible accu- rately to solve the problem just stated. As will be seen later on, we can, however, solve it within certain limits by first turning our attention to the following simpler case. Problem: Let us suppose electrolysis to take place in at the Electrodes in a Solution. 51 a cylindrical vessel bounded at both ends by its electrodes. Let F g.-equivalents of salt be uniformly and constantly removed at one end, per unit of surface and time, and let the distance from the electrode forming the other end be so great that changes of concentration occurring there do not affect the concentration at the electrode under consideration. Further, let the initial concentration be uniform and equal to £0 g.-equivalents per unit of volume. Find the concentration in the interior of the liquid and at the electrode at any given time ¢ under the suppositions, that changes of concentration are neutralized by diffusion only, that this takes place according to Fick’s law, and that it is not affected by the passage of the current through the liquid *., As the concentration at any point of the liquid cannot be influenced by the nature of the cause producing the removal of the salt, it will be the same as that in a similar liquid in which a flow F was produced by a suitable gradient of con- centration being artificially kept up immediately behind the electrode. In sucha solution, and therefore also in the one under consideration, we have for the determination of the state of the liquid the first equation : : Ge = a ae ct Mae as” veg ii ae (1) bo ale if concentrations at any point are indicated by c¢, distances from the electrode by #, and the diffusion-coetfficient of the salt by K. pe The uniformity of the concentration at the beginning of the experiment affords us the second equation : Cam ICO see ate hn wath ee Nap cise) vats he (2) between «=0 and z= for t=0, and the general expression of Fick’s law gives us the third : OC _y OC Si Se errtat il wetntey al aoe ot Oa” (9) Hguations 1 and 3 are satisfied by the following general solution : F Le nt ee n=0 * Note.—The equations given here as far as No. 5 have already been given by H. F. Weber in the elaboration of his beautifully conceived method for the determination of the diffusion-coefficient of ZnSO, (Wied. Ann. vii. p. 539). Concentrations in a solution subjected to alternating currents have been recently examined by Warburg (Wied. Anz. Ixvii. p. 495). , HK 2 52 Dr. H. J. 8. Sand on the Concentration and in order that equation 2 may be fulfilled, viz. that F erat ni » oe — a oy geeae Comma “=z cos i & ) between c=0 and x=], n=0 we must, according to Fourier, make j r oa Lye »p—l1le—1 _fP 7 0 Y F NTL PE la, = (c —- v) cos (“ dxz= — — 57; (cos nm — 1), . i LS i ) mn? K which is equal to 0 or 2° mn? K according as 7 is even or odd. Substituting these values in equation (4), we obtain ri] 17 a2 * t= Soran (ces Te ie oes : cos Bee BR me (5) or | EF AIF /, _. By ae _DKt 1 Ba c= etcom mae (Sm gant tes & ayps @ L ) and remembering that : Ya 1 i ial = LP =e 52 ae ean Dre eee we find ey a F ML Se l LB _n—12 Ke C= ret oe AC be [i= COS (2n—1)r Fe [2 sk The infinite series in the above expressions for ¢ converge so slowly for large values of /, as to make them useless for numerical application. For 7=« all the single members of the series in the last equation become infinitely small, and the series assumes the nature of a definite integral. We * This equation also fulfils the condition F=K ce for 7. legean es therefore be taken accurately to represent the concentration in a cylinder of length 4, filled e.g. with CuSO, into which F g.-equivalents are introduced per unit of surface and time at the anode and the same amount is being taken away at the cathode, a fact which is utilized by Weber. at the Electrodes in a Solution. 53 shall convert it into a definite integral and make / infinite by the substitutions : ze dq’ ed) a di ues = dq being the differential of the variable g which assumes successively the values dg, 2dq..... een. oo, and « an arbitrary positive constant. We thus obtain : 2k AES (ee pear . 2q NY c= Ketan aR | dy 1a ( penne iG w)e ; ). The value of « being arbitrary, we can make : =—=1, ie«=2?vKi, and we find Fr ANA ee |e CL? LOR is ) Ce tO eK veil = es CO ay cen’ ce} This expression is further simplified in the following manner: we differentiate twice according to 2 and obtain Bae My) SO e ee rege ta Qa? K TR! we The value of the integral occurring here being known to be Vo rer es 4Kt, we have: RCO nl TARTS ae Ox = K Ve @ 4Kt, and making use successively of equations (3) and (2) we find F iE ee C=C)— —~——)| — ée 4kt; Pe G Be Oe 6 ° VatK Jo Vt 6) an equation from which it is not difficult to obtain numerical values for c by one of the approximation methods. For the concentration at the electrode for which «=0, this equation assumes the extremely simple form cman tla / pa q—1ieser y/* ee a) Experimental application of equation (7).—(a) Application to the Solution of a Single Salt. If we electrolyse the solution of a single salt, for example that of pure copper sulphate, we know that the value of F at 54 Dr. H. J. 8. Sand on the Concentration | ° r.-@e ul ie ° the cathode in am ’ is ‘i cm.” sec. Hh Na ae uU1—ne) i 96540 ~~ 96540 ” e e ° ° am e | a 2 being the current-density in ats , n, the transport value of m. the anion SO,, and n, that of the cation Cu in the solution. The concentration at the electrode after electrolysing for ¢ seconds will therefore be ees. pee 11284 Aes o= Co e5ag VK — oO 96540 This formula can be employed for the determination of K if coordinate values of c and ¢ are known. Before, however, further attempting to apply it to electrolysis, it will be necessary to consider to what extent the conditions on which it is based can be fulfilled in electrolytic experiments. Let us suppose electrolysis of a pure copper-sulphate solu- tion to take place in a cylindrical vessel of length /, bounded at the top by a horizontal cathode, at the bottom by a horizontal copper anode. In such a vessel, kept at constant temperature, convection-currents will be reduced to a mini- mum, as the lighter layers of less concentrated solution are continually being produced at the top, and the more concen- trated ones at the bottom. Our formula being based on the assumption of an infinitely distant anode does not comprise the fact that the anode of the real vessel we are now considering is causing a con- tinuous flow of salt into the liquid at the distance / below the cathode, which is equal to the flow out of it. It is, how- ever, not difficult to see that the following statements are correct :—(1) The real concentration at the anode and in the solution is greater than that given by the formula. (2) The difference between the real concentration and the calculated value is a maximum at the anode, and decreases continually as we approach the cathode. These first two statements can be inferred from the principle of superposition. (3) The real concentration at the distance 5 below the cathode is (either according to Weber’s formula (5) or from considerations of at the Electrodes tn a Solution. 55d symmetry) constantly cy; the difference between real and calculated values therefore is FE 4 pep a ST Re P It is easy to see that as long as t gene ae Ac=-— at the Electrodes in a Sohition. “i ii It is of importance to know by how much the value of ae differs when determined by either the one or the other of K these equations. This calculation does not offer sufficient interest to give it in detail, we shall therefore only state the t result that the ratio of the difference between K eoleuiated by (11) or calculated by (8) is given’ sufficiently Coo by the expression 2x 0-047 coe | e264? ty zeaae which for values of C= 0 2096 DSI. and c=0, em.? y) the only ones employed in the experiments, amounts to about 24 per cent., z.e. K, calculated by (8), is 25 per cent. smaller than calculated by (11). In concluding these remarks it must be mentioned that, according to Wiedeburg’s * careful investigation of the diffusion of copper sulphate, this does not accurately follow Fick’s law, the diffusion-coefficient decreasing slightly with increasing concentration. A thorough examination based upon Wiedeburg’s law would, however, lead beyond the scope of this paper. (b) Application of Equation (7) to a mixture of Copper Sulphate and Sulphuric Acid. As has already been stated, we shall in dealing with mix- tures be obliged to confine ourselves to obtaining upper and lower limiting values for the concentration at the electrodes, which will enable us to follow the real values in broad lines in their dependence on initial concentration and current density. Great accuracy in these values will not be required, and we shall be justified in wholly neglecting influences which only slightly affect the results. We shall thus suppose, that in a mixture of copper sulphate and sulphuric acid, the diffusion of the former is not affected by the presence of the latter. We first proceed to determine limits for the flow F, defined by Fdt being the quantity of copper brought by diffusion in the differential of time to each unit of surface of the electrode, when copper alone is being deposited on it. Using the same * Wied. Ann. xli. p. 675. 58 Dr. H. J. 8S. Sand on the Concentration notation as above, the flow of copper out of the solution at the electrode is | | 2 g.-equiv, 96540 em.?sec.’” | and the flow towards the latter, due to electrolysis | ac % g.-equiv. « 96540 cm.” sec.” The flow F due to diffusion is therefore i (i-“ ia 96540 ae This quantity is variable, increasing continually from its a year nale e e h C ' 6540? sips it assumes when has gone down to 0. The quantity pies which we may original value to the value call the transport value of the copper in the solution, can, as 1s known, be determined experimentally for the values of concentration and conductivity which exist at the beginning of the experiment. For this purpose it is necessary to pass an arbitrary quantity of electricity q through the solution, and to determine the decrease in copper in a region bounded on the one side by the anode, on the other by solution still having the original composition of the liquid (making the necessary correction for copper dissolved from the anode). ; ae g.-equiv., and has been determined by Schrader * in the case of certain mixtures — the same mixtures which have been employed for this present work. If the value of this decrease in grammes be a, and the quantity of silver deposited in a silver voltameter by the current employed be @, both of these values having been given by Schrader, then ac This decrease is equal to — GE Gana ta GS aes «x 96540 31°39? =: 96540 __—:107°6 6 and ill eu ee ie “3 a oy e e e e (12) the numbers 31°59 and 107-66 being the equivalent weights of copper and silver respectively. . * ZLischft. f. Elektrochemie, iii, p. 502. at the Electrodes in a Solution. 59 We thus find that if we pass a current of constant density 2 through an acid solution of copper sulphate, until the con- centration at the cathode has gone down to zero, the values of F at the beginning and at the end of the experiment can both be calculated, and we shall be justified in assuming that: the concentration actually attained at any time ¢ could also n't tee 96540 ying some- where between the extreme values of F had taken place- Thus, as far as variability of F is concerned, we can express the concentration at the electrode at any time by the formula VBL i, [2 Se CACO Or Al) NV K? ° : St rey ert ( ) n’ being contained between 1 and the value of 1—n, given in equation (12). We now come to the consideration of the effect of the passage of the current through the liquid on its con- centration. As has already been stated, this is expressed for a positive ion by the equation Ce | have been attained if a constant flow F’= Boras So (2) ot 96540 Oa\ ne] In the case we are now considering the concentration c¢ of the copper will vary extremely rapidly as we approach the cathode, the conductivity « of the solution on the other hand will remain fairly constant, as the solution, while becoming poorer in Cu and SQ, ions, will at the same time become richer in H ions, which are brought to the electrode without being liberated there. As we only desire to obtain rough values, we shall therefore be justified in assuming « constant. and equal to the conductivity at the beginning of the experiment. The mobility of the copper we also assume constant. We thus have OC i | OE Ot 96540 « Oa As a is always positive, we can conclude that the passage of the current will have the general effect of raising the concentration in parts of the liquid near and at the electrode where oe is of appreciable magnitude. The value given by Oz equation (13) must therefore be regarded as a lower limit. 60 Dr. H. J. 8. Sand on the Concentration Still more must i “ 1:1284 . “he t C> Co— OB5A0 d- K 6 . A 5 A pe) ‘, We can also find an upper limit for c, by determining the increase of concentration Ac at the electrode due only to passage of the current through the solution, by a precisely similar method to that employed for finding the corresponding decrease in the case of pure CuSO, on page 56. In the way shown there, it can also be seen here that the value obtained is too large when taken to represent the combined effect of diffusion and passage of the current. As the final result, we obtain vee ke 1! an! ae °—~ 96540 K” S¢5407e * Note.—If we had made no assumption about @ and « this inequality ‘would be 1:1284 ,. t tdi 8 ea) OSs way) xt. 96540 aa ( a from which, in conjunction with inequality No. 14, can be concluded Oe Weleeeieo | ee Un ION eS Of 2x 9NS4OV Kt 9654090 Lx « being a number contained between 0 and 1. This formula enables us to obtain some further information about the ratio L in which two monovalent metals can be deposited, which is mentioned in the note on p. 49, if we suppose that in the mixture assumed there the two salts diffuse independently of each other. The equation | 04 _ P, oe, Hae ot | ea ot then leads to et 1:1284 0,7, p iE: ra) (481) Be P,_ 2x 985400/K, _* 96540 “¢ Ca Or, Ps of EM 11284 Nyity : os Vt @ AC. ac 296540“ Ke ~ 96540 Ac _ Ox from which for t=0 we obtain, remembering that for this value of ¢ v Te D Ey 2 2 By 2 PCL Mey) = FE, Jeg ma Ne, ) K, n'=1—ne; and also that _ This equation for the limiting value of the ratio in which the two metals separate out in the first differential of time is based on no other assumption than that the two salts diffuse independently of each other, according to Fick’s law (besides those assumptions stated on p. 47. at the Electrodes in a Solution. 61 co—c being always positive, this inequality can also be written ily 1284 n! $ ie Wat eo— 9) = “96540 “WV KO 965408 K” where € is a number smaller than 1. The values of 2 Ne obtained from this quadratic equation are JS Bee Gye om are (co—c)ex 10-43 ot = 5447 — = (e 447 I Sp Now as. we know that for t=0, also cy—c=0, we con- clude that only the negative sign before the square root is / applicable. Remembering also that = is always greater than the value 1—n, of equation (12), we can transform this equation into the inequality —4 Mt Ans c es 10 J (54878 =\- = 93:20 7) ae 5) | the dimension of the number 5°447 occurring here is amp. Xsec. . : ; ; milliamp. Xsec. +" or, which is the same thing, Ee 44! g.-equlv. mg.-equlv. So) eee illiamp. x sec.\? | and the dimension of the number 93°20 is (= Hae ee ) : mg.-equiv. In the following Table (I.) I have given the concentrations of the solutions examined experimentally in g.-equivalents per ae =i They have | been made to correspond to solutions examined by Schrader’. The concentrations given by him have a slightly different meaning to mine, as his indicate the number of g.-equivalents contained in the copper-sulphate crystals which were dissolved in one litre of pure water. The quantities a, 8, and «, given by Schrader, as well as the values for a taken from Kohl- rausch’s tables, which have been used; will also be found in the table. Under the headings “ 2?t) max.” and “ 7¢) min.” will be found the maximum and minimum values of 7%), calculated from the expressions (15) and (14) respectively, t) being the time required for c to go down to zero. In the column marked “ 2*t) acc. to (16) ” I have given values of #t, derived from the formula 11284 t : 96540 (t= —7n,)t' 7 ee (16) litre, or, which is the same thing, in 6 = Cy— * Zeitschr. f. Elektrochem. iii. p. 502. 62 Dr. H. J. 8. Sand on the Concentration 1—n, being found by equation (12). These values are intermediate between those in the other two columns and given merely for comparison with the experimental numbers. At the end of the table I have also given the concentration of the solution of pure copper sulphate examined, and the value of 2 derived for it from equation (8), m_ having been taken as 0°63 %*. ‘ TaseE I. | My solutions. Schrader’s solutions, a ps ee Cone. of | Conec.of | Cone. of | Cone. of | aing. | Bing. ant ey ee wsiaa H,SO, in Cu in H,SO, in mg.-equiv. | mg.-equiv. | mg.-equiv. | mg.-equiv. ce. ce. ce. ce. A 4 0°1634 00881 | 01670 00926 0:1743 | 0:00828 | | B 5 0:2407 01327 02490 01375 0:2057 | 0:00988 C 2 006618 | 00275 | 0:06618 | 0:0275 00903 | 0:00360 | D. 10 01483 01804 0:1483 | 01804 0:2501 | 0:00860 E 0:2096 Table I. (cont.) M - C in #t, max. (in | 2?¢) min. (in | 272, acc. to 16 N a (ohm yi ee eu cm" ___|milamp., sec.,] milamp., sec.,| (in milamp., eg “ —* JohmX mg.-equiv, cm.) cm.) sec., cm.) A 0-027 lo x10=8 1609 836 1246 _B. | 362 x 10690 x 10-8. 15x 10-3 33380 1773 27°6 C. |79:5 x 10690 x 10-8. 17+10—3 265 141°0 192°3 D. |891x10690x10-8.| 15x10—3 1064 691°5 O25 He MC RANE Biemtosecis | Pi =10-9X1:195 (inilamp., sec., cm.). | 4) Note.—The value of « for solution A has not been given by Schrader. ‘The number 0:027 is an approximate value, calculated from Kohlrausch’s tables. ‘ * According to Kohlrausch’s tables, its value at the concentration mg.-equiv. 3 0:2 is 0°643, and at the concentration 0-02 it is 0°62. at the Electrodes in a Solution. 63 In the calculation of #¢, Wiedeburg’s value for the diffusion- coefficient of copper sulphate at 18°, . em.? Kyg = 44°79 x 10-11 —3-467 0) was employed. Here the concentration ¢€ is supposed given CuSO L elineyes . mg.-equiy. =. when it is given in ST the number 3 : = 0:2761 must be taken instead of 3°467. The value of K for c=0 has been taken in calculating the numbers contained in the columns “ 72¢) max.” and “2?t) ace. to (16)”’ ; and the value of K for the initial concentration in calculating the number 7’t)min. From the quantities 2?¢) given in the table, which are based upon the diffusion-coefficient of copper sulphate at 18°, we should find 2% at @ degrees by the formula Pte = itys[ 1 +0:026(0—18°)], in which 0°026 is the temperature-coetficient of diffusion assumed by Wiedeburg. EXPERIMENTAL PART. Determination of Time required till Hydrogen appears in the Electrolysis of an acid solution of Copper Sulphate. A first series of experiments was performed to ascertain the time required till hydrogen first began to appear on electro- lysing the mixtures of copper sulphate and sulphuric acid arranged in the preceding table, the solutions electrolysed being contained in cylindrical vessels, bounded at the top by horizontal cathodes. The values obtained are compared with the limits calculated by the formule given in the preceding table. Had hydrogen ever appeared before the lowest limit of time was reached, this would have proved conclusively that it was given off before the concentration of the copper at the electrode had gone down to zerow The upper limit could not be exceeded unless there were some considerable error in the experimental numbers em- ployed. Preliminary experiments were first carried out to study the subject qualitatively. It was found that on electrolysine the solutions with low current densities, horizontal cathodes being employed, which could be lit up for observation, at first only copper was deposited, after a certain time, however, varying greatly with the current density, the total surface ee SSS —aSESESESEE—ESESEaEyEaEEE—— SS 64 Dr. H. J. S. Sand on the Concentration of the electrode would suddenly within about half a minute become uniformly covered with tiny bubbles of hydrogen. The current was at the same time observed, the measuring instrument, as described later on, being either a Weston millivoltmeter or an Ayrton-Mather D’Arsonval galvano- meter. When employing the former, the current seemed to remain absolutely constant till shortly before the hydrogen bubbles were visible, when suddenly a considerable drop would take place. In the actual quantitative experiments in which the Weston instrument was employed, the time which passed from the beginning of the experiments till this drop of the current occurred was taken as the time which elapsed until the hydrogen came off. When employing the D’Arsonval, however, it was seen that the current at first kept slowly decreasing, until it would after a certain time drop considerably and then become fairly constant again. It was seen that after the drop had taken place, the hydrogen bubbles always began to appear. In the experiments in which the D’Arsonval was employed, the time when the sudden drop was completed was taken as that when hydrogen bubbles first appeared. In these experiments a Thomson-Varley rheostat was always intro- duced into the circuit, by regulating which the current was kept perfectly constant until the large drop occurred. The behaviour of the Weston instrument was probably due toa slight sticking effect. Three types of apparatus were employed, which will be understood from the accompanying figures 1-3. Tubes of the first type were employed for experimenting on solution A. The cathode consisted of an engravers’ plate. It was fixed to the end of the tube, which was ground perfectly flat, by Chatterton cement. As it allowed a spirit-level to be placed on its top, the apparatus could be adjusted so as to make the cathode perfectiy horizontal. The anode in this apparatus consisted of copper gauze. As seen from the figure, the tube was closed by a rubber stopper, into which a groove g was cut to allow air-bubbles to be easily removed. The rubber tube r was filled by introducing a long thin glass tube into it, down which the solution was poured by means of a funnel. In the first few experiments tabulated, the original surface of the plate was employed. In the later experiments it was amalgamated in order to secure as uniform a deposit as possible. Apparatus of this type, of which several were made, showed the disadvantage, that the plate forming the cathode occasionally came off, besides it could not be readily removed for examination and cleaning purposes. at the Electrodes in a Solution. 65 All the experiments on golutions B, C, D, and part of those on E were carried out in apparatus 2. It consisted of a polarimeter-tube. The top being originally bevelled had to be ground Be ectly flat. The cathode consisted of a copper ig. -COT# HAA eRe Ne, ZZ 7B elle aN S a y ey 4 Yijun my plate which was made perfectly flat, then polished and finally amalgamated. This was done by cleaning it with nascent electrolytic hydrogen, after which it amalgamated extremely readily, on dipping it into mercury. It was then again polished on perfectly clean chamois-leather, excess of mercury being removed from the edges by a pipette, drawn out to a fine point. ‘This process of cleaning and polishing was repeated after each experiment. In order to avoid any liquid coming between the cathode and the surface of the glass forming the end of the tube by capillary action, this was greased with a trace of vaseline, so much enly as could not be removed by a piece of dry filter-paper. The cathode was always fixed on the apparatus before introducing the liquid, by placing it in the cap, into which it fitted accurately, Phil. Mag. 8. 6. Vol. 1. No. 1. Jan. 1901. iy 66 Dr. H. J. S. Sand on the Concentration and then screwing down the glass tube on it. By always proceeding in this manner, all risk was avoided of any vaseline being spread on the surface of the electrode. ‘The method of obtaining metallic contact through the cap by means of a drop of mereury will be understood from the figure. On the top of the cap a piece of plate glass was laid and on this a small spirit-level, it having been previously ascertained that it was possible to level the end of the polarimeter-tube by this means. ‘The rest of the apparatus will be sufficiently understood from the figure. As seen, it was jacketed with water. The surface of the cathode was measured by accurately determining the length of the polari- meter-tube, and then weighing it out with mereury. Jt was found to be 0°699 sq. em. F ig. 3, Z ae Vo QML ALLL, ace Washer ry 1a),\ \\ On kde, LSS PLZZ LLL LL LLL 5 The apparatus 3 was only employed in the series of experiments on pure copper-sulphate solution, and only the last three values of Table VI. have been obtained withit. The cathode here again consisted of an engravers’ plate, which reached beyond the surface of the tube and allowed a small level to be placed on its projecting part. In this apparatus the cathode could be easily observed, when suitably illu- minated. Its surface was calculated as that of an ellipse from the length of two diameters of the tube, taken at right angles to each other with a screw-caliper. Its value was 3°782 sq. cm. Yor the experiments the tubes were tightly clamped to a at the Electrodes in « Solution. 67 very heavy tripod stand of 14 inch iron tubing, which was adjustable by three | valine Seer As I was anxious to avoid vibrations, which are exceedingly great at Mason College, I followed a suggestion of Prof. Poy nting’s, and mounted the stand on three 50 ke. weights, each resting on three pieces of rubber. Before each experiment the tubes were allowed to rest for at least twelve hours. - The solutions for electrolysis were prepared by diluting the: requisite amount of carefully standardized copper sulphate and sulphuric-acid solution to 1 litre. The former solution, which was prepared from purest commercial copper sulphate, recrystallized twice, was analysed by electrolytic copper: determination, the ites by precipitation with BaCl. The electrical arrangements, which were in principle the- same throughout all the experiments described, will be readily fo) understood from the accompanying diagram (fig. 4). The Fig. 4 AA adiustable Pole tu omuter Tesestance battery Potentiometer wire a tl ae aetectin galvano KrLowe ne: ak nesistance mats ee aoe DDINN)NINIV A fae Main femme. (atte ry = oa Electrol 2a cell. current from a suitable number of accumulators was passed through a known resistance, an adjustable resistance, the electrolytic cell, and the measuring Instrument, which, us already Aen tened consisted in all experiments cies of an Ayrton-Mather D’ icons or a Weston millivoltmeter, in either case suitably shunted. The measuring instrument was carefully ealihtsted. and also standardized before each expe- riment by taking its reading when a current of approxi- mately the same magnitude as that employed in the experiment Ry « MEASHRL SG LnWStrumenr 68 Dr. H. J. S. Sand on the Concentration was passed through it. This current was measured, as will be sufficiently understood from the diagram, by determining the voltage on the ends of the known resistance by means of a separate potentiometer circuit. As regards the degree of accuracy obtained in the experi- ments, the upper limit is probably reached by those arranged in Table V. The experiments here having all been repeated, this table shows the degree of coincidence which can be obtained in a series of determinations. The readings have in general been taken to within five seconds. The most serious errors are no doubt brought about by changes of temperature which cause convection-currents in the liquid. The accuracy of the experiments contained in Tables B and C, which were carried out in winter, has certainly been con- siderably reduced, owing to the heating arrangements of the building. Indeed, differences of as much as 10 per cent. have here in single cases been obtained in successive experiments which could not be accounted for in any other way. I have nevertheless not hesitated to give these earlier values as the ranges of the times obtained are so great, that even differences of as much as 10 per cent. do not preclude a comparison with the theoretical values. These being calculated for 18°, should be multiplied by 140-026 (@—18). if the experimental values have been obtained at 6°. I have instead made the corrections at the experimental numbers themselves, dividing them by 1+0°026 (@—18). It must be acknowledged that some uncertainty is introduced by this huge temperature correction. The temperature-coefficient for the diffusion of copper sulphate never having been experimentally determined has, as was also done by Wiedeburg, been assumed to be the same as that of other substances. From the tables it will be seen that the experimental values are in all cases contained between the theoretical limits, and their differences from those calculated by the intermediate formula are in most cases not great. When we consider the extremely great ranges in which the times can be made to vary by varying the current-density, and also the numerous causes of experimental error, I think the medium formula No. 16 will be considered sufficient as an empirical expression. of the results. From the fact that the values are always con- tained between the theoretical limits, and, besides, are far distant from the lower limit, I think we may conclude that these experiments prove within the limits which our theoretical knowledge of the processes taking place in the electrolyte allows, that liberation of hydrogen from an acid solution of copper sulphate takes place only after the concentration of the copper at the electrode has gone down to zero. at the Electrodes in a Solution. 69 A New Method for the Determination of the Digfusion- Coefficient of Pure Copper Sulphate. A second series of experiments was performed in order to study the behaviour of a pure copper-sulphate solution after the concentration of the copper at the electrode had gone down to zero. TaBLe II. Solution A, see Table I. Experiments in Apparatus 1. Experimental Values. Theoretical Values. 3 | Current Surface | Current- | Time. Tame |e 4 ce! yoni | ¢ max x in of density in | observed|Temp.| cor- toca Looper eae | NO- | milli- electrode milliamps. in im ° C. rected 1246 236 1609. amps. [iN sg.cm.|~ em 2 seconds. Ose. = {=—_| iP ia | 2s —— mine es ae im = | Bs 9°33 13°53 0-690 2480 16 | 2617 2618 | 1756 | 3380 | Boee.|. 181 16°76 1-081 1010 14) 2128 1068 EE Voie Be y..| 20°D 13°53 1515 510 afl 524 543 364 Ol 4...; 409 13°53 3°02 110 15 IS) 137 92 176 | )...| 516 13°53 3°88 75 13 86 85 o7 107 | i ,..| 528 13°53 3°905 73 1) Sl 82 a9) 10a" 5) ii.-) 5-4 13°53 4:24 62 15 67 69 47 90) aes 1G 2 15°53 5°78 28 13 32 37 25 48 | | | Taste III. Solution B, see Table I. Experiments in Apparatus 2. Surface of Cathode °699 sq. centim. Experimental Values. | Theoretical Values. | | | ; ee ase iz Current- | Time olkirae Weyieae ee es | No ea density in |observed| Temp.) cor- ee ea NG re ety een | ) Balas milliamps. in in ° C.| rected || 10 | milliamps. cm2 | seconds. to 18°. ee | Og. Ps a | ie ie 2 oa | | | | —— --—— —— (qaee 0-776 1-111 2025 | 12:4 | 2371 || 2201 1437 2698 bee =. 1-131 1617 945 | 138 | 106U || 1038 678 1274 a. 1183 1936 630) 7) 13:62) 711 || 97125 73 889 ae 2-09 2°99 ZOO 1SSe i ole | ols 199 372 ee el, <250 © 358 1/0-| 148 185 212 138 260 622... 21617 374 165 | 136 186 |} 195 el 238 ha x.|) 358 512 85 | 12:8 98 || 103 68 127 mS .2 5°10 7°30 40 | 13: 45 51 80 | 62 nee G22 8°20 25 | 136 29 || cee 22 | 42 70 Dr. H. J. 8S. Sand on the Concentration TABLE LV. Solution C, see Table I. Experiments in Apparatus 2. Surface of Cathode °699 sq. centim. = - ee [ = Experimental Values. Theoretical. Values. | | = — | | | } | \ | | } } si : t ace. ¢mini- | ¢ maxi- Current ee ane 1 T Time to eq. 16.) mum. mum. LN ne ee In | obseryec | oe oar Sue milliamps. in in .| rected | ; 2 milhamps. eae eceanils: fo 18° |e 192-3 ae ; AD | - z 4 1 OPI23 am 2O304 1940 12:0 | 2299 2084 1528 2868 | 1 2 0:2202 0315 1960 13:0 | 2253 1938 1421 2671 ies 0:280 0-400 1040 12:3- | 1208 1202 881 1656 | 4 0-406 0-581 550 13:6 621 570 418 785 | | 5 0502 |; O718 330 13:2 378 373 274 lay ke a | 6 0768 1-099 150 14:2 166 | 159 ay ZO | hee een 1621 67 12'8 78 | ore D4 101 | 8 1801 2-576 23 13°8 26 | 29 | 21. 40 Is y _ TABLE V. Solution D, see Table 1. Experiments in Apparatus 2. Surface of Cathode 699 sq. centim. Experimental Values. | Theoretical Values. 3 ut: tace. | ¢mini- | ¢ maxi- Current- | Time Time | i Current si iba : ‘to eq. 16.) mum. mum. aise i density in | observed) Temp.| cor- | Tie aces milliamps. in in ° C,| rected || ae) = : ‘milliamps. ga cae lua @ Il, eee 691-5 1064 | em.2 seconds. tO) Loos — == AZ 72 iz 2500 Bia 29700) 2801 209-4 3218 eile 0:402 0-575 | ihe 0:405 0-F 80 2600 | 12°7 | 3016 2753 2058 3163 hens 0°556 0-795 1355 | 125 | 1580 1465 1093 1684 24 0557 O797 1370 | 12:0 | 1604 1457 1089 1675 | 3 0-734 1051 750 “| 12:0 888 839 627 263 | 3a 0°737 1-054 750 =| 12:0 888 833 622 958 [aan 1182 1-691 305 | 12°4 307 || eee 242 372 | 4a 1174 1680 295 | 12°3 345 328 245 S77 [oD >. 1847 2°64 120} 124 140 | = 183 99 153 | 5a 1885 DOr ZO eS 0 128 127 96 146 | Ou 222 4:03 55 | 134 63 |) oT 43 66 | at the Electrodes in a Solution. ek After this is the case, diffusion can no longer bring sufficient copper to the electrode to carry the current, for the formula shows that if the current were still conducted in the same manner as it was before, the concentration of the copper would become negative. It might therefore be supposed that it would be impossible to keep the current at its former strength. This is, however, found not to be the case. In 184£ Smee* described an experiment, in which he electrolysed a solution of pure copper sulphate ina tall vessel, in the upper part of which he placed the cathode. His description of the varying appearance presented by the deposition of the copper as the concentration of his solution went down to zero runs:—“ On the action of the galvanic force bright reguline copper first appeared at the negative pole, this was followed by a brittle, this by a sandy, this by a spongy deposit, this by black powder, and finally hydrogen was evolved.’ I have in general been able to verify Smee’s observations as well as the fact, mentioned by him, that eepper hydrate is formed at the electrode after the black powder has begun to appear. I have, however, in no case— neither when employing apparatus 3, nor when a form of apparatus was employed in which the solution was not con- tained in a closed vessel—been able to observe bubbles of hydrogen.. It is therefore probable that Smee’s copper- sulphate solution was more acid than mine. In my experi- ments the black spongy deposit always seemed to grow into the solution; in single cases it became intermingled with bright branches of metallic copper. The black deposit is evidently not pure copper, for it disappears when left for some time in dilute sulphuric acid. It is probably a copper hydridef. The behaviour of the current while electrolysing a solution of pure copper sulphate was quite similar to that when an acid solution was examined. The black deposit always ap- peared after the large drop had taken place. The completion of the drop in the current was taken as the time when the concentration of the copper had gone down to zero. From a knowledge of this time and of the current-density employed, it is possible to calculate the diffusion-coeflicient of copper sulphate by means of the expression given at the end of Table I. ‘This has been done in Table VI. (p. 72). * Phil. Mag. xxv. p. 437. + See Poge. Ann. lxxv. p. 350, £2 Dr. H. J. S. Sand on the Concentration TABLE VI. Determination of Diffusion-coefficient K of copper sulphate. Solution E. Experiments 1-3 in apparatus 2; surface of cathode 0°699. Experiments 4-6 in apparatus 3; surface of cathode 3°782 sq. cm. , eae Ko by formula K,,° by Raprent eae Time ob-| 7 g| (Lable 1.) formula Mean No Bie “iatmne, [served in| ~°™P Ke 10s2 Kk, .= value *} milli- | milliamps. in ee a Ka ete Toe seconds. alata Mipvet Ki 3: res in cm.2/sec. | 1+0-026(0— 18) ik: ‘675 0-966 3390 14:4 3°79 xX 10-6 4:16 x 10-6 Dea L-OO+ 1-436 1530 14:2 3°19 X 10-6 421 x 10-6 Bee 038 1-485 1515 13°8 3°99 x 10-6 448x10-6 |446x10—-6 4...| 668 1-766 1095 154 408 x 10-6 4°38 x 10-6 De. OAl 1-694 1285 15:0 2Pael S<1O=6 4°78 x 10-6 G...| O3s 1-683 1275 14:4 4°31 x 10-6 4°76 x 10—6 According to Wiedeburg the diffusion-coefficient of copper m.? sulphate at 18° is 4: 479 x 10-65 a and 4:220x 10-6 ot, at the eco, of solution E (see p. 63 & p. 57). Although the mean value for K,, in the above table is about what should be expected from Wiede- burg’s determinations, yet the differences between the single experiments, none of which were known to have gone wrong In any respect, is too great to justify the recommendation of the method in its present form for more than a rough deter- mination of diffusion-coefficients. at the concentration 0, “aperiments on the Hffect of Convection-currents on the Re- lative Quantity of Hydrogen given off in the Electrolysis of an Acid Solution of Copper Sulphate. The following experiments deal with the relative quantity of hydrogen produced by electrolysis of an acid copper- sulphate solution when considerably greater current-densities are employed than those used in the preceding experiments. ‘This subject has been experimentally treated by Schrader in the paper already quoted, and by Houllevigne”. Both investigators employed vertical electrode: and neither - promoted nor hindered the natural convection-currents of their electrolyte. They found that their results were roughly expressed by hyperbolical functions. * Ann, Chim. et Phys. [7] 11. p. 851 (1894). at the Electrodes in a Solution. 73 From the results obtained in the foregoing part of this paper, the electrolytic evolution of hydrogen from an acid solution of copper sulphate is explained in the following manner. ‘The concentration of the copper goes down to practically zero with great rapidity, as shown by the formule, when current-densities are employed which are considerably Jarger than those used in the preceding experiments. Alter this, diffusion no longer brings sufficient copper to the elec- trode to carry the current, and hydrogen is given off too in ever Increasing quantity, until either the concentration of its ions has gone down to practically zero, or convection-currents bring new liquid to the electrode from which copper alone is again deposited. It will thus be seen that convection-currents play as great a part in the determination of the ratio of the two constituents as any of the other conditions of the ex- periment, and always have the effect of diminishing the relative quantity of hydrogen given off. A lower limit of this quantity, when sufficient convection takes place, is thus always 0 per cent.; and the question might be asked, Is there an upper limit when we employ a given current-density, and use a large quantity of electrolyte ; and what is its magnitude? I do not propose to discuss this question fully, but only to point out that, owing to the fact that convection-currents always have the tendency to diminish the production of hydrogen, such an upper limit can for all practical purposes be taken as represented by the relative quantity of hydrogen produced in a solution in which no conyvection-currents whatever interfere, at the time when the concentration of both copper and hydrogen ions at the cathode has gone down to practically zero. It is also possible to see from the formule given which are the main influences that determine this limit, by determining the lengths of time during which copper only and during which mainly hydro- gen have been given off. They are, in the first place, the = for the hydro- ame gen and the copper ions, and, toa smaller degree, the relative values of the dittusion-coefticients of sulphuric acid and copper sulphate. 1 have discussed this question in view of some experiments that have been quite recently performed by 'Toepffer*, a short account of which will be found in the Zeitschrift fir physi- kalische Chemie, xxx. p. 570. He deposited alloys of iron, cobalt, nickel, and zine from mixtures of several of their salts, with the result that when his so-called low current- * Fully described in his thesis kindly sent me by the author, relative magnitudes of the expressions i 74 Dr. H. J. 8. Sand on the: Concentration densities were emploved, the metal requiring the higher H.M.F. for its liberation was always deposited in relative quantities which far exceeded its relative concentration im the solutions. Firstly, as regards the values of the lowest current-den- sities used by the author, it seems probable that these would have been sufficient to make the concentrations at his cathode go down to zero in times varying from ten to one-tenth of a second if no convection-currents had interfered. This can Le taken from the values given for concentrations and current- density in the thesis referred to, if, in order to obtain nume- rical values, we assume that diffusion-coefficients &e. had been the same in the author’s solutions as in mine. None of his current-densities can therefore be described as small in the sense used in this paper; and I do not think there can be any doubt that if sufficiently small values had been used, the metal requiring the lower W.M.F. for its deposition would have preponderated in the alloy formed. As regards the actual preponderance of the baser of the two metals, a great deal of light could no doubt be thrown on this by determi- nations of transport values in the solutions examined, as will be seen from what has been stated above. If, as Toepffer assumes, the nobler metal has the tendency to form complex anions to a creater extent than the baser, this would certainly greatly influence the transport values in the direction required to explain the results. The main purpose of the experiments I am now about to describe is to show to how great an extent the relative quantity of hydrogen, given off in the electrolysis of an acid solution of copper sulphate, is influenced by convection- currents; and also to show that when these are artificially increased by stirring, the hydrogen can be made to disappear altogether, even in cases in which otherwise more of its equivalents than of those of copper would have been liberated. : For this purpose the apparatus was devised, shown in the accompanying figure (fig. 5), which allowed the course of the electrolysis to be continually followed by measuring the quantity of hydrogen given off, and in which, at the same time, the solution above the cathode could, when desired, be rapidly renewed by vigorous stirring. It will be seen that it resembles a desiccator in general appearance, but has two openings in the side and two in the lid.. Through one of the side-openings the tube a passes leading to the cup ¢, which 1s filled with mercury, forming the cathode, uniform deposition ot the copper being thus ensured. ‘The glass tube 6 passing . a = - i at the Electrodes in a Solution. °— TS through the other side-opening is continued by the rubber tube vr. It contains the wire leading to the anode, formed ot a piece of pure electrotype copper, which lines the inside ot the vessel. This tube also serves to pass hydrogen into the iw coer SSS A > RxsS4WVOD, a VD | “ Ki 77, G 4s reer) ZZ solution before each experiment. The tube 7 leads through the lid to the gas-buretite. The gas-tight joint g, through which the stirrer passes, will be understcod from the figure. It may be described as an inverted cup rotating in a ring of mercury. Glycerine is placed at the top of the mercury, and after the cup had become well moistened with the glycerine it could be made to rotate up to over 500 revolu- tions per minute without any considerable leakage occurring. When rotating at these very high velocities, a very slight escape of the hydrogen contained in the vessel took place ; but this was in the nature of diffusion occurring through a porous cup, for it seemed independent of the pressure of the gas, and a correction could theretore easily be made for it. ‘The stirrer s may be described as a modified Witt’s stirrer. It has four hollow arms out of which the liquid is thrown by centrifugal force, being replaced by solution drawn from above the cathode. Owing to the great extent to which it causes the liquid in the vessel to rotate, which ‘hinders’ thie 76 Dr. H. J. &. Sand on the Concentration flow to the electrode, its efficiency decreases somewhat after it has been going for some time, and its velocity must be increased in order that the former efficiency may be obtained. ‘The stirrer was fixed at its top to the end of the shaft from which it derived its motion by means of a short piece of rubber tube. It was also in connexion with a speed- counter. In the experiments the apparatus was nearly filled with 600 ¢.c. of solution. Before use, a rapid current of hydrogen was passed through it for about half an hour by means of the tubes d, 6, r, the gas escaping through a tap in the gas- burette. After this, mercury was poured down the tube d, which made a gas-tight joint and besides formed metallic contact for the wire leading to the anode. Hither before or after each experiment, the apparatus was tested for leakage, the stirrer always rotating at about the same speed as it did in the experiment. The apparatus was mounted inside a Jarge water-bath, to which also the pulleys &ec. for the stirrer were fixed. It was made to order by Messrs. UC. EK. Miller & Co., of High Holborn, W.C. The measuring-instrument for the current was in these experiments always the millivoltmeter mentioned above, the electrical arrangements being in principle exactly the same as those employed for the experiments described above. The solutions employed are Nos. A and B of the previous experiments, which have also been examined by Schrader *; the minimum current-density employed by me being greater than the maximum value of 36 milliamperes per sq. cm. used by Schrader. Some results are given in the following tables. The quantities of hydrogen observed are corrected to 0° and 760 mm. The percentage ratio of the hydrogen given off to the total number of equivalents liberated has been calcu- lated from the current employed. The time required for the concentration of the copper to go down to zero, calculated by means of the empirical equation 16, has been given in each case. It will be seen from the results that when the solution is not artificially stirred, the quantity of hydrogen liberated decreases rapidly after the experiments have been going on for some time. This is evidently due to the rapid convection- currents brought about in the liquid by the electrolysis, and not to slight changes in the average concentration of the liquid, for when it was allowed to stand for about a day, the * Taken from his thesis kindly lent me by Prof. Warburg, in whose Jaboratory the experiments were carried out. Tuble of Experiments on Influence of Convection.—Solution A. Surface of cathode 2°14 sq. cm. = @urrents Time Average volume | Percentage ratio | Time for concentra-| Revolu- rea ieee of hydrogen of equivalents of | tion at electrode to | tionsof | Temp. 7 Current | density im from esas ee 1 - : uh NOP cease emilliamnel besianine\-to end of liberated per | hydrogen to totai |become zero without| stirrer of Ps. | oe minute. |minute, corr. to 0° equivalents convection by . per bath. cm. of minute . . y ‘ & 760 mm., in c.c. liberated. eq. 16, in seconds. minute. aul 0 120 56 1 st a) Phan 0:51 61 per cent, 0-4 0 12° i a Orde nen 8th 0:37 44 " % rs Oe hy dn 0:23 3 5 | % s | < i Toth). 22nd 0:23 28 rr 5 7 8 ; : 23rd, 28th 0-17 20 ‘ eee : 8 la. - a sts 4th 0:00 0 a 180 5 B 2. 0 200 93°5 1 lear Ist 0°64 46 O14 0 12? =. ” ” 2nd 99 6th 0:51 on 99 ” ee | 8 5, | a 7a, ALI 0:43 31 nf <3 re & b a 12th =. oe a oN 0:38 27 3 Bs i 4 ‘ ‘ th . 38th 0:37 26 | ¥ _ eis ~~ 2 a. - Pr lst. . #9 3rd 0:06 4 | f 540 ie | & | 3 | 0-400 187 Is pn lee 1:44 51 | 0.035 0 13° 2 3 a Di os 2nd 0:90 32 ve | + 3 RS 99 9 ord 3 5th 0:76 27 ” ” ” ke zs Gilliveeays 9th ():48 Way “5 9 ” = 3a, - ” ist=. “4, Ist. 076 27 | oe | 325 x = 5 ” 2nd 5 2nd 0:47 V7 ” ” ” 3 55 ef, SUC w tee 4th 028 10 | ” ” r | \ Solution B. 1. 0120 £61 | ches is) Shih 052 62 0-56 0 13° ” 29 10th ” llth 0°48 ‘ d7 ” ” ” | ‘ ee Est oe th 0:43 51 . ais : i | 5 rn | 14th i 17th 0:38 | : 45 ” ” ” PY) 1G | 18th ” 19th O31 ) 37 ” a9 ” ‘ ” os | 20th a 30th | 0:27 32 , Lio ” ” way enh es | 14 Otel eel ravrayay 0 cit 9O0 joo ‘ 78 On the Concentration at the Electrodes in a Solution. values found at the beginning of the experiment were again approximately attained. The experiments in which the solution was stirred were performed on different days to those in which no artificial stirring took place. It will be seen that in cases where otherwise over 60 per cent. of the equivalents given off would have consisted of hydrogen, the hydrogen oeenl be made to disappear altogether. When a current- -density was employed which would reduce the copper to zero in about 0:035 of a second, the stirrer could not make the hydrogen disappear altogether, but only decrease during the first minute to the extent to which it would have decreased if no stirring had been going on, owing to natural convection alone, after three minutes. SuMMARY OF RESULTS. An eqnation (No. 8) has been derived and rigidly proved or calculating the concentration at the electrode of a solution of a single salt from which the metal is being deposited under the conditions that (1) the solution is contained in a eylin- drical vessel bounded by the electrode ; (2) that no convection- currents occur; and (3) that the diffusion of the salt obeys Fick’s law and its transport values are constant. This formula can be made the basis of a method for roughly determining diffusion coefficients. In the case of mixtures, it is possible to arrive at limits for the concentration; and it has been experimentally proved (1) that hydrogen always appears at the electrode of an acid solution of copper sulphate in which no currents of liquid are taking place, between the limits of time for the concentra- tion to go down to zero; and (2) that the time when it appears differs only slightly from that calculated by equa- tion 16, which is the same in form as equation 8. It seems, therefore, that this formula can be taken as a sufficient empirical expression for the concentration at the electrode of a mixture too. Lastly, the great part played by convection-currents in determining the ratio of the two constituents given off at the electrode ae an acid copper-sulphate solution has been shown, it having been proved experimentally that by artificial stirring hydrogen can be made to disappear altogether in cases where it would otherwise have presented over 60 per cent. of the equivalents carrying the current from the solution to. the electrode. : The experiments described here have been carried out entirely in the laboratories of Prof. P. F. Frankland and Specific Velocities of Ions in Discharge from Points. 19 Dr. D. K. Morris, at Mason College, Birmingham, pre- liminary experiments having been performed in London at University College in the laboratories of Profs. Ramsay and Callendar. I have pleasure in expressing my thanks to these gentlemen, as well as to Mr. A. W. Porter, of University College, London, for friendly interest shown in my work. IV. On the Specific Velocities of Ions in the Discharge from Points. By A. P. Cuarrock, Professor of Physics, Oniversity College, Bristol; and Winirrep EK. WALKRR, B.Sc., and BE. H. Dixon, B.Se., Associates of University College, Bristol*. N a communication to the Philosophical Magazine for November 1899, it was shown by one of us that under suitable conditions the pressure of the electric wind furnishes a means of determining the specific velocities of the ions con- cerned in its production ; and results obtained in the case of air were given in illustration of the method. Subsequent experiments on other gases, while leading to values which were roughly in accord with the velocities of ions obtained by e-rays, have remained unpublished on account of the behaviour of hydrogen. The results for the negative ions in this gas were found to vary between the very wide limits 5°7 and 8°3, and in later work 4°7 and 10:0 centi- metres per second in a field of one volt per centimetre. It istrue that, owing to the smallness of the wind-pressures for hydrogen, exceptionally large errors were to be expected in the readings of the pressure-gauge, and hence in the deduced velocities ; but the magnitude of the observed varia- tions was much too great to be accounted for in this way, and it seemed possible that these might be due to real changes in the specific velocities themselves. Analysis of the results now obtained, without being abso- lutely conclusive, leaves little room for doubt that this view is correct. Specific ionic velocities have been measured in the five substances, Hydrogen, Carbon Lorde, Air, Oxygen, and Turpentine according to the formula V=z/ep, where c is the current from the point, and p the increase in the total wind-pressure corresponding with a shift of the dis- charging point through < along the axis of the discharge- tube (J. ¢.). * Communicated by the Authors. 80 Prof. Chattock, Miss Walker, and Mr. Dixon on the In the following tables these specific velocities (V+ and V—) are given for the positive and negative ions in centi- metres per second in a field of one volt per centimetre; ¢ being the current from the point in microamperes, n the number of values for which V is the mean, z, z. the distances in centimetres from point to ring used in the “ double position ” method (/.c. p.413), and V the mean of V+ and V—. FTydrogen. Red toner | VSR Ry, May ye) eee | [2k 1D GS RB TRS 80 30 Tube A. 22 1 eal ee ee ees va Bie: = a2 3 56 85 70 1:67 Curves. Tube B. I. 32 FG 56 7-0) CSie leo 92 3-7 Tube B. II. 16 919 538 7-2 963, aukse 3 ee 0:87 919 | 520 168 =) Gone aol : is 1 aes Bey 19 niet 78 tel ee RS a Tube B. III. 16 19 Sa T2 me ae ss > , - 332 a 54 ony ae me Curves. Tube B. LV. 3:2 7 ak 76 r be Curves. Tube B. V. 2:0 ce 540 743 641 1:38...Weighted means for Tube B only. Tube A in all the tables is the tube used in the original experiments on air. Its length was 34 centimetres, and its internal diameter 6°3 centimetres. Owing to the high values of the ionic velocities in hydrogen, it was necessary to use greater distances between point and ring than in other gases to obtain measurable pressures. This brought the discharge region so near the ends of the tube, that it became doubtful whether it was safe to assume that the ends were at an infinite distance from the wind. For this reason a second tube B of ebonite, 55 centimetres long and 5:6 centimetres internal diameter, was used in the later work ; the decrease in diameter possessing the twofold advantage of decreasing the convection-currents in the gas and of increasing the pressures to be measured. In the experiments with Tube A the readings were all taken under the same conditions, as the positive and negative discharges for the larger current were sandwiched both with each other and with those for the smaller current. All these values are therefore comparable. The same is true of each of the separate groups of experiments with Tube B, marked respectively I., IL, 11I.; and the remark applies to the tables’ for the other gases as well as for hydrogen. Specific Velocities of Ions in the Discharge from Points. 81. Except in those experiments marked “ curves,” the “double- position ” method was used. The hydrogen in the case of Tube A was less pure than that used in Tube B. It was obtained from commercial hydrochloric acid and zinc, and was passed through strong sulphuric acid and over phosphorus pentoxide. In ‘the other experiments the hydrochloric acid was pure, and the gas was passed through tubes of caustic potash, sulphuric acid, phosphorus pentoxide, and glass-wool, in that order. In all cases a very slow stream of gas passed through the dis-- charge-tube during the experiments at a pressure greater than that of the atmos phere by a few centimetres of water. The ring used in Tube A was the brass ring used before with air, cleaned and slightly vaselined on its “surface. In Tube B. I. in every table a flat ring of brass, 1 millimetre thick, was embedded in the Sven so that ia inner edge was flush with the inner surface of the tube. By this device the whole pressure cf the wind is measured on the pressure- gauge, but against this has to be set the disadvantage that conduction over the inner surface of the tube becomes appreciable for smaller distances between point and ring than in the other arrangement. The ring in experiments II. to V. was an exact copy in platinum of the ring used in Tube A, and was never vaselined. This also applies to all the tables. The point was usually of fine platinum wire cut obliquely with scissors to a very sharp end, and sheathed, except a millimetre or two at the end, with glass. In a few of the experiments this was replaced by aluminiom, filed sharp, but the change did not cause any certain difference in the results. Carbon Dioxide. e nN. V+. V-. ve V-/V+. 2. z h2 15 O76 O8 O81 113 60 20 °° £TubeA. Pett §«6(0-82 094 «688 CISC C34 4S Tube B.T. O07 11 O81 092 O86 1:13 ae ee lll 18 O8 O92 O88 108 62 82 Tube B. II. Pecks, -..5. 0°33 0-925 088 1-L1...Weighted means for Tube B only. | As regards the condition and arrangement of the apparatus and the production of the gas, the same remarks apply here as in the case of the hydrogen table, except that for zinc is to be read marble and for caustic potash water. -In II. also the length of phosphorus pentoxide was nearly quadrupled, Phils Mag. 8. 6. Vol. 1. No. 1. Jan. 1901. G 82 Prof. Chatteck, Miss Walker, and Mr. Dixon on the and a second tube of glass-wool was inserted between the kipp and the drying-tubes. Air. C. nN. V+. VW—-. V. V-/V+. 2z,. z 30 26 L538 ge SO icon ele 52 3°6 Tube A. 2:0 3 L226. Sle Gow ale2 6 34 0-4 Tube B. 1. 32 15 1233 eS easeaalcas 62-1. 372 Tube B. IT. 16 15. 1S) Sle OG wel 3S 0°8 15 LSliy Lae Wh oe 1eSS +7 a9 73 17 19 97 29 129 2 eA Sel G33 5 x Tube B. IIL. | TE a i Tey eae II Z e Tube B. IV. Oe 1329 80 ea Neb e Means of Tube B. II. The experiments with Tube A are in this case the ones already published. In II. the air was drawn through glass- wool, caustic potash, sulphuric acid, phosphorus pentoxide, and glass-wool, in that. order. In II]. some of the air was afterwards found to have been drawn in past a badly-fitting cork, so that it did not all pass through the drving-tubes ; the effect of which is probably to be seen in the lower value of V—/V+. InIV.the air was wet, its treatment being otherwise the same as in IT. The air was not passing through the discharge-tube during the readings, but fresh air was pumped through after every two determinations of V. Oxygen. Be nN. Veate 6 eV Vis V—/V-Ee 2p oes | 19 if 142 184 163 130 62 382 Tube BIL. i392 14 138 - 190 161 143 "5, awnentnesB aimee iG) 1-93) 1862) 159 on 5 Oop ae 4 125) 078. Ao oe | 1:9 ex, 1:30 1:85 1e57/ 1:42... Means of Tube B. ITI. The gas came from an ordinary oxygen cylinder over phosphorus pentoxide and through glass-wool. The platinum ring was alone used. ‘The gas passed frequently through the. discharge-tube between the experiments, as in the case of air, but was not flowing while the readings were being taken. — Hxperiments IL. were made directly pies a long series on hydrogen, and have been omitted from the mean on account Specific Velocities of Ions in the Discharge from Points. 83 of the high value of V+. On emptying and filling the dis- charge-tube with oxygen, the readings changed to those of B II11., and showed no further tendency to fall. It is worth noting the similarly high value of V+ for air in the case of B.I., as it was also obtained directly after discharging in hydrogen. Turpentine. It was of interest to see whether non-conducting liquids could be treated in the same way as gases, and several experiments were made with that object, mostly on tur- pentine. It was of course necessary to modify the apparatus to measure the discharge pressures, and after some failures the design shown in fig. 1 was adopted. Eis Te 4 b WM T is a glass discharge-tube of about 10 square centimetres: cross-section, into the side of which are sealed the ends of the loop AABB; the lower portion of the loop being fastened to a metal slab C at BB. ( is pivoted at D, and supported G2 84 Prof. Chattock, Miss Walker, and Mr. Dixon on the at its other end by a micrometer-screw 5S with a large divided head. P is the discharging point and BR the ring, both of them supported by glass-sheathed wires and capable of motion in a vertical direction.. The apparatus having been completely filled with tur- pentine, mereury was introduced at F until it stood at AA, a layer of water separating it from the turpentine in each limb ; the cross wire of the microscope M was then focussed on the mercury surface in the right-hand limb. Change of level due to discharge was measured by turning 8 until the mercury surface again appeared on the cross wire, after which it was of course a simple matter to calculate the pressure of the discharge. ! The chief difficulty met with was the tendency for ions to pass from the ring to the point, and so reduce, and in some cases even reverse, the pressure. Brass rings were very troublesome in this respect, no doubt owing to chemical action of the turpentine on the brass; for which reason platinum was adopted. Dust particles in the liquid also reduced the pressures, presumably by playing the part of secondary discharge-points ; and tbe pressures were found to rise as the purity of the turpentine was increased. In Curves I. are plotted the pressures in arbitrary units as ordinates, observed in the purest turpentine we were able to obtain, between a platinum point and ring; the distances between these, in centimetres, being the abscisse. The current was about 0-2 microampere, and each point is the mean of 24 observations. The full curve is for positive discharge, the dotted for negative. Both curves show the existence of “ back-dis- charge” from the ring, this being most marked for the negative. It will be seen that at a distance of 2 centimetres the curves have become practically straight, so that velocities should be calculated for distances above this value (see previous paper). Unfortunately, the effect of conduction along the sides of the tube then makes itself felt, the pressures at 2°4 centimetres fallirg below their proper values, and the curves at still greater distances tending downwards. It is thus unsafe to go beyond 2 centimetres, and we have therefore calculated V from tangents drawn to the curves at this point. ‘The results are thus possibly rather too high, and must be regarded as approximate only in the absence of experiments with a wider tube, which there is no immediate prospect of our being able to make. The following are the values obtained :— Cc. ~V+~ V—. V—/V+. iO <0:0013 <0-0015 1:15 Specific Velocities of Lons in the Discharge from Points. 85 Kohlrausch’s value for hydrogen in the ordinary electrolysis of solutions is 0°003 ; our values thus lie between those for hydrogen and for many of the other metals respectively. Curves I. Pressure in arbitrary units, Centimetres (z). Variations in the Value of V. It is of course inevitable that the calculated values of V for given conditions should differ to some extent among them- selves owing to errors of observation; but when, as in the case of negative discharge in hydrogen, the probable errors of observation are not sufficiently large to explain the differences observed, it becomes a question whether they may not be due to real changes in the motions of the ions. In fig. 2, (p. 86) 2, 2, represent the two positions of the point in the “ double-position ” method, and jp, p, the corresponding pressures. zis measured from Q, the centre of the plane AB drawn to touch the front surface of the ring R. If z, is the distance of the point where the straight part of the pressure- 86 Prof. Chattock, Miss Walker, and Mr. Dixon on the curve prolonged cuts the axis of z, it is clear that Pile =(2;—Z9)/(zo— Zo)e Fig, 2. 4 y q , ie u 5. AX/S. OF 2, OISCHARGE TUBE Provided zo is constant, a real change in V will bring about an alteration in the pressures such that their ratio is still (2;—2)/(¢2—2Zn); whereas if the change is apparent only the ratio will alter. It is thus possible to discriminate between the two kinds of variation of V, and for this purpose it is important to know the value of 2. The table on page 87 contains the values of zp caleulated for the various groups of experiments given above, and one or two others. zo for the embedded ring is measured from the plane iiiough its centre instead of from O. As the brass and platinum rings are of the same size and shape, the values of z) obtained with them should be com- parable with each other, though not with those for turpentine and the embedded ring. If we leave out of account the two latter sets, it will be seen that, apart from the negative dis- charge in hydrogen, the value of z) does not vary more than about 2 millimetres on either side of 0-06 centimetre, its mean value. | That variations in z) should occur with a ring which catches any of the wind-pressure is of course intelligible ; for the amount caught will depend on the paths taken by the ions in approaching the ring, and these must depend to some extent on the relation between the current-density and the potential slope in that region, which will vary with the gas as well as with the sign and strength of the current. This is borne out by the way in which the discrepancies between the values of 2) for air and for carbon dioxide almost vanish when the embedded ring is used ; for there is then no reduc- tion in the force of the wind by the ring. In the case of hydrogen, the same argument leads to the conclusion that the large value of 2) for negative discharge is not due to the stoppage of an abnormally large amount of Specific Velocities of Ions in the Discharge from Points. 87 wind-pressure by the ring; since practically the same value is obtained with the embedded as with the other rings. Substance. ae Z, in centimetres. + — iydropen ......... 33 0-2 0-8 A. Brass ring*. | 3°2 Ol 0-9 B. I. Embedded ring. | 32 Ol 13 B. II. Platinum ring. 16 O01 Il 2» 33 ” 08 0-0 he ” ” co) 32 : 08 BELLE ¥ | 16 ie 08 ‘ i vs | 3:2 O01 ne B. IV. Curves. II. 32 1-0 BV s ws | Carbon Dioxide.. 1:2 --0:2 0-0 A. Brass ring *. 1-1 —0:06 —U:035 | B.I. Embedded ring. jest —O0-2 0-0 B. IT, Platinum ring. LSE 30 0-3 01 A. Brass ring. 2-0 0:00 0-05 | B.I. Embedded ring. 32 0-2 O-1 B.II. Platinum ring. | 1-6 0-1 0-0 . _ at oe 08 0-0 OL 3 ” 2” | 1-9 0-0 Ol B. III. Impure air. | 1-9 0-0 00 B.1V. Wet air. Oo | 19 O1 0-1 B. I. Platinum ring. 32 Ol 0-0 iBalhiE B 5 16 0-0 0-0 . ¥ : 0-8 02 0-0 > r3 saan =e ~ | ———_---— Binet 2 Turpentine......... 0-2 =—0 9 S079 Platinum ring. —_—_—— The only other way of accounting for the high values of z in this case is by assuming the presence in the tube of ions travelling against the wind, and therefore of similar sign to the ring. These might conceivably be liberated at the surface of the ring, or else in the gas itself by the passage through it of the ions from the point ft. * In the Hydrogen and Carbon Dioxide experiments with tube A the values of z, are unfortunately not known to within a constant. The con- stant is, however, the same for both gases; and the closeness of the agreement between the values for the brass and platinum rings in the case of CO, makes it probable that the constant we have assumed is about correct. Tt Townsend, ‘ Nature,’ August 9, 1990. (p) Millis. of water approximately. gro? 88 Prof. Chattoek, Miss Walker, and Mr. Dixon on the Now, if they are formed in the gas, the process may be expected to occur chiefly in the strong field near the pomt, in which case it is practically equivalent to lengthening the discharging point; that is to adding a more or less constant quantity to the values of z of from 8 to 13 millimetres. That this has not occurred seems to follow from Curves II., the Curves II. S HYDBROGS 32 MICRO-A Centimetres (2). pressure-distance curves for hydrogen. In these each nega- tive point is the mean of ten, and each positive of four observations. The positives (full curve) were not sandwiched with the negatives (dotted curve) as usual, in order to obtain ereater constancy in the negatives. There is a bend in each curve near ¢=1-°2 centimetre, due no doubt to the shifting of the region where the current enters the ring from the frent to the inner surface of the latter as the point approaches. It will be seen that these bends are vertieally over one another ; ulso that the pressure vanishes at about the same value of 2 Specific Velocities of Lons in the Discharge from Points. 89 for both curves. There is thus no evidence that the negative curve has been shifted bodily along z to anything like the extent required; and this renders it very improbable that the gas is ionized in the region of the point to an appreciable distance from it. The only alternative seems to be a back-discharge from the ring into the gas ; and as this is also consistent with the shape of the curve, we shall assume that it oecurs in the case of negative discharge through hydrogen. Coming now to the fluctuations in V, it looks at first sight suspicious that it is precisely in the case in which back-dis- charge is high that these fluctuations are so marked; for it the ions of the back-discharge travel as far as the part of the tube in which the pressure measurements are made, changes in the amount of this discharge must give rise to apparent changes in V. This, however, would mean that dp/dz must increase as <. increases; whereas inspection of the negative curve for hydrogen shows that for points beyond <=1°8 centimetre the curve is straight. We may therefore conclude that in the region beyond that distance from the surface of the ring back-discharge ions are not present in any appreciable number. Hrrors of observation being also insufficient to account for the apparent changes in V, the possible explanations of these thus reduce themselves to a, Fluctuations in the back-discharge outside the region of pressure measurements. b. Real changes in the value of V. Now fluctuations in the back-discharge must affect p, and pz about equally on the average, and they will therefore pro- duce the same sort of effect on V as the accidental errors of observation. Itis true that the amount of the back-discharge may depend, for a given current, on the field at the surface of the ring ; and it might be objected that, as this field is greater for p, than for p., owing to free electricity in the tube, p, Should be more reduced than p. But if fluctuations in the amount of this free electricity are to account for changes of 50 per cent. and more in V, the free electricity itself must produce a far greater effect in increasing the apparent value of V; from which we should have to conclude that our value of V— is too high, the true value falling considerably. below that of V+. This would be contrary to the results. obtained by other observers however, and the objection. thus, falls to the ground. | At the same time it is quite possible that our value for V — 90 Prof. Chattock, Miss Walker, and Mr. Dixon on the in hydrogen may be somewhat too high from this cause, and we have therefore marked it doubtful in the summary of results. The effect of real changes in V being to alter the difference Pi—p2 without altering the ratio p,/p., while fiuctuations in the back-discharge alter the two pressures independently, and on the average equally, we may apply the test of pro- portionality between p, and p, to distinguish between the two alternatives a and b. Take <2, z.as before for the two distances from point to ring used in the “ double-position ”’ method, and let p; po, p,/ po be two pairs of pressures observed at these distances which give different calculated values of V. In case a there will be no particular connexion between these pairs of pressures; but in case 6 we shall have pif P= py | Pa! = (2; —20)/(<2 — 20) = constant. This may be shown graphically as in fig. 3, by plotting p, with py and p,’ with p,’; the higher pressures being ordi- nates, the lower abscissee. If the above equation holds, the two points thus obtained will lie on the line BB, of which the tangent of the angle with the horizontal is (¢, i: (co—Z). Fig. 3. In fig. 3 besides BB two other lines AA and CC are shown at right angles to each other and at 45° to the vertical. CC is obviously a line for which p,—p, and therefore V is con- stant ; points faliing above CO giving values of V below that for CC, and vice versa. : Suppose that in the case of an actual determination of V the point O represents the mean value of, say, n individual observations. If these were plotted separately in the figure they would lie symmetrically within a circle centred at O for case a; but for case 6 they would all he on BB. | Arrange the n values of V with their corresponding pres- Specific Velocities of Ions in the Discharge from Points. 91 sures in columns according to the descending order of V; divide each column into two at its centre ; take the means ot the pressures in the upper and lower halves of each column respectively; and plot the two pairs of corresponding pressures thus obtained, In case a these points will fallon AA, sayat LL; in case 6 they will fall on BB at MM; and in the latter case, Fig. 4.—Hyprogen. n=19. B. II. Negative. 9.6 va Microamps. .. as there cannot fail to be errors of purely accidental character also present, we should expect the points to show a trace of the “a” effect by falling somewhat off BB as at NN. In fig. 4 are given the results of the application of this test 92 Prot. Chattock, Miss Walker, and Mr. Dixon on the to the hydrogen pressures for tube B. 1I., the pressures being expressed approximately in thousandths of a millimetre of water. As explained above, observations belonging to sepa- rately labelled groups were sandwiched together when made, and the results for the different strengths and signs of dis- charge are therefore comparable. AA and BB have the same meanings as in fig. 3. The dotted line joins the two points N, N. The fundamental difference between the positive and nega- tive discharges is very apparent. In the former the dotted line is short and roughly coincides with AA ; in the latter it is longer, and the coincidence is with BB. We conclude, therefore, that while the small variations in V+ are due to errors of observation and chance alterations in the condition of the hydrogen, the much larger ones in the case of the negative discharge correspond with real changes in V—, Fig 6 Age. 215, By IL. Negative. Microamps ..... In figs. 5, 6, 7, and 8 are given the results of similar tests applied, where possible, to the pressures for air, oxygen, and carbon dioxide; as well as a second set, taken by itself, for the . negative discharge in hydrogen. The latter is closely in . accord with the set in fig. 4, though the variations are not so Specific Vecocities of Ions in the Discharge from Points. 93 Fig. 6—Oxyern. n=14. B. III. Neaative. Fig. 7.—Carpon DroxipeE. n=18. B. IL. Negative. Positive. 14 15 16 py 17 18 p, Microamps. = 1] large; perhaps because no positive discharges were taken with the negatives. V— in air and oxygen shows the same ten- dency to vary more than V+, though it is not nearly so marked. V+, on the other hand, varies more han in hydrogen ; but this may be due to the formation of ozone. In carbon dioxide the effect seems to be absent. 94 Prof. Chattock, Miss Walker, and Mr. Dixon on the As the current is reduced the effect of accidental errors should become increasingly important, the dotted line tending towards AA. This is well shown in the figures. In the case of the highest negative discharges in hydrogen the dotted line Fig. 8.—Hyprogen. n=19. B. Il. Negative. has actually crossed BB, which is not in accordance with theory. If this is due to more than an accident, it may be explained by supposing that the more rapidly moving ions give rise to greater back-discharge than the slower ones, which seems reasonable enough. If the conclusions arrived at above are to be accepted, we have, in considering the case of hydrogen, to reconcile variations of something like 100 per cent. between the extreme values of V — with practical constancy in the value of V+. The only obvious changes in the conditions of discharge were those of temperature, pressure, and purity of the gas, which must have been extremely small in our experiments ; and it seems hardly possible that they should be responsible for such large effects. A solution of the difficulty is perhaps to be found in the fact that the negative discharge from a point is apparently much more closely dependent upon the condition of the point surface than the positive. It is an instance of this that a needle-point which when discharging positive electricity 1s covered with a smooth velvety glow, often discharges negative from a single spot on its surface, the position of which will move irregu- larly and suddenly in a manner suggestive of local surface changes. The frequent and large fluctuations in the strength of the field close to a point discharging negative electricity—changes Speeric Velocities of Ions in the Discharge from Points. 95 which do not occur with positive discharge—furnish another ‘Instance *. So also does the gradual and permanent increase in the strength of this field when the point is discharged from for long periods ; an increase which is not shared by the field for positive discharge from the same point™. If, then, we may assume that the starting-place of the positive discharge is in the gas surrounding the point, while that of the negative is at or just below the surface of the metal, it may quite well happen that while the positive ions are all formed of hydrogen, some of the negative ions consist of gases other than hydrogen occluded in or condensed on the point, which, by occurring in greater or less numbers, give rise to the fluctuations observed in V. Our value of V— for hydrogen may thus be too low. Summary of Results. In the following table are collected the most reliable of our values for V; the results of Rutherford f and of Townsend t being added for comparison. Numbers in square brackets are for wet gases. ‘The velocities are in centimetres per second in a field of 1 volt per centimetre. The value of V— for hydrogen may be too high or too low for one or other of the reasons already given. | | V. Vi /V-E | Substance. ; é Rutherford. | Townsend. Point- Townsend. Point- | Discharge. Discharge. | Hydrogen ......... 5-20 6°60 6°41 1-54 1:38 S21 aie | ne eri] Carbon Dioxide... 1:07 0-98 088 TIEN 1-11 (OO ea [1-04] 2 ee 1-60 1°39 1:55 1:54 1:36 [1-341] [1:56] [1-09] eZ RV PON Ss 5260522565: 1-40 1-29 1-d7 1-48 1-42 (eS es ee sen e [1-24] PRMEPEDEMOg tcc) eecem | | ceen ce requires that c’?>gh, while the negative value requires gh>c*. We have thus two waves with different rates for every value of the modulus, and, from (22), these will have also different values for p. These waves will, in general, be necessarily accompanied by a motion of drift, for if we remove the purely periodic part from the right-hand side of (20) we shall remain with ’ E \ c2—oh fletiy=(atr%)—" oti) +-. Long Waves in Shallow Water. 109 showing that the drift will exist unless E In the extreme case when «=1, the solution represents waves of the solitary type. We shall then have either A=1 and w=0, or A= —1 and p= The solutions are therefore Se I (et+ty) = Ces IMIOOR | Be eee Ca gh wt (?—gh/3) h- which represents Scott ae Solitary Wave, or 2 gh— fet) =— 3B“ Ge tiy) V/2(gh—c?) (c? ae BAe gh— «ety Ms ¢ Tea N OieeGhaN i This last solution represents a comparatively slow-travelling solitary wave of elevation, which is essentially accompanied by a perceptible drift. As far as I know it has not been observed, and the method of transmitting the wave by re- flexion at the ends of a trough, ue in Scott Russell’s experiments, would not be likely to disclose it. The need of an accompanying drift for the progressive transmission of these long waves, and the fact that long waves can be observed which are not accounted for by this. method, seem to point to the probability that some more com- plex motion of the fluid than a uniform drift may be necessary for the exhibition of these phenomena, and to raise a doubt whether the artifice of reducing the motion to one of steady motion is attended by advantage in studying this species of wave. I have ventured to describe these waves as of the type of those discovered by Drs. Korteweg and de Vries because of the similarity of the form of the free surface; but the relations (20), (21), and (22) do not lead to results identical with those of the authors named. The equation which my results give, as a first approxima- tion, for the free surface is Za) c?— A(e2—gh) wx = A(1—x?) + Ax?en? J f( Be are ae ee ’ (24) (26)) 110 Prof. K, Pearson on some Applications of the whereas in the paper referred to the oe equation is 3(B +") Ah? [eiar a where £ is the amplitude of the wave, and @’ a eae G+ BD) mod y-= pen? The similarity is seen on writing B= Neh = ia and. therefore C ¢ Ac? — gh) = NN 2(¢? —gh/3) h? a/ ee -— gh/3)h = 4/24 approsimately, which will become af ER (Sue eran) a B+Pp° This would require 6?4+@86’+B8?= c = 2h? to make the results identical. . ~ VIII. On some Applications of the Theory of Chance to Racial Differentiation. From the Work of W. R. Macdonell, _A_A., LED; and Cicely, D» Faweett, Bese lan aie men, Pearson, F.RS., University College, London +. (1) - a memoir published in 1894 I have dealt with the problem of resolving the frequency of hetero- geneous material into two normal components. The object that [ had then in view was that of differentiating races which could not be definitely separated by any special outward characteristics. But the method of course applies to all statistical investigations wherein there is any suspicion that the material has been drawn from two heterogeneous sources. The objections to the process of resolution suggested in my memoir are threefold :— (a) The heterogeneous material may consist not of two diverse types, but of three or more §. A development of. theory is required here, which shall act for statistics like harmonic analysis in physics ; in particular a mechanical analyser would be a great boon, resolving any given curve into a series of normal curves. My method gives only an approximation to the two chief types, supposing the ‘first. two terms of the series to be largely preponderant. * Loe. cit. p. 430, eqn. (20). + Communicated by the Author. { Phil. Trans, vol. 185. pp. 71-110. § Ibid, p. 72. Theory of Chance to Racial Differentiation. 1b ()) The assumption is made that the frequency type is normal. My iriend Prof. Edgeworth has kindly described the method asa beautiful ‘ conception ”’*, but I fear he has done so solely because on this occasion I dealt with that “ normal’ atmosphere in which he lives and moves and has his being. I can only recognize the occurrence of the normal curve—the Laplacian curve of errors—as a very abnormal phenomenon. It is roughly approximated to in certain distributions ; for this reason, and on account of its beautiful simplicity, we may, perhaps, use it as a first approximation, particularly in theo- retical investigations. That is the only justification for my method, for I cannot recognize any special claim in expe- rience, as apart from the weight of authority, for the use of this normal curve f. (c) The process is said to be laborious. Prof. Edgeworth writes (R. Stat. Soe. Journ. loc. cit.) :— ‘‘ The method is attended with one disadvantage: it is very laborious.” The method certainly involves the soiution of a nonic, but when once that equation has been determined its numerical solution is not difficult, especially as in most cases * R. Stat. Soc. Journ. vol. lxii. part i., December 1898. + It is through no want of courtesy that I have not replied to the very numerous criticisms of my methods which Prof. Edgeworth has pub- lished during the last six years in the R. Stat. Soc. Journ. and elsewhere. Partly I have been overwhelmed with more urgent work; partly I believe that if one’s position is strong—and the solid ground of nature is stronger than any mathematical reasoning—it is as well to let your opponent exhaust his ammunition before replying. In a paper published in the Phil. Mag. for July last, I have to some extent criticised the usual text-book treatment of the curve of errors. Prof. Edgeworth in a humorous letter tells me that while I have been getting my Long Tom into position, he has retreated under a bomb-proof casement. By this I understand him to refer to his “method of translation” (R. Stat. Soc. Journ. vol. lxi. Dec. 1898). In this every member of a group is supposed to be some function of a member of a hypothetical group which obeys the normal law. In other words, the generalized type of frequency is given by Z=2,e-T), Since f is perfectly arbitrary, it is clear that Prof. Edgeworth’s method covers every type of frequency-curve that can be suggested. My own skew-curves can be looked upon as giving values of # which correspond to close fits. The generality of Prof. Edgeworth’s method cannot be denied. We might even venture to put z=F (x), F being unknown! But I am inclined to look upon this method rather as a complete dis- persal of Prof. Edgeworth’s forces, than the erection of a bomb-proof easement. For, after all, is not the problem before us the discovery of a suitable value for F, or, if Prof. Edgeworth likes, for f? Some day I hope to show him that the logical and philosophical arguments in favour of my form of f are even greater than he supposes. 112 Prof. KX. Pearson on some Applications of the the frequency distribution itself suggests the limits betweem which the required root must lie. The determination of the moments, on which the constants of the equation depend, is such an every-day task in statistical investigations that the trained statistician soon performs it with the greatest rapidity. In laboratories where such work is regularly done, the Brunsviga and the Comptometer are always at the disposal of the calculators, and reduce this labour to the lightest of tasks. During the past five or six years I have had a number of workers training for statistical research, and have made a point of their resolving at least one heterogeneous frequency distribution. The result is that we possess a considerable number of cases relating partly to the animal and vegetable kingdoms, partly to economic statistics, in which it has been ossible to differentiate heterogeneous material. We have dealt with flowers, insects, fish, human characters (eyesight, judgment, skull-measurements, &c.), price of investments, and other topics. The object of the present paper is to illustrate the method by a selection of this material from one field—that of skull-measurements. We hope thereby to emphasize the type of problems for which the method offers some solution, and further to indicate that it is not so laborious that it cannot be used whenever it seems likely to be of service. 3 For our present purposes I have selected data bearing on one character only of the human skull, namely, the cephalic: index. (2) Illustration 1.—One of the most difficult and yet important problems in craniology is the identification of sex. There is a considerable element of speculation in the sexing of skulls, and a control-investigation wonld be of great value. Now it is clear that any skull-material before sexing, even if from a pure race, is heterogeneous, consisting of two groups, male and female. Hence it occurred to me that my method of differentiation might be used as a control ex- periment to test the sexing of the expert craniologists. I chose the cephalic index for two reasons: (i.) because the absolute dimensions of the skull change considerably and the cephalic index hardly at all with age ; there would thus be no danger due to a casting-out of juvenile skulls, which might to some extent be really female. (ii.) From rather extended observations on the cephalic index, I had noticed that it approximated more to normal distribution than other measurements. Against these advantages must be set the disadvantage that the cephalic index is not a very markedly sexual character. I accordingly chose the French race, in Theory of Chance to Racial Differentiation. 113 which there appears to be a sensible difference between male and female in this matter. From some statistics with which M. Manouvrier kindly furnished me, there appears to be a difference of some 1°5 units in the cephalic index of male and female Parisians, and this whether the material be drawn from the West End er the City *. I have the data for upward of 1000 French skulls obtained from the Paris Catacombs, and measured by MM. Broca and Manouvrier, I owe to the courtesy of the latter distinguished anthropc- Jogist a transcript of the measurements and. sexing from the degistres Craniométriques of the Laboratoire JAnthropo- logie at Paris. So far as the cephalic index was concerned, we obtained the following results :— No. Mean. | Standard Deviation. Won, 25a 730 1 Oona LT 4451 4-078 Vg ae) eee oe 283 78°1380+°169 4:220 +7120 | | | If the sexing here be correct, there can be no doubt that there is differentiation in cephalic index between these men and women. Turning to the variability, there is a difference in the standard deviations of *231, and the probable error of this difference ='143. Thus variability seems also, if less certainly, a sexual character. We have accordingly a ‘mass of material which, if the craniclogist be right, consists of two fairly marked groups. Plotted as a curve f (fig. 1) (p. 114) it has a distinct skewness. Is ilis due to the mixture of sexes? If it be, can it be possible that only some 28 per cent. of the women’s skulls have surviv ed, as against 72 per cent. of the men’s f{ ? Clubbing male and female skulls together, [ handed the material to Miss C. D. Fawcett, B.Sc., and asked her to mathematically investigate the possibility of resolving it into two Laplacian distributions. Her results were afterwards verified by Dr. W. lt. Macdonnell. His constants, based upon Mr. W. F. Sheppard’s improved expressions for the * ‘The Chances of Death,’ vol. 1. p. 352. + I have to heartily thank Mr. K. Tressler for preparing the diagrams. t There is generally a preponderance of male skulls in sexing, owing to their greater strength enabling them to survive batter ; but I have never before come across such an immense disproportion as in the Catacombs. Pipl Mag. s: 0; Vol. ty Now 1. Jan. 1901. i 114 Prof. K. Pearson on some Applications of the Index. ya Mii Le Pea mien at oeaco me. Saluda Cea MES eRe eS er ae oe ao eee a Oe ae ee ae a en a ae Oe ee ee el Saal Ae a LEC er Re Ree |. Cee eee eae ‘ S oO N rt Oo fer) (e.@) = Ne) iia) ~— ian) N Ce) Frequency. Theory of Chance to Racial Differentiation. GM moments, differed very slightly from her’s, and made no difference whatever in the final result *. There were, including now those of doubtful sex, 1146 skulls ; and using the notation of my first memoir on the Mathematical Theory of Evolution (Phil. Trans. vol. 185. pp. 81-83), the following were obtained :— Mean Index= 79°1824. Moments: po= 19°534932, jis 30 160070) #4=1136°6665, fis=o (Lo On0sv: Other Constants: A,= 24°5229, XN; = 3466°2776. Hence we have the nonic :— : po — 28°6667 po! + 1,854°345 p,® —121,618'21 p.? —1,188,506-5p." +16,841,221°5p,3 + 150 441,450°2 9,” + 50,071,456°6 p, —1,889,286,562-4=0. Sturm’s Functions gave the following results :— ign- ; ; Checes,| Px | Ae) | A@)-|A@)-|.A@| A@)-| £)-| A). 3 a) = — + + = + te 3 1 —~ =F ate + oi a + 3 2 Sipe earted raat) ems | ibe die lia 3 3 = + a + = 4 aie 2 4 = Same) Wea 01) ye ce) eco. dl orcad eat 2 +a | + a5 ats = - a 1" Thus there exists only one real root and it lies between 3 and 4. Its value was easily determined to be 3:0443. Whence the other constants :— 3 $°4465, py= 27745. The quadratic for the distances of the means y, and y, of the two groups from the mean of the mixed material is thus : y—2 714574 3°0443=0. This has tmaginary roots. In other words, no resolution of the Parisian skulls into a male and female group is possible on the assumptions: — (i.) That we are dealing with a homogeneous race ; and (ii.) That the distributions for either sex are given by the ordinary curve of errors. * Dr. Macdonnell found A4y=245229, ,=3466:2776, against Miss Faweett’s A,=24:5727, ;=38466:1421, differences. which are of no importance, 3 116 Prof. K. Pearson on some Applications of the It may be that there are other sources of heterogeneity than sex in the skulls of the Paris Catacombs; the skulls were collected about the year 1800 from graveyards which had been used for several centuries. Or, it may be that the cephalic index for the Parisians has in itself a distribution so markedly skew that the skewness due to sex-difference is completely masked. (3) With a view of considering this point I suggested to Miss Fawcett that she should endeavour to fit the material with a skew frequency-curve. She found the following equation to the curve:— ; x 13°88905 on 79372 7— On 631(1— ene, (1 se ioe 9 where y6z is the number of skulls with indices between « and w+6a. The modal value is 780988, or 78:1 say, and this is the origin of z. The total range of cephalic index is from 66°2894 to 112°3155, corresponding to an observed ranze from 68 to 97. The observed and calculated frequencies are given in the table on p. 117, e being their difference. Forming the value of y?=S(e’/y), where y is the theoretical frequency, we find: vy? = 23-0121. Hence following the method described in the Phil. Mag. June 1900, pp. 163-164, we deduce * IPSSrslake.. That is to say, in upwards of 81 cases out of a hundred random samplings we should have obtained a system of frequencies for our cephalic indices, differing as much or more from our theoretical curve as the observed system. In other words, the skew-curve is a remarkably good fit. Fig. 1 shows this graphically, We thus conclude that in this case the skew-curve achieves what neither one nor two normal curves ean do. If it be supposed that possibly the Paris skulls are a triple racial mixture, then the diagram suggests that one of these components will have a mean cephalic index as high as 87 to 88, 2. e. a value 2 to 3 units above that of the medieval Jews, and corresponding, as far as [am aware, to no race likely to be found in Paris from 1600 to 1800. IJ-seeno hope * It has been suggested that in the paper cited I have used the normal distribution to prove that the normal distribution is of no special value. The suggestion, however, overlooks the point, which I readily admit, that the normal curve is a good fit to a binomial distribution, and that it is precisely such binomial distributions to which the errors of random sampling belong. Theory of Chance to Racial Differentiation. 117 of satisfactorily resolving this material, and hold it best to treat it as having a homogeneous character but a skew frequency *. | Index ...... ie OMe 68. 69. 70. Hie (Y= 73. 74. 49 he i) (lee) — op Or [w) Or uae (Se) Ot ly’, Observed ...| 0 y, Caleulated...; -O1 “39 | 23h | -7-53.| 16:97,) 3041) 46:57 | 63:32 Se gee te Wg eon, ecient _€, Difference ... { ‘Ol 65 20 WS Ae 459| 307} 14°32 index 25...04) ° 75: 76. Tie 78. (ee 80. Sl. 82. |y', Observed ...| 88 | 895 |1035 | 1125 | 97-5 | 885 | 89 | 745 | y, Calculated...) 78°71 | 90°90} 9869 101:61| 99°81) 93°99 | 85:14) 74:36 5 | paar + a pata ats a ae ¢, Difference ..{y99| 140/ 401 1089] 231| 549| 386 14 | Pndex.......| .8d. 84. 85. 86. 87. 88. 89. 90. | y', Observed ...| 62:5 | 545 | 295 | 25 |23 | 225 | 125 | 115 y, Calenlated...| 62°74} 51:19] 40:43] 30:92] 22-89) 16-40| 1136] 7-60 (=e aig 5 lias sy eae é, Difference i 1-24 3°31 10-93 | 5:92 “11 6:10 eet: 3:90 index 5. ...3- 91. 92. 93. 94. 95. 96. 97. | Total. y', Observed ...| 6 1 0 L 0 5 9) 1146 y, Caleulated...| 4:90} 3:04} 1:81 |} 103 | -36 20) LG) L146) | e, Difference .. { ia + Be ats we 1 LO 2 Os tes 703 | *56 Al “34 a | (4) In the previous investigation we have seen that sex differences are not sufficiently marked, as far as the cephalic andex 1s concerned, to form a hasis for the resolution of unsexed material into its two components. On the other hand, when we have a mixture of two markedly diverse races we ought to be able to differentiate the components by my method even if they should diverge somewhat from the normal type. To illustrate this point Dr. Macdonell has dealt with * Like, of course, so many other homogeneous but certainly non normal series, 118 Prof. K. Pearson on some Applications of the the Row-Grave skulls of Southern Germany and the ancient skulls of our own country dating from the British period *. In both these cases, I take it, we have a prior historical evidence for the probability of a racial mixture. A resolution therefore will tell us, although somewhat roughly, the pro- portions of the racial mixture, and to some extent point out the racial factor -vhich has survived to the present day. Hence the importance of such investigations. (5) Illustration Il. The Row-Grave Skulls.—These skulls date from the fourth to the fifth centuries,—the latter part and close of the folk-wanderings. The Row-Graves are found prin- cipally in Baden and Bavaria. O. Ammon, in his work Die natirliche Auslese beim Menschen, Jena, 1893, gives (p. 66) Kollmann’s results for 675 Row-Grave skulls. He compares them with the modern German distribution in the same districts, and concludes that there has been an evolution in the shape of the Germanic head. This investigation appears to me very incomplete ; it does not settle the main question at all, 7. e. whether evolution has gone on by (1) survival of the fitter inside a homogeneous population, or (2) survival of the fitter of two races, both of which were in existence at the time of the folk-wanderings. It is this question upon which Dr. Macdonell’s investigation seems to throw strong light. The following table gives the observed frequencies, sexual differences being disregarded }. aE ee Frequency. ae is oy Frequency. 67 1 81 40 oe 1 82 31 69 2 83 D5 70 8 84 98, 72 13 86 20 73 3H) 87 9 TO 49 89 6 16 59 90 10 ts 70 92 3 v9 54 93 2 80 58 94 1 J * I had previously dealt with these cases to a much rougher numerical approximation, and diagrams of the component distributions were exhibited some years ago at a Royal Suciety Soirée. _¥ In cases where! could sex the Row-Grave Skulls (see ‘The Chances of Death,’ vol. i. p. 861), I did not find the cephalic index a marked sexual character. Theory of Chance to Racial Differentiation. 119 Using the same notation as before we find for the funda- mental constants :—- Mean = 78°846. Moments: po= 21°268,109,. f3—) ol O82 olay fy == 1488°723,449, Ms = 8358°086,377. Other Constants : 4y= — 245°177,507, Xs== 6919-938, 389. The fundamental nonic, writing p.= 10x, 1s X° + 2°86 yi +3°914 y* —35°911x — 7-669 x4 + 129°429 3 + 95°675 y° — 22°202y—17-772=0. A root of this was localized between 0 and —1, and by successive approximation was found to be —°9685. Hence po= —9°685. Thus p3= —49°637 and py =5°125. The quad- ratic for the means of the two components is y — 9°125y—9°685=0, which leads to y;= — 14685 and y.=6'5935. Working out the other constants for the components we have, finally, the following results :— First Component. Second Component. Meanmi index: 25... ...:+4- Ta op lce) $5°4395 Number of Skulls...... 992°05 122°95 Standard Deviation... 3°3926 34518 Modal Frequency...... 64°917 14-210 The equations of the two components referred to their means are :— y = 64917 e—2°/23:020 y= 14°210 e—27/23'880, The frequency-distribution, the two components, and _ their compound curve are given in fig. 2, and it will be seen that the result is very satisfactory*. We have a mixture of a mesocephalic and a hyperbrachycephalic race in the pro- portions of 81°8 and 18°2 per cent. The second component is remarkably high ; it stands between the modern Germau 83-84 and the so-called Disentis type of His and Rutimeyer (Crania Helvetica, p. 25). The first component is almost identical with that of His and Rutimeyer’s Sion type with * Much more so than the fit of a skew-frequency curve which I have aiso tested on these data, £20 Prof. K. Pearson on some Applications of the me Tense er) ee SE Sal! Sees Ee Pole e Saas a ae GmR meee n nes Jae) ae Cephalic Index, Car |_| ase T Buccensesssgeee! = S| a aa ae See ia eRe eS es, eS nol, awe Oh Se coe tay tat ee Frequency. cephalic index = 77°2 (Crania Helvetica, p. 12). The Sion ‘ type may witha very great degree of pr anine be attributed to the Celts of Southern Germany. The Disentis type i approaches closely that of the dominant element in the modern Theory of Chance to Racial Differentiation. Lan South German, and of the old Alemanns. Our conclusion therefore must be :—That the Row Graves contain a mixture of two populations, possibly Celtic and Germanic, in the ratio approximately of 4 to 1. The latter element has largely sur- vived in the race struggle in Southern Germany. That the cephalic index at present is somewhat lower than 85 may be due either to evolution within a pure Germanic race, or to the continued presence of a small element of the Celtic race. In the distribution of the head-index of the modern Baden population there is, however, scarcely a trace of that skewness which is so characteristic of the Row-Grave skulls (see for example Ammon’s diagram, loc. cit., p. 68). This result strengthens the conclusion which is pressed upon us by other investigations, namely, thut man evolves largely by the survival of a race rather than mainly by the selection of special types within the race. Both processes are probably at work, but I believe too much stress has been laid on the latter. (6) Jllustration 1I.—We have not for Great Britain as ample data as for Southern Germany. In the Crania Britannica I can find only 114 skulls in all attributed to the ancient Britons, taking male skulls alone. The probable errors in dealing with such small numbers must be large, but it seemed of interest to attempt the same sort of resolution as we have carried out for the ancient Germans. It is needless to say that the frequency distribution had been previously observed to be very skew and to suggest heterogeneity. The data are given in the following table, where for the purpose of plotting such very irregular material, the smoothed values are given obtained by taking the mean of each three groups. Of course the constants have all been calculated from the unsmoothed frequencies :— | oa eal | | Frequency. Frequency. | Frequency. || Frequency. | Mit iem=ns7 77 lidex.|—-.-. || Index|... — — | Index. | | Actual.| Smd. | Actual.| Smd. | Actual.| Smd. Actual.) Smd. | B2a iO oI 0 ie ae 4a) Set SOes| Gee are 89.l00 1 & | 635..| 0 = 72 is Geri Sl 7 62 90 0 O | Gae5.). 5 73 ft 74 ||: «82 i 63 91 0) a 65...| O z 74 8 82 | 83 5 D3 92 1 || 662.) 0 2 75 11 74 84 + 42 93 0 5 | Oils: iiss 2 76 3 12 85 ) 33 94 0 Opa 68...| 4 yar 77 9 63 86 2 53 95 Gor.| 3 78 7 62 87 4 24 96 Reels: F4 oo Mei 79 | 4 53 88 1 2 97 122 Prof. K. Pearson on some Applications of the The following numerical results were obtained, still using the same Saletan : oe Mean Index = 77°3246. Moments p, = — 307342,028) 2; =) Fo Ms 24s: eo 2261-25" ehor 45 = 8050°185,852. Other constants A, = 1501°893,855, As = 9018°523,444. Putting p.=10y, the fundamental-.nonic is :— x°—17-°522x" +3894" + 85-093y° — 49-43 1y4 — 207-1382? —14°776y? + 13°510y—-017=0. A root was localized between —1 and —2, and x was found to be ~1°54599. This gave po= —13°41599, ps=—5:0906, p,='3290. Hence the quadratic determining the means of the com- ponents is v2 —3290y — 15-4599 =0, which leads to y;= —3°771 and y,=4:'100. Proceeding to the determination of the other quantities we find First Component. Second Component. Mean Index, .i2..6.1.5: 73°5536 81°4246 Number of Skulls...... 59383 54617 Standard Deviation... 3°7397 3°9822 Modal Frequency...... 63349 54719 The equations of the two components. referred to their means are :— ¥ — 6°3349 2) — #279708, y= ATI e— 27817120 , The two components and their resultant, as well as the smoothed observations, are plotted in fig. 3. I think they ought to be considered as distinctly good, having regard to the paucity of the material and the possibility that a certain amount ef the variation in it is due to distortion of the skulls*. According to this resolution the population here classed together as Ancient Britons consisted of two races mixed in * See ‘The Chances of Death,’ vol. i. p. 362. Theory of Chance to Racial Differentiation. Frequency. N ey teh bE I ‘quouo0duoy IST jo uvoyy g jo uvayW ‘xapuy oipeydeg SoTI9g 9TOU AA ‘quoucduog pug BOCES Ole! Nae W Agi ye Ae Lo fee SVAEE IS Pocecrer ee OR ee AS ee Col ee ee a 124 Some Applications of Chance to Racial Differentiation. the proportions of 52°1 and 47:9 per cent. The slightly larger element was a dolichocephalic race with an index of 73°554, and the smaller element a brachycephalic race with an index of 81:425. For the Long Barrow male skulls I have found a mean cephalic index of 71°77 (60 skulls) and a variability of 3°89 ; for the Round Barrow male skulls a mean index of 80°92 (25 skulls) and a variability of 3°82. There can be small doubt that one of our components coincides with the Round Barrow men or the “Celtic” element in Britain. The other component is somewhat less dolichocephalic than the Long Barrow skulls I have referred to above, but there is little doubt that it represents the Iberian element. Thus the mean index at Cro-Magnon was 73°34, and in the Caverne de Homme Mort 73°22. The Brito-Celt differs indeed sensibly from the Germano-Celt* in his cephalic index (80°92 as com- pared with 77°38), but this is a point which has been much considered by anthropologists, and I need not reopen that discussion here. It would seem therefore that if we had had no knowledge of the nature of the burial-places of our skulls, we could still have differentiated them into two groups—the Iberian and | Celtic ; and this, certainly, ought to give us confidence in the usefulness of the method. | (7) I have chosen in this paper, out of a wide range of material, three cases dealing with one character only, because that seemed to me to give most force to the illustrations. I have no doubt that the method, in the hands of a competent craniologist, would lead to most interesting anthropological results. But in itself the method is perfectly general, and applies to any material with which we may venture to deal on the basis of the old-established mathematical theory of chance. How far that theory has itself to be superseded is a question I do not propose to enter on here, but I would urge by means of these new illustrations of my method, which have been worked out, by competent mathematicians it is true, hut still by comparative novices to statistical work, that the process is not so laborious that it need be discarded for rough methods of approximation based upon dropping the funda- mental nonic and guessing suitable solutions to what then become indeterminate equations. * Assuming with His and Rutymeyer that the Sion type with an index of 77:2 is really that of the ‘‘Celtic ” element in South Germany. Pe Dee | IX. Aleasurement of the Expansibility of a Hard Jena Glass. ye deh. BorromEny, Aw Oise, L.1,S., and W.T. Evans*. ‘ia the course of RESIS None which we are carrying out on the subject of Thermal Radiation it became necessary to construct an Air-Thermometer which should be capable of being used at high temperatures, above the softening- point of ordinary English glass. The form of air-thermometer employed is that which was described in the Philosophical Magazine for 1888+ by one of the present writers. In this thermometer, which is a constant-volume air-thermo- meter, the volume-gauge and pressure-gauge are seprirated, and only connected by means of indiarubber pressure-tubing. The instrument has proved eminently satisfactory, and convenient to work with. The volume-gauge is the only part which it is necessary to make of hard glass, and, after some trials with specimens of the Jena glass of Messrs. Schott & Genossen, who specity three kinds of hard glass, we determined to use the glass termed by them ‘‘ Verbrennungsrohrenglas.’” ‘This is a very hard glass, little acted on by water or alkalis (though this property was not of much consequence for our purpose). It is slightly green in colour, and slightly opalescent. It is just possible to work it with an ordinary blowpipe, but for any complicated construction an oxygen flame is required. In order to use this glass for the volume-gange of the air- thermometer, it was necessary to determine the expansibility of the glass, This. we have done; and the present note is tied in the hope that the results may be of use to others. We were surprised to find so small an amount of expansibility. This property makes the glass of special value for thermometric purposes, at high temperatures. To determine the expansibility of the glass, the weight- thermometer method was used, and the ‘cubical expansion was found directly. This seemed more satisfactory than the determination of the linear expansion, and the inference, therefrom, of the cubical expansion. The bulb of the air-thermometer is a tube of Jena glass 12 cm. long and 1°5 cm. in diameter inside. A similar ‘tube * Communicated by Lord Kelvin. + J.T. Bottomley,“ On a Practical Constant- Volume Air-Thermometer,” ‘Proce. Roy. Soc. Edin. Dec. 19th, 1887, and Phil, Mag. August 1888. 126 ~=Dr. Bottomley and Mr. Evans on the Measurement was taken and fitted with a T-tube of narrow gauge, as shown in the figure, and a reservoir F, to aid in the process of filling the bulb EH. This apparatus was carefully weighed, and it was then filled with pure mercury ; an extra quantity of mercury being left in the reservoir F. To effect the filing, the end C was closed with a stopper, and the bulb F partially filled with mercury. \ ns as, at any rate, a first approximation towards a representation Mixtures of Liquids and of Solutions. 145 of the viscosity of a physical mixture in terms of the viscosities and natures of its constituents. Like other empirical formule, it will in time be replaced by a formula founded on theory and capable of including cases in which the liquids, owing to some chemical action on each other, give rise to mixtures having viscosities outside the limits of those of their con- stituents. Since a liquid at temperature ¢ may be regarded as pro- duced by a mixture of suitable proportions of the liquid at temperatures 0 and ¢, respectively, the above formula for the viscosities of mixtures should be capable of expressing the variation of the viscosity of a liquid with temperature. If 1 c.c. of a mixture at temperature ¢ is supposed to result from mixing v% c.c. of liquid at 0° C. and v, cc. of liquid at #,° C., t=v,t,; and if the viscosity is 7) at 0° C., at ¢°C., and m, at t° C., then (=a 0 10 ui -OHO-OH sativa NP m1 No a LENE 1 : where ee (”)"— i}. t, L\7 Hence No Uma aaa (1+ at)n an empirical formula proposed by Slotte*, and found by him, and more extensively by Thorpe and Rodgerf, to be applicable to all liquids on which experiments have been made. The values of m for most of the mixtures mentioned in the preceding tables vary between *20 and °50; and Thorpe and Rodger have found its values in Slotte’s temperature-variation formula to lie between *22 and °3 for alcohols, and to be about 6 for water, benzine, ether, and chloroform. In the following table the values found suitable for expressing the viscosity of a mixture in terms of the viscosities of its constituents, are compared with those found best for expressing the variation of the viscosity of each constituent with temperature. * Ofv. Finska Vet. Soc. Forhand. xxxii. p. 127, formula (11) (1890). t+ Phil. Trans. A. 189. p. 96 (1897). Phil, Mag. 8. 6. Vol. 1. No. 1. Jan. 1901. L 146 On the Viscosities of Mixtures and of Solutions. Values of m. Liquids. In Temperature In Mixture |. Variation Formula, | Formula. Carbon Tetrachloride and Benzine...... "58 * 64 * © 49 Nitrobenzine and Benzine ............... ‘67 t . 64 ‘50 | Ethyl Ether and Benzine........ sobageenes 68 64 °50 Ethyl Ether and Alcohol.................. 68 "23 adel Ethyl] Benzoate and Toluene ............ “50 t ‘61 "30 Glycerine and Water ......... peti eba "12§ “65 "22 & °25 40-per-cent. Sugar solution and water. “455 || 65 ‘50 20-per-cent. NaCl solution and water...) —_-66 | "65 3°0 to —*25 "* The numbers in these two columns, with the exception of those for nitro- benzine, ethyl benzoate, and glycerine, are taken from Thorpe and Rodger’s papers. if; from observations of Pribram and Handl, Wien. Ber. II. lxxviii. _ Gs ‘ + Calculated from observations of Rellstab, Inaug. Diss. Bonn, 1868. § Calculated from Schottner’s values, J. c. f || Calculated from Hosking’s values, 7. c. ‘The agreement between observed and calculated values may be seen from the following tables :— 40-per cent. Sugar Solution. » Viscosity. Temperature. Observed. Calculated. 0° C. "148 148 10 "895 903 20 ‘607 605 30 423 “430 40 313 "320 50 241 ‘247 60 191 "195 70 "155 "158 80 129 "130 90 "109 "109 20-per cent. NaCl Solution. ) 0267 0267 10 197 197 20 154 153 30 124 123 40 102 102 50 87 86 60 74 74 70 65 65 80 57 57 90 51 51 Sparking Distances between Plates for small Distances. 147 _ Although in the above examples of non-electrolytic mixtures and solutions there seems to be some connexion between the values of min the formula for the temperature-variation of the viscosities of two liquids, and its value in the formula for the viscosities of mixtures of the two, the number of instances is too small to warrant ageneral conclusion being drawn. In the case of the electrolytic solution (NaCl) the values of m for the mixtures at different temperatures vary greatly from one another, although the values in the temperature formula are practically identical. Possibly the magnitude of the heat of solution of NaCl places it outside the class of simple mixtures considered in what precedes. The result of this investigation may be summed up as follows :— (1) No one of the three theoretical formule (1), (2), (3) represents the viscosity of a mixture with sufficient closeness. (2) The empirical formula (; ) =0,(7 )+0(2) with a U] m1 12! suitable value for m gives a satisfactory representation. (3) It leads also to Slotte’s formula for the variation of viscosity of a liquid with temperature. X!. The Sparking Distances between Plates for small Distances. By Rosert I. Harwarr™*, Hf STORICAL.-—Previous to 1860, several series of measurements on the difference of potential required to cause a spark to pass between plates separated by a stratum of air, had been made. These earlier experiments by Volta (identita, p. 53), Riess (Pogg. Ann. vol. xl. p. 333), and others possess little more than historic interest, the means at their disposal for measuring differences of potential having been unreliable. The first trustworthy series of measure- ments were those performed in 1860, under the direction of Sir William Thomson (now Lord Kelvin) (EHlectrostatics and Magnetism, p. 250). In the series of measurements referred to, the plates were separated by known distances, the distances being determined by a micrometer-screw. The potentials required to cause a breaking down of the inter- vening dielectric were measured by the absolute electrometer. The results obtained show that the difference in potential necessary to break down the medium is not directly pro- portional to the thickness of the separating medium. This has been amply verified by other observers. Various * Communicated by the Author. L 2 148 Mr. R. F. Earhart on the Sparking Distances theories have been offered to explain this phenomenon : among them the hypothesis that a certain amount of energy is necessary to tear asunder an air-film which may surround the surfaces in question, the assumption being that, in the neighbourhood of bodies, the air possesses a more or less definite structure, and that in this condition the dielectric properties of air differ from those which it possesses in the ordinary gaseous form. A much more complete series of obser- vations on the spark potential were undertaken by Dr. Liebig in 1887 (Phil. Mag. vol. xxiv. p. 106). In these experiments the distances were varied from ‘0066 cm. to 1:144.em. The methods of measuring both distances and difference of potential were similar to those employed by Lord Kelvin. Object.—It seems desirable to obtain measurements for very thin strata of the dielectric, and if possible to ascertain the potential necessary to break down the air-film itself. To accomplish this, a much more delicate method of measuring the thickness of the separating medium is imperative if the limiting value is to be approached. The modern form of the interferometer is particularly suitable for measuring small distances, and may be readily adapted to this experiment. The conditions to be fulfilled are extremely simple : we are required, 1st: To measure a small distance accurately ; 2nd: To measure differences in potential accurately. To fulfil the first condition. Consider two plane parallel surfaces in contact. Let one of them be rigidly attached to a fixed support. Let the other be mounted on a movable carriage which bears one of the mirrors of an interferometer. Upon separating the surfaces, a succession of fringes (pre- ferably circular) will move across the field of view. By counting the procession of fringes, the distance through which the carriage is moved, and therefore the distance of separation of the plates, will be given directly in terms of wave-lengths of light. It may readily be shown that a passage of one fringe across the field corresponds to the movement of the carriage through a distance of half a wave-length. Again, since fractions of fringes can be measured readily to one-tenth of a fringe, and since the wave-length of sodium light is approxi- mately equal to °59 w, we shall be enabled to measure distances of ‘03m if desired. Any departure in the motion of the movable plate from a plane not parallel to itself will be indicated by the appearance of the circular fringes. Experience has shown that it is practically impossible for between Plates for small Distances. 149 parallel plates to be brought into contact throughout the entire extent of the surfaces. This is probably due to the existence of a gaseous film surrounding the surfaces. In exerting a pressure sufficient to squeeze out this last vestige of the air, strains are introduced which destroy the parallelism of the plates. Apart from this the electrical conditions render it advisable that one surface be convex. Description.—In the experiment here described, one of the surfaces is convex, the other plane. In the accompanying diagram, let ““D” be the fixed body, rigidly attached to a firm support A. This fixed body consisted of a steel bicycle ball, heavily nickel-plated, and 2°52 cm. in diameter. This was carefully insulated from the support, and connected with the binding-post “ B,” to which the necessary electrical connexions were made. ‘The complication due to the sphe- ricity of this surface is not so great as might be supposed, since the distances to be measured are of the order of a wave-length of light, whence a radius of curvature of 1°26 cm. is comparatively large. The surface ‘ D’”’ consists of a brass disk ground plane, then heavily nickel-plated and polished. This was mounted on a movable carriage, “ C,’ which bears the mirror, “ M.” The mirror M constitutes one arm of the interferometer. The surface D’ could thus be brought into contact with D by shifting the carriage. The point of contact was determined by means of a sensitive galvanometer with a small E.M.F. in circuit. The carriage having been pushed back until the point of contact was reached, the motion of the carriage was reversed ; the distance through which it was moved could be ascertained by counting the number of fringes which passed during the displacement of the carriage. The second condition imposed requires the measurement of differences of potential. In the experiments of Lord Kelvin and Liebig an absolute electrometer was used. The smallest difference in potential was approximately 2 ©.G.S. units E.M.F. in the electrostatic system. In this experiment the measurements of potential were made in the electromagnetic system, the readings being expressed in volts. The values obtained can therefore be transformed into electrostatic O.G.S. units by dividing by 300. A standard Weston voltmeter reading directly to volts was utilized in measuring the differences in potential. The instrument used was compared with a standard volt- meter recently calibrated by the Weston Company and kept in the laboratory for standardizing purposes. Source of E.M.F'.—The E.M.F. used was supplied by a 150 Mr. R. F. Earhart on the Sparking Distances bank of 2000 storage-cells so arranged that they might be used in units of 25 cells, or by special connexions of single cells. The cells were intended primarily for supplying small currents at high voltages, and had small capacity. It is highly desirable that small capacity be used ; otherwise, owing to the disruptive discharge, the surfaces would be greatly marred upon the passage of a spark. Surfaces.—The surfaces as described above consist of one spherical surface and a plane surface. These were made optically perfect, free from scratches, and were polished with dry rouge. It is necessary, owing to pitting of the surfaces due to discharge, that a fresh surface be presented each time a reading is taken. This may be readily accomplished by rotating the bodies about an axis not in the line of symmetry. The means of accomplishing this will be apparent upon con- sulting figure 1. Method of Procedure.—The surfaces were brought into contact and separated by a distance considerably greater than a given difference of potential required for discharge. The number of fringes crossing the field during the displacement was noted. Call this number a. The potential was then established and the motion of the carriage reversed. The number of fringes of retrograde movement untii discharge a—b 3 = distance in wave-lengths between plates, since the passage of a fringe corresponds to one-half wave-length displacement. of the carriage. In fig. 2, the plan of the electrical portion of the apparatus is indicated. As in fig. 1, D and D" represent the surfaces. These are connected to binding-posts B and B’. Circuit 1 contains the H.M.F., which may be varied from 2 volts to 5000 volts. Circuit 2 includes the voltmeter. Circuit 3 includes the galvanometer and small H.M.F. (about 1/100 volt) for determining the point of contact. All circuits are provided with suitable double-pole switches. After the plates are separated, circuit 3 is opened, and a difference in potential between D and D' established by closing circuit 1. The voltmeter will register this potential- difference. Upon the passage of a spark the resistance of the dielectric breaks down, causing a sudden drop in the potential existing between D and D’. Thus the voltmeter serves not only to measure differences in potential, but also to detect the point where discharge occurs. Before the readings the surfaces were polished with dry rouge, and freed from dust-particles by blowing them with a jet of dust-free air. occurred was noted. Call this number 6. Then between Plates for small Distances. 151 It was found that the apparent resistance of the dielectric depends in a measure upon the manner in which the potential- difference is established. A sudden rise in potential trom zero up to a definite amount will cause a spark to jump Figs. 1 & 2. To a considerably greater distance than if the potential were built up gradually. This is perhaps what might be expected ; for if we regard the energy due to the presence of the electrified bodies as existing as a strain in the separating medium, then the sudden application of such a strain would cause the medium to break down more readily than if the strain were applied gradually. The readings given in the table are those in which the potentials are built up gradually, or, what amounts to the same thing, a given difference of potential being established, the plates were made to approach one another gradually, thus confining the strain to a more limited portion of the dielectric. It is for this reason that 152 Mr. R. F. Earhart on the Sparking Distances the plates were separated a greater distance than the potential seemed to require, and then gradually brought together. Results—Yable I. and the corresponding curve designated I. (fig. 3) show the results from distances of *5 X sodium light to 185A, 27. e. from *3 micron to 109 micra. In this case the dielectric was air under atmospheric pressure. ‘The readings were taken during the winter months, and it was not deemed necessary to guard against water-vapour. The readings given in the following tables were taken in the spring and summer months, when the humidity is likely to be larger. In these cases the air was passed through suitable drying- tubes. Tas.Le [.—Air, Atmospheric Pressure. Distance in Potential in Distance in Potential in Wave-lengths. Volts. Wave-lengths. Volts. oh 38 16:0 360 ih 46 175 400 Wii 52 18°5 408 8 84 20:0 408 1:0 100 22-0 416 1c 106 22:0 416 1-2 108 28:5 454 1:3 111 MIs 460 15 152 39:0 512 2:0 202 52:0 556 2:5 240 64:0 604 2°5 250 770 664 30 300 78:5 670 3:0 304 99-0 712 4:0 312 119°5 | 820 50 336 125:0 864 50 344 1640 986 8:5 348 185:0 1080 13°5 350 14:0 360 From the results indicated in Curve I. (fig. 3) it will be observed that from readings from *5 to 3 wave-lengths the po- tential required for discharge varies directly with the distance. Between ,wave-lengths 3 and 4 the curve takes a sudden bend, and proceeds in nearly a straight line, varying with the distance, but according to a different law. If we accept the hypothesis of an air-film surrounding the surfaces of the bodies, the sudden variation in the form of the curve between wave-lengths 3 and 4 would seem to be another argument in its favour, and would indicate the thickness of such a film as being 1°52 sodium light, 7. e. about °9 pw. It is of some interest to compare the portions of the curve indicated with those given by previous observers. The obser- >YYIIW N/ FINYLSIO between Plates for small Distances. 153 Fig. 3. _ SESSA See (oa ee oes J ee eee re ee | ee a 2) oA) ies aes coe iva 2) Se a pte Pe pura | | | S68 2 ea POTENTIAL IN VOLTS 154 Mr. R. F. Earhart on the Sparking Distances vations of Dr. Liebig, previously mentioned in this article, are perhaps more complete for relatively large distances than those given in any published table. Dr. Liebig has two values which fall within the limit of this experiment. Reducing his observations to the scale here used, they show a very close agreement. They are indicated in fig. 3 by a dagger, together with the letter L. Liffect of Pressure-—Tables II. to V. indicate the values obtained for the pressures indicated. These results are represented graphically in fig. 4. The values obtained indicate that for varying pressures the general form of the curve is the same as that under atmospheric pres- sure, but that after passing a certain limiting distance, the second straight portion of the curve makes a different angle with the X-axis, the inclination depending on the pressure. Tor pressures greater than one atmosphere, values of the potential up to a distance of three wave-lengths seem to coincide very closely with the values given for one atmosphere. After passing this “ turning-point,” the curve again becomes a straight line. For pressures less than one atmosphere the values indicate that, in the first straight portion of the curve, asmaller potential is required to cause the spark to pass a given distance. The character of the curve would lead us to believe that for very low exhaustions the resistance of the air-film, if such does exist, becomes much weakened, and that for minute pressures we should have a curve lying close along the Y-axis. The discharge through a Geissler tube is probably of this character. In obtaining the readings under pressure other than one atmosphere, the entire instrument was enclosed in an iron box provided with suitable windows. The movement of the TasLE II].—Air, 40 em. Pressure. Distance in Potential in Distance in Potential in Wave-lengths. Volts. Wave-lengths, Volts. 10 52 15:0 328 WEE) 1) 19:0 356 15 82 21:0 360 2-0 104 30'5 412 25 146 40-5 464 2°5 150 54-0 496 3:0 152 67:0 552 4:0 170 750 592 4°5 204 1250 66U a0 304 178°5 720 5:5 320 between Plates for small Distances. Tas LE I]J.—Air, 15 em. Pressure. Distance in Wayve-lengths. Potential in Volts. 85 106 122 156 200 300 | Distance in Wave-lengths. 53°5 78:0 103°5 160°0 29:0 200°0 Potential in Volts. 320 360 400 412 468 512 _ Taste [V.— Air, Two Atmospheres Pressure. Distance in Wave-lengths. Heise SP OUTS eo toe SASAKRSSAKRS — | Potential in Volts. 96 130 142 200 302 312 _ 824 356 376 376 | Distance in | Wave-lengths. Potential in Volts. eee TasBLe V.—Air, Three Atmospheres Pressure. Distance in Potential in Distance in | Potential in Wave-lengths. Volts. Wave-lengths. Volts. 1-0 107 15-0 512 2°0 194 17-0 512 25 240 | 19-0 568 2°5 260 24°5 660 30 304 | 315 768 8:0 368 | 38°0 886 Ito £00 42-0 1024 130 480 plates was controlled by a aie a cece working eee a stuffing- box. Carbon Dioxide. The only other gas experimented upon was CO,. The gas was allowed to pass into the iron vessel described in the previous paragraph, the air being removed by displacement. The results obtained are given in Tables VI. and VII., and represented graphically in fig. 5. Both curves are for CO, under atmospheric pressure, with this distinction: that in the upper branch of the curve a gentle flow of CO, was 156 Mr. R. F. Earhart on the Sparking Distances Fig. 4. ee ae ef dy A ee tel oe Socanmaiel oe [eee | icone BEERiZEES ol | | Ua BREESE o| | tt | J 4 eA -i Af More iwee: poee fea PCT ie CCH eC 7 SCD Pee ee A et ale Ve ae SoA eee POTENTIAL tN VOLTS ET] N/ FINYLS/IOC between Plates for small Distances. 157 TaBLE VI.—Carbon Dioxide (surface blown). Distance in Potential in || Distance in Potential in Wave-lengths. Volts. Wave-lengths. Volts. 1:0 100 9°5 364 15 150 15:0 412 1°5 182 22:5 408 2:0 250 alts) 420 2:5 250 36:0 480 2°5 300 | 52-5 560 3°0 300 | 62:0 592 40 304 1 93:0 630 4:5 340 | 110°0 736 5°5 360 | 125°0 780 9-0 376 Taste VII.—Carbon Dioxide (surface not blown). Distance in Potential in | Distance in Potential in Wave-lengths. Volts. | Wave-lengths. Volts. 1:0 104 17:0 568 2:0 212 18°5 582 2:5 260 30°5 618 3:0 300 38°5 660 i) 320 52°5 678 4°5 360 hess 732 5:0 412 84:0 768 | 15 464 107°0 870 12°0 516 maintained over the surfaces, while for the lower branch the gas was quiescent. This distinction gave rise at first to what appeared to be inconsistent readings, but the apparent wide discrepancy in the readings was found to be due to the cause indicated below. In the case of the gas in motion, a jet of CO, was allowed to impinge on the contact-surfaces ; not,. however, at the point where contact would take place, but remote from the region of contact: thus it was hoped to secure a gentle flow of the gas, which would naturally spread out over the surfaces. The values from which the lower limb of the curve were obtained were those taken after the CO, had filled the box and the supply had been cut off. The readings were taken in from two to four minutes after the box was filled. The separate readings are indicated for the upper curve (surface blown) by a cross (x). The read- ings for the lower curve (surface not blown) by a circle (o).. As an explanation of the two branches of the curve I submit the following hypothesis :—We know from general. | 158 Sparking Distances between Plates for small Distances. considerations, such as the pressing together of parallel plates, various experiments with a coherer, that an air-film is tenacious. In the case of the upper curve this air-film remains intact, but the CO,, having displaced the body of Fie, 5. ELLE TTCLCEL Plt Le PLCC pt LPL CCC aa SeRGG See ces . Lee MMe ot [LC A Sa SP ee we e4nnne: AR doe eb ae POTENTIAL, #N VOLTS VYIIW N/ FOINYLSIC On the Refraction of Sound by Wind. 159 air, furnishes the remaining resistance. When the gas is flowing across this surface the molecules of the gas are too greatly agitated, too much stirred by convection-currents, to group themselves into anything like the semblance of a film. In the case of a gas quiescent, the CO, meeting a limiting surface and not being disturbed, a film of carbon dioxide forms, which is superposed over the air-film. The fact that the upper portions of both branches are parallel indicates that they differ, in this region at least, by an additive constant. Several readings taken after the CO, had remained in the vessel for about thirty minutes, seemed to indicate a greater resistance of the dielectric for a given distance. It seems probable that a time-factor enters into this con- sideration. The readings, however, are too few in number to base any further statement thereon. In conclusion, it becomes my pleasure to thank Prof. A. A. Michelson not only for suggesting this experiment, but for encouragement and advice always freely given throughout the course of the work. It is also my pleasure to thank Prof. 8S. W. Stratton for many courtesies rendered during the progress of this experiment. Ryerson Laboratory, University of Chicago. Sept. 13th, 1900. XIL. On the Refraction of Sound by Wind. By Epwin H. Barton, ).Sc., P.RS.E., Senior Lecturer in Physics at - University College, Nottingham*. N his treatise on Sound (vol. ii. pp. 182-4), Lord Rayleigh discusses the refraction of sound by wind where the rays are everywhere but slightly inclined to the wind, and obtains an approximate expression which, in the numerical illustration adduced, gives a result differing by only a few minutes of are from the strict value. The theoretical interest of the wave propagation in this case seems, however, to warrant a slightly fuller examination of the problem on the basis of Huyghens’s principle of wavelets and envelopes. Let us retain Lord Rayleigh’s assumption as to the distribution of the wind, -namely, that it is everywhere horizontal and does not vary in any one horizontal plane but is different at different levels. Then, confining our examination to rays in the same vertical plane as the wind, we find the following results :— (1) The direction of propagation is not usually at right angles to the wave-front where there is a wind, conse- quently the cosecant law for the wave-front needs * Communicated by the Physical Society: read Nov. 9, 1900. 160 Dr. E. H. Barton on the supplementing by another expression giving the direction of the ray. (2) Total reflexion cannot occur if the wave-front is initially horizontal. (3) In a region where the horizontal wind increases uniformly as we ascend, the rays instead of forming a catenary describe a more complicated curve which,, however, reduces to a parabola in the special case of rays whose wave-fronts are horizontal. Relation between Direction of Propagation and Wave- Front.— Let a region be imagined in all parts of which the wind is horizontal of speed u; let a plane wave-front be inclined @ to the horizontal, and let the direction of propaga- tion of this wave of sound be inclined ¢ to the vertical. It is required to find ¢ in terms of 0, u,and v, the velocity of sound. Let AB in fig. 1 represent the wave-front at a certain instant, and let CD represent it after the lapse of a short time Fig. 1.—Drift of Sound-Rays in a Wind. denoted by ¢. Then the Huyghens’ wavelet whose origin is A may be conceived as radiating from A in every direction. at speed v compounded with the horizontal velocity u. Hence the wavelet from A after any time ¢ is a circle whose radius is vt but whose centre is transferred a distance wt horizontally in the direction of the wind. Thus, lay off horizontally AA‘=ut, then from A’ describe with radius vt the are HCF, and we have the wavelet required. Similarly we get the wavelets originating at B and at any other points along AB. The new wave-front is the envelope CD of these wavelets, and is obviously parallel to AB. Also the direction of propaga- tion of the wave is AC, making the angle VAC=¢ with the vertical ; whereas A’C is perpendicular to the wave-front Refraction of Sound by Wind. 161 which itself makes the angle BAD=8 with the horizontal. From C let fall GN perpendicular to the horizontal line AN. Then, for the relation between @ and 6, we have by con- struction NAY. NAC AVA fan NOS = CN” GN CA’ cos NCA’ tanp=tan d+ — seed. . hy, orm Oy or Accordingly the ray, instead of making the angle @ with the vertical as it would if normal to the wave-front, makes the angle @, which usually differs from @ whenever there is a wind in the region in question. An exception occurs when @ is 90°, } being then 90° also. Refraction of Waves and Rays on crossing into a new Wind Zone,—Consider now two wind zones divided by a horizontal plane; let the wind in the lower zone be everywhere horizontal of speed up, and in the upper zone in the same direction but of speed uw, Let a plane wave-front in the lower zone, inclined @) to the horizontal, assume the inclination 6, after refraction into the upper zone. It is required to determine the relation between @; and 6). Fig. 2.—Refraction of Sound by abrupt change of Wind Speed. Q In fig. 2 let AC represent the wave-front incident at A upon the plane of separation AB of the two zones. Draw CB’ at right angles to AQ, and lay off B’B, making B/B: CB/=w:v. Then, by previous paragraph, CB is the direction of propagation in the lower zone. And, if ¢ be the time occupied from C to B, we have CB/=vi and B/B=ut. To construct the new wave-front in the upper zone it is necessary to consider A as the origin of a wavelet as in the first case, Phil. Mag. 8. 5. Vol. 1. No. 1. Jan. 1901. M 162 Dr. E. H. Barton on the The wavelet is obviously a circular one of radius A’'Q=vt described about a centre A’, distant horizontally ut from A. From B draw BQ tangential to this arc, then BQ is the refracted wave-front required. And we have by the figure cosec QBA!= Bae er eee ee NO? vt _ BIA — ut—uot re Ob en ae (ly ell or cosec 0, =cosec 6. -———.. (2) v This result is obtained very simply by Lord Rayleigh by consideration of the velocity of the trace of the wave-front on the surface of separation, 7. e., referring to fig. 2, the velocity of the point G along AB. This velocity is seen to be susceptible of two expressions according as G is treated as a point on I*G or as a point on GH. Rayleigh thus obtains — | v v sin 6) © °~ sin, |“ ere (3: which is identical with (2) already found by Huyghens’ principle. The advantage of the longer method adopted here lies in its power to treat the direction of propagation also. Thus, by equation (1), or by fig. 2, in which QN is perpen- dicular to AB, we have | tan d,;=tan 0; + A sec 6, re which completes the solution. i Refraction through any Number of Parallel Wind-Zones.— Consider, now, any number (n+1) of horizontal zones, in each of which the wind is everywhere the same and hori- zontal, but let the wind-speeds in the different zones, beginning from the lowest, be wo, wu, wo, ... u,, and let the angles which the wave-fronts make with the horizontal and the rays with the vertical be denoted respectively by 6 and @ with corresponding subscripts. Then from (2) we have cosec 8, =cosec 6) — (uy — U9) /2, cosec @,=cosec 6, — (ut2— 1) /v, cosec 6,, = cosec 6, -1— (Un— Un—1)/v. Hence, on addition, we obtain Un =U cosec 0, =cosec 0,— ———. Bea ae Vv Also by (1) or (4) we have for the final direction of propagation Un ; tan dn=tan O,+ > see 0, = ae (6) We thus see that the final inclination of wave-front and direction of propagation are each independent of the constants Refraction of Sound by Wind. 163 characterizing the intermediate zones. It should be noted, however, that a cosecant cannot have a value between + 1 and —1, so that if any of the zones required this, the series must cease there, equations (5) and (6) not holding for higher zones. This brings us to the next topic. Total Reflexion.—Although the cosecant law for the wave- front obtaining here differs from the ordinary optical law of refraction, we still have, as in optics, the phenomenon of total reflexion possible. And it is in this connexion that the distinction between wave-front and direction of pro-| pagation is most striking. ‘Thus, for the wave-front, if the angle of refraction @, is put 7/2, we have from equation (5) the critical case expressed by Une sa Uo cosee 8, — ——— Sot rete eee ET) v Hence any pair of values of 0) and (t#—ug) which violates (7) affords an example of total reflexion, the last zone not being entered by the beam. Suppose now that we have a series of wind-zones in which the wind-speed increases as we ascend: then, provided the initial inclination of the wave-front were /inite, it is clear that at some point we must have total reflexion. But if, on the other hand, the wave-front were initially horizontal, we should then have @)=0, and, by equation (5), all the 6’s would be zero also. That is, we should have no refraction of the wave-front, and consequently no total reflexion any- where, whereas the ray, as we ascend, deviates without limit from the vertical, for equation (6) now reduces to i. Oy Uae ea et ewes =. (0) So that in this case we have ¢cero refraction of the wave-front associated with unlimited refraction of the rays, total reflexion being impossible. - On consideration of the case by Huyghens’ principle, it is seen that where a zone cannot be penetrated, and total reflexion occurs, the reflexion follows the ordinary optical law, angle of reflexion equals angle of incidence. Path of Rays where Wind increases continuously with Height.—Let the wind be everywhere horizontal, and in the ‘same vertical plane, but let its speed vary from one level to another according to the equation (8 A ae a (9) where u is the speed of the wind, v that of sound, ¢ and a are constants, and y is measured vertically upwards. The « co- ordinate will be taken horizontally to leeward. It is now required to determine the inclinations of the wave-front and of the rays at any point, 7. e., we require 0, , and w for any given y. The equations for @ and ¢ are derived immediately 164 _ Dr. E. H. Barton on the from (5), (6), and (9). Thus, dropping subscripts, we have cosec 6=cosec O)—ay 10 or cosec 0=z=b—ay 4 ae) where z=cosecO)—ay, and b=cosec @; also tan 6= = =tan9+(ctay)sec@, . . (11) whence ox} dy ai (‘teow ges /22—1 /z2—1 - The first integral here represents the catenary found by Lord Rayleigh for the path of the ray when taken at right angles to the wave-front. The second integral is a small correction for the obliquity of the ray, and arises from the second term on the right side of equation (6). On evaluation (12) yields ; ae Qax= (b+ 2c) VP2-1— (b+ 2c +. ay) V27—1+ log bot lisa 2 ¥ “2+ /2—-1 Thus, for any given ordinate, the abscissa is the sum of three terms, the first being a constant, the second forming with y a curve of the fourth deyree, while the third is the abscissa of a catenary. This is the general expression ex- hibiting the relation between x and y, and therefore completes the required solution. In considering various special cases it will, however, often be simpler to go back to equation (10) and (11). 3 Ray with Horizontal Wave-Front.—We now have &=0, b=cosec 6)>=, and (13) becomes indeterminate ; so, either by evaluating it or by use of (10) and (11), we obtain 22=2ey+ay’, . «2 see 1. €., the path of the ray is the parabola ON? e (y+ =) =<(2t+5\ - 2. + (18) If the ray starts in still air, put e=0, and we obtain y= 28a, 2 on a parabola with vertex at the origin. Numerical Illustrations.—To exhibit the two phenomena of total reflexion and the parabolic path of rays with total reflexion impossible, take the following numerical data. Let the region be specified by equation (9), where c=0'02 and a= 0°0001, i. e., speed of wind y being expressed in feet. Then, if the temperature is such as to make the speed of sound 1100 feet/second, the wind- speed at the origin is 22 ft./sec., = 15 miles per hour. Whereas at 1000 feet high the speed of the wind would be 20 miles per hour. In this region let sound at the origin of Refraction of Sound by Wind. 165 coordinates start down-wind and in the same vertical plane, and with (1) its wave-front initially inclined at 60° to the hori- zontal. Then it suffers total reflexion at a point about 1547 feet higher than the origin, and at a horizontal distance of about 6195 feet to leeward of it. The intermediate inclina- tions of wave-fronts and rays are given in the accompanying table, and graphically exhibited by curve AA of fig. 3, in which the numerals along the axes denote thousands of feet. Table of Inclinations of Waves and Rays. Coordinates. Inclination of Inclination Angle between | Wave-front to | of Ray to Ray and Normal | the Horizontal. the Vertical. to Wave-front. | cis ac: 0. . ~—O. | Pig coeds ft. aes | es Evy L420 | 0 60 | 60 34 0 34 | 1005 500 64 dl 66 27 1 36 2383 1000 71 28 73 26 1 58 3359 1250 7612 77 =(56 ipa 5059 1500 | 84 27 85 15 0 48 6195 1547 90 90 OPO. Fig. 3.—Continuous Refraction of Sound by Wind. \ \ s a , Zag O\ i 2 3 A 5 6 N: (2) Let sound start from the origin, with its wave-front horizontal, then the curve BB (fig. 3) represents the parabolic path described by the ray, the wave-front remaining hori- zontal throughout. But although the wave-front is neyer refracted, the ray at a height of 8000 feet has drifted more than 500 feet to leeward. It would, however, never suffer total reflexion, but would asymptote to the horizontal at an in- finite height, the ray and the wave-front tending to coincide. Rays intermediate between AA and BB would suffer total reflexion at greater heights than 1547 feet, and rays below AA at less heights. University College, Nottingham, Aug. 22, 1900, r 166° 3 XIII. Notices respecting New Books. Die Partiellen Differential-Gleichungen der Mathematischen Physik. Nach Riemann’s Vorlesungen in Vierter Auflage neu bearbeitet von Hernrich Weser. Erster Band. Pp. hone Braunschweig: Friedrich Vieweg und Sohn. 1900. ELL-NIGH half a century has elapsed since the time when Riemann first delivered the course of lectures on partial differential equations which was subsequently published in book-form, and which is well known to all students of mathe- matical physics. The first three editions of this important and, at the time of its appearance, unique work were practically identical in form and scope, the last edition appearing in 1882. Meanwhile, the subject was making enormous strides, the rapid progress of experimental investigation constantly opening up new vistas of problems, and calling for fresh methods of dealing with them. The gradual abandonment by leading physicists of all action-at-a-distance theories, and their replacement by theories based on the transmission of strains and stresses through a continuous medium, have in no small degree modified the methods of dealing with various classes of problems. Quite apart from the stimulus received by mathematical physics from the accumu- lation of new facts and the development of new theories, rapid progress was also being made in various branches of pure mathematics, and some of the results obtained were shown to lend themselves easily to the solution of important physical problems. Among such developments may be mentioned the modern theory of functions of a complex variable. Accordingly, when the demand arose for a new edition of Riemann’s work, the publishers, realizing that a mere reprint of the former editions would no longer meet modern requirements, entrusted the task of bringing the book up to date to the able hands of Professor H. Weber. The work is not yet complete, for the book before us is only the first volume, and a second is promised shortly. Some idea of the magnitude of the task undertaken by Professor Weber may be gathered from the fact that the last edition of Riemann’s work was a small volume of only 325 pages. The first volume of the new edition contains over 500. Practically the outcome is a new treatise on mathematical physics by Professor Weber. Riemann’s method has been re- tained, but the scope of the book has been enormously extended. - The volume is divided into three sections. Section I. is devoted to an account of the analytical methods used in the solution of physical problems, and deals with the following subjects :—definite integrals, Dirichlet’s and Fourier’s integrals, infinite series, Fourier’s expansion, multiple integrals, functions of a complex variable, differential equations, and Bessel’s functions. Section IT. contains an account of certain fundamental geometrical and dynamical propositions, including the subject of strains, vector- analysis, the theorems of Gauss and Stokes, the ho of Geological Society. 167 potential, spherical harmonics, the principles of D’Alembert and Hamilton, and Lagrange’s dynamical equations. Section III. deals with the mathematical theories of electricity and magnetism : electrostatics and the problems connected with it, problems in magnetic induction, electrokinetics, electrolytic conduction, steady electric currents, conduction in sheets and solids, and the theory of electrolytic phenomena. Problems on electromagnetic waves and the propagation of currents along cables are not dealt with in this section, as they are, no doubt, reserved for treatment in the secoud volume, which is to be devoted to the theory of heat, wave-theory, elasticity, and hydrodynamics. ~The book is an important and timely contribution to the literature of the subject. In one or two cases, indeed, the treatment would seem to be capable of improvement. Thus, in considering the problem of the potential of an ellipsoid, the author simply writes down the potential functions, and shows that they satisfy the required conditions. Although this mode of treatment is, no doubt, commendable on the score of brevity, it is hardly satisfying to the mind of the student, who is more con- cerned to know how the functions in question were obtained, than that they furnish a solution of the problem. Such a method, in fact, savours too much of a mere conjuring trick, and cannot be considered to have much educational value. Among minor blemishes we may note that the names of Enalish physicists appear to be frequently mis-spelt. In the last section of the book Professor Weber has embodied some of his own researches, more particularly in connexion with electrolytic conduction—a subject which does not lend itself very readily to mathematical treatment. All students of physics will feel grateful to Professor Weber for having undertaken the task— an ex- eeedingly arduous one—of bringing Riemann’s book up to date, and for having so admirably carried out the first portion of the work. XIV. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from ser. 5. vol. ]. p. 536. | June 6th, 1900 (con.).—J. J. H. Teall, Esq., M.A., F.R.S., President, in the Chair. 2. ‘Note on the Consolidated ASolian Sands of Kathiawar.’ By Frederick Chapman, Esq., A.L.S., F.R.MS. The name miliolite-formation was originally given by Dr. H. J. Carter to certain granular calcareous deposits occurring on the coast-line between the peninsula of India and the mouth of the Indus. The foraminifera and other organic remains in the rocks must have inhabited moderately shallow to littoral marine areas. The minute granules are worn and polished; the prevailing genera of foraminifera are roundish, and would be easily moved by wind; remains of larger organisms are absent; and the deposits are false-bedded. AJl these phenomena are explicable if the deposits represent the accumulation of material derived from littoral calcareous sand of 168 Geological Society. marine origin, mixed with mineral detritus from adjacent hills. The rocks can hardly be older than Pliocene; and there is nothing in the general character of their organic remains which is incon- sistent with a still more recent date. The tests of some of the foraminifera have been filled with limonitic substances or with the yellow, brown, or green varieties of glauconite. Six specimens are described in detail, and lists of the contained foraminifera given. In one instance the granules are all invested with a thin, dark layer, which seems to be the first stage towards an oolitic structure. A note is appended on the foraminiferal, wind-borne sands of Dog’s Bay (Galway), discovered by Welch. 3. ‘On Ceylon Rocks and Graphite.’ By A. K. Coomara-Swamy. Ceylon is surrounded by raised beaches, and has been elevated in recent geological times ; fluviatile deposits also occur: the gems for which Ceylon is famous are obtained from gravels in the Ratnapura district. With the exception of these recent deposits, the island probably consists entirely of ancient crystalline rocks. Pyroxene- granulites are recorded from several localities ; they are dark in colour and greasy in lustre. Foliation is not evident, but it may appear in thin slices. The minerals most frequently present are augite or hypersthene, or both, plagioclase (usually labradorite), orthoclase - microperthite, garnet, quartz, amphibole, magnetite, apatite, zircon, and biotite—-the pyroxene and felspar alone being essential constituents. Varieties approach gabbro and eclogite. The texture is granulitic or granular. Centric structures are very characteristic, probably resulting from the corrosion of garnets. Normal granulites are white or grey and usually contain red garnets. The minerals are quartz, orthoclase- and microcline-microperthite, plagioclase, and garnet; biotite, mag- netite, ilmenite, apatite, and zircon are often present; and the texture is granulitic. Microcline-gneiss, sometimes with hornblende, occurs in conical hills, originating the term domoid gneiss employed by Prof. Walther. The minerals include ortho- clase- and microcline-microperthite, quartz, plagioclase, biotite, pyroxene, amphibole, pyrite, magnetite, apatite, and zircon. An- orthosite-gneiss, gneissic granite, and pegmatite are also described. Dark diorites (containing amphibole, plagioclase, quartz, pyroxene, biotite, magnetite, apatite, and zircon), dolerite, hornblende-gabbro, and ophitic quartz-norite are also present. The white, crystalline limestones usually contain pale mica and blue apatite; sometimes also colourless pyroxene. Banded scapolite- and wollastonite-bearing rocks are found at Galle. Certain rocks, apparently vein-products, are also described, which contain quartz and calcite micrographically intergrown. Graphite occurs chiefly in branching veins in igneous rocks, which at Ragedara are granulites and pyroxene-granulites. The relations to the matrix are described, and are held to favour the idea of the deposition of the mineral as a sublimation-product (Walther), or from the decomposition of liquid hydrocarbons (Diersche). Ana- lyses of several of the minerals, including mangan-hedenbergite, are given; and a bibliography of the geology of the island 1s appended, Phil. Mag .S.6.Vol.1 PLI. — — e— Without centres of inversion : 4 Ay ia is e ” a = eI A, Mirroramage Forms a a Seas F g Es | 4 gS , 13) of: a moon ” 3s : <3) = -) x B i) | ee a = y NE ih he ze i ra f van ° Ba \ Lae ee ais Wer TT Rect dS NO we EOE | Sane canna xe oe « » is ae Noxe / 5 PSO ee Fie uke Zoe SS i=) is 2 = Phil. Mag.S.6.Vol.1.PL.IL 1. TL, Phil Mag. S.6.Vol.].P1. II Knantiomorphous Forms Mirror image Forms With \centres of inversion Without centres of inversion XXVI Phil. Mag. 8. 6. Vol. 1. Pi. III. No. 1.—Continuous spectrum below. Same deviated by cyanin prism of 17’. | Nos. 2, 3.—Same with prism of 22. No. 2 taken with Aurantia screen to reduce effect of blue; No.3 without. Nos. 4,5.—Same with prisms of 35” and 2’ 51” re- spectively, showing continuity of curve. No. 6.—Several exposures with prism of 28' 30”. \ — —— — tne _ — —————— Phil. Mag. 8. 6. Vol. I. Pl. LV. i t i i THE LONDON, EDINBURGH, axpv DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. | se [SIXTH SERIES. ee he Ak ¥ VOL, XV. On the Stresses in Solid Bodies due to unequal Heating, and on the Double Refraction resulting therefrom. By Lord RAYLEIGH *. j Boe phenomena of light and colour exhibited in the polariscope when strained glass is interposed between crossed nicols are well known to every student of optics. The strain may be of a permanent character, as in glass im- perfectly annealed or specially unannealed, or it may be ‘temporary, due to variations of temperature or to mechanical force applied from without. One of the best examples under the last head is that of a rectangular bar subjected to flexure, the plane of the flexure being perpendicular to the course of the light. The full effect is obtained when the length of the bar is at 45° to the direction of polarization. The revival of light is a maximum at the edges, where the material tra- versed is most stretched or compressed, while down the middle a dark bar is seen representing the “neutral axis.” It is especially to be noted that the effect is due to the glass being unequally stretched in the two directions perpendicular to the ‘line of vision. ‘Thus in the case under discussion no force is operative perpendicular to the length of the bar. Under a purely hydrostatic pressure the singly refracting character of the material would not be disturbed. When a piece of glass, previously in a state of ease, is unequally heated, double refraction usually ensues. This is due, not directly to the heat, but to the stresses, different in different directions and at different places, caused hy the * Communicated by the Author from the Lorentz Collection of Memoirs. eae Mag. =. 6. Vol. tl. Nox2. feb. 1901. N 170 Lord Rayleigh on Stresses in Solid Bodies due to unequal unequal expansions of the various parts. The investigation of these stresses is a problem in Hlasticity first attacked, I believe, by J. Hopkinson*. It will be convenient to repeat in a somewhat different notation his formulation of the general theory, and afterwards to apply it to some special problems to which the optical method of examination is applicable. In the usual notationt if P,Q, R, 8, T, U be the com- ponents of stress; wu, v, w the displacements at the point L,Y, 23 , the elastic constants; we have such equations as du dv. dw du P=a(ita,t \+2e a ee) These hold when the material is at the standard temperature. If we suppose that the temperature is raised by 6 and that no stresses are applied, ——S i SS while dw/dy &c. vanish. The stresses that would be needed to produce the same displacements without change of tempe- rature are P=Q=R= (3042p) x6, S=T=U=0. Hence, so far as the principle of superposition holds good, we may write in general du dv dw du ey ie +7, ae) + eae —(3V+2u)K0, . (3) <1) fd. av S=a(F +a ee with similar equations for Q, R, T, U. If there be no bodily forces the equation of equilibrium is deed ON aadale ie Ay heh ee) * Mess. of Math. vol. viii. p. 168 (1879). + See, for example, Love’s ‘ Theory of Elasticity,’ Cambridge University Press, 1892. Heating and on Double Refraction resulting therefrom. 171 with two similar equations ; or with use of (3) and (4) d T l a+) £(% dv dw dé eee fy 22 alee Ls da\ dx * dy ct 7) teY SY’ dx Paid AB) if GW (ON A) Reams! ee Te ET) One of the simplest cases that can be considered is that of a plate, bounded by infinite planes parallel to wy, and so heated that 0 is a function of z only. If, further, 0 be sym- metrical with respect to the middle surface, the plate will remain unbent; and if the mean value of @ be zero, the various. plane sections will remain unextended. Assuming, therefore, that u, v vanish while w is variable, we get from (3) and (4) dw . 1 Pal se alee TO ig a ok oie gh SNS a0e sy Re. ae CO) In (8) R is assumed to vanish, since no force is supposed to act upon the faces. From (8), (9) cepy ee aie Pi — LET GA Karis died (11) If the plate be examined in the polariscope by light tra- versing it in the direction of y, the double refraction, de- pending upon the difference between R and P, of which the former is zero, is represented simply by (11). Dark bars will be seen at places where @=0. If the direction of the light be across the plate, z.e. parallel to z, there is no ten- dency to double refraction, since everywhere P=Q. in the above example where every layer parallel to zy remains unextended, the local alteration of temperature pro- duces its full effect. But in general the circumstances are such that the plate is able to relieve itself to a considerable extent. A uniform elevation of temperature, for instance, - would entail no stress. And again, a uniform temperature gradient, such as wouid finally establish itself if the two surfaces of the plate were kept at fixed temperatures, is com- pensated by bending and entails no stress. In such cases before calculating the stress by (11) we must throw out the mean value of @ so as to make | Pdz=0, and also such a term proportional to tne distance from the middle surface as Ne 2 172 Lord Rayleigh on Stresses in Solid Bodies due to unequal shall ensure that Be dz=0. Otherwise the edges of the plate could not be regarded as free from imposed stress in the form of a force or couple. The assumption in (1), (2) that u=v=0 is now replaced by u=(a+82)2, V=@+ B2)y) ae eee and wow —tB(2+y7),... 28 See where w’ is a function of z only. We find R= (A +2p) 2 +2r(a + Be)—8, . «oan / P=Q=aot + (20+ 2u)(a+8z)—yO, (14) S=TSU=00« os re Since R is supposed to vanish, we get pega wer [=e — 6]. ae K In (16) a and £ are to be determined by the conditions \Wde 0: Ped: 07 or, which comes to the same, we are to reject from @ such linear terms as will leave \0dz=0,\. \Ozdz=0, \. 2s aero Since w! and @ are independent of wz and y, the equations of equilibrium (5) are satisfied. It is of interest to trace the influence of time upon the double refraction of the heated plate when light passes through it edgeways, e. g. parallel to y. Initially @ may be supposed to be an arbitrary function of z, while the faces of the plate, say at 0 and c, are maintained at given temperatures. Ulti- | mately the distribution of temperature is expressed by a linear function of z, say H’+ Kez; .and, as is known from Fourier’s theory, the distribution at time t may be expressed by @=H’+ Ket SA,e-'sn——, oe are C where n is an integer and p,, depending also upon the con- ductivity, is proportional to n*, After a moderate interval Heating and on Double Refraction resulting therefrom. 173 the terms corresponding to the higher values of n become unimportant. In the subsequent calculation it is convenient to tike the origin of z in the middle surface, instead of as in (18) at one of the faces. Thus O=H+4+Kz+ Ayen*i" cos — Ase Pst cos oF 4. oe: We Tce at him — A,e—P2 Sean A3e- -st( cos + m=) OT — Ase -tat( sin = ane *<) + A,e- et( sin = z Ba . (20) c Y dee After a moderate time the term in A, usually acquires the preponderance, and then @’=0 when cos (7z/c)=2/m7. When the plate is looked at edgeways in the polariscope, dark bars are seen where z= +°280c, c being the whole thickness of the plate. As a particular case of (19), (20) let us suppose that the distribution of temperature is symmetrical, or that K vanishes as well as the coefficients of even suffix A,, Ay, &e. Hi then represents the temperature at which the two taces are maintained, and (19) reduces to O=H + Aye-Pi¥ cos “- —Age7Ps" cos ae ym Cale) If we suppose further that the initial iemperature is uniform and equal to ©, we find by Fourier’s methods 4 4 4 A\=-(®-H), A=; (@-H), A=- (0-H), and Bee (4) LS carat oe ee ir =) eee DME ch 2 a @L Ee“ PA (cos Fit rea Hi (cos + 5) Dine oe a2 p77 Pst S — ___ sj —— ee (cos 6 =) (23) where also ope Ps=25 M1, Oday toe zs) 174 Lord Rayleigh on Stresses in Solid Bodies due to unequal At the middle surface, where z=0, the right-hand member of (23) becomes emt(1— 2) —Jortmt(1 + 2). 2. Oa Initially 1 2 1 if (25) 1-54 oo. -(l+pt+pt ) a Da } Loe Boe as was required. If we pute-?'=T, (25) may be written 9D 2 " 2 aca era AN 4728 (4 2 eee r( ) yT(14 5 )+4r (1 5 ) 22% 3 (2G) and (26) may be tabulated as a function of T, and thence of ¢. It vanishes when T=1 and when T=0. The maximum value occurs when T='747. When T is less than this, which cor- responds to an increased value of ¢, only the first two or three terms in (26) need be regarded. The above value of T gives Pit = Fae) 24 3 and if, as for glass, the diffusivity for heat in C.G.s. measure be 004, we get 2926 0047?) Thus if a plate of glass be one centimetre thick, so that c=1, the light seen in the polariscope at the centre of the thickness is a maximum about 74 seconds after heat is applied to the faces. The following small table will give an idea of the relation betweev (26) and T. (27) T. (26). T. (26). 0-0 0:0000 0:6 | 02139 01 0:0363 0-7 0-2381 0-2 0:0727 0:8 0:2371 0:3 01090 | 09 0°1823 0-4 0:1453 1-0 0:0000 a O8 0:1809 In his paper above referred to Ilopkinson considered the strains produced by unequal heating in a spherical mass, Heating and on Double Refraction resulting therefrom. 175 under the supposition that the temperature was everywhere the same at the same distance from the centre. A similar analysis applies in the two-dimensional problem, which is of greater interest from the present point of view. We suppose that everything is symmetrical with respect to an axis, taken as axis of z, and that @ is a function of r, equal to (a? +4’), only. The displacements in the directions of z and r will be denoted by w and u ; in the third direction, perpendicular to z and r, there is supposed to be no displacement. We may commence with the strictly two-dimensional case where w=0 throughout. This implies a stress R whose magnitude is given by du in which du. u ; dr + Pp ° ° . e ° e ° (29) represents the dilatation. The other principal stresses operative radially and tan- gentially are dl P=(A+2u) 7 + —— 9, 0 Bo) li | A Q=r—- +(A+2)=—y8 . . - (81) “The equation of equilibrium, analogous to (5), is obtained by considering the stresses operative upon the polar element of area. It is ES (aan) i, tele CS) Substituting from (30), (81), we get du ldu iu y 0 dr ‘+ dr Tr? X+ 2 ar so that au, + U V0 pane 2 by Sg et te aie ye IO SES dr 2 yr A+2Qpy alae (33) where « is an arbitrary constant. Integrating a second time we find TU = S| Ae dialars OM RUN ek 3054) SD xc ence 176 Lord Rayleigh on Stresses in Solid Bodies due to unequal in which, however, @ must vanish, if the cylinder is complete through r=0. From (84) 1 P=(A+p)a— ane 5 | Oran, 2 oh ae N+ 2p r? 6-04 pat eed, Ve be A+2u 7 Jo A+ Zp’ and | a af ee = P— = ads 2 \‘erar }. Sk SoRie (37) It is on (P—Q) that - double refraction depends when light traverses the cylinder in a direction parallel to its axis. “Th (35), (36) ar) en 2 | Ordr 0 represents the mean temperature (above the standard) of the solid cylinder of radius 7. It is to be remarked that the double refraction of the ray at v is independent of the values of @ beyond r, and also of any boundary-pressure. If @ increases (or decreases) continuously from the centre out- wards, the double refraction never vanishes, and no dark circle is seen in the polariscope. In the above solution if the cylinder is terminated by flat faces, we must imagine suitable forces R, given by (28), to be operative over the faces. The integral of these forces may be reduced to zero by allowing a suitable expansion parallel to the axis. Regarding dw/dz as a constant (not necessarily zero), independent of 7 and z, we have in place of (28) R=a(f 4") + + 42p) 2 98. eS) The additions to P and Q are A dw/dz, while (P—Q) remains unchanged. If the cylinder is long relatively to its diameter, the last state of things may be supposed to remain approximately unchanged, even though the terminal faces be free from applied ‘force. In the neighbourhood of the ends there will be local disturbances, requiring a more elaborate analysis for their calculation, but the simple solution will apply to the greater part of the length. The case of a thin plate whose faces are everywhere free from applied force is more difficult to treat in a rigorous manner, but the following is probably a sufficient account of Heating and on Double Refraction resulting therefrom. 117 the matter. By supposing R=0 in (88) we get Chip ep du ==). 27x as rx an Z In this position the reflector is distant : from the oscillator. This is in accord with experiment, and justifies the assumption of a change of phase of 180° by the reflexion. This phase- change is given by Hertz’s theory. * The —7 is introduced: to take account of the change of phase by reflexion. Its meaning is clear in what follows. 194 _Mr. G. Pierce on Indices of The amplitude of the first maximum enables us to determine k. Forex= ) I= (14+%?+2kh) . f(a) = (EEO 5 (a) Say (2) (experiment). Whence (1+ h)?= 3, (mallee The square of this & is the coefficient of reflexion of copper for norma! incidence. With this approximation, other maxima are seen to be at v=3r/2, DA/2, ..-.5. and minima at 2=A2Naeo eee Hence the value of « that gives maxima and minima is independent of &, and in the experiments on indices of refraction, if observations are made on nodes and loops whose double distance from the oscillator can be neglected in com- parison with a, absorption by the medium would not introduce error into the value obtained for the index of refraction. Returning to the general case, let us solve equation (1) for maxima and minima, by differentiating I with respect to w und equating to zero. The derivative of f(7) with respect to r is denoted by /f'(7). DIN? 2G @) of Ca) — 2h. f(a) .f(at+2). cos — + 2k. f(a) .f(at+2) ‘gin ee NS = (). 27x 2X eS he 2a os) Fata) Ne 2a aa) r ey) ‘ which may be written briefly sin @ = A coz 6--B, Whence sin where 27x Pie Seay _ xX f@te2) ~ Yar f (a+a)’ ute l t'(at a) Zan a) B Refraction for Electric Waves. UG: Solving, 3 1— cos? 6= A? cos? 6—2AB cos 6 + B’; (A2+1) cos? @—2AB cos €=1—B’; 2g 2AB 36 A?B? ee ae OSS a rn ai Ea De a A?+1 (A?+1)? pees eee aly tor (ae De AB 1 cos = meen ae | VO —-p 1. As a step tow rard amore general treatment of this equation, let us investigate the case ahoce fo ae fi (r)=—1/r. then We should have Whence it is seen that in our iparticular problem where ‘\=4-4, and a=18, ‘ dul Se il 2 S |) A” is less than = (8) which is negligible in comparison with unity. B? is less than A? and is also negligible in comparison with unity, cosO@=AB+1. But AB is less than A® and may be neglected in com- parison with unity ; cos 0@= +1, ora i itis Pe p ? nr C= 9? j where n is any integer. 196 Mr. G. Pierce on Indices of This is a solution of the equation of condition for maximum or minimum, with an error in cos @ not greater than ‘0013. cos 0 = + (1—:00138), 0 =n7 +°05, a8 =n +05, : _nr “0dr tae at 20 mr = — + Joo, centim. The last term, making a difference of less than + millim. in the value of 5 is negligible. Coming now to the general case, let us assume f(r) any function of rv, analytic everywhere outside of a small cylinder about the oscillator, and of which all the derivatives exist. Let 7(r) vanish at infinity to such an order that r./(*) is finite—an assumption suggested by the fact that the rate of propagation of energy through any closed surface about the oscillator is finite. Then we can expand /(7) in the form of « descending power series with undetermined coefficients, thus Gn 5 Gy 4) © Ba Ds LT Y i 7(r)= Differentiating term by term (assuming the proper con- vergence of the series), we have Whence where 7 is written for (a+). Whether or not this expression squared is negligible in comparison with unity depends on the values of the co- efficients c. Theoretically, 7(7) can be obtained as an integral, from Hertz’s equations and the elementary theory Refraction for Electric Waves. 199 of the composition of waves. This integral I have not been able to treat, so I have attempted to obtain empirically the coefficients ¢ with sufficient approximation for the problem under consideration. With the oscillator at various distances from the resonator (r, in the following table) relative intensities at the resonator were measured by the relative deflexions of the instrument. These are placed in the second column of the table. The square-roots of the relative intensities give /(r)//(a), which are placed in the third column of the table. Hquations were then formed on the assumption that terms of f(r) after the fourth vanish, and four coetticients obtained. They are G=2 10, C2 le (Eps 11) C4= —°83. With these values of the coefficients, /(r)//(a) is calculated for the several values of 7, and placed for comparison in the fourth column of the table. | | r. I/I obs. S(r)/flajobs. | f(r)/f(a) eale. | 13 1:93 1:39 1:27 15:5 1-23 11 evi 18 1-00 1:00 101 20°5 "86 ‘93 92 23 69 "82 86 25°5 62 “78) 79 28 | 51 ell 74 30°5 | AT ‘69 66 33 | 46 ‘68 65 It is seen that within the range actually employed in the experiments on indices of refraction (r=18 to r=380), the agreement between the observed and calculated values of 7(r)/7(a) is close enough to show that no large terms in the series occur after the fourth. Employing these experimental values of the c’s we can form an estimate of the size of A and B for any value of r. For example, when r= 18, fee boot n6-F1- 00 = "32. 44 1 60) 2m 13 1538-784 °34—-03 ~ 623° 18° 100" Hora —s5o: XM 1:°83—"464+1-65—-024 44 1 ‘dil 2a 33°83 —"23 +°055—-006 ~ 628° 33699" For both these values of r, and for all intermediate —— A=— 198 Prof. Townsend on the Conductivity produced in values of 7, the square of A is seen to be negligible in com- parison with unity. | Now B is less than A, for & is less than 1, and a+a is greater than a. Hence, B? and AB are negligible in com- parison with 1, and our equation for maximum and minimum reduces to the form 27x CS in > ap i. whence mr t= 7) ; where m is any integer, Whence it follows that with the arrangement of apparatus adopted in the experiment on stationary wave and index of refraction, the diminished amplitude of the reflected wave and the absorption by the dielectric placed between the oscillator and the reflector could have no appreciable effect on the position of the maxima and minima. Jefferson Physical Laboratory, Harvard University, Cambridge, Mass. XVII. The Conductivity produced in Gases by the Motion of Negatively charged Ions. By Joun S. TownseEnp, .A., Wykeham Professor of Physics, Oxford*. i. iia a paper published in ‘ Nature,’ vol. lxii. August 9th, 1900, I gave a brief description of some experiments Which showed that negatively charged ions, moving through a gas, produce other ions, although the torce acting on them is very small compared w vith the force necessary to produce the ordinary vacuum-tube or spark-discharges. The present paper contains a more complete account of the principal experiments and also some investigations founded on the theory to-which I have been led by the experimental results, Tn all the experiments with which we are here concerned, a number of ions are generated in the gas by some external source, such as Rontgen or Becquerel rays. The nature of the conductivity produced by these rays has been investigated by several physicists, and it has been generally concluded that when the electric force is increased, the conductivity approaches a maximum. ‘Thus, in the paper t published on this subject by Professors J. J. Thomson and E. Ruthertord, it is stated that “for a given intensity of radiation, the * Communicated by the Author. + Prof. J. J. Thomson and Mr. Rutherford, Phil. Mag. Noy. 1896. Gases by the Motion of ‘Negatively charged Ions. 199 current through the gas does not exceed a certain maximum value whatever the electromotive force may be.” ‘Numerous experiments have also been made with electrodes of various shapes, and it was found that the conductivity is not altered when the electromotive force is reversed. From the experiments which are described in the present paper, it will be seen that the relation between current and electromotive force is not characterized by either of these properties when the conductivity 1s produced in a gas ata low pressure. ‘There is no critical pressure or force at which discontiguity occurs; but, as the pressure is reduced, the connexion between current and electromotive force gradually loses the simple properties which hold at high pressures. At low pressures the current may be considered to pass through three stages as the electromotive force is increased. In the first stage, ‘the current increases with the electromotive force ; in the second stage, the current remains practically constant and shows only ‘small variations for comparatively large changes in the force ; in the third stage, the current rapidly increases with the electromotive force. Also, for certain shapes of electrodes, a great difference can be produced in the conductivity by reversing the electromotive force. This is particularly noticeable “when the current passes between two electrodes, one of which surrounds the other; but when parallel plates are used, the conductivity shows only slight alterations when the direction of the current is changed. In the latter case there would be no alteration whatsoever if the two plates were made of the same metal. We shall therefore begin by describing the nature of the conductivity between two parallel plates 1 when the gas between them is at a low pressure. 2. ‘The apparatus used for the investigation is shown in fig. 1 (p. 200), and consists of two parallel plates inside an air-tight vessel connected toa Topler pump. The lower plate A was a thick sheet of zine with a circular window W which was covered with a dise of thinaluminium. The junction between the aluminium and the zine was sealed with elastic glue, so as to make the joint air-tight. A sheet of aluminium foil was stretched over the surface of the zine plate so that a plane face should be presented to the movable brass plate B. The tube T, by which the vessel was exhausted, was soldered to the back of the brass plate. The brass plate B was 10 centimetres in diameter, and the circular aperture W was 4 centimetres in diameter. The neck of the glass covering C was closed with an 200 Prof. Townsend on the Conductivity produced in ebonite plug through which a brass tube U was passed, and the junction between the tube and the ebonite was made air- tight. The tube T fitted exactly into the tube U and could be moved up and down in it; by this means the distance Fis. 1. T 3 between the two plates A and B could be varied, and a scale S ruled on the tube T gave a means of determining the distance between the plates. A piece of rubber tubing was put over the upper end of the tube U, so as to prevent air getiing into the apparatus between the two tubes. _ The pressure of the gas inside the apparatus was found by a Macleod gauge. The electrical connexions were made in the usual manner. The zine plate A, which was supported on ebonite legs, was Gases by the Motion of Negatively charged Ions. 201 connected to one terminal of a battery of lead cells, the other terminal of which was connected to earth. The upper plate B was connected by the:tube 'I to one pair of quadrants of an electrometer, the other pair of quadrants and the ease being connected to earth. The wire joining the tube T to the quadrants passed along the centre of brass tubing which was connected to earth, and thus formed a screen for the wire. Strips of tinfoil were gummed round the glass vessel C both on the inside and the outside, and were kept at zero potential by means of earth connexions. The lower edges of the bands were within 2 centimetres of the zinc plate, so that no charge could leak trom tae plate A over the surface of the glass and influence the potential of the upper plate and the tube T. The ebonite legs supporting the apparatus rested on a box, covered with lead, containing a Rontgen-ray focus-bulb, and a Ruhmkorff coil. A circular hole was cut in the lead covering, and the bulb was placed so that the platinum anode should be vertically under the centre of the aperture. The direct rays traversed the space between the two plates, above the aluminium window; and the insulated disc B, which was of thick brass, prevented the radiation from penetrating into the upper part of the apparatus. At the sume time the brass plate gave out a secondary radiation which increased considerably the ionization between the plates. 3. The experiments were conducted in the following manner. The wire connecting the upper plate to the quadrants was put to earth and the lower plate was raised to the required potential ; the upper plate was then insulated. The deflexion on the electrometer-scale, produced when the rays were acting for 10 seconds, was observed. The electrometer showed no leak until the bulb was excited; and after the rays were stopped, the electrometer reading remained perfectly steady, showing that the current between the plates does not continue after the rays have ceased to act. The connexion between current and electric force was thus obtained for five different pressares, and the numbers - obtained are represented graphically by the accompanying curves, figs. 2, 3, 4, 5, and 6. The current between the plates varies slightly, in magnitude, on reversing the electro- motive force. The mean of the two currents obtained by reversing the electromctive force is represented by the curves. The ditterence in conductivity is generally small and could have been avoided by using two aluminium plates; but the advantage thus gained would not compensate for the joss Phil. Mag. 8. 6. Vol. 1. No. 2. Feb. 1901. P 202. ~=Prof. Townsend on the Conductivity produced in of conductivity arising from the larze secondary effect due to the brass. In Section 9, an account is given of the effect produced by reversing the electromotive force between the plates. Fig. 2.—Pressure 4:13 mm. 480 Current. 200 80 160 240 3820 400 480 560 640 720 Volts per centimetre. Three seis of observations were made at each pressure for distances of *5, 1, and 2 centimetres between the plates. The curvee corresponding to these distances are marked °5, 1, Gases by the Motion of Negatively charged Tons. 203 and 2, respectively. The forces X are given in volts per centimetre [(potential of A) + (distance between the plates) ]. The unit of current is 1*410- amperes. The curves have Current. Fig. 3.—Pressure 2°12 millim. : ee ee ie ye an ea : anal Oe Volts per centimetre. not been traced back to the origin, as we are at present only coneerned with the connexion between current and electric foree when the potential-difference between the electrodes P2 204 Prof. Townsend on the Conductivity produced in exceeds 10 or 20 volts. The curves show that the current increases, sometimes very rapidly, after the second stage (to which I have referred) is passed. ig. 4.—Pressure 1:10 mm. i Coe 320 Bis at ieee ‘ F Bae Hes Current. 00 160 120 80 40 80 160 240 320 400 480 560 640 720 Volts per centimetre. These experimental results are completely accounted for if we consider that all ions produced by the rays, including the secondary rays, are collected on the electrodes when the electromotive force is small oe the current independent, . Gases by the Motion of Negatively charged Ions. 205 practically, of the electromotive force ; and that the negative ions produce others by collisions with the molecules of the gas when the electric force is increased, the new negative ions thus produced having the same property as the negative ions produced initially by the rays. Fig. 5.— Pressure ‘332 mm. Current. 80 160 240 320 400 480 560 640 720 Volts per centimetre. If both positive and negative ions produced others by collisions with the molecules, it is evident that the current 206 Prof. Townsend on the Conductivity produced in would not cease when the rays are stopped. We must therefore attribute the increase in conductivity to ions of one kind; and it can be clearly shown from experiments with one electrode inside the other, that it is the negative ions which produce the large increases in conductivity. Fig. 6.—Pressure ‘171 mm. aaa 220 200 180 Current, 20 80 160 240 320 400 480 . 560 640 720 Volts per centimetre. 4. The first step towards an explanation of these results is to find trom the curves the number, a, of ions of one kind that a single negative ion will generate in moving under an electric force through a centimetre of the gas. The number of positive ions which are generated is equal to the number of negative ions, so that in what follows we need consider only the negative ions ; it being understood that when a negative ion is produced, a positive ion is also produced. Let a force X be applied to N, negative ions in a gas at pressure » and temperature ¢. Let N be the total number of negative ions after the No ions have travelled u distance #, Gases by the Motion of Negatively charged Ions. 207. The new negative ions travel with the same velocity as the original N, ions, so that all the negative ions will be found together during the motion. The number of negative ions produced by N ions travelling through a distance dv will be aNdzx; where @ is a constant depending on X, p, and ¢. Then i adN=aNdz. Hence N= Nije7 e . ° * e e e (1) Let nol negative ions be distributed uniformly between two plates at a distance / apart, and let the force X be applied to them. The number of ions C that arrive at the positive plate is 1 o=| nye da = fs) (e**—1), 0 a and the ratio of this number to the original number is C 1 al fal = a (€ — i): Hence if Cy denotes the number of negative ions produced by the primary and secondary rays the total current in the gas is = S(et_1), baa ia esl ae) C, the current when no ions are being produced by collisions, is represented in each curve by the (y) ordinate at the point where the tangent to the curve is practically parallel to the axis of X, Hence the ratio if is a function of /; and by making simple 0 calculations it can be shown that equation (2) completely explains the relative shapes of the three curves in each diagram. The value of a can be found by substituting the experimentally determined ratio, = and distance between the plates / in equation (2). 8 The small values of a are determined, most accurately, from the curves corresponding to /=2; but in the following tables some uf the values have been obtained from two curves, and the agreement between these numbers shows that the effect of separating the plates is completely explained by the theory. The tables give the values of a for different forces X:; the determinations made from curves corresponding to distances between the plates of 2, 1, and °5 centimetre are given in the second, third, and fourth columns respectively. A separate table is given for each pressure. 208 Prof. Townsend on the Conductivity produced in TABLE I, TABLE II. Pressure 4°13 millims. Pressure 2:12 millims. its ne Pus =isp | Caleu- ue re Callie Me PSB, | 1) et5. | 8 |) | eee 120) 3-13 eae no "135 80} °13 a3 ee 14 160} -28 30 aus ll 120| -42 “40 an "44 200; °5O bl 160! -:90 ‘90 ae ‘91 240 ae "99 ae "95 200 ae 1:60 320 sa 2°1 2 Nale9'5 240 1: 2°39 9:35 | 2:4 , 400 3°6 36 SLOT: 4] 40 4:2 480 53 =| 5:0 400| ... ee 6:6 560 fel) ASO ee ve 78 8:0 640 89 |8-7 HAO. 9-4 L | |640 168 |113 TABLE ITI, | TABLE LV. Pressure 1°10 millim. Pressure °385 millim. | | | ee zit _.¢ | Caleu- Pe ts _.p | Caleu- X. | d=25) l=1. | l=". nea: Xe) 7=25) aS ee inte 80| °45 wen fe “44 40| -34 35 120} 1:11 19 ak 1:20 80) 1:3 13 160 | 2°02 1:98 a 2:05 170 | 2:0 iE ZOO) hs: 23 | ; 160} 2:8 29 2°9 2°8 UA) Pg Bicol 4:0 4:0 200 vas 34 34 a2Oi iene 54 5:5 Dai ZAO WS ce 38 38 39 400 a aie 6:8 SMe oe Lis 4:5 4°5 480| ... ee 80 8:5 AGO tae ree 50 HOON, Bua ie 9-3 480 ah 54 53 G40) 2 aie 10°6 | 10°5 560 58 ding 640 62 | 58 TABLE V. Pressure *171 millim. fe atk ne Caleu- X. aa eat | peo). cal 20 “24 40 65 Ss 66 80 | 1:35 | 1:36 hay 120 | 18 GON | 2:25 aa 2:1 al 240 en 2°45 xa 2°4 320 tae 2-69) te, 2°6 480 Bee yh 3:15 2°8 640 at nee 3°25 30 The numbers in the fifth columns of these tables were calculated by the method explained in Section 7. Gases by the Motion of Negatively charged Ions. 209 5. We may now proceed to investigate the relation connect- ing a, p, and X, the temperature being constant. Let v be the velocity acquired by an ion in travelling freely between two points differig in potential by P (volts). Let ¢ be the charge on an ion, and m its mass. Then : ee a as Reale) 2 300 Let n be the number of molecules ina c.c. ofa gas at atmo- spheric pressure (10° in c.G.s. units.), and temperature 20° C. (which was about the mean temperature at which the experi- ments were made), and w the mean velocity of agitation of a particle of mass 7 immersed in a gas at temperature 20°. The velocity wu is given by the equation SMa tie LOLS cae yeaa ah (AS) Hence from equations (3) and (4) we obtain GU In ose: 3 -_= 9 OG = Dole se) U since Gee MeO! qe aoee Hence the velocity acquired by an ion in travelling freely between two points differing in potential by 4 volts, is ten times as great as its velocity of agitation at ordinary tem- peratures. This result is independent of the mass of the jon. Under the circumstances with which we are dealing, there is a remarkable difference between the positive and negative ions. The latter produce new ions when moving in a field of force which is too small to maintain a continuous discharge. It is therefore reasonable to suppose that the negative ions with which we are dealing are the same as the negatively charged particles which are given off when ultra-violet light falls on a zine plate. It has been shown by Professor Thomson that the mass of these particles is 51, of the mass of a molecule of hydrogen t. Becquerel and Curie have also shown that the radiation emitted by radium is composed of similar corpuscies. lt seems probable in the present case also that the negative ions are very small, and that the positive ions differ little from ordinary molecules as far as their mass is concerned. lf we adopt this view, it is easy to see that the velocity of * John 8. Townsend, Phil. Trans. vol. exciii. 1899. t J. J. Thomson, Phil. Mag. vol. xlviii. Dec. 1899. 210 Prof. Townsend on the Conductivity produced in agitation of the negative ions is 80 times the velocity of agitation of the molecules of air; and the velocity acquired by an ion in travelling between two points differing in potential by 4 volts would be 800 times the velocity of agitation of the molecules of air. The latter velocity is therefore so small in comparison with the velocities of the negative ions, that it may be neglected, and the molecules of the air may be con- sidered to be at rest. Let us now consider what happens when an ion is con- strained to move with a fixed velocity (greater than its velocity of agitation) through a gas at pressure p. ‘The number of collisions that the ion makes with molecules of the gas in going through a centimetre is independent of the velocity and is proportional to the pressure. Let Bp denote the number of collisions ; then — will be the length of the mean free path, expressed in centimetres. According to our theory, the new ions are produced by collision, and if the velocity with which the ion is constrained to move is suffi- ciently great, it will produce Bp new negative ions and an equal number of positive ions, in going through one centi- metre of the gas. Since the collisions are not all of the same kind, an arbitrary velocity of the ion might be sufficient to produce ions on some occasions without producing the maximum number (8p). We would expect, therefore, that there is not a fixed minimum velocity of impact necessary to produce ions, but the greater the velocity, the nearer wiil the number of new ions produced approach the value Gp. Using these principles as a basis for our theory, we may proceed in the following manner to find an expression for a in terms of X and p. 6. The free paths described by an ion as it moves through a gas will not be all of equal length. Out of y paths the number which exceed the length x is Ye ¢, where ¢ is the mean free path. In going along a centimetre an ion has Bp free paths, so that the number of paths which exceed the length wx is Bper*, | The number of paths intermediate between wx, and 2, 1s Bp (e— P71 — eqire2)s Let Ip be the velocity acquired by an ion in travelling Gases by the Motion of Negatevely charyed Ions. 211 freely between two points differing in potential by P volts. Let a,x X=P and 2, x X=Q, X being the force acting on the gas. . Then the number of times that an ion collides, with velocities intermediate between Ip and Ig, in going through one centimetre is ea ‘ eae rlG) assuming that after a collision the velocity of the ion is small compared with its velocity before collision. (This assumption would not be legitimate for very large velocities of impact, but the hypothesis may he applied to the velocities with which we are dealing, and leads to simple analysis.) If the potential P is large, then, aczording to our theory, a pair of new ions will be formed at each of these collisions, but when P is small (about 10 or 20 volts) new ions will only be made on some of the more favourable occasions. Let Bp be the number of negative ions formed in # collisions when the velocity of impact is between Ip and I p41. Then BpP __ Bp(P +1) a=p 3 Bp (e * -e - Je oe Cs) The maximum value that any of the coefficients 8p can have is B. Equation (7) can be expressed in the more general form : =s(5)s 5 OE OS ee and if no restriction is placed on the form of the function /, it is not necessary to assume that the velocity of the ion is small after impact. We can test whether the values of a which we have deter- Hoe can be expressed by means of an equation of this orm. If we plot a curve for each pressure, taking as coordinates a ° ° e ‘ ~ and —, the five curves should coincide, since they have T] each the same equation (8). The points on the accompanying diagrams which are marked 1, 2, 3, 4, and 5, have as coordinates the values of E aud 7, deduced from Tables I., IT., III., IV., and V. respec- tively. Me ; 124-3 212 ~— Prof. Townsend on thé Conductivity produced in As the variables extend over large ranges, the points are given on two diagrams, figs. 7 ral 8; one for values of Soe than 320, and the other on a different scale for the larger values of the variables. The positions of the points on the diagrams show clearly that they all lie on the same curve, so that ine results of the experiments confirm the result to which we have been led by theoretical considerations, AECL SRaaeantanse | SEPZeeeeeee 60 80 100 120 140 160 180 200 220 240 260 280 300 X=p. The problem of determining a in terms of p and X is therefore considerably simplified; a0 the three variables a, x p, and X have been reduced to two: ~ and = Before we proceed to determine the coefficients in equation 7 we may here mention an interesting ‘geometrical property of the curve (fig. 8). 320 Gases by the Motion of Negatively charged Ions. <0 © = MM F'O! * @ oan = 2 os Hb k ro) = i) 213 214 = Prof. Townsend on the Conductivity produced in When X is constant, there evidently exists a certain pressure for which @ is a maximum: if p is large no new ions will be formed since the original ions never acquire a large velocity, and if p is very small there will be too few collisions to allow of a large value of a. The value of p for which @ is a maximum is obtained by differentiating the equation, X “= #5} with respect to p. We thus obtain the following equation to determine p in terms of X :— i(2)-27)=0. ioe Sen Since this equation involves X, and p, in the form x , we conclude that for a given value of X the value of p which gives the maximum value of « is proportional to X. The value of as which satisfies equation (9) can be obtained immediately from the curve in fig. 8. aa Xx Bes da | an ee Substituting X, for pe for FS) and ax for AG in equation 9, we obtain This relation between the coordinates of a point on a curve [a,=7(%1)] shows that the tangent at the point passes through the origin. X Hence in order to find the value of — which satisfies equation (9) it is only necessary to draw a tangent to the curve from the origin, and find the abscissa of the point of contact. xX The value of — thus obtained is 380. Hence the value of e e e e e e oe xX p in millimetres for which ais a maximum is 580" where X is expressed in volts per centimetre. The corresponding value of @ 1s. 66x & 380 7. Having established the general relation obtained in = ‘0174 X. Gases by the Motion of Negatively charged Ions. 215 equation 8, we may simplify the notation by using a and X, for ~ and —. The new variables denote the values of a and X when the pressure is one millimetre. When X, is greater than 400, the tangent to the curve fig. 7 tends to become parallel to the axis of « when a, is increased. This shows that the value of «, approaches a maximum for large forces. The greatest value of a, as obtained from the experiments at ‘171 millim. pressure is 19. When this value is reached, the increments of a for large increases of force are small, so that the number of collisions 8 cannot much exceed this value. In order to represent the curve by an equation similar to equation 7,in which the coefficients Bp are less than 8, it was found necessary to take 8=21, which, as we have seen, must be about the correct value. For the purpose of getting an expression for a, in terms of X, which will agree approximately with the experimental curve, we shall take seven terms in the expansion of a, When the velocity of the ion on impactis less than I;, the probability of producing an ion is very small, The number of ions formed by cvllisions in which the velocity is less than I, may be neglected. Letting p=1 we see from equation (6), Section 6, that the number of impacts per centimetre in which the velocity ef the ion is intermediate between I, and Ti 18 (fo) Let 0b, be the average number of new negative ions generated by a single ion in going one centimetre with a velocity intermediate between I, and I;. Tne total number of collisions will be 8 in this case. Hence when the ion is moving under an electromotive force X,, the number of new ions produced by collisions in which the velocity of impact is intermediate between I, and I, is FT om ie b,(¢ ue"), Hence a can be expressed by the sum of terms :— fe _5B 5B 108 af Y, Pale Ei) 4 &e. (10) 216 Prof. Townsend on the Conductivity produced in In order to obtain values of @ for the range of forces that, has been used, it is necessary to find 7 coefficients in equation (10). When @ is taken equal to 21, the coefficients so found will be less than 8, and, according to the theory, it is neces- sary that the coefficients should satisfy this condition. _ When the following values of 6 are substituted in (10), the equation will represent very accurately the curve through the points in figs. 7 and 8. b,= 03 when the velocity of impact is intermediate between I, and I, b= a) ” ” 5) gi Ii Da—eae ” 2 Tio ” Ls b= 90 ” ” Dis jeueleo b = 13-0 9 ” 20 99 I, 5 0,=16°0 a) r) 4195 9 T50 b,= 20-0 for velocities over Is, The values of a have been calculated for the different pressures from equation (10), by replacing 3 and s for a and X,, and taking the above values of the coefficients. The results are given in the fifth column of the tables in Section 4. We have thus obtained results which enable us to find approximately the number of ions that would be generated by a single ion in moving through a gas with a fixed velocity. The maximum number is 21 x p per centimetre, which corre- sponds to large velocities. The number is 13x p when the velocity is about I,., and for velocities of the order I; the number is comparatively small. 8. The mean free path which we have deduced can be shown to agree with what we should expect from physical considerations of a more familiar kind. re The mean free path of a molecule of air at pressure 760 mm. and temperature 0° C., is * 0°96 x 10-° centim. We may therefore take the mean free path in air at 20° C. to be 1:03 x 105°. The free path here has not quite the same meaning as the free path that we have been considering—that of an ion travelling through a gas supposed to beat rest. The formula used in finding the mean free path from the coefficients of viscosity takes into account the fact that all the molecules are in motion. The collisions that a single molecule would make with other molecules would be less frequent if the * Meyer, Kinetic Theory of Gases, Gases by ihe Motion of Negatively charged Ions, 217 latter were at rest. The mean free path of a molecule travelling in an atmosphere in which the molecules are at rest would be greater in the ratio ,/2=1°41 than the free path when all the molecules are moving with their velocities of agitation *. We therefore conclude that a molecule of air moving with a great velocity through a centimetre of air at 1 millimetre pressure would make 90°7 collisions. An ion under similar circumstances makes 21 collisions. Hence the ratio of the free paths is 43:1. This bears out the conclusion to which we were led from other considera- tions, that the negative ion is small compared with a molecule. If we disregard the charge on the ion and con- sider that it is a material particle whose dimensions are small compared with those of a molecule, its free path would be four times the free path of a molecule. The ratio which we have obtained 4°3 : 1 shows that the number of collisions made by an ion, estimated according to the theory of vis- cosity of gases, would be 7 per cent. greater than the number of collisions in which it is possibie for new ions to be formed. Let 2S be the distance between the centres of two mole- cules of air when a collision ocsurs, and let d be the dis- tance between the centre of a molecule and the centre of an ion when new ions are formed. Then LSe aes Fe areal Hence = -96 Sa It is usual te assume that S is the radius of the sphere of action which surrounds a molecule, and that the radius of the molecule is much smaller. If we adopt this view, it will be found difficult to explain the results at which we have arrived. It would appear from the above value of d that new ions are made when the original ion comes inside the sphere of action of a molecule, provided that the velocity of the ion is sufficiently great. The effect of a collision under these circumstances ought to diminish as the velocity of the ion is ‘increased ; the experiments, on the contrary, show that the roduction of ions increases as the velocity is increased. It therefore appears from the results of the present experiments that some part of the molecule itself must extend to a distance 8 from the centre, in order that an ion should produce two new lons when d="96 8. * Maxwell, Phil. Mag. xix. (186)). Phil. Mag. 8. 6. Vol. 1. No. 2. £eb. 1901. Q I | 218 Prof. Townsend on the Conductivity produced tn We can find § from the present experiments since it is practically the same as d. The number of collisions made by an ion in going cheoven 2 a centimetre of air at one millimetre pressure is : a 2 7 “= 21 , n being the number of molecules in a c.c. at atmospheric pressure. Taking for n the value 2 x 10, we obtain = OK ls”: I may mention that the mean free path of an ion in air is shorter than its mean free path in hydrogen, but as the experiments with this gas are not yet compieted, I must reserve the account of them for a future paper. The number of ions produced in a gas by a single ion moving rapidly through it could be easily found by another method. Jt has been shown that the char ge on the corpuscles emanating from radium can be measured +t, when a highly active specimen of the substance is used. The ratio of the ionization produced per centimetre of a gas to the charge carried by the corpuscles would give the number of ions pro- duced by each corpuscle in travelling through a centimetre. I have made experiments with a view to finding the above ratio, but the specimen of the radio-active substance at my’ disposal was so weak that it was impossible to detect its charge although a very sensitive method was employed. ‘The ex- periments, however, showed distinctly that each corpuscle in, travelling through a centimetre of air at atmospheric pressure produces at least 10,000 ions. According to the theory which I have described, the number should be 7160: X 2p oe the absorption of the radiation by the gas be neglected. I hope to be able to repeat this investigation with some highly active radium and obtain an accurate result. 9. I have already mentioned that the conductivity be- tween the two parallel plates is altered when the electro- motive force is reversed. The difference between the currents in the two directions is a direct consequence of an effect discovered by Curie and Sagnact. They found that the secondary rays, which are given out when Roéntgen rays fall on a metal, carry a small negative charge. It would therefore appear that the ionization produced by secondary rays is due to charged corpuscles emitted by the metal. The bodies which produce the greatest secondary ionization also emit the largest charges. ‘Thus the brass * John S. Townsend, Phil. Trans. vol. exciii. (1899). + M. P. Curie et Mme. Curie, Comptes Rendus, vol. exxx., 5th Muscle, 1900. t P. Curie et G. Sagnac, Comptes Rendus, vol. exxx., 9th April, 19090, Gases by the Motion of Negatively charged Ions. 219 plate in my experiments gives out more negative corpuscles than the aluminium plate through which the Roéntgen rays pass. The corpuscles emitted by the brass plate have an effect upon the conductivity between the two plates which we shall now proceed to investigate. Let C, be the current when the lower plate is positive, and Cy the current with the same electromotive force when the lower plate is negative. Let D be the number of negative corpuscles emitted from the brass plate, and C the number of ions (positive or nega- tive) produced between the plates in the volume of the gas. Then C= CD, Cs = ce C,+C, 3 oe Hence C = Boer 0 that the correct value of C is ob- tained by taking the arithmetic mean of the two currents. The experiments at ‘171 millim. pressure give C,=7°6, and C,=4°6 when the plates are one centimetre apart and differ in potential by 10 volts. The corresponding numbers for 334 volts are 30 and 27:5. In the experiments at higher pressures the ratio of D to C is smaller. The negative corpuscles D are probably emitted with different velocities, so that when the pressure is increased, some of them are stopped by the gas before they get to the aluminium plate. It is evident from the experiments at °171 inillim. pressure that an electromotive force of 334 volts has little effect in stopping them, since the currents differ by the same amount for high and low potentials. When some of the corpuscles which start with a small velocity are stopped by the air at higher pressures, the equation C,=C—D does not hold accurately, for although D corpuscles start from the plate, some of them are stopped by the gas and driven back to the plate by the electromotive force. In these cases the mean current does not differ much from either of the currents tC : C, or ©, so that the equation C = ts represents with sufficient accuracy the number of ions produced in the volume of the air. At 4:13 millim. pressure C;=37°5 and C,=41°5, when the potential-difference between the plates was 20 volts. ‘The correct value of C probably does not differ from 39°5 by as much as 2 per cent. When the force is increased and larger conductivities are obtained, the ratio of D to C dimin’shes. Q 2 220 Prof. Townsend on the Conductivity produced in The distribution of the ionization produced by the rays between the two plates is not quite uniform, which gives rise to small differences in conductivity when the forces are large. The errors arising from this effect are also eliminated by taking the mean of the two conductivities. The large difference in conductivity which can be obtained by reversing the electromotive force, when one electrode surrounds the other, is not due to either of the causes men- tioned in this section. The explanation of this result is given in Section 12. 10. An estimation of the energy required to ionize a molecule can be deduced from the results obtained in Section 7. When an ion collides with a molecule, two new ions are produced if the velocity before the impact is sufficiently great. It has been shown that new ions are formed when the velocity is equal to I;. The kinetic energy of an ion moving exo =10-" ergs ; and we conclude that 30U the energy required to produce two new ions is not greater than this amount. An estimation of the energy required to ionize a molecule has also been made by Prof. Rutherford *, and he concluded that the energy required was equal to the work done in moving an ionic charge through 175 volts. If this number is correct, we should not have got any definite increase in the conductivity between two plates by increasing the force, until the difference of potential between the plates con- siderably exceeded 175 volts. It would therefore appear from the present experiments that this estimute of the energy is much too large. 11. In the short account of the present theory which was published in ‘ Nature,’ I mentioned that the results obtained by Stoletow +, in connexion with the conductivity produced by ultra-violet light, could be explained on the collision theory. We shall examine these results in detail and show that they all agree with our previous conclusions Stoletow investigated the conductivity between two parallel plates, and found how it varied with the pressure of the air, the distance between the plates, and the electromotive force. The following results were obtained by Stoletow :— 1. When the pressure and force were constant, the con- ductivity Increased with the distance between the plates. with this velocity 1s * KE. Rutherford, Proc. Roy. Soc. vol. Ixvii., 14th Noy. 1900. + Stoletow, Journal de Physique, série 2, vol. ix. Gases by the Motion of Negatively charged Ions. 221 2. When the pressure and distance between the plates were constant, the current increased with the electric force ; at very low pressures the current reached a maximum, and remained constant tor large forces *. 3. When the electric force was constant, the conductivity attained a maximum value for a certain critical pressure, which was accurately proportional to the force and independent of the distance between the plates. If we suppose that a certain number of negative ions are supplied initially by the action of the light on the metal surface, we can explain all these results by the theory which we have been considering. Stoletow’s experiments at low pressures show that the number of ions supplied initially cannot vary much with the pressure. Tora given force the conductivity would therefore be a maximum for the same value of p as makes a a maximum. We see therefore that the third result relative to the critical pressure agrees with the conclusion arrived at in Section 7 relative to the maximum value of a, and moreover a remark- . s < e x able numerical coincidence exists between the value of — for 2 : ; D. a Waleed 4 which # is a maximum, and the value of — which gives the maximum current with ultra-violet light. The following table is given by Stoletow :— H is the electromotive force between the two plates, the unit being the electromotive force of a Clark cell. Lis the distance between the plates in millimetres. p is the pressure for which the current is a maximum. The values of 10! for the different experiments are given in the fourth column. RC. 2 Gnillim:). _p (millim.). £10 ie 165 “25 25°3 333 165 "AT 13°5 384 65 ‘AT od 343 100 *83 4:7 389 65 833 30 385 60 83 2°5 386 63 aoe 1°3 352 65 371 67 382 40) 3°60 “43 BCT * This corresponds to the results obtained at ‘171 millim. pressure, as can be seen from the curves, fig. 6. 222 Prof. Townsend on the Conductivity produced in When E is expressed in volts and / in centimetres, I find from the above numbers that the mean value of - is 372. So that if X is the force in volts per centimetre, the value of p for which the conductivity is a maximum is p= 379° In Section 7 we found that the value of p for which @ isa maximum when X is constant is given by the equation p= oe so that the empirical law discovered by Stoletow is completely explained by the theory of collisions. The other results obtained by Stoletow can also be ex- plained, but the numerical coincidence is not very aceurate in some cases. The discrepancies occur when the con- ductivity between the plates is very small, and it is possible that the experimental results are not so accurate in these cases, but on the whole there is a very good agreement between theory and experiment. Let us consider how the current depends on the distance between the plates when the conductivity is produced by ultra-violet light. The following table gives some of the results obtained by Stoletow w chen the difference of potential between the plates was proportional to their distance apart /. For the largest distance (1°08 millim.) the potential was 165 x 1°43 volts. D. =108 655 393 262 750 i= 762 74k). 1739) a ae 69 1837 1799 1782 1676 7 491 1127 «482 832-7 For the larger pressures an increase in the distance between the plates has little effect on the current; but for the pressure 7°7 millims. the current becomes very large when the distance between the plates is increased. If we suppose as before that the ions created by the action of the light start from the plates, then the current should satisfy the equation (as), Section 4, N — Wee where 2 denotes the distance between the plates, and @ is a constant. Gases by the Motion of Negatively charged Ions. 223 - Taking «=34:1 it will be found that the following numbers are proportional to N when the distances / given in the above table are expressed in centimetres :— ADI: FETS 4832, Sid, which agree with Stoletow’s values of the current when the pressure is 7°7 millims. Ei The electric force (x = 4 used in these experiments was 2186 volts per centimetre; and although no forces exceeding 800 volts per centimetre were used in my experiments, never- theless the value of e calculated from the curve given in Section 7 is in good agreement with the above number. Shas 45 = = = 284, the corresponding value of a, deduced from the curve is 4°8, so that 2=36°9. In order therefore to explain the variations in current which oceur for different distances between the plates when X is constant, it is sufficient to assume that the number of ions given off by the action of the light is independent of the distance between the plates, and that other ions are produced by collisions *. For pressures lower than 70 millims. it would appear from Stoletow’s experiments that the number of ions generated by the action of the light is practically constant, but at higher pressures the number of ions given off by the plates seems to diminish. Thus the conductivity at 750 millims. is about half the conductivity at 69 millims. when the force is 2186 volts per centimetre ; and since the current is practically independent of the distance between the plates, this effect cannot be explained by the collision theory. The following considerations, however, show that at a pressure of 750 millimetres, the force of 2186 volts per centi- metre is not sufficient to bring all the ions that are generated at the surface into the gas away from the plate. When the ions are set free by the light at the surface of the plate, they tend to move in all directions with their velocities of agita- tion; and unless the force acting on them is large enough to give them a velocity away from the plate greater than the velocity of agitation, some of them may, after colliding with molecules, come into contact with the plate and be discharged. The mean-free path of an ion in air at atmospheric pressure . * These experiments cannot be explained by the theory of surface- layers, since the density of ionization is largest at the points furthest from the plate. 7 224 Prof. Townsend on the Conductivity produced in is, according to this theory, 4°3 x 10-° centimetre. In going through this distance, the ions only acquire a velocity, cor- responding to a fall of potential of 2186 x 4°310~ (=:1) volt, which is about 1:5 times the velocity of agitation (Section 5, equation (5)). When the velocity of an ien before impact is nearly the same as the velocity of agitation, the effect of the collision on the ion may reverse the direction of motion without diminishing the velocity. Under the present cir- cumstances it 1s to be expected that some of the ions move back towards the plate after colliding with molecules of the gas, and lose their charge by coming into contact with the surface at which they were generated. In order to ensure that nearly all the ions generated by the light should get into the gas, it would be necessary to have the electric force above a certain value. It would appear from the experiments that a force of 2186 volts per centimetre would be sutticient for this purpose when the pressure is 69 millims. The fall of potentialin a length equal to the mean free path is about a volt in this case, and the velocity acquired is five times the velocity of agitation. Much smaller forces would be necessary for lower pressures in order that the fall of potential in a length equal to the mean tree path should be of the order of: one volt; thus we have xX —,=1l or — =21. It will be seen from the curve fig. 6 px Bp P X that the value of a, corresponding to the value of —= 21 is very small. Pres Hence if the force X is constant and the pressure gradu- ally lowered the conductivity increases slowly until — is about 20; at this point practically all the ions generated by the light traverse the air-space between the plates. Further diminution in p produces an increase in conductivity owing to the formation of new ions by collisions, the increase being very great for the larger distances between the plates. When ~* is about 372, the value of a is a maximum and p is the Pp the number } x critical pressure ; for values of p less than 379 vo of ions formed by collisions begins to diminish ; and finally, when the pressure is very small, the conductivity approaches the value corresponding to — = 20. 12. We may here compare some of the conclusions at which we have arrived with the results obtained from the coeffi- cients of diffusion of ions. Gases by the Motion of Negatively charged Ions. 225 The present experiments have led to the conclusion that there is a great difference between the positive and the negative ions at low pressures, and that the negative ions are ‘mach smaller tuan molecules. At atmospheric pressure the ions diffuse more slowly than the molecules of the gas in which they are generated, so that each ion is associated with a mass lar ger than the mass of a molecule of the gas. Also, there is no great difference between the rates of diffusion of the positive and negative ions. Subsequent experiments* at pressures varying from 750 to 200 millims. gave no indication of any change in the size of the ions. Theslow rate of diffusion of the ions may be explained if we suppose that a number of molecules are collected round the ions, and that the whole group moves about in the gas with the carrier of the charge: the rates of diffusion of the positive and negative ions would depend on the size of the groups accompanying the ions. The particles of matter on which the negative charges reside might be very much smaller than the partic! es which carry the positive charges, and at the same time their rates of diffusion might be nearly equal. When the pressure is reduced, and the ions are acted on by forces which cause them to move rapidly through the gas, the groups of molecules which surround the ions probably disappear, and the negative ions move in the gas as if they were accompanied by a mass which is small compared with the mass of a molecule. It is possible that this effect could be produced at any pressure if the electric force was large enough to make the ion move with a velccity greater than its velocity of agitation. It is difficult, however, to arrive at any definite conclusion on this particular point, as our know- ledge of the behaviour of ions under the various conditions 1s very limited. 13. When the current passes between two electrodes, one inside the other, the conductivity is practically unaltered by reversing fli current when the electromotive force is small. If the electromotive force is large, the conductivity depends on the direction of the force in a remarkable manner ; the current obtained when the inner electrode is positive may he five or ten times as big as the current obtained when the inner electrode is negative. The reason of this can be easily explained by the theory of collisions if we attribute the production of new ions to the negative ions, * John S. Townserd, Phil. Trans. vol. exev. 1909. | 226 Conductivity produced in Gases by Negatively charged Ions. The ionization preduced by the rays in the space between the electrodes is practically uniform. Jn order that new ions should be produced by collisions, it is necessary that negative ions should pass through the gas near the inner electrode where the force is large. When the inner electrode is | positive, all the negative ions pass through this region and a | large conductivity is obtained. When the inner electrode is | negative, only a few of the negative ions pass through the space where the force is large, and consequently the con- | ductivity is not rauch inere ane It can be easily seen: that by varying the shapes of the electrodes, the conductivity may undergo various changes; and by having the inner electrode very small, a phenomenon resembling unipolar con- ductivity can be obtained. | These results show that the increase in conductivity must be attributed to the negative ions, and that the positive ions | do not generate new ions in the cases which we have been | considering. We have thus obtained experimental evidence i to show that positive and negative ions have very different physical properties. | 14. The conclusions which have been arrived atin this paper ae help to explain some other phenomena connected with the | passage of electricity through gases. The cases I have dealt with are probably the simplest; the experiments can be | easily arranged so as to test the theory, and furnish data from which we can arrive at definite conclusions. i Professor Thomson * and Dr. H. A. Wilson f have given explanations of some of the phenomena connected with dis- charge-tubes based upon the supposition that ionization 1s produced by ce ions. In these cases, the phenomena are very complicated, and it is by no means evident that the | ionization is principally due to this effect when the electric il intensity is small. | Thus in the positive column where the force is of the order i of 80 volts per centimetre, the ionization produced by moving M ions must be very small as can be seen from the curve fig. 7, which gives the values of @ for small forces. Moreover, there is evidence of other effects which produce ionization. It has been found by EH Wiedemann { that rays are produced in a discharge-tube which are analogous to Roéntgen rays, and produce ionization, so that their effect cannot be neglected in the investigation. If we consider the results of experiments on the potential : * J. J. Thomson, Phil. Mag. September 1900. i + H. A. Wilson, Phil. Mag. June 1900. ; ii | } E. Wiedemann, Zeitschrift fiir Electrochemie. Electric Inertia and the Inertia of lectric Convection. 227 gradient in the positive column, we are again Jed to conclude that the ionization does not arise principally from collisions. It has been found, in some cases, that the force per centi- metre in the positive column is almost independent of the current strength, so that the velocities of the ions would be the same for different currents, and the rate of recombination would be proportional to the square of the current. The rate of production of ions by collisions would be proportional to the current, and the new ions thus produced would not com- pensate for the loss due to recombination. These and other considerations show that it is impossible to infer from pheno- mena connected with discharge-tubes that any ionization is produced by collisions when the force is as small as 30 volts per centimetre. The results which we have obtained show that for a large range of forces, the positive ions do not contribute to the generation of ions, but it is probable that positive ions would produce ionization in stronger fields. XVIII. On Electric Inertia and the Inertia of Flectrie Con- rection. By Arraur Scuuster, /.R.S., Professor of Physics at Owens College, Manchester*. ie Ge calculations of self-induction are based on the assumption that the currents which traverse a con- ductor fill it continuously, the flow being treated as that of an incompressible liquid. The assumption is generally recognized not to hold in the ease of electrolytes, where electricity is con- veyed by a number of irregularly distributed ions. In the immediate neighbourhood of such an ion, the magnetie field will be many times greater than that calculated cn the supposition - of continuous distribution,-and hence the total magnetic energy is underestimated. What is universally recognized in the case of electrolytes must also be conceded w ‘hen the current is con- veyed by a gas, and the idea is gaining ground that even in solid conductors the current consists of mov ing positive and negative electrons. It is the object of this paper, to calculate the additional terms which become necessary for the evaluation of self- induction, and to discuss the possible cases in which the cor- rections may affect experimental results. 2. I begin by calculating the total energy of a number of electr ically charged, equidistant particles, placed i in a straight row and all moving with the same speed (u). If the charge (g) of each particle i is taken to be spread uniformly over a * Communicated by the Physical Society : read Dec. 14, 1900. 228 Prof. A. Schuster on Electric Inertia and spherical surface of radius a, the magnetic energy is g?u?/3a*, so that the particle behaves as if it had a mass 2g?/3a. With- out making any assumption, as to whether the magnetic forces are to be taken as vanishing within the electron or not, we may use the above expression, taking a to be a linear quantity, not necessarily the radius of the electron but of the same order of magnitude. If there are n particles per unit length at a distance d apart so that nd=1, the energy per unit length will be g?w?/da, as far as the magnetic field established by each particle is concerned. The mutual energy of different particles has to be added in order to obtain the total mag- netic energy. A pair of particles at a distance 7 from each other will have a mutual ener ey of q?u?/r, and each particle with its nearest neighbour on either side will therefore con- tribute a term 2e? wd. Taking the remaining particles in pairs we get for the mutual energy of a central particle and p pairs on either side 2q°u* re PA ges : (tb++ ie eile aa . The series 8 may be added up and the result expressed in the form S=B + log p, where B is a number approximately equal to 0°577. If p is very large, the total magnetic energy per unit length of the central portions of the row will be negrar{ 25 + 77) =0°(2B +2log p+ aa) re GS) where C stands for the current. 3. I now compare this expression with that calculated on the usual supposition, which is, that the electrification is not confined 4o electrons but ‘Alle continuously a rectangular space having a square cross-section with sides equal to d, and having a length equal to (2p+1) d, tor which we write 2D. The total ma genetic energy in this case will be the same as that of two linear conductors of the same length, and at a distance apart which is equal to the geometric 1 mean of the square section 7%) where ro= "AAT d. For unit current in each of the conductors, the linear ele- ments of which are ds,, ds, the magnetic energy between the conductor s, and the element ds, is 1 dy dds (, + 9 ds ih * Heav Fiside, Phil. Mag. April 1889, p. 324. the Inertia of Electric Convection. 229 The well-known ambiguity, as to the expression under the integral sign, disappears in our case, because we are only com- paring the magnetic energy on two suppositions, and must therefore consistently use in both cases the same expression for the mutual energy of two current elements. As D is large, the value of — for small values of s, will be sensibly 1 equal to #1 according as sz 1s large on the positive or negative side, and consequently we find the above expression to be equal to = ds,(— 1+ { ay 0 V1 +52 2ds,(log (D+ W7,.2+ LD?) —log7y>—$). - - (2) We may substitute pd for D, and the above expression then becomes, neglecting 7 compared with D, 2nd ds(2 log a —l ). The bracket being independent of s, we conclude that the central portions of the column have a magnetic energy which for a current C and unit length is or C72 log p+2 log = —] \=C(2 log p +.1°996). 0 The excess of (1) over this will be the required difference in the magnetic energy. Introducing the numerical value for B this difference becomes "(37 — 842). ies ete This expression being proved for any portion of the circuit which can be considered straight for a length which is large eompared with the distance between the electrons, may be taken to hold for the complete circuit, as, excluding sharp angles, every circuit may be divided into portions satisfying this condition. 4, Some additional explanation is necessary for ordinary conductors whose cross-section is many times larger than the distance d between the electrons. The cross-section of such conductors may be divided into square elements, each square having sides equal to d. If we imagine the electrons to be placed at the centre of each square we may calculate the mutual energy of anv two parallel columns and thus obtain further correcting terms. It is easily seen that these terms 220 Prof, A. Sehuster on Electrie [Inertia and will be positive and tend to diminish the negative term ‘in (3). They will also be small and of the same order of magni- tude as other quantities we neglect. It serves no useful purpose therefore to calculate them out in detail. If A is the area of the cross-section, the number cf electrons spread over it will be An?, so that the total correction to the mag- netic energy beccmes Anigru*( : feS St ag If d is large compared with a the second term may be neglected. In that case, writing 2 for the current-density n°ug, and N for n® which represents the number of electrons in unit volume, we obtain for the correcting term per unit volume of the conductor | ita where w stands for 2/3aN. The flow of electricity will behave, therefore, as if it had inertia, the apparent mass for unit current-density aud unit volume being »w. ‘The dimension of w, as pointed out by Hertz, is the same as that of a surface. 1 We may conveniently use the expression ‘‘ electrie inertia ”” for the quantity ~; the energy due to electric inertia is the energy of the magnetic field due to the moving electrons over and above that which is calculated in the usual way. 5. The investigation has been restricted to the case of a number of electrons moving in one direction, with the same speed and keeping the same equai distances from each other, but the result holds more generally. The magnetic field established by a positive electron moving in one direction is the same as that of a negative electron moving with the same speed inthe opposite direction. Superposing on our system of one kind, a second one carrying opposite electricity in the opposite direction, N being the number of electrons of each kind and Az, Az, the currents conveyed in the two directions, the energy per unit volume becomes (i,? + i,?)/3Na or Menace 2 tS fi; Fig)? BNa’ The assumption that two sets of electrons move s0 as to keep equal relative distances is not of course satisfied. The change in the relative distance will increase the mutual energy between the electrons, but the increase will be of the order of magnitude which we have neglected, and the term we have the Inertia of Electric Convection. 235 retained is not affected by the relative distances of the electrons. For the purpose of this paper it is not therefore necessary to go beyond the above expression, The correction to self-induction for a conductor of ibngeh I : : l and uniform cross-section A will be - i; or 141 4-2«(«—1)}/3NAa, where « is that fraction of the total current which is conveyed by the positive electricity. If both kinds of electrons take egual parts in conveying the current, the correction becomes. l/6N Aa. The correcting term increases in importance with diminish- ing cross-section, and might be made large, if the cross-section could be reduced so as to be comparable with molecalar ae ae . We must now enter into a discussion of the numerical Fe oe involved. In the case of metallic conductors we, may, in the absence of contrary evidence, reasonably take N. to be of the order of magnitude of the number of molecules per unit volume. Taking the molecular distance to be LU~$ this gives N=10*. As regards the linear quantity a, observations made on, cathode rays determine it, in my opinion, and in any case fix a lower limit. ‘The deflection of these rays by the magnet shows that the moving electron has itself a mass or is car nrc by a small mass. J. J. Thomson adopts the latter view, but if seems to me to be more natural to take the inertia of the cathode particle to be the magnetic inertia of the electron. If m is the mass, real or apparent, of the particle carrying. the negative charge, we may determine the ratio g/m. Measurements of this quantity were first made by myself’ in. 188) *, and since then more accurate determinations by my original method or by cther and better methods have been carried out by J. J. Thomson, Kaufmann, Lenard, and. Wiechert. Taking the latter’s timate as being deduced from the most cen! method, I shall use 1°3 x 107; in. electro- magnetic measure for the value of g/m. If g, as was assumed by me and afterwards proved by J. J. Thomson, is the same quantity as that carried by the ion in a liquid, we know that in’ the case of e. g. hydrogen g/m'= 10+, if m’ denote the mass of ' an atom of hy ‘drogen. Now trom the density p of the gas and ’ the number N/ of hydrogen molecules per unit voluine, we _ # Bakerian Lecture, Proc. Roy. Soe. vol, xlvii. p. 526 (1890). : . ny 232 Prof. A. Schuster on Electric Inertia ant may caleulate 2m’=p/N’. Taking p=q x 10~?, N=21 x10") we find m'=2 x 10-*4, and hence g=2 x 10-20 *, Also ee =4 <2 x 10-2 % 1°3 x 107=1°8 x 10. The linear dimension of the electron would therefore have to be about thirty-thousand times smaller than the molecular distance in solids, but I can see nothing more astonishing or improbable in ie than in the Aer native assumption aa particles having masses thirteen-hundred times smaller thai the masses of hydrogen atoms. The electric energy per unit volume and unit current density was found to be 1/3aN, which in the case of solid eonductors would therefore become 2x 10—!2 C.G.S. units. We po-sess fortunately a series of experiments by Hertz in which he investigated the possibility of electric inertia, and found that if it exists it must be smaller than 18 x 107-8 for uit current-density and unit volume. The effect we have calculated is much smaller than the number given by Hertz, and as this represents the Jimit beyond which he could not push his experiments, we must for the present give up the hope of testing the results of our theory. There seems only one chance—and not at all an impossible one-—that in some cases the effects may be considerably larger than those caleu- Jated above. Perhaps in some bad conductors like carbon, the distance between the moving electrons is greater than the distance between the molecules If it is fitty times as great, we should get within the limits to which Hertz worked. 7. In the case of electrolytes the electric inertia of moving ions is small compared to their mass inertia. The latter must to some extent affect the motion of electricity in electrolytes, and it becomes a matter of interest to obtain, if possible, some experimental evidence to establish the eteee of this mass Inertia. If N molecules of a dissociated salt are dissolved in unit volume of water, and if 4, w. represent the velocities of the ions having masses mm, m»., the energy per unit volume is | LN (mjity? + gute”). If the masses of the ions contained in each molecule referred to hydrogen are aj, ds, and a represents the ratio between the mass sae charge for a hydrogen atom, which is numeniggiiy equal to 10 Ax LOR M1 =A,2d, Myg=—AzQaq. * Owing to some arithmetical blunder, this quantity was put down as 3x 107 in my Bakerian Lecture. the Inertia of Electric Convection. 233 Introducing the current-density t=No(uj tu), and the weight p of dissociated molecules per unit volume, which is related to the other quantities used by the equation p=N(m + m) = Nag (ay +p), we obtain for the energy of ionic motion Roel Gk sf iui + dots’ | ght = > ae 2 2 eee (uy + U2) If uw, refers to the kation, the ratio w2/u,;+u_ is Hittorf’s constant deduced from the migration of ions. Denoting this by x we have finally = mes a?(a,(1—n)? + a9n”). Taking for instance nitrate of silver, for which n=*53, a =108, a,=62, the energy of ionic motion per unit volume and unit current becomes equal to 3°8 x 10~°/p, where p is the number of grams of nitrate of silver per c.c. of water. Hertz gives in the paper quoted for the same salt the number 7°8 x 10—*, which is nearly double the value I find. As Hertz does not indicate his method of calculation, it is not now possible to trace the discrepancy, unless there is some slip in the above reasoning. In order to discuss the possibility of an experimental veri- fication of the increase in self-induction due to electric inertia, we may consider two narrow tubes placed side by side. If the tubes have an internal diameter of 1 mm., their axes might be placed 2 mm. apart and the coefficient of self- induction would in that case be equal to 6°6 per em. of ‘the double conductor. The ionic inertia would increase the value by 76x10-°/pA, which is nearly equal to 1 if p=:01. The increase in self-induction amounts therefore to about 15 per cent., but the whole quantity is so small that it could not be measured very accurately. When the dilution of the electrolyte becomes great, the ionic inertia may become considerable. Thus in the case of the purest water obtained by Kohlrausch, he estimates that there was *08 mg. of dissociated hydrogen per cubic metre. This sives p—( 2% 10%) In order to avoid making any assumption as to the quantity n, we may substitute that value for it which gives the smallest Phil. Mag. 8. 6. Vol. 1. No. 2. Feb. 1901. R 234 .. Prof. A. Schuster on Electrie Inertia and value to w. This is found to be n=a,/(a,;+a;), so that if Qj=2, dg=16, e=108x10- p— tee = I | a? = 480 = Aa = ° Sida The energy of straight parallel currents close together as in the above example would therefore in this case be almost entirely due to the ionic motion, but it will appear in § 9 that the chances of experimental verification are not very great, as long as an increase in the value of u« is accompanied by a cor- responding increase in the resistance. 7 8. The case of gases presents several features of special interest. The effect of inertia on the deflection of the cathode ray has already been alluded to, and the fact that in the positive portion of the discharge, the current is conveyed by a com- paratively slow diffusion of molecules has been proved by me in 1885*. In the positive part of the discharge the number of ions is proportional to the current, as follows from Hittorf’s experiments. ‘To make an estimate of the inertia involved in the diffusion, I take as an example one of my experiments for which I have calculated approximately the ratio of the number of ions to the total number of molecules as 1:2 x 10-6 at a pressure of 4 mm., at which the density of nitrogen is 5x10-7. The quantity called p above is in this case 10-®, and taking a,=a,=7, w= 49 x 1002 = 5-4 x 10°, This value holds for a current-density of 1:5 x 10-4, and will be inversely proportional to the current-density. The electric energy of convection in gases may therefore be very large and exceed many times the magnetic inertia calculated on the usual hypothesis. As an example I take a circular tube of radius 7 bent into the form of a circle of radius R, and as a first approximation we may take the expression L=47R (log oe —1°75); the electric energy of convection per unit current is wR/r’, so that the total energy per unit current becomes 3 [e+ (og = —1-75)]. With r=1, R=10 the numerical value of the second term * Bakerian Lecture, pp. 548, 550. the Inertia of Electric Convection. 235- is 34, and this term is therefore quite insignificant compared with the first. A coil might be made of a good many windings still leaving the inertia of convection great compared to the magnetic inertia. In any problem in which the self-induction of gases has to be calculated, the ordinary methods would give erroneous results. 9. The general equations of electric motion will be altered by the introduction of the inertia, whether it be the inertia of the electron or, as in the case of liquids or gases, the inertia of the ion. If E represents the component of electric force in any one direction, and wu the flow in the same direction, the ordinary equations of electric motion are pu=H, with two other equations giving the components in two other directions, p being the resistivity of the medium. If, however, the electric flow possess inertia, the electric forces will be doing work in increasing the energy of convection, the rate of doing work per unit volume being mwuu. Hence the complete equation will be putypu=H. In the case of conductors, we may put Meher idle «di Hs ae tae) avy being the electrostatic potential and F the X component of the vector potential, and introducing the conductivity « for 1/p, the equation becomes dF dw du ute dp tM gy =9> 2 or, as V*EF= —47u, with the corresponding equations for the other components of the vector potential. The electrostatic potential disappears in the usual way by introducing the components of magnetic induction (a, b,c) for those of vector potential, the typical equation in that case being da d mK, = (1+«u5)v% R2 236 Prof. A. Schuster on Electric Inertia and If the flow is periodic so that a, ,¢ are proportional to e*, where 7 stands for “ —1, we obtain by dividing out the time factor AtKip 24 — Vie eke Kip This equation shows that the inertia will affect the mag- netic induction and consequently the lines of flow only when «up becomes an appreciable fraction. But m itself we have found small in liquids and solids, while « is never greater than 10-*. Hence kup cannot produce appreciable effects until p becomes of the order of magnitude which holds for luminous radiations. But that case will require separate treatment as our equations are not correct for rapid variations of the currents. In the numerical example given in § 8, w was found to be equal to 5:4 106 for a current-density of 15x 10—-% The product xy in the case considered will be independent of the density. The fall of potential in the experiment was 5 volts per cm., so that the conductance was °3 x 10-”, and the cross- section being 2 the product «xu becomes *8xX10-§ This product would be considerably larger at lower pressures, and when the frequency is of the order of magnitude of leyden- jar discharges it is very likely that the term depending on the inertia of convection is very appreciable. Some of the facts brought to light in J. J. Thomson’s work on luminous discharges produced by induction in tubes without electrodes seem to point in that direction. When «up becomes large compared to unity, the equation reduces to a Beans Vo ee pe so that, for instance, DIN ae »” COS pt would represent a possible disturbance. | 10. The effects of inertia may become very appreciable in the case of luminous vibrations, to which our equations do not apply, as the term depending on the specific inductive capacity has been left out of account. In forming the more complete equations a difficulty presents itself which is due to the fact that the displacement currents may also to some extent have inertia or what is equivalent to inertia. The apparent masses will not be in general the same as those involved in the conduction currents, though in the case of the Inertia of Electric Convection. 237 displacements of electrons in the molecules, the order of magnitude may be the same. If 4p’? represent the energy per unit volume due to electric inertia where 7 is the displacement current, the complete equations for the magnetic induction become, for a medium of specific inductive capacity K and conductivity «, ANCE NG oe ae ioe ee (1 frees ae re ie) AYE a=Kae + dK with the two corresponding equations for } and c. If a varies proportionally to e~’”‘ this reduces to IK 2 (1 —ippK— a) Va=— (Kp? + 4rxi)a. In non-conductors the terms involving « disappear, and a=e'® is a solution provided that IZ 2 e(1-" 2 )=Ky, Ar which gives for the velocity of propagation p/q the equation Pol es. g. K a? dividing by V’, where V is the velocity of light in vacuo, we obtain for the refractive index of the medium (n) soap ¢ ok por ee dO MiG If the second term is small we find to the first approxima- tion, writing 7) for Vv K, i 3 (pd LEAD N=Ng-+ 2 SPS se J. Willard Gibbs * nearly twenty years ago deduced from the mere assumption that the medium possesses a fine-grained structure an equation for the relation between velocity of waye-propagation and wave-length which is identical with the above, and it was pointed out by him that his equations include the case in which the medium is endowed with electric inertia. It seems of interest to determine the order of magnitude of the quantity uw’. The coefficient of 1/A? may be calculated from the optical dispersion and for ordinary flint-glass is * American Journal of Science, vol. xxiii. p. 262 (1882). 238 = Electric Inertia and the Inertia of Electric Convection. found to be about 107°, the corresponding value of np being about 1°6. Hence p/=10-" approx. This value does not differ very materially from 2 x 10—!, which is the estimate of # which has been made for solid conductors in §6. As the latter estimate depends on the cube of molecular distance which was assumed to be 10-74, the difference between the two numbers falls within the possible errors of estimation. I do not, however, attach much importance to the apparent equality of the numbers and mention it only as a remarkable coincidence, which probably is accidental. For the quantity called w diminishes with increasing distance between the molecules, and for gases at atmospheric pressure would be 90,000 times smaller than for liquids. There would therefore be a very wide discrepancy between pw and yp’ in the case of gases. Should the coincidence between mw and yp! in solids prove to be more than accidental it would prove that the greater part of the kinetic energy in a luminous vibration traversing a transparent solid is accounted for by the kinetic energy of the electrons attached to the molecules and set in motion by the vibration. This proposition is obviously not true in the case of gases, but may hold for solids. It would be of some interest to discuss the effects of metallic reflexion in connexion with the equations which are given at the beginning of this paragraph. H. A. Lorentz * has already introduced a term depending on inertia in the equations of motion of light, and pointed out that without such inertia the electromagnetic theory of light could not explain the known experimental facts. But even the inertia term introduced by Lorentz, was not sufficient to account for all the discrepancies between theory and experiment. My equations differ from those of Lorentz by the introduction of two constants w and p! which need not be identical, for there is no a prior reason why the inertia of the conduction current should be the same as that of the displacement current. The numerical results of Lorentz’s investigation are not easily interpreted, as he used the Helmholtz form of the equations, which involves a large and unknown coefficient. Attention may be drawn in conclusion to several papers by P. Drude + “On the Electron-theory of Metals.” * Zeitschrift fiir Math. u. Physik, vol. xxii. p. 197 (1878). + Annalen der Physik, vol. 1. p. 566, vol. iii. p. 369, and Physik. Zeit- schrufe,, (ol. i. p. VG: [ 239 ] XIX. On Astigmatic Lenses. iby kt. 3. SOWTER, B.Sc. A.n.C.Se.* LENS which so acts on light falling on it as to produce two focal lines in the refracted-ray system is termed an astigmatic lens. Sturm (Comptes rendus de ? Académie des Sciences de Paris, t. xx.) investigated the refraction of a circular pencil of light by an asymmetrical surface or lens with circular aperture, and showed that for a convex refract- ing lens the ray surface was a skew surface (surface gauche) bounded by two right lines. Fick (Mediz. Physik) has written on the subject; and Knapp (Archiv f. Ophthalmologie, Band viii.) has mathematically determined the form of the whole refracted-ray surface. Donders, Reusch, and others have investigated the optical properties of asymmetrical or astigmatic lenses; and more recently Prof. 8S. P. Thompson has, in his paper on ‘ Obliquely-crossed Cylindrical Lensesf,” deduced a very simple geometrical construction for the sphero-cylindrical lens equivalent to two obliquely-crossed cylindrical lenses. The intent of this paper is to simplify the systematic investigation of the properties of astigmatic lenses, and to show the relation between a general type of astigmatic lens and its equivalents. The quadric surface is the surface of lowest degree which is capable of representing the general type of thin astigmatic Jens. An ellipsoidal lens is here considered as the tunda- mental form or type. Thin lenses only are treated, I. Ellipsoidal Lenses. A system of parallel and axial rays of light after passing through an ellipsoidal lens becomes a system of rays inter- secting in two straight lines. These lines are at right angles, are the focal lines of the lens, and are separated by an interval —the focal interval of Sturm —which depends on the ellipticity of the lens. The focal lines are parallel to the elliptic axes of the lens, and correspond to the lens powers in those directions, i. e. to the maximum and minimum powers of the lens. If, in comparing the curvatures of various arcs, a constant or common sagitta is chosen, the curvatures are proportional to the squares of the semi-chords of the arcs; and if the sagitta of an are is properly chosen, the curvature of that arc is measured by the square of the semi-chord. It follows therefore that the power of a lens or a surface in a given * Communicated by the Physical Society : read November 9, 1900. + Phil. Mag. Mar. 1900; Phys. Soc. Proc. 97, July 1900. 240 Mr. R. J. Sowter on Astigmatic Lenses. direction can be represented by the inverse square of a length, that length being the semi-chord for the surface in the direction considered. Lens properties may be established by a consideration merely of the arrangement or distribution of refracting material in the lens—by a materialistic method one might say—and this material distribution is determined or indicated by contours of equal thickness. A curve drawn through all points on a lens where the material thickness is equal or constant, may be said to determine a natural aperture for the lens. From the natural aperture of a lens the power in any direction of the lens is at once determined, for the power is as the inverse square of the radius vector from the centre of the aperture to the edge in the given direction. An ellipse is the natural aperture for an ellipsoidal lens, and may be taken to represent the ellipsoidal lens. In the ellipse shown in fig. 1, the semi-axes are a and 6, and this ellipse is the natural aperture for an ellipsoidal Jens with focal powers, A and B say, where iL A — ae? 1 b— Fe I The power of the lens in the direction OR (1, ¢) is R= - = A cos* d +B sin’, since 1 cos*d | sin’ gem aa It is obvious that the sum of the powers in any two directions in the ellipse. Mr. R. J. Sowter on Astigmatic Lenses. 241 at right angles is equal to the sum of the minor and major powers, 2 e. A+ The cornea of an eye affected by corneal astigmatism may be taken as an illustration of an ellipsoidal lens, for the curve of equal thickness or natural aperture for the asymmetrical corneal surface is an ellipse. | For a spherical lens, which is a particular form of ellip- soidal lens, the natural aperture is a circle, the powers are equal in all directions, there is a focus and no focal interval. A cylindrical lens is a particular form of ellipsoidal lens, it produces only one real focal line and has an infinite focal interval. For a cylindrical lens the natural aperture is an infinitely long rectangle, fig. 1 a, and the lens power in any direction is given by the inverse square of the radius vector. Riomiva. Thus if A is the equatorial or focal power of the lens and OA=a, then A= = Also it is evident then that an ellipsoidal lens may be repre- SSS 5S SS SS 242 Mr. R. J. Sowter on Astigmatic Lenses. sented by an ellipse such that the semi-axes are the reciprocals of the square roots of the focal powers, and that a cylindrical lens may be represented by a pair of parallel lines at a dis- tance from an axis equal to the inverse square root of the power of the lens. Il. Cylindrical Lenses crossed at Right Angles. Let two lenses of powers A and B be crossed at right angles, and let the lenses be represented by their natural apertures as in fig. 2. Then the lens equivalent to the crossed lenses is one in which the distribution of refracting substance is the same as in the combination. This distribution is determined by the natural aperture for the combination. Now taking the lens axes as axes of coordinates, the equation to the curve of equal thickness, for a thickness equal to the greatest thickness of either lens, is Az? + By?=1. The natural aperture is therefore an ellipse, and the com- bination is equivalent to an ellipsoidal lens with focal powers A and B. In fig. 2 the lenses represented have powers in the ratio 9:4 and are equivalent to the ellipsoidal lens represented by the ellipse inscribed in the rectangle of which the sides are as 3:2. Mr. R. J. Sowter on Astigmatic Lenses. 243 The power of the combination in any direction OQ at an angle @ to OA is ae where OR is the radius vector of the inscribed ellipse, and is also equal to A cos? 6+ B sin? ¢. If the lenses are equal, A=B, the ellipse becomes a circle, the power in any direction is A say, and the crossed lenses are equivalent to a spherical lens of power A. The point R on the ellipse may easily be determined as follows :— Draw OP’ at right angles to OP and make OP’=OP. Join Q,P’, and make P/P”=OP!=OP, and draw P"R parallel to P’O. Then Ris the point on the ellipse, and cage = epg Oe Sg en OR? OP2 * OQ? *™ Ree, OM lf OR EOO? er vOn 0k yj OR - OPR0g ; If Pand Q coincide as at C, then the point F on the ellipse is found by drawing the semicircle OHC and making OF = OH, where EH is the extremity of the radius perpendicular to the diameter OC. Ill. Cylindrical Lenses crossed obliquely. Let the two lenses A and B be crossed obliquely, and let the acute angle between their axes be @. The curve of equal thickness or natural aperture for the combination is easily determined. The axial thicknesses of both representative lenses are equal, and the equation to the curve for a thickness equal to that axial thickness is A sin? ¢ 27+ B sin? dy’=1, the curve being referred to oblique co-ordinates coinciding with the axes of the lenses. That is, the natural aperture is an ellipse, and the crossed cylindrical lenses are equivalent to an ellipsoidal lens repre- sented by the ellipse inscribed in the parallelogram as shown in fig. 83. The lines OC, OD are semi-conjugate diameters of the ellipse. If the major and minor axes of the inscribed ellipse are 2a and 26 respectively, then the equivalent ellipsoidal lens is one with focal powers 2 and 2" The magnitudes of the axes may be geometrically deter- mined as follows :— Draw OC’ at right angles to OC, make OC’=OC, join 244 Mr. R. J. Sowter on Astigmatic Lenses. C'D, O'D!, produce D/C to D", making C’/D”=('D, and from C’D! cut off C'D!"=C’D. Then DD! = 24, and Dipve= oF To determine the direction of the axes the following procedure may be adopted :— ‘With O as centre and a length a=4D’D” as radius, cut the parallelogram in the points d, ¢, e, f, and draw dF and cF perpendicular to the sides of the parallelogram to intersect in F. OF is then the direction of the major axis. To prove the above constructions, let OC=—2 00a Then, since ¢ and d are conjugate, (Ge eda (il.) cdsind = ab. Now DC? = 0C’?+0D?—20D. OC’ cos DOC; DC”? = c?+d?—2cd sin d = (a—b)? by the relations (i.) and (ii.). Therefore DO’ =a—d. Mr. R. J. Sowter on Astigmatic Lenses. 245 In a similar manner it may be shown that CD! = a+b. Hence DAY Zar 1D aD ieee Again, the circle cdef is the locus of the feet of the _perpendiculars from the foci on the tangents to the ellipse ; therefore the points FF’ are the foci, and the axes are determined in direction by the line OF. Analytically a and 6 are easily determined in terms of e and d from the equations (i.) and (ii.). Further, Gi ee (iv.) = B sin? ; and from the equations (1.)....(iv.) a and are readily deduced in terms of A, B, and @. Thus, since an ellipsoidal lens with powers «= S and b=5 is equivalent to a spherical lens of power a and a cylindrical lens of power B—« or a if C is the cylin- dricity of the sphero-cylindrical lens, it is easily shown that 1 1 vo (c?+d?)?—4c?a? sin?h € = 2507 aD — = 6b? a 7d? sin? MS ca ee | 2 1 — 2 S/W Fea ena = ABsin oa/ A? sint ob si B? sint d ar AB sin? $ ee b = V B+ A?+2AB(1—2 sin? ¢). * C= VA?+ B?+2AB cos 26; and a parallelogram-construction with sides A and B, and angle 2, as was shown by Prof. 8. P. Thompson *, gives the eylindricity in a sphero-cylindrical lens equivalent to two crossed cylindrical lenses, A and B, at an angle ¢. | The angle of inclination of the cylindrical lens in the sphero-cylindrical combination to the direction OC is the angle between the major axis of the inscribed ellipse and the axis OC. The equivalence of a sphero-cylindrical combination and an ellipsoidal lens follows at once from the method of contours * Phil. Mag. Mar. 1900; Phys. Soc. Proc. 97, July 1900. 2) 246 Mr. T. Mizuno on the Function of or apertures. In fact, crossed cylindrical lenses, whether the lenses are at right angles or are inclined obliquely, and also spherical and cylindrical combinations, may be replaced by their equivalent ellipsoidal or quadric lenses, or for an ellipsoidal lens a pair of cylindrical lenses, or a spherical and a cylindrical lens, may be substituted ; for the arrangement or distribution of refracting substance is similar in such lenses or combinations. And, moreover, the preceding geometrical constructions afford a ready means for effecting the trans- formation from any assigned type of the combinations named to the type of any other. The method is applicable to astigmatic lenses or combinations in which the curvatures are not all of the same sign. XX. The Function of Self-Induction in Wehnelt’s Interruptor. By T. Mizuno *. 7 EHNELT + discovered a very interesting interruptor and made a minute investigation on its properties. Soon after this discovery, Simon { also carried out experi- ments on the new interruptor and gave the theory of its action. According to his theory, an electric current 7 sent through the interruptor of the resistance w grows logarith- mically, and finally attains such a value that the Joule’s heat expressed by the integral | 0-24 | wdt,. 3070 500 3070 2500 3070 2700 3070 2700 Contacts changed ... 2940 2920 2940 2920 Breathe on once —> 3000 1000 3100 2C00 3100 1500 3100 1500 Before leaving this pseudo-coherence two more tables will be given. In Table III. the gradual increase on the contact of water from the air, with the accompanying adherence, can be traced. The effect is small but quite distinct. In Table IV. it is seen that water at the contact can be quickly dissipated (by heating and electrolysis) due to a passage of a moderate current. Investigation of the Simple Coherer. 273 TaBueE III. In this case in order to sunder the wires currents must be reduced, 7. e. resistance must be increased. | Resistance to Resistance to Remarks. overcome overcome torsion. sticking. | i ed |» 3 eee Adee 2.2 te ee B eee 205 A damp day. 1 710 720 ‘Contacts clean. J 710 720 710 740 710 740 710 760 = | TABLE IV. Resistance to Resistance to Remarks. overcome overcome | torsion. sticking. | A damp day. | Current passing. | Breathe on once —) 2550 | 1000 2570 2530 2570 | 2560 | 2570 2560 All the following observations were taken when the air was dry, the extra precaution being taken to rub the wires with well-dried blotting-paper before using, and to repeat this process every few minutes. We cannot suppose that the condensed oxygen and nitrogen on the surfaces, which played such a prominent part in the recent observations * of Mr. Spiers, can be in liquid form, and therefore cause surface-adherence, though, as shown above, the average pressure over the area of contact is 200 atmos; for, as pointed out by Prof. Oliver Lodgef, their critical temperatur es are far too low for this to be possible in the usual sense. But it will be seen presently that they seem to produce a marked effect on the resistance of the contact, when the pressure is small. * Phil. Mag. Jan. 1900; Proc. Phys. Soc. 1900, p. 39 &e. t Phys. Soe. Pres. Address, Feb. 1900; Phil. Mae. xlix. (1900). 274 Mr. P. E. Shaw: 5. Direct-Current Coherence. Dorn *, and Guthe and Trowbridge t have pointed out that the initial high resistance of a coherer is due apparently to a film of condensed gases on the surfaces. I also found this; for if the wires, just cleaned, be brought into contact a cur- rent, though an uncertain one, passes; the voltmeter-readings flutter, and, after a few contact “makes” and “breaks,” the index comes to rest, showing that resistance is practically infinite. Now this is quite unlike true coherence, which is accompanied by perfect steadiness, for any length of time, in ammeter and voltmeter. When, either by direct current or alternating discharge, true. coherence i is effected, stopping or reversing the current will not produce any change, and in twelve hours’ time the surfaces will still be found to hold perfectly. Table V. is an illustration of the point; after two readings there is no coherence, and the voltmeter-reading goes to its full amount. TABLE V. R.T. is the column showing resistance to overcome torsion. RS. 3 oe u FS sticking. Remarks. eS re al RUD |! SRISe Voltmeter. Contacts cleaned Novcurrent "| 2720. |> 2700 with emery-paper | | and wiped. C.D. 2720, | ~=—2620 O45 | C.D. i 2720 2620 0:50 C.D. | 2700 -| 2680 1:40 C.D. | 2700 | 2680 1-40 C.R. | 2700 2680 1°39 CR. | 2700 “| "2680" | aa 38 6. Coherence Proper. Having cleared up some obscurities, we have now to deal with coherence as usually understood ; 7. e., due to vibrations from some discharge falling on the contact. It may be stated at once that coherence occurs at a contact when radiation falls on it even when no independent current is passing through the contact, and even when the contact- * Dorn, Wied. Axn. lxvi. + Guthe and Trowbridge, Phys. Rev., Aug. 1900, p. 22. Investigation of the Semple Coherer. 275 circuit is not completed. If the radiating source is near, as in the following experiments, coherence occurs at once; 2. €., without capacity and self-induction in the receiving system being in any way changed with a view to resonate the vibrations from the source. The spark-gap was placed at distances of from 50 cm. to 3 cm. from the contact ; and it was customary to make one spark only by pushing the induction-cvil hammer forward once. Sometimes more sparks were used, but in all cases the amount of discharge was in this way well under control. The process adopted was as follows :— (1) Bring the wires together to firm contact, noting the resistance in the galvanometer-circuit R.T. There is no coherence and no current through the contact. (2) Pass the spark; coherence at once occurs, and the voltmeter and ammeter give definite steady readings which are recorded. , (3) Change the galvanometer-current till, the resistance being R.C., the wires are sundered, as shown by the spot on the scale moving. (4) Bring the wires together as in (1), the resistance R.T. is the same as before; but there is an important change, for on the wires touching this time they will almost invariably be found to cohere, a current passing. Read the ammeter and voltmeter. By continuing the process of “make” and “ break ” the coherence caused by the original one spark will gradually die out. When all traces of it have gone a fresh set may be taken. We have then this ascertained fact, that whatever physical change occurs in coherence—whether mere fusion, allotropic change, or the formation of a string of particles asa “ bridge” —there is associated with it some polarization or a change simulating polarization. This change of the surface particles departs aftera few ‘‘makes ” and “ breaks,” leaving the sur- face quite normal. Let us call this change Orientation, leaving for the present any explanation or conception of it. There are four distinct sets of results for orientation according to the methods of examining it; they will be given in the four following sections. 6A. Direct Currents. In this section the current is always sent through the contact in one direction and is constant in strength, about ,!, ampere. The following table consists of five parts corresponding to 276 Mr. P. E. Shaw: the five times a spark is sent to the contact. After each spark the orientation is gradually lost and disappears before the next spark is put on, the voltmeter also returning to its maximum in each ease. Tasie VI. Radiation. R.T. R.C. Voltmeter. One spark......... 2730 2000 O27. 2720 2530 0-7-0°8 hovering 2730 2730 1:42 Oue spark ...... . 2790 2700 0°20 2790 2770 2790 2760 0-7 hovering 2790 2790 1:42 One spark......... 2790 1590 0-20 2790 2590 13-14 hovers 2790 2790 1-42 One spark... 2790 2000 0-20 | 2790 2490 0:6 hovering |» 2790 2790 1-42 One spark.......-. 2790 1590 0:20 | 2790 2790 1°42 6B. Mirect and Reverse Currents. In this section, radiation is sent to the contact sometimes when the circuit is open and sometimes when a current is passing: the results appear to be very much the same. After breaking the coherence and treating as in the last section, all orientation appears to have gone ; but it is not so, for, if the current be then reversed, at once and always there is a pronounced coherence. It seems as if the particles at the contact have a strain or some latent peculiarity which a reverse current brings into effect. This phenomenon is dis- played clearly in the following tables and curves. In column 2 it is stated whether contact is made once or often ; for it was found that repeated make of the contact-circuit often brought out coherence, when a single make failed to do so. The last traces of orientation may thus be brought out and removed from the contact. Investigation of the Simple Coherer. 207 Tasie VII. C.O. Circuit open. C.D. Current direct. C.R. Current reversed. | Circuit. Making of Contact.| R.T. R.C. Voltmeter. One spark C.O. sts 2000 C.D. Make once. | 2600 2600 0°35 | C.D. iC “ | 2600 1-42 | C.D. ‘. ug 2600 C.D. es 2 2300 0°45 C.D. “ = 2600 C.D. ‘3 < | 2000 0°45 C.D. i. S41) 2600 | C.K. a 4 1000 0-9 hover. C.R. eS 5 _ 1000 C.R. 5 st 2600 1-42 C.R. ~ 3 2600 C.R. bs i | 2600 1:42 C.D. o}) ” 9 99 C.D. 3 bb] ” 99 C.D. Made often. se zs rp, C.D. ” ” ? 39 C.D. 29 »” oi) 9 TasLe VIII. Circuit. Making of Contact.| R.T. R.C. Voltmeter. One spark C.0. 2600 2000 C.O. a 2600 C.D Make once. ‘ 2600 0-5 hover. C.D. ” > 2600 0-7 hover. CR: a3 8 1500 C.R. s ,. 2600 1-42 C.D s x 2600 i C.D Pe ‘ 2600 | - CR i i 1600 | 1:88 C.R 3 ‘ 2600 C.D. |}. ie . 1600 1°35 C.D. a ie 2600 1-42 C.R. 39 99 2 ” C.R. ” ” ” y C.D. 29 9 oe) } C.D. 39 ” ” Cm. 4 i 1600 | 06 C.R 2600 1°42 C.D. “ - “3 Pe C.R. ” ” ” ” | C.D. ” ” ” ” | C.R. 99 » ”? 9 The two curves show that reversing the current, especially putting Reverse (R) after Direct (D), causes a most pro-- 278 Mr. P. E. Shaw: — nounced coherence to be displayed, until, at the end of each curve, no coherence is obtained by any means ; all orientation has now gone. | hee a im La Lele fa ie ei ie Li HAE} See Bie See GERBERA E Ace SSee aI ‘ee! MESTEAE| ‘iz Bal APES PUSS eaeSeese eo UI i Hi | | S PES NBe ies Curves for Tables VII. and VIL, [| a ‘a ia A a a im le R VE SUCCESS/ ee | i iia eee eae ea a ae ae tes Se Dimes —& SINSIYSHOD SO FSIHOSY Investigation of the Simple Coherer. 279 6c. Strong and Weak Currents. _ Having the wires freshly cleaned, if the spark-gap is put, say 40.cm. (7. e. comparatively far) from the contact, then on producing a spark a weak current, say 0:001 ampere, will refuse to pass the contact, and no coherence will occur. But repeat the operation with the resistance in the circuit reduced so that the current, if it passed, would be a large one, say 0:02 ampere, then coherence does occur, and the current passes. On proceeding with the observations, two things will be noticed : (1) coherence becomes greater at each fresh trial with the strong current ; (2) coherence now occurs always for a weak current. Thus a strong current seems to prepare the contact in some way both for coherence and for the easy passage of a weak current. See Table IX. TABLE IX. Resistance Radiation.. in Contact | Ammeter. | Voltmeter.| R.T. 1 Or Circuit. One spark. 1050 53 0-01 520 530 One * 150 oe 0:13 Pa 530 One ‘, 50 88 0:27 Fe 600 One 99 39 9 ” ” 660 Without ” ” oF) ” 530 One ” ” ” ” 9 800 Without ,, a . - 530 One 29 ” ” ” ” 730 Without ,, 1050 53 0:01 a 530 One ,, a 9 %) 9 S00 One. 2 > 99 ” 800 6D. Direction of Discharge and of Current. Another relation observed was between the direction of the contact-current and of the discharge ; the latter was seen by attaching a Geissler tube to the terminals of the Ruhmkorff. It was found that when the direction of the discharge agreed with that of the current, coherence was much greater than for opposition. This is shown in Table X. and curve (p. 281). The curve is easily understood; the four highest peaks are obtained when radiation and circuit-current agree; the other peaks, five in number, are produced when R and C are opposite. 280 Mr. P. E. Shaw: 7. Dimensions of the “ Bridge.” Instead of considering the two wires forming the simple coherer to be in actual metallic contact, suppose each wire to TABLE X. f 1 pers une fe ser eecnan me Tu Paresh | >ycllunctoe irection. direction. R.D. C.R. 2800 2000 0°30 se. 2800 R.D. C.R. 4 2000 0°30 = 2800 ; R.D. C.D. es 1600 | f 2800 - R.D. C.D. 5 1300 0°32 a 2800 R.D. C.R. ee 2400 0:28 i 2800 R.R. C.R. # 1200 0:27 3 2800 R.R. C.R. Ss 700 0:34 » 2800 R.R. C.D. 4. 2000 0-19 2800 R.R. C.D. Ps 2000 0-19 Ae ' 2800 have a layer of condensed gases over its whole surface. Suppose that this layer is not all squeezed out when the wires are brought together with the small pressures used in these experiments. This layer remaining is very thin, but if it does remain, as we suppose, it will produce a discontinuity there, so that practically no current can pass. When, however, violent changes in the E.M.F. are pro- duced across it, it will be pierced and a “ bridge” of particles may be formed between the metal surfaces. This bridge is not formed of loose particles, but has the full strength of solid metal; so that. though very small, it has considerable strength and stability, and as such might exhibit the forces of coherence. As previously stated, the resistance of the contact could be written down at any time ; thus, for example, take Table I[X.; the resistances after coherence range from 8@ to 25, but if R=resistance of ‘ bridge” (say 10), k=specitic resistance (00000017 for copper), =length of “ bridge,” a=radius of area ot contact, then pee ee TA ee Investigation of the Simple Coherer. 281 FORCE OF COHERENCE. a ae ee Eh tS ee CEH SS as ee Pee | pT PE ae NS Te eT ei lie aeoao co ae ece eee me Poi ie Pee sles ieee oe Yi aa TO I CS ie ee WEE braless See eae ae Oe Ts ae ee fee a ef oe fe Pl ee I aes Scale eT eS oe. SEE 2 Wee SiN Sed Pee eine fas la L ae SHYVSG FSAISSTIIING EE SEE Sal [TS aie fissietantis PEEEEPENEEEN Ee BS maemo ot eT eas 8 J naa ea ae eens _—_ === eS PERE eee aoa. Te eeeenieee eee a JIE SSa2 2a nulla Paez Ney Aas al Vet a "YX 9[QVy, 1Of oAINs) but in Section 3, @ was shown to be of the order 10-° cm. Hence we have a. | Ta, ki. l. 105-2 yi ow lO 3 x LU Phil. Mag. 8. 6. Vol. 1. No. 3. March 1901. U 282 | Mr. P. E. Shaw: This rough value of /, though small, is not small enough, for I have frequently examined the surfaces after cohesion with a microscope and have never seen any markings even with high-power objectives. The bridge is assumed to be all over the area of contact, wa*. If we assume that the bridge is formed over lh of the area of contact, / would be os as much *.. 7 ‘ Knowing the area of cross-section of the bridge and the force required to break it, 2. e. to sunder the wires, we can determine the breaking-stress (F) per unit area of the material. Let the force be 1 dyne, then 1 r= Aas ap @ KOE? CLERSY 2 but this is about the breaking-stress per unit area for copper, so that there is good agreement between theory and experiment. When current passes through the contact, it is obvious that melting will occur over a very small area—-but as s20n as any melting occurs, the area in contact rapidly increases, and the conditions are changed. Consider the case of a current =0'00la@ and resistance =10o. Suppose the copper acted on has an area 10—* sq. em. and a depth 10-* cm. ‘Then, if the density is 9 and specitic heat 0-1, the rise in temperature in one second: eye at £0. MAK _ (0:001)?x 10 | 1 a ee 10-§ x 10-8 x 9x O-1 =2x 10° about. Suppose only +,4, of the heat produced is effective, we should have a rise in temperature in one second of 2000° about. ‘This would be ample to weld the surfaces under the pressure existing, which has been already shown to be of the order 200 atmos. lf the resuits obtained above are rough, it must be re- membered that considerable conjecture has had to be made : * The latter would probably be the case. If 2 = » J=3X10_5, which is a more reasonable result. n 1000 Investigation of the Simple Coherer. 283 moreover, the surfaces of the wires are not, as supposed, perfect cylinders but, examined minutely, would obviously appear most irregular. The calculations serve to show that the conception of a bridge and its consequeaces are not by any means incompatible with the data so far obtained. 8. The Lonic Theory of Conduction. According to the recently developed theory, conduction occurs in metals by much the same process as in electrolytes and gases, 7.e. by ionic movements. Under electric force atoms are split up into negative and positive ions ; these, or at any rate the small negative ions, are carriers of electricity, each having a unit charge. Any atom receiving a negative ion maintains its neutrality by at once losing a similar ion ; thus the charges are banded on from atom to atom throughout the metal. If the current became great per unit area of cross-section, we can imagine that the majority of the atoms would be in action at any instant, and that the commotion among them would be very great. Prof. J. J. Thomson™* recently suggested that an ion may attain such speed as to shatter an atom on meeting it, producing from it many ions. Another view of conduction is that held by Mr. Suther- land t, who considers the shattering of the atoms an un- necessary assumption ; he supposes that electricity exists in neutrons which split under electric torce into positive and negative electrons ; these have an existence independent of the atoms and pass the charges along on some Grothuss-chain system. Adopting these views, imagine the current passing through the simple ‘coherer. In the wires themselves, the agitation of atoms (or neutrons) would be moderate ; but at the place of contact, where the area of cross-section is so restricted, the commotion would be intensified in inverse proportion to the area (say 10° times). A loosening of particles and formation of a “bridge” would be most likely to occur, with sudden drop in resistance of the contact. The particles of the bridge being deposited or laid in this peculiar way would be likely to have some “ orientation” or arrangement for maximum conduction. When the radiation stops, the bridge is com- * Phil. Mag. xlvii. 1899. + Phil. Mag. Sept. 1900. Other writings on this subject are:—J. J. Thomson: A paper read before the Paris Congress on Physics, 1900; Riecke, Wied. Ann. lxvi p-. 9998. U2 284 Mr. P. E. Shaw : plete, the atomic agitation is reduced, but coherence is now accomplished. When the wires are pulled asunder the bridge is snapped ; but traces of orientation may be seen for some time when the surfaces are brought together again, as shown in Tables VI., VES Ve, The difference between the state in the wire and at the contact will be evident from the simple relation N=T.q, where n=no. of ions per c.c.; r=mean free time; g=no. of ions formed per sec. per c.c. Now the velocity of ions might vary as the potential gradient if ; : ? - which would be enormous in the bridge; but the mean free-path would increase probably at the same time, so that t would not increase fast enough to prevent n and g from becoming very 2reat. It is possible that some part is played by ionization of the air-film between the wires ; but, so far, there seems no direct evidence of this. 9. Hesults of other Investigators. During the last three years a great deal of experimental work on the nature of coherence has been published. The theories of Lodge * and Branly +, the pioneers of the subject, are well known ; these opposing views have been subjected to many and varied tests. The view of Lodge has been repeatedly shown to stand the test of experiment, and is at present pre-eminent. The following brief summary will give some idea of the experimental results so far obtained :— Aschkinass t considers that, since chemically clean copper coheres well, the oxide film is not essential to coherence phenomena. [But a condensed air-film may exist apart from any oxide as such; his observation makes the ease for a condensed air-film stronger. | Blondel § found that the thickness of the film of oxide or sulphide on the metal filings must not be greater or less than a certain amount. [I shall show later that a very thick film will not oe bridged over when discharge occurs ; also a thin film will not provide sufficient insulation. | * Phil. Mag. i894, xxxvii. p. 94; Electrician, 1897, p. 87. + Comptes Rendus, 111. p. 786, and 125. p- 939, { Wiedemann’s Vo 1898. § Eclairaye Electrique, 1898. Investigation of the Simple Coherer. 285 D. van Gultk * observed that if two free platinum wires were separated by as much as 0:0004 cm., then, when radiation reaches them, a spark pierces the intervening di- electric, and particles pass through the hole thus made, forming a bridge of particles from wire to wire. [I have found a maximum striking distance of 0°000012 cm., but my surtaces were rigidly fixed. ] Sundorph +, using an iron coherer, found a string of particles formed from one contact-surface to another. On observing that heating destrovs coherence, and that cooling does not do so, he inferred that the chain breaks up under end pressure but not under tension. [But suppose orientation to oceur, then heating loosens the particles and orientation would be destroyed, whereas cooling would have a contrary effect. | Branly { observed small surface-resistance in copper, zinc, brass, silver, german-silver, and large resistance in aluminium, iron, lead, bismuth. [The difference between the two sets is certainly not in readiness to form oxide; it may depend on power of condensing air on the surface. ] Tommasina§ and Hérdén || showed that when coherence occurs a chain of particles is formed by the orientation of small fragments under the influence of the electric field. Guthe § Trowbridge 4.—The experimental method used has some points of resemblance to the aphometer method described above ; one contact of two metals was used, the. pressure of the surfaces being controlled by a screw. One important result was that the high initial resistance was not produced until some hours had elapsed after cleaning. They also found that the potential-difference between the ends of the contact rises to a definite maximum when current increases. This is a curious and striking result. It is evident that when the maximum potential-difference has been obtained, any increase in current is attended by a pro- portional decrease in resistance of the contact. The authors suggest that there is a layer of condensed, badly-conducting gas, possibly water-vapour. A current then produces ions in this layer, and resistance falls. One would like to try, as a test of this conception, whether co- herence occurs between platinum wires which have been * Wied. Ann. 1898. + Wied. Ann. July 1899. Tt Comptes Rendus, 1898, p. 219. § Comptes Rendus, July 1899. || Llectrotechn. Zeitschr. April 1900. 4] Phys. Rev. July 1900, p. 22. 286 Mr. P. E. Shaw: heated to redness 7m vacuo and left in the same vacuum. Also, if there is this electrolytic action at the contact, we ought to be able to get more direct evidence of it than has been furnished so far. Bose*, having made an exhaustive investigation of the more common elements, metallic and non-metallic, found : (1) that some elements (e. g. potassium) show an increase and some (e.q. iron) show a decrease in resistance after receiving electric radiation ; these opposite effects he named nevative: and positive coherence respectively : (2) that a- coherer resistance is liable to “ fatigue” and “reversal” effects, if the radiation be maintained for long. His theory is that the radiation produces an allotropic modification on the surface of the substance on which it falls. This being a skin effect, and the allotropic modification being unstable, | there is a tendency for the contact to return to the normal state. Thus radiation sets up a backward influence against its own action, which increases as time goes on. As less and less effect seems to result from radiation, “fatigue” is seen. The same influences might produce a further effect under certain conditions, so that a positive coherence would give place to a negative one and wice versd: this is “reversal.” “ Fatigue” and “‘reversal’’ are displayed by a very inter- esting series of curves. Now, that molecular changes, with the production of Tele forms, do occur in his experiments, seems indis- putable. For when once coherence has occurred, it is an undoubted fact that metallic conduction occurs throughout the system (the air and oxide films, with their uncertainties, being excluded), so that, there being continuous metal, the “ fatioue” and “reversal”? must be due to changes zn the’ metal. But whereas Prof. Bose seems to consider that these allotropic changes occur over the whole surface of the bodies used (2. e. wherever radiation can fallt ), surely only the contacts themselves influence the results! It isin the very restricted area of touch of two surfaces that all changes in resistance occur; obviously this bridge region must have a preponderating influence in his experiments. I have already shown what seems to be evidence of molecular change or “ orientation,’ but to use the term allotropic scarcely seems at present justified. All allotropic change is no doubt molecular, but not conversely ; so that the more general expression seems preferable in the present state of our (want of) knowledge of molecules. * Roy. Soc. Proc. Aug. 1900. . + This is the only rendering which seems possible frcm his paper. Investigation of the Simple Coherer. 287 After reading the above paper, I looked for reversal, and frequently found rapid changes in resistance of the contact ; thus on one occasion, on sending successive sparks, the follewing veitmeter readings were recorded :— 1-42 0-5 1°42 1:42 0-26 0-3 0:28 0°26 0°32 1-42 0-5 0-24 Further sparks produced no change, the voltmeter remaining at 0°24. T. Mizuno* has recently made a careful study of the change in resistance of coherers made of filings (in one case he used two lead balls touching) as successive sparks were received. ‘This individual-spark method, which I also used, is the ehvious way to measure off radiation and to watch its quantitative effect. A set of curves are given showing the relation of number of sparks to resistance. The general tendency after the first spark is for the resistance to fall to a fairly constant value ; but in bismuth (specially), zine, iron, and antimony the resistance-curve rises distinctly. Bismuth gives peculiarly high resistances, confirming my own results (see later). The inference to be drawn from the whole paper seems to be that the bridge formed by the first spark is as a rule strengthened (by acquiring new particles or by molecular change ?) by succeeding sparks, but that for a few metals the bridge is weakened by some contrary action. It will be seen in the above summary (1) that most writers agree that a protecting film of some sort exists at the surface ; but whereas they all seem to consider an oxide actually formed, it appears to me that a layer of condensed air might answer all the requirements in some, at any rate, of my own experiments: (2) that many writers uphold, in some cases on direct experimental evidence, that a bridge of particles is laid between the metal surfaces: (3) that a strictly molecular change occurs in the metal is upheld, with ample evidence, by Bose and by him alone ; but he seems } to have paid little attention to points (1) and (2). 7 My own views are expressed at the end of this paper. * Phil. Mag. Nov. 1900. + Principal Lodge writing, partly in reference to the work of Prof. Bose, in a letter to the ‘ Electrician, Oct. 12, 1900, says:—‘“ There seems a, tendency to regard the metallic coherence as a theory, whereas it is a fact.” He goes on to say that the coherence can be felt; it can also be seen when particles are made to hold together in a string. 288 Mr. P. E. Shaw : 10. Various Metals and Carbon. All the work so far mentioned was done with a copper- copper coherer ; we will now come to other combinations. Complete observations of coherence were taken, but only a table summarizing the results will be given. The phe- nomena displayed are so diverse that it might almost be said that every pair of metals behaved differently from every other pair. It was interesting, in trying different combinations, to watch for idiosyncrasies, as one had ever new and peculiar effects. Coherence for direct current is abbreviated to C.D.C. ox » Yadiation a Be One, two, or three stars in a column shows whether the effect is weak, strong, or very strong respectively. This table shows :— (1) The general principle of the important réle which oxide plays at the contact—for all the more oxidizable metals show such rapid oxidation of the contact that no coherence will take place after a few “makes” and “ breaks”; then a new place has to be chosen on the wires. Moreover, platinum-platinum, the least oxidizable of all cases, shows wonderful cohering power. (2) A fluttering, lasting for many minutes, occurs in the voltmeter readings when the current is weak in the case of some metals. This is a noteworthy peculiarity, it certainly does not occur as a rule. Now since the pressure of the wires on one another is constant and vibrations are excluded, we must infer that some (molecular?) breakdown and recovery are going on at the contact. It is only found for weak currents and is most pronounced in the alloys, platinoid and manganin. ‘The current seems to be ‘critical,’ more current would break down opposition and give the molecules a permanent “set ”’ or orientation, while less current would be quite ineffective. (3) Hvidence of some fragile bridge certainly for graphite-fusemetal and platinum-platinum. It pressure was increased in these cases, but not apparently in others, the bridge between the surfaces seems to have been crushed and coherence destroyed. (4) Lead seems to make contact in a remarkable way: each time the wires touched, a singular noise, like a creaking door-hinge, was heard in the telephone of the contact circuit. =P) ‘ @) N ye the Simple Coherer. of vestigation In Combination. rr nn ee eee Tron-Iron ......... ST ohiad ee Becca Copper MusP= wine Meee rere ses deareee ase. oe Fuse-wire—Fuse-wire ....... es aioe Sh Graphite-Graphite ......./........ aoe oie CA DINILC I NISO=WATES sac eseseur scart ster eas 0: Aluminium—Aluminium ........ tes PEF 8 | WCAG SMCAC: Hivesecevesteces: a, Pe eer TIN AVO Oe saree A a | Platinum=Platiaum ,....... AES Blea ene EA Goren laite —P latimlina, seeaecpan cen eete snes one Magnesium—Magnesium ....... a anaes is Platinoid—Platinoid .......... eae a a German silver—Gernian silver.............. Manganin—Manganin ...... samen ers siete ari (ia eth awash stance Se netaee ace : H Myo] ed FU Gjb0(0) (6 fuer A en Re ee ee | Platinoid—German silver .....:............. ~Cadmium-Cadmium ...... PER ted, BISIUMU MS OISITAUIUIO saves seeauiees cence see one sats | Iron-—Bismuth .......... A estc cs eee Any? eeceee % x Bridge. Coherence depends on the state of the surface. Bridge broken if pressure is put on. Contact soon ruined by oxide. Creaking heard in the telephone. Wonderful sticking O,D.C. for large | currents, Voltmeter wavers. Voltmeter wavers. Orientation observed. | Very high resistance of contact. | 290 Mr. P. KE. Shaw : It is well to point out such peculiarities as this one, until we can fully explain them ; for who can say how important such apparently isolated phenomena will become when the day arrives for framing a comprehensive theory of molecules to satisfy the demands of Physics ? 11. Tests with the Electric Micrometer. Having observed coherence effects so far described with the Aphometer, I turned to an apparatus, the Electric Micro- meter, which I had at hand, for some further tests. The above instrument is described by me in Phil. Mag., Dec. 1900, where it is shown that measurements of 10-6 em. can be accurately made. Briefly expressed, the principle is to have a screw s with a large graduated plate g (fig. 3) anda Cell R | r= Condenser series of levers a, 6, c, d, e, f, so that when a small movement is made of the graduated disk g an exceedingly small move- ment may be obtained at the far end z. The movement of w may be made forward or backward. Touch is made between the surfaces « and y electrically, a small current passing, 7. ¢. sufficient to sound the telephone T in the simple circuit shown. Suppose that x is brought gradually very close to y, sparks Investigation of the Simple Coherer. 290 being produced at the spark-gap near at hand, then we shall be able to observe, by listening in the telephone, whether any discharge or coherence occurs at the contacts a, y. The same process may be continued when the surfaces just touch, or when, going further, they press one another hard. Suppose coherence occurs when the surfaces are, say 5x 10-7 em. apart, then on drawing 2 away, y will hold to it for a small distance, but severance must occur, the surfaces being now, say 1x 10-°cm. apart; the difference between these two distances will provide some information as to the force of coherence. We can also find what is the limiting distance at which coherence will occur, whether any bridge is formed, and we can look for orientation, &c. Tt is evident that in such an arrangement we have a valuable auxiliary means of examining coherence problems. As in the last section the observations, except for three short tables, will be curtailed to a mere table summarizing the results. Two stars show when the effect is a pronounced one. CDG: C.R. Combinations. | fone Remarks. | Coher- “sg »| Coher-| Limit of 4 “Snap. at | ence. | ence. Striking. ESS On ee in a ae 2 i ee Copper—Copper ...... geese Se oe 3 12x10-* em. = _Copper-Fuse-metal... , Het PE WOE es sat * Copper-Iron ......... ae ae Bae “ Copper-Carbon ...... Mr Al cae IN. Baad (tons ..... | Small effects only. Seopper-Elatinum.:....) » + | « x Carbon-Platinum ... 0 Bg Wi hla? sel ~Carbon-Carbon ...... S ) Oe Boy eee ae aie . Large region of in-| Patna tridio- complete contact. | ple TMA Sees aaron On 0 i 10x10-Gem., «x Platinum-Platinum... =, 0 S 8x10—-6cem.) ,. » | Distinct “fatigue” shown. The following table was taken to ascertain the “ striking ” distance for Copper-Copper and the effect of the coherence on, the contact. By the striking distance is meant the greatest distance of separation of the contacts with which coherence can be produced by radiation from the given source at a known distance. Taser XI. ee i ae aire | Distance t Micrometer Readings for contact. -{rom 3 . | Distance | No. of , spark-gap arks, |?Part of the Remarks. | to sparks: | contacts. Next Next “ | Make Diff. . contacts. *| Break. Make. 60cm, 3. |25x107° 470 | 670 | 5x10~8 480 |) ‘Thesereadingswere | Nor | taken after the con- Peete F 480 | 6380 | 37x10 500 | } tactshad been pressed | a, | home; there was al- if at 4990 | 620 | 33x10 510) waysabridge of loose ue 28 | particles which were |. Le i BOSC NG DIO | 400 AiO thus pressed flat into ibe | the contacts. ff 75x10 590 | no cojherence. i e 530 | 940 | 10x107~° | anal 10x10-°) 560 | 920 | 9x10-° | | aes | | { A discharge in tele- | 0 12°5x 10 O10)= | aoc) erence: 5) tere aml | phone at each spark, | et 256 _{ but no coberence. | i 75X10 580 | 730 5x10 The next table is for Copper-F' ER for strong ‘steady currents, no radiation. TaBLe NII. | Resistance} Diff. between make and Remarks. In cireuit. break x107° em. | 1000 none. E.M.F. in cireuit is about 2 yolts. | 200 5 to 12°5 | 100 9 to 15 30 25 | these soon A pronounced “snap” oceurs when \ get less + the contacts are separated—not | 20 36} (oxide ?). noticeable for the high resistances. The following is for Platinum-Platinum for strong steady currents. TaBLE XIIE. Resistance} Diff. between make and Remarks. in circuit. break x 107° em 5000 incomplete contacts. 200 50, 19, 125, 7:5, 5, |) Between the first and second line | was a pause of 4 min.; between the | Wey 8) ‘second and third a pause of 10 | mins. Each line shows some WS kee, ) “fatigue” and each pause some recovery. 100 AQ, 17, Investigation of the Simple Coherer. 293 The accompanying curve displays this peculiar fatigue, and the recovery in the power of the surfaces to hold one ‘another. AMOUNT OF COHERENCE. SIHUM, IAISSFIING co isi sie ma Bega de eee ra PEEPS Bae = 20 ee | ae Ea [L eat J eae ae ee ee top at tT Senos, 0s | _ SRS eae eee ae ae TS a an ARS 2 meat BEE er | | cloacal alle cif Vile ILD Bee eee ee eee ak eae I a Se ae | aes O[QVyT, lof OATNS) MMIC MAIC E Om be [ohio oe i oe eRe eee Ae ee The conclusions arrived at from these tables are :— (1) The “ striking ” distance under the conditions stated seems to be about the same, viz. 10~° cm. for the three cases 294 Mr. 2. BY Shaw's tried. A bridge at once forms, if the distance is less than this amount. There are two ways in which the surfaces might come into contact when set at this small distance apart: (a) by a shattering of the surface particles under great electric stress, a bridge of particles being laid across ; (6) by the diaphragm bending until it touched the other contact. Taking Lord Rayleigh’s measurement* that the ratio force/displacement of an ordinary diaphragm =10' ¢.¢.s., then the displacement 10-° cm. would only require about 100 dynes. If this force came into action on the diaphragm, it would meet the other contact without the help of (a). While allowing that (b) may influence the result, it can with certainty be said that (a) does occur, for repeatedly there was evidence during the experiments of a quantity of loose particles or of some easily-crushed bridge which formed during coherence. It seems again that it must be a thin bridge and not loose particles, for the surface always made a sharp contact of a distinct sort. The evidence of van Gulik on this “‘ striking ” distance has already been quoted. (2) A pronounced rending apart of the surfaces, observed as a “snap” in the telephone, was found after coherence with the more fusible copper-iron and fuse-metal, but not with carbon, platinum, and iridio-platinum. (3) The action of platinum (Table XITI.) is remarkable. It calls for some explanation. The only one seems to be that orientation occurs due to coherence which enables the surfaces to hold one another a/ter discharge but not before; also there is a remarkable fatigue and recovery involved. (4) A measure was found of the distance of incomplete contact of hard carbon. It is a very variable quantity due to the soft, friable nature of its surfaces as compared with metal surfaces. The extremes were 5 x 107-® cm. to 50 x10-® cm.; 2. ¢., for complete contact the movement necessary was sometimes as much as the first number and never more than the last. This property alone would indicate carbon as the material par excellence for microphone contacts, no metal used in any way resembling it in this respect. In working with carbon coherers it is well to bear this action in mind. 12. Summary of Results. The Electric Micrometer has proved of service in studying the Simple Coherer, for by it we obtain some idea of the * “ Quantitative Theory of the Telephone,” Phil. Mag. xxxvii. 1894.. Investigation of the Simple Coherer. 295 distances as well as of the forces involved. The Aphometer is less delicate in action, is not concerned with small distances, but is an incomparably better instrument for determining forces and is more under control. The Simple Coherer alone has been used, the idea being to reduce the problem of coherence to its simplest possible terms. Yet the results obtained are involved and complex, so much so that it seems as though it would be hopeless to expect a satisfactory and full explanation of coherence to ‘crystallize out’ from a study of the usual complex coherer. For in the Simple Coherer, at any rate, the conditions at one contact can be fairly well kept constant or varied at will. As much cannot be said of the ordinary coherer. To mention some chief points in conclusion :— I. The insulating layer between the surfaces of the contact is of importance before the first coherence has occurred. It _has been shown that a condensed-air layer might produce all the well-known resistance, at any rate in many cases, in my investigations. Oxide as such asserts itself when strong currents pass with certain easily oxidized metals, but this is a special case and does not aftect the statement above. II. The term bridge has been used throughout to express the region between one metal and the other. Even if, as some may suppose, the metal surfaces merely compress one another so as to touch over a small area (calculated in section 3), and there is actually no length to the bridge ; still, it is necessary to have some term to represent the narrow space, call it a doorway, into which the current is compressed in going from wire to wire. Whether it more resembles a narrow bridge or a doorway, its strength is un- mistakable as the tables in this paper will show. There actually is a bridge in certain cases which have heen pointed out—but they may be exceptions or they may not. III. The (molecular) change called in this paper orienta- tion seems the most interesting fact brought to light. It should have an important influence on our conceptions of molecules and their relations to currents. The observations of Prof. Bose, already referred to, seem to point in the same | direction. Some curious stray phenomena noticed during the research have been mentioned ; others have been omitted, but are none the less interesting. Of the problem of coherence itself, many of the facts are left, so to speak, in the raw state. There is, quite obviously, a great deal of work yet to be done on the subject. at 296 Dr. Richardson and Mr. Laws on Changes in the Magnetic For instance, the Aphometer might be put bodily into the bell-jar of an air-pump, the wires passing into it. By this means the experimenter would have a better chance of success, as some distressing complications would be eliminated when a dry neutral atmosphere surrounded the contacts. [ am glad to thank Professor W. H. Heaton, M.A., for his kindness in always placing the resources of this laboratory freely at my disposal. XXIV. On some Interesting Changes in the Magnetic Condition of an Alloy of nearly Pure Iron and Aluminium (2°42 °/,) due to successive Heatings and Coolings. By 8S. W. RicHarpson, J).Sc., Principal and Professor of Physics at the Hartley College, “Southampton, and 8. C. Laws, B.Sc., Research Student at the University College, Nottingham *. THXHE behaviour of alloys is attracting so much attention at the present time that the authors felt that the curious phenomena which they have observed might be of interest to some observers who are studying this subject, althongh the investigation of the magnetic properties of the specimens dis- cussed in this paper is far from complete. An account of some experiments on the same subject by one of us is given in the Philosophical Magazine for January 1900. In this paper it is shown that the effect of temperature on the magnetic behaviour of impure alloys of iron and aluminium is very different from that on the behaviour of iron itself. It is shown that the curves connecting the permeability and temperature for a constant field have at least two maxima, which is explained by assuming that the specimens investi- gated consisted of two distinct constituents. Subsequent microscopic examinations have shown the presence of crystals in all the specimens except one. This demonstrates to us clearly that there are at least two constituents present in the specimens. The subject was of so interesting a nature that it was decided to continue the investigation, dealing in the first instance with very pure specimens. A series of these were accordingly obtained from Professor Arnold, of Sheffield. The behaviour of the first one, which is the only one we have investigated so far, was so striking that we thought it worth while to publish at this early stage a short account of some of our experiments. The specimen’ referred to contained about 2°42 per cent. of aluminium. * Communicated by the Authors. Condition of an Alloy of nearly Pure lron and Aluminium. 297 It did not contain any large amount of impurity, as is shown by the following analysis :— VUITTON. Fp. ew eae ee CARON? ouiviy Lethon ete OO MaMoaneses, V5 prs) etree a wOpOo UO Sih iakce cy. an rd ae ORO Ehosphoriise 20 3 - «~ o)s.u.0:02 Supt ewe se os ae 10008 fron (by difference) . .° . 97°29 This specimen was cast in the form of a disk. A ring was turned out from this disk, and was wound with primary and secondary coils carefully insulated with asbestos paper. The ballistic method was used for measuring the induction, and the temperature was determined from the resistance of a platinum wire furnished with compensating leads. The specimen was heated by means of a current flowing in a non-inductively wound platinum wire. By this means a constant and easily adjustable source of heat was obtained. A detailed account of the apparatus and method of expe- riment will be found elsewhere. The specimen, which had not been annealed, was slowly heated or cooled over a considerable range of temperature, and the induction was measured from time to time when the temperature had become steady. It was found that no two successive curves were the same. For a low field (H=0°5) the permeability increased with each heating. The curves at first showed three very distinct maxima, which, however, became less and less marked with each heating. In the first experiments it was found that the induction increased slightly at first, and then very rapidly diminished, having a very small value at about 300° C. On further heating the induction increased again up to 470° C. It then diminished, though not to any large extent, until the temperature reached 510° C. _ On still further heating, it increased rapidly to a tempe- rature not much below that of minimum permeability, when it fell off very abruptly. The curve, however, on nearing the axis of no induction bent round gradually, showing, as has been previously demonstrated by one of us, that these specimens do not abruptly lose their magnetic properties as the temperature approximates to that of minimum permeability. As the heatings and coolings are continued the curves. Phil. Mag. 8. 6. Vol. 1. No. 3. March 1901. xX 298 Dr. Richardson and Mr. Laws on Changes in the Magnetic ‘become smoother and smoother, and the second maximum very soon disappears altogether. new maximum, however, begins to develop between 500° C. and 600° C. This maximum will be seen clearly in ) eurve VII. 4 The following particulars will enable the changes taking place to be followed by the reader. TES Q ® 2) g b = | 2 rt} Vi @ ‘ 4° i Ny a iD 7 a = ay 1 Rm, we i Pp —o—P = tee i So i o~/t. Se a hat cette (A) These electric forces will tend to produce currents which are of the same type as those assumed to exist, but turned through a right angle in a direction opposed to that of the angular velocity. This is seen by comparing equations (1) and (2) with (3) and (4), and noting that the latter becomes proportional to the former when (¢ “ie 5 | is substituted for ¢. Hence the effect of these forces will be to add a system of eurrents which will have the same effect as a rotation of the original system in a direction opposite to that of the rotating sphere. 4, To show that the whole system of currents will rotate in the body and to determine the period of rotation some further calculations are necessary. The system of currents we are considering will produce a uniform magnetic field, M, within the sphere, which is equal to Sarl. The energy of the total magnetic field is easily found to be pen 2 ane, Now imagine such a system of currents as we have been con- sidering, in which the current crossing an element ds, of the arc QA (fig. 1) is Isinads;, and let electric forces equal to A sina act at each point on the system of currents. If ds, is an element of the line along which the forces act, the rate of doing work in the surface element ds,ds, is AI sin’ a ds,ds». Hence the rate of doing work over the whole sphere is { Al sin? a ds, dsy=2mAla? {rs sin’ ada 0 = a Ald’. The currents will increase in intensity and the rate of doing work must be equal to the rate of increase of energy. Hence, 318 Prof. A. Schuster on Magnetic Precession. 7 denoting time ays nh oi gue ae 3 Ald’, or dl 3A dr 87a’ This equation will determine the rate of increase of the system of currents due to a given system of forces of corre- sponding type. In the system of currents with OQ as axis, we may take the current-intensity I, at the points at which a= a to be the variable, which is now to be considered a function of the time tr. We also take I’ to be the corresponding variable of a_ ‘system of similar currents having OR as axis. Introducing, the forces due to the rotation of the sphere, we find that iu 3 dt 87at*® ol, a 4 ne Reo epee From which we deduce T=], cos Or, == ly sin Wap. where O0= ae and Ip is the initial value of I. Q is the angular velocity with which the whole system of currents revolves. 3. The rate of rotation of a system of currents in a rotating spherical sheet which has been determined in the simplest case, can also be calculated when the distribution of currents is of a more complicated character. Let there be a current function a® on a sphere of radius a from which the current-intensities are derived, so that if ws and we are the currents in the direction of the axes of X and Y respectively: : (e = Introducing polar coordinates and taking dw = ad6, dy=a sin ddd, we find as in the previous paragraph that the electric forces Vz and Vy, acting towards the south and Prof. A. Schuster on Magnetic Precession. 319 east respectively are expressed by Vs=2pueur cos O/t Wp = —2pwrig cos 6/t, or | 2uw cos 0 dd 2 VY3s=— Rabie de’ e ° ° s ©) _ __ 2a cot 0 dD Put d® d? Essa eCaeaae Puan toa UN and | d® d? ee ene co a ahaa on eee) where « is a constant and H and K functions of ¢ and @, which are to be determined. If an operation is performed with the equations (7) and (8), which may be represented by the symbol 47) — in g 8) a sin 0 16” the left-hand side of the resulting equation becomes Te eile — cos 8 oe asin oe | dp” a0 do "de dd’ on the right-hand side we have = he i d g d , dH _ dKsin@ «| Sin ad? dd" quag|®+ do dO Hence dH dKsné@ _ d d IL eee Sp Gi P. dd dO onl ae Ee qu seas aii nl The right-hand side vanishes, if ® is a surface harmonic of degree n, provided that n(n + 1) =1/k. Hence we may put in that case, _ dQ = el) © de aan Odd Equations (7) and (8) will now become A 7 a ha 3) ala ie n.n+1 SEs eT gi ete XY) meh 2.0 iL OF dQ : pee Yn=~> t ts n+1 qesg sin a) (0) 320 Prof. A. Schuster on Magnetic Precession. As ® only depends on ¢ in so far as it contains terms which have coso@ or sino¢ as factors, the effect of dif- ferentiating with respect to ¢ is the same as a multiplication by o and a change of of to of+ a Hence the terms depending on ® will be proportional to the original current- intensities if of is replaced by of + = In other words the currents which the forces Vy.and Vy tend to produce are of the same type as the origindl currents, but turned through 7 e e e e e e an angle 5—round the axis of rotation, in a direction opposite 20 ? to that of the angular velocity of the body. If the original current function has been proportional to cos o@ or to sin o¢, inertia will tend to produce currents of the same type but proportional to —sinod or to cosa@ respectively. The _ final effect of these will be a rotation of the system of currents. 6. The terms depending on Q in (9) and (10) will not produce any permanent currents, but an _ electrification having —2u@Qa/t for potential. We obtain Q from (8), by substituting K=dQ/sin @dd. After integration with respect to @, it is thus found that ~ oe Q=® cos 0 «sin 07, ‘ This may be put into the standard form of tesseral har- monics, if we write @=T, cosod and ao, aN : where 7X=cos@ and P, stands for the zonal harmonic of degree n. | | By differentiation we obtain T? = sin’@ sin go 1 =0 cos 6 T? —sin@ Trt, We have also the following general equations :— (2n+1) sin OT7*°= (nto+1)(n+o)Ti_1—(n—o +1)(n—o)Ti 4); (Qn +1)eTi=(n—o +1)Triit+(n+o)Ti 1. Combining these equations we obtain n.n+l1.2n + 1Q=(m—c+1)n?T7 1 cos od +(n+1)?(n+o)Tz_, cos od. Prof. A. Schuster on Magnetic Precession. 321 7. To obtain the angular velocity of the system of currents, we may proceed as in the simple case, which has already been discussed. A current-function a®, of degree » produces a magnetic potential which inside the sphere is equal to n+1 Torte ‘ ~~) QD, and in the outer space Bee Peas The energy of eee stress is easily calculated from this and found to be Wane a *{ as. 2n+1 If there is a force-function ®’ from which the electric forces are derived in the same way as the currents from the current-function, the rate of doing work in a rectangular element bounded by the linear elements ad@ and asin 6d will be "GD hey dP dev! IS. le Odbsin@db dé dé an But ee AP’! { sin Odd — sin Odd as ® and © only contain ¢@ in the form of a factor cos op or sin o@. By partial integration, if again X\=cos 8, db dd! one de! 3 9 a e {Sn On er in —(¢ a sin 26 —— vA dn; so that the total rate of doing work will be ; dD’ acon 2) {e { 258 6 ~ nny dn } an which by the characteristic equation of tesseral harmonics becomes dS= sae sin? @ é n.n+ 1/ BO‘ds. The rate of doing work is equal to the rate of increase of energy ; hence 87a dD Sn ee Pee / ER Coben (A, cos 2na+ B, sin 2na) from a=h, toa=o0. n=1 H | The integration of (6) now gives Hl | x | i | 2a a2\ (0 4h) Pp ae ss a Mi | 1=—" (H+ al e? .dy +- _[e AE A Pee vE| | i Ne 7-5 se fs Jae ie JH | i | 2 V4(H—hs) N= co Sz nes MH | + — Eg! (ayo Ss "cos (2nH— a2 Vn) Ki | WV oT iclonct & n=1 iH V4(H—h,) is . + Be?” "sin (2nH— « Vn) i | n= V4(H— he Jp 2 Mi | fo ee (A, cos 29nH + B, sin 2nH) ( COS 5-5. e-? . dy TW n=1 2/9 y) Ht iS V4(H—h3) > 2 | : I | N= 0 2 NL : Ii | ute >(A, sin 2nH—B, cos anti) sin dy E79” Lay een 0 Wh | i | V0 n=1 Let us next suppose that H varies continuously, so as to Magnetic Induction in Lron and other Metals. 339 cover an exceedingly large number of periods. The changes in I become then truly cyclic. For if in (9) we put, in place of H, H+ ™ Z, and ultimately nN make Z=> millim., and a discharge sent through, then on letting a small quantity of air rush into the tube, a beautiful luminous wave was seen to travel up the tube into the bulb. This phenomenon admits of a ready explanation in the light of Mr. Newall’s discovery. (10) At the meeting of the British Association at Oxford Iread a paper ‘‘ On the Luminosity produced when a Vacuum Bulb is broken ”’ (see also Phil. Mag. Jan. 1895). It was then shown that a luminosity must undoubtedly have been produced by the collision of the particles of glass when the bulb was broken, a view which was verified by breaking a glass plate at the mouth of a tall glass receiver, as a number of luminous spots were distinctly visible at various parts of the receiver. And it was also found that two bits of glass, when. struck, produced a bright flash. Nevertheless there was a continuous glow as well to be explained, especially in the case of vacuum-bulbs when broken, and this may easily have been due to the “ pressure glow,” since in a glow-lamp the same change may have been brought about, and energy stored up almost indefinitely in the gas, as by the passage of’ a spark through it. The spark or flash from the collision of glass may also have produced some ionization. (11) Since the pressures at which the after-glow, and the “ pressure glow,”’ occur are within the one range of pressures, it suggests at once that the two phenomena can be traced ultimately to the same cause. However, they differ in this one respect, that whereas the after-glow gives a continuous 354 Mr. J. B. B. Burke on the spectrum, the ‘‘ pressure glow ” gives a band spectrum and is the same as that which Schuster had observed in the negative glow of oxygen. We are now referring to the spectrum of the glow in gases in which oxygen is the predominant element, ‘but we have reason to regard—after a careful study of the "question—the presence of oxygen somehow as a necessary condition for the production of the glow in every case, although, as has been shown, it is not in ‘itself a sufficient one. The connexion at once shown, by the identity of the spectram between the negative glow in oxygen and the ‘pressure glow” in the same gas, appears to be of the utmost importance in the study of the cause of phosphorescence in gases, since it reveals the operation of a process in the pro- duction of the latter phenomenon such as is known to take place in the neighbourhood of the cathode by the passage of an ordinary discharge through the gas. As has been pointed out, the glow ina gas produced by a discharge between electrodes is confined to the neighbourhood of the cathode, but the degree of exhaustion requires to be much higher than in the case of the ring discharge ; the pressure at which this glow is conspicuous is about 34 mm., about that at which the resistance of the gas to a discharge between electrodes placed as in the tube is least ; just as the pressure at which the after-glow with the ring-discharge is produced is in the region of that at which the resistance of the gas to the electrodeless discharge is a minimum. The after-glow, however, which follows a discharge between electrodes in an ordinary tube is one which I have never observed to be particularly brilliant. Nevertheless, when there is a stream of gas passing through the discharge-tube, the glow, as in the experiment w hich Professor Dewar showed at the Royal Institution (loc. cit.), is very marked. This is what might have been expected, since the removal of the phosphorescent particles, whose existence has been demon- strated, from the destructive influence of the cathode should or eatly increase their persistency, since the experiments described in art. (5) show that cathode-rays destroy the glow whilst the positive discharge may be sent through the olowing gas without materially affecting it. It is to some process occurring at the end of the dark space that the negative glow is obviously due. J. W. Capstick (Proc. Roy. Soc. 1898) has shown that the cathode-fall at the boundary of the dark space is the same in oxygen, air, nitric oxide, and nitrogen with traces of oxygen ; thus indicating that oxygen is fhe: carrier of elec= Phosphorescent Glow in Gases. 35d: tricity in each case, just as we have seen that it is the active and necessary agent in the production of the phosphorescent pressure-glow, which by its spectrum may be identified with the spectrum of the negative glow in oxygen. The Hon. R. J. Strutt (Phil. Trans. vol. exciii. p. 393) has shown that the minimum spark-potential, or cathode-fall— which he has proved to be of the same magnitude—is in atmo- spheric air 341 volts and in ordinary nitrogen between 347 and 388 volts, but that in nitrogen specially freed from all traces of oxygen it was as low as 251 volts. A gas appears to have the capacity to store up energy when a spark is sent through it, just as a certain amount of energy is necessary before a discharge can be made to pass ; and this: extra amount appears to be about the same in all gases in which there is a trace of oxygen. This minimum amount of work which has to be performed is done in the boundary of the dark space, near the region also of the negative glow. It is most probable that the effect of cathode-rays is to: increase suddenly the brilliancy of the phosphorescence to such an extent as to reduce its duration. As in the destruc- tive effect of infra-red rays on phosphorescent substances, discovered by Becquerel, which has been explained in this manner as a particular kind of thermo-luminescence. This is what might be expected from the fact that the negative glow is at all possible in the presence of the cathode- rays when a discharge passes ; since, as we have seen, the glow lasts much longer when it is removed from the influence of the cathode. (12) Returning io the tube, fig. 3, another observation of sume importance may be described in connexion with the negative glow. Thus if either of the bulbs A or B had been standing for some time unused (say A), and a ring-discharge was sent through it, the pressure in the tube being such that the after-glow was produced round the cathode when a discharge was sent between the electrodes ed: 1t was found that there was no visible effect accom- panying the ring-discharge in the neighbourhood of the electrode c, except when a discharge had previously been sent between the electrodes cd, ¢ being cathode: then a brilliant fluorescence accompanied the ring-discharge just round the curved portion of the end of the side tube at c; and this effect was obtained a considerable time after the passage of the discharge between ¢d—on one occasion, fully an hour after. When ¢ is anode the phenomenon does not occur- Philipps (‘ Hlectrician, Sept. 1900, and B. A. Bradford, 1900) ——s SS SSS 356 On the Phosphorescent Glow in Gases. has shown that there is an emanation of gaseous particles from the cathode for a long time after the discharge has passed. It seems probable that the emanation of particles from the cathode for so long a time may be connected with the observation I have described. It is difficult to say whether this phenomenon is one of fluorescence of the glass or of a layer of gas on the glass round the cathode. The effect appears to be instantaneous, and to accompany the ring-discharge ; but it occurs only when the pressure in the gas is so low that the phosphorescent glow appears round the cathode c when the discharge is sent between cd. Meissner and also Dela Rue and Hugo Miiller have shown that when a discharge passes through a gas there is a sudden change of pressure, in some instances amounting to 30 per cent. ‘They have shown that this is not due to heating. The experiments of Hertz (Wied. Ann. xix. p. 78, 1883) also show that the discharge is an explosive effect, and that this is more vigorous at the anode than at the cathode. For instance, a tube with a narrow mouth had the cathode close to the open end and the anode at the bottom, and the whole was in the interior of a bell jar. When a discharge was sent between the electrodes from a leyden-jar, a glow was pro- duced which was blown out of the tube to some distance from the open end. This would explain the fluorescence round the cathode e (fig. 3), since the explosive effects of the ring-discharge would be to compress the gas round the electrode e. That the phos- phorescence does not last long may be compensated for by the tact that it is extremely brilliant, and the phosphorescence is always a time-integral. The explosive effect of the ring-discharge would also account for the curious fact, that the after-glow in one of the long tubes at pressures of about 7y mm., when the glow is at its best, appeared to start at the end farthest from the bulb as well as in the bulb, the two moving in opposite directions until they | met, when it became uniform throughout the tube. This was doubtless again due to compression at the end of the tube. [To be continued. | ial Oo Ou +] ee far \ “Ca \\ \\ ’ ; | XXXI. Note on the subject of a Paper by Prof. L. T. More = “On the supposed Elongation of a Dielectric in an Electro- static Field” *. By Dr. P. SACERDOTE fT. ROF. L. T. MORE, of the University of Nebraska, has recently published an account of a series of experiments in which he purposed measuring the elongation experienced by a glass tube forming the dielectric of a cylindrical con- denser when the condenser is charged. In none of his experiments did he succeed in observing any elongation or contraction of the tube: from this he concludes that no electrical deformations of dielectrics exist, and that those observed by Govi, Duter, Righi, Quincke, &. were only due to disturbing causes. In the present note I shall show that the conclusion to be drawn from Prof. More’s paper is quite different. By the very disposition of his experiments the tube should not experience any appreciable elongation; thus the negative result of his experiments merely proves that they were carefully performed. 1. For the description of the apparatus I refer to Prof. More’s paper, merely recalling that it consisted essentially of a glass tube A, 2°5 mm. thick, and of two coaxial metal tubes B’ B”’, which constitute the armatures, the one Bb’ interior, the other B” exterior to A, from which they are separated by an interval ; the arrangement for magnifying the dilatation was such that one division of the micrometer eye- , : ae piece corresponded to an elongation of A of 755 micron f. First Hxperiment.—The space between B’ and A, as well as that between A and B”, is filled with an insulating liquid ;. then, the armature DB’ being earthed, B” is charged by an electric machine. In no case did Prof. More obtain any displacement of the reflected image by the amplifying mirror.. Second Experiment.—The cylinder B” is removed and replaced by tinfoil 45 cm. long cemented on A. The space between B’ and A is filled with acidulated water forming the internal armature. Prof. More still obtained no elongation or contraction, even on charging this condenser to high _ potentials corresponding to sparks of 12 mm. to 20 mm. between two brass knobs of 2 cm. diameter. * Phil. Mag. vol. 1. pp. 198-210 (1900). + Communicated by the Author. { I omit all criticism relative to the apparatus, although in my oyinion,. for such small displacements, direct measurement by interference-fringes . is the only one that can be relied on, and it is in any case much prefer-- able to any mechanical process of amplification. B58 Dr. P. Sacerdote on the supposed Hlongation of 2. Discussion of the Second Experiment.—In this experiment ‘we have to do with a condenser of which the dielectric is the glass and the armatures are adherent to the dielectric and follow its deformations ; these conditions are quite analogous to those in the experiments of Righi, Quincke, and Cantone*, ‘On the basis of the figures obtained by this last author, we ean calculate a priori the elongation which the tube should undergo in the experiments of Prof. More. Let | be the length of the condenser, Al be its elongation when charged to the potential V, e be the distance between the armatures, which is here equal to the thickness of the dielectric. A : , : Al Cantone’s experiments give for the expression o X73 T values { varying between 4°6 and 7:1 x 10-18: let us take the mueano x Imi. Denoting by x the elongation to be pre- Beles for the ‘eae in Prof. More’s experiment (for a spark- Jength of 12 mm., V=110c.a.s.), we have a oe Zoe Peso? Tee * In a long criticism of the experimental work on this question (Sacerdote, “ Recherches théoriques sur les déformations électriques des .diélectriques solides isotropes,” Annales de ph ys, et chime, sér. 7, t, XX. pp. 289-377 ; abstract, Journ. de Phys. sér. 3, t. vili. Sept.—Oct. 1899) I have already shown (pp. 344-369) that the experiments of Duter, Right, and Quincke should only be considered from the qualitatwe point of view ; while those of Prof. Cantone (Rendiconti della R. Acc. der Lincei, ser. 4, t. iv. pp. 844-853, 471-477, 1888), in which the elongation is measured directly by the displacement of interference-fringes, present far greater guarantees of accuracy, and that these are the only ones the numerical results of which can be depended on. Prof. More does not appear to have been acquainted either with my paper or with the experiments of Prof. Cantone. + The formula for the electric deformation of a thin cylindrical con- denser with adherent armatures is = (a+ ae = in which a, k,, K are Hiden depending solely on the nature of the dielectric (for the proof of this formula and the eee of the co- efficients see Sacerdote, loc. cit. p. 307) ; the quantity “ xe should thus be sensibly the same in the experiments of Prof. Mee and in those of Prof. Cantone. t See Sacerdote, doc. cet. table on p. 368; these numbers have just been confirmed by recent researches (Cantone & Sozzani, ‘‘ Nuovo Ricerche intorno alla Deformazione dei Condensatori,” Rendiconti della £. Istituto Lombardo, sey. 2, t. xxxiii. 1900). a Dielectric in an Electrostatic F. veld. 359 whence BO [es oe de hoe © = Fg uueren =, which corresponds to only 34 divisions of the micrometer eye- piece t—a displacement which evidently could not be observed with certainty, since on pp. 202, 203 of his paper Prof. More mentions displacements of the zero of the micrometer which exceed 3 divisions t. Discussion of the First Lxperiment.—In the second experi- ment we had to deal with a thin condenser with adherent armatures ; the dilatation being in this case given by the formula § Al KH? aris) ery atts, Wowie fa 2 (1) H denoting the intensity of the electric field in the glass (H=V/e). In the first experiment we have, on the contrary, a condenser with armatures independent of the glass tube, since they are separated from it by a liquid dielectric ; the dilatation is thus given by the formula || él Ki? 7 al ere a age ee) h denoting the new intensity of the electric field in the glass. Butas: (1) The coefficient k, is considerably smaller than (2) The field 4 is much less intense than H, since the potential-differences were the same and the distance between the armatures much greater. The elongation J will thus be much smaller still than A/, and consequently absolutely inappreciable. * For a spark-length of 20 mm. (V=130 c.a.s.) puis. micron—that is to say, less than 5 divisions of the micrometer, 100 + Prof. Cantone used tubes having a length of 60 to 70cm. and a thickness of only 0:4 to 0-6 mm. ; and we know that the dilatation increases in proportion to the length and in inverse ratio to the square of the thickness. { Prof. More, who had also the trouble to make this tion, hoped to obtain elongations of 20 to 30 divisions; but, as he wasnot aware of the work of Prof. Cantone, he based this expectation on the experiments of Righi and Quincke, which, I repeat (see note (*), p. 358), are altogether to be rejected from a quantitative standpoint, § See note (t), p. 358. || For the proof of this formula, see Sacerdote, Jou. de Phys. Feb.— Mar. 1901. 4] (See Sacerdote, loc. cit, p. 372.) k, is of the order 10—12 C.G.s. and a nearly equal to 1:6 10—-12.¢.¢.5. preliminary calcula- T2360" q XXXIT. Intelligence and Miscellaneous Articles. To the Kditors of the Philosophical Magazine. The Gamble Institute, St. Helens. Feb. 11, 1901. GENTLEMEN, F. NANSEN points out in his work on Hydrometers that the employment of hydrometers of total immersion was first sug- gested by Prof. Pisati, and that such instraments were afterwards used by N. Reggiani and an account of them published in 1890. I regret that ignorance prevented me acknowledging their work in my paper on Hydrometers of Total Immersion, published in your Magazine in December 1899. I trust that you and your readers will excuse me, on the ground that I am only a chemist and have but little acquaintance with modern work in physics. Yours faithfully, Arraur W. WARRINGTON. OBITUARY NOTICE : PROFESSOR FITZGERALD. We deeply regret to have to announce the death of Professor G. I’. FirzGeraxp, which took place on Thursday, the 21st. The following paragraph, which appears from a correspondent in the ‘Times’ of the 25th, describes so well his amiable character and eminent position among men of science, that it will be appreciated by all Physicists. In him we have lost a most kind and judicious adviser :— “‘ Professor FitzGerald was recognized as being among the foremost men of his generation in physical science; the most ungrudgingly helpful to ail other scientific men; looked up to by his contem- poraries, not merely with respect, but with such genuine affection that this paragraph conveys not merely a news of disaster to the progress of science, but of a personal calamity to great men of science all over the world. He was the indefatigable helper of his students, a number of whom are Fellows of the Royal Society. He was the colleague and inspiring friend of all men who were trying to do good in the world, but more especially of men who were trying to help Irish industry and Irish education of all types. In every department of applied science, in any kind of engineering, his advice was known to be valuable, and he was always ready to give it. His life was devoted to the interests of others in a whole- hearted way. He seemed perfectly unselfish, quite disinclined to have his name honoured, and yet perfectly alive to his own worth. His friends in England have not known that he was very unwell. It was thought advisable to perform an operation; this was successful, but he had not sufficient strength to recover.” TH & LONDON EDINBURGH, axp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERTES.]———._ . aw doers scans > ak = wd ae a ¥ ef “ep. a bt APRIL 1901. APR ID ) 90} cx | Ui WS. XXXII. Onakind of easily Abdeb6H Radiation produced by » the Impact of slowly moving Cathode Rays; together C) lies 00008 volt 2 169 2°359 $3727 70 below ZnSO,+ 3 118 BOY 35148 120 100H,O, 4 056 4341 36376 182 5 5321 3°7260 237 Lussana’s observations. Sols. ZnSO,| E.M.F. Bie eee an Eecal saiga GO E.M.F. from in 100,000 g.| _ volts or iGGoG cease normal soln. water. (differences) ; Volts x 10~4. 120 |. 9.9059 0-110 40414 —166 | By _ interpolation 13°8 S 93 0-149 4:1732 114 -normalsolution lies 12:7 x 30) 0-724 48597 31 0:0031 volt below 195°8 < 114 1:791 3°2531 + 49 727 ZnSO, solu- 556'3 4-150 36180 163 | ‘tion. Temperature about 23°. a Force and Osmotic Pressure. 3989 Concentration-cells without migration. Moser’s observations. | E.M.¥F. in lal sea fineres log C E.M.F. in | Denciee) 6) 1000Ie! | =~. | voltsx10—4 | ZnSO,+800H,0. = 0 146 | 41644 ZnSO,+100H,0. 0:0227 V1OG. > pl SOs) are oto Goodwin's observations. | | gm.-equiv./litre. ye E.M.F: in | 1000 ©. Se area? : | 02 to002 | 4301 to 5301 497 ' 01 to001 — 4-000 to 5-000 440 | With PbSO, as | te * = epoleicaten 0:02 to 0002 5301 to 6-301 522 i (vii.) New Experiments. To test the accuracy of the relation between electromotive force and osmotic pressure as given in the foregoing theo- retical treatment, and to provide data for calculating the osmotic pressure, it is clearly necessary to make more syste- matic and complete experiments than has so far been done. In endeavouring to fill up this deficiency, I chose in the first place the salts of zinc, because zine electrodes are well known to give results of a satisfactory degree of constancy. The measurements so far made have been on the chloride and sulphate of zinc: the former possesses the advantage of an excepticnally great solubility, allowing of investigations in the regions of concentration which are especially interesting from the point of view of this paper. The sulphate is, however, preferable in the matter of purity, and neutrality; whilst as the course of the molecular con- ductivity curve is considerably different for the two salts, a comparison of results will give some indications as to the properties common to salts in general. Materials.—FYor electrodes, zinc rod (obtained trom John- son and Matthey) was cleaned with emery-cloth, and amal- vamated: or when liquid electrodes were to be used, some of the same zine was dissolved by gentle heating in about 100 times its weight of mercury. The zine rods on standing for days in a zine solution sometimes became coated with a 390 Dr, R. A. Lehfeldt on Electromotive flocculent black deposit, the nature of which was not determined with certainty, but’was probably metallic indium. The deposit appeared to make no difference to the electro- motive force, and after repeated cleaning of the rods gradually ceased. | The zine sulphate contained no iron, or other appreciable impurity ; solutions were made up from it, as obtained, and merely filtered into stock bottles. Several strong solutions were weighed out direct: those below normal strength were made by diluting a strong solution with pipette and measure- flask. The zine chloride, in the form of fused sticks, contained no appreciable impurity except zinc hydroxide: a strong solution of the chloride was found to dissolve an appreciable amount of the hydroxide, which is precipitated on dilution. To obtain a neutral solution the sticks were dissolved in water and hydrochloric acid added till the liquid just began to turn litmus red: the density was taken, and the concen- tration calculated from the tables in Kohlrausch and Holborn’s Leitvermégen der Elektrolyte: weaker solutions could be pre- pared by dilution, without further inconvenience. The mercurous sulphate (Harrington’s) was that used for Clark cells ; it remained perfectly white in use. The mer- curous chloride at first contained traces of mercuric chloride, but on washing proved quite satisfactory. Cells—-The cells used are here referred to for brevity as “mercury ” and “ concentration ” cells. The former are of the types, } Zn : ZnCl, : HgsCl,, :-Hg, Zn : ZnSO,: Hg.S8O,: Hg, the latter | Zn: ZnCl, (dilute) : ZuCl, (conc.) : Zn, Zn : ZnSO, (dilute) : ZnSO, (cone.) : Zn. The “mercury” cells were of two kinds, “rod” and “amalgam.’ The rod cells were made up in short wide test-tubes, closed by corks with two borings: one of these held in place the glass tube through the end of which a platinum wire was sealed for communication with the mercury : when the mercury had been poured in and the platinum fixed in place, the depolarisator and the solution were added through the other boring, and lastly the zine rod fixed in it: the platinum wire consequently remained clean and dry. The amalgam cells were made up in H form, with similar precautions. ‘ Force and Osmotic Pressure. 391 ' After a good many failures a form of “concentration ” cell was designed which satisfied the requirements of facility of setting up and cleaning, freedom from diffusion, and low internal resistance: it served equally for rod or amalgam electrodes. A pair of glass tubes, AA fig. 2 (8 cm. x2), have each a short side tube, B B, blown on at about halt their length: the side tubes fit by means of short pieces of rubber tubing inside a straight tube C (3 em.x1) which carries the porous diaphragm ; this is a fragment of a porous soup-plate D, filed round and fitted in by a ring of india- rubber. Hach tube A is closed by a rubber stopper with two holes, one for the electrode; the other, made merely for convenience in filiing, is eventually closed by a glass rod. By working the side tube B backwards and forwards in the central tube C, the air can be driven out of the latter. The cells were placed—up to six at a time—in a wooden holder by which they were held in a sink filled with water; the sink was provided with a thermoregulator, and. kept within one or two tenths of 20°-2 cent. The Clark cells were kept in the same thermostat. Electrical measuring arrangements.—The E.M.F. of the concentration-cells, or in the case of the “ mercury ” cells the difference between their E.M.F.’s or between each one and a Clark, was measured by the compensation method. At first a Crompton potentiometer was used, but. subsequently given up on account of the necessity for frequently readjusting ; a P.O. box was then adopted, the resistance being always kept greater than 100 ohms. Under these circumstances the accumulator (charged fortnightly, and discharged for half an hour at maximum rate before using) gave such a constant E.M.F. that it was only necessary to take a reading with the Clark cell once a day to standardize. The connexions are 392; Dr. R. A. Lehfeldt on Electromotive shown in fig. 3. The accumulator A was connected to the terminals of the box ad: 1000 ohms taken out of the arm be, and about 430 from ed, making the H.M.F. between 0} and c equal to that of a Clark cell. The Clark or other cell was Fig. 5. connected by a multiple switch from the tapping-key at ¢ through a Crompton “midget” galvanometer to c, the wire touching on the way at the other tapping-key /; putting down the latter short-circuits the galvanometer and damps it, while the right-hand key puts the experimental cell in circuit. The E.M.F. between a and d having first been found when the Clark is in circuit, may be regarded as known for the subsequent experiments ; for although the total resistance between a and d varies, it is always so large as to leave the E.M.F. between the terminals of the ac- cumulator practically unaffected. The results obtained are shown in the following tables and also on the accompanying diagram (p. 397) :— | ZInc CHLORIDE. 1st Series.—Solution («) prepared as described above. Den- sity 1:1238 at 19°7 (referred to water at 4°) : corre- sponding concentration calculated to be 2:19 times normal, Amalgam cells. EN ar EMF. EME. EMF. So Uy) log C= —w. observed. differences. | from normal. (1000 C). Volts. | Volisx 1024 velepalgee 2=719 3-340 10406 +249 | 2/2 3-039 > 220 4 99 = DA a4 4-738 > 225 196 2/8 4-437 > 23 _ 496 2/16 4136 | > 228 epost #/32 5 835 as = 869) > | 393 con- ~~ Force and Osmotic Pressure. 2nd Series—Solution (y). Density 16049 at 20°3: centration 12°33 normal. Amalgam cells. gm.-equiv./litre lone) BM. He observed rain normal. (1006 C). : Volts! Volts x 10-4. y=12'33 2-091 0:9378 +1263 y/10 3-091 10573 2 GS y/100 4091 1:1298 — 657 3rd Series.—Solution (y) as before. Amalgam cells. | gm.-equiv./litre Se E.M.F. | | (1000 C). log C=— eat we | from normal. : Volts x10—4. | y= 1233 | 2-091 0-9382 +1288 | y/2 3790 1-0005 + 665 | | yA | 3°489 10300 + 370 | | y/8 3188 1-0528 + 142 | y/16 | 4 887 1-0755 — 85 | | y/80 | 4188 11269 — 599 | ! | 4th Series—Solution (z). Density 1:9538 at 20°. Since this density lies beyond the range of the tables, another was prepared from it, by mixing 40 e¢.c. of (z) with 20 c.c. of water. The density of the latter (2/3 z) was 1°6624 at 20°: whence the concentration (from the tables) =13°51 normal, and thence that of the original solution is 19°94 normal. The solution (2/3 <) was diluted similarly to form (4/9 z): density of the latter 14536 at 20°, whence concentration 9°089 normal : it was then diluted to (4/90 s) with pipette and flask in the usual way. Amalgam cells. E.MFE. | | Solution. log C=—~. pee cree oe from normai. olts. 1 VoltssqloSa | 2 1-000 0°8539 Hoyas | | 2/3 z 218 09246 +1406 | 4/9 z 3-958 0:9740 gta Lis 4,90 z 4-958 1:0683 = ol | Phil. Mag. 8. 6. Vol. 1. No. 4. April 1901. 2D 394. Dr. R. A. Lehfeldt on Electromotive Mean electromotive force of a cell containing equivalent, normal ZnCl, solution and 1 per cent. zinc amalgam (from the four series) =1°0054 volts. Concentration-cells (with migration). a E.M.F. Solutions. log C=—w, Volts x 10-4, y : yj10 2091 : 3-091 1309 y/10 : y/100 3091 : 4-091 427 ZInc SULPHATE. lst Series.—Twice normal solution and its dilutions. Rod cells. gm.-equiv./litre. CK ee eee see 1U00 C. log C— —wp. Op See a erences. _ normal. Volts. Volts x 10-4. | Voltsx 10-4. 2 ou 14558 vee 55 58 2/5 ‘602 ~105 Ss 1 if 3 2/25 5 903 2 a _996 2nd Series.—Twice normal solution and its dilutions. Rod cells. | ine: EMF. EMF. oe aatue ears log C=—vwv. ditferences. from normal. | : Volts x 10-4. Volts x 10-4. fe | ee ee a 2 3°301 se a Za lei): i 3090 0 = = 80) 1/2 4 699 — 80 | as a) | 1/4 4°398 —159 x ae Gr, 1/3 4097 236. Force and Osmotic Pressure. 395. 3rd Series.—Solutions made up directly by weight. Rod cells. iv./li E M.F. E.M.F. ; ae log C= -¥. ne differences. | from normal. ; pigs Volts x 10-4, | Volts x 10-4. (Clark) 3800 nearly (14285 4.855 e if assuined.) |> 81 33 3715 ie 4974 = a Nise 3 S477 +142 7 = 2 5301 oY 60 | noe V3 3.239 Mt 28 | nas 4th Series.—Solutions made up directly by weight. Amal- gam cells. ee WM.F. ae io C= a Pee from normal. : olts. Volts x 10-4. 33 3-715 14306 +296 3 3477 14452 +150 2 3-301 1:4520 a? | V3 3-239 1:4545 J. 57 Concentration Cells. Solution. leg C=—y. See. NG: a2 S715 : 3301 162 ea /5 3301 : 4602 131 215 + 2/25 4602 : 5-908 111 Noel 3239 : 5-000 47 Ae te 55 3:60 : £602 65 1 = 4/10 3000 : +000 178 £53 1//100 3000 : 5:000 307 2D2 Dr. R. A. Lehfeldt on Llectromotive AS) a LA 396 Electromotive Force of Concentration Cells (without migration) at 20°. Finechionae: “| I.M.F. from normal solution. | Volts x 10-4. 4 | gm.-eq./litre| log C from | 1000 GC). | ==w. con- or!) eae Cale. by Cale. ductivity. equation (2).| (Nernst). | curve). 0-001 6-000 2108 2363 2°888 2 -301 1861 2108 2-852 5 69) 1544 1776 2-782 0-01 5000 | —1537 1310 1525. 2-728 2 ‘301 1301 1083 1278 2 658 3 477 1158 956 1137 2-604 , 699 976 199 961 CE 0-1 4-000 747 588 720 2-446 | 2 ‘301 526 392 487 2340. 3 ‘477 392 286 359 2-22 5 699 999 158 199 2-146 ] 3 000 0 0 0 1:970 | 2 301 SLE) re - 1-706 | 3 ATT 865 i 580 4 -602 465 1-406 | 5 699 5d6 1:336 v1 “845 734 12904 1 2-000 1016 1128 15 176 1580 . 20 301 2116 | ieee Zine Sulphate. 0:001 6-000 — 1250 2 Ay 1-841 2 301 1098 1258 1-788 5 699 906 1035 Lol | 0-01 5000 | — 743 770 908 1627 9 “301 617 639 763 1554 | 3 ATT AGT 567 683 1509 5 699 369 AT] 581 1457 —| 0-1 4-000 272 361 449 1395 | 2 301 190 247 302 1343 | 3 A 14] 182 929 T3159 4 5 699 80 104 126 1:276 1 3-000 0 0 0 1-227 D) SOL eonee ie 1172 | 3 “ATT 146 1-133 | 4 602 295 1-102) | 5 ‘699 293 1:077 | 6 ‘778 356 “ | Volts, Force and Osmotic Pressure. 397 No PECs stig DRL RRBeaes ba —---- Ss eee \J lait Eas +e BONS ee LOSS EERE SNENEES ane a Be PEPER EE EEE ETS eae Pgee Sec ee nee na males 0 cof sn oee BEET ea ai BEL _J_ bE RED ER ERE e tee ee oe: See Seesaw suse tnbpees ps uusentueeesneue <.7oseceeceeresaeate N pe | a | ds (Pa RE PS Eee EE _Te eta tae aaa se FEELS ade ia Por avaeea OT tH tt wal Hp Te SEOLAdza@conE Geen ate BOGae semen SReSSB005 Tt ese Pere ale ila (ae el eep Neale ar |e ea d SERRA SSESSRER ERA See RER eee ia = gaauaun iia Sci seteeicisiak (eal a Oe eS |e | tT ol See ne rer eeseaen |_| ROmEROGEMONSneMC a: | a a aes es Seo aie eS ear Eee SE CCRER REE D S225 Tha ee a aS a | PTT tS | BEN UREESANGS Saggy Ee ee eee eee cee eee PEER EEE EECA BRO aR Re eee eaeeewaee ea se A a [| ea a ey ese omt ea reereetae ain eet ie leet taiale eae ae 7 20 25 3°0 35 4°) =log (c. c./gm. equiv.). The general character of the results arrived at is clearly indicated by the diagram. Considering, first, the case of zine chloride, ani starting from the lower end on the curve, representing the most dilute solutions, the relation should, 398 Dr. R. A. Lehfeldt on /lectromotive for indefinitely great dilution, be that given by Nernst’s equation oll Os ; Bee ar log. ahs = 2°3026 x —h5) 5 di 1. é., graphically a straight line witha slope — a = 87 millivolts for unit difference in the common logarithm. Since, how- ever, the disscciation of the salt is sensibly incomplete even for very dilute solutions, the straight part of the curve does not come within the range of experiment ; the electromotive differences are those calculated from equation (2) above, and ee in table. These are: from j,,, normal (W=7) to “ane normal (yr=6) 84 millivolts, from milli- to centi-normal (y=6 to y=5) 80 millivolts, from centi- to deci-normal (yr=5 to w=4) 72 millivolts, the curve consequently being convex upwards. ‘The experimental results agree satisfactorily with the calculated over the range centi- to deci-normal, showing—as might be expected—that the deviation from the value given by the logarithmic formula is accounted for by the incomplete dissociation of the salt, and does not imply any departure from Boyle’s law as applied to the solution. Goodvin’s observations made over the range from p=6 to ar=4°3, which, to save space, are not shown on the diagram, follow satisfactorily on my own, extending the curve into regions of greater dilution. Goodwin compared his observations with the results of the formula (due to Nernst) where y is the degree of dissociation. This formula is conirary to that arrived at thermodynamically above, and I think is wrong. _ Unfortunately there is no means of de- eiding hetween them, since for great dilution they, give values not far apart, and the experimental numbers lie between, while for strong solutions beth formulee are vitiated by the inapplicability of Boyle’s law. It may be noted, however, that strong solutions of ZnSO, and ZnCl, show a maximum of conductivity (and so rameeranena bl of irre con- centration), and thus Nernst’s formula would make the concentrated solution anodic to the dilute, which is not the case. Beyond this point, however, the curve, which on account of incomplete dissociation should continue to bend downwards, is found instead to pass through a point of Force and Osmotic Pressure. 399 inflexion and then bend quite sharply upwards, indicating that the effect of departure from the gaseous laws greatly prevails over that of incomplete dissociation. Thus the values calculated for the range decinormal (y=4) to normal (yr=3) and normal to ten times normal (y=2) on the assumption of Boyle’s law are 59 and 34 millivolts respect- ively : the observed values are 75 and 102. Instead of any distinguishable point of inflexion, the curve shows a long portion that is practicaily straight. In this region, then, the osmotic pressure may be calculated very simply. For then we may put H=—ay+b=—alogyV +), whence diy dE a ee dy iN oasi0: But from (3), for a cell without migration, ren if VdP, whence ' dis =\/ dP LING = dV? and dP = —7¢ Z ay 4 Nog 10, giving Parew 10 Tea@Omsin a4 eus eer Ga) The constant term is small, since the straight part of the curve extends into regions where the deviation from Boyle’s law is negligible. 1t follows, therefore, that we may put : a approximately Le Oe ear and regard the combined me effect of varying dissociation and the finite CONCH Ton of the solution as simulating the behaviour of an idea! gas. ¥rom the value 0°0747 volt for ~=4 to p=3 we get POO 2. 193089 x 0 0747 log. 10 23026 = 6264 joules. Now for an undissociated solution obeying Beyle’s law we should have at 20° PV=RT=8-316 x 293= 2437 joules ; the ratio is 6204 400 Dr. R. A. Lehfeldt on Electromotive But van’t Hoff’s factor as determined by means of the electrolytic conductivity is 2°45 for decinormal, 1°97 for normal solution : hence the osmotic pressure may be reckoned to exceed that calculated trom the laws of gases by about 11 per cent. in the former case, 38 per cent. in the latter. The curve for zinc sulphate shows the same general trend, but differs in certain respects. I could not obtain measure- ments with mercury cells of concentration much below decinormal. Goodwin met with the same difficulty, and: attributed it to some secondary reaction of the Hg,SO,. I um inclined to think that it is mainly due to the appreciable solubility of that salt, which prevents it from constituting an ideal depolarizing electrode (see Goodwin’s work on TiCl loc. cit.). In either case the difficulty remains ; but if it be permissible to associate Goodwin’s measurements with PbSO, as depolarisator with mine, as shown on the diagram, it will be found that the curve bends sharply down to the right, as it should do, since for limiting dilution the value of = ( should be 0-058 volt for unit difference in common logarithm (2/3 of the value for the chloride, since there are only two ions); while in the straight part of he curve i has the abnormally low value of 00272 volt. ‘On account of this sharp curvature the integration constant in (7) cannot. be neglected, and the approximate estimate of the osmotic pressure given in the preceding paragraph fails. The few observations I have made with concentration-cells of the ordinary type were for the sake of verifying the previous work of Moser, Wright & Thomson, and Lussana, This they do satisfactorily ; but I do not consider that, at present, the measurements are sufficiently exact to justify: » calculation of Hittorf’s transference ratios in this Wily lt may be seen from the curve that w increases for ZnCl, from, about O°6 in dilute solution to more than unity in strong solution, in agreement with the results of migration experi- oo) ments ; but before calculating the values in detail 1b will be necessary to extend the experimental data, and to take into theoretical account the successive (“ stufenweise ”) dissociation which undoubtedly occurs in this salt. | (vill.) Calculation of the Osmotic Pressure. To caleulate the osmotic pressure we have re =|VdP Foree and Osmotic Pressure. 401 Hence The integral was evaluated graphically by the method de- scribed in the following ‘‘ Note on Graphical Treatment,” being first transformed, as there shown, into P=re[ HC]—r el E dC, where OL1v | is the concentration. It was assumed that fer a centinormal solution the osmotic pressure might be ecaleu- lated according to Boyle’s law, from the concentration and the degree of dissociation as indicated by measurements of conductivity ; Meme —aulee. or Zach, wer have 2.128. tor ZnSO, Aes 627 from Kohlrausch’s data; C being 10-7 gm.-equiv./litre. Hence ie — Sole <205 xX 27125 x 105?=0:658iatmos (10° dynes/sq. em.) for zinc chloride, and : FP oollod x 293 x 1627 x 10727=0°396 atmo for zinc sulphate. The differences in pressure between centi- normal and the more concentrated solutions were then measured by the planimeter, with the results shown in the following table :— Zine Chloride. ; F smoti ressur Vik: | Gim.-equiy. /litre. Ds Ny . BNE ee | | 0-01 0658 65°8 gal) | Ol 6°65 66:3 de 1 63°7 63°7 32°3 | 2 1236 61°8 onl 3 193 | 64:3 4-0) 4 270 67°D 6 446 74:3 8 660 82:5 10 1006 100°6 12 1475 1229 1+ 2029 144°8 16 2670 166°9 18 3396 188 5 . 20 4207 2103 pi The numbers in the column PV show at first apparent irregularities ; but I think these are not due to errors of 402 On Electromotive Force and Osmotic Pressure. experiment, but are real fluctuations due to the combined effect of the decreasing dissociation of the salt and the in- creasing departure from Boyle’s law. This complication can Ue be partly eliminated by taking the quotient re b determined from the conductivity. Undoubtedly the values of van’t Hoff’s factor ¢ so arrived at are somewhat uncertain, but they are probably near enough to the truth to serve the immediate purpose of bringing out the character of the devia- tions from the gaseous laws. Assuming the values of « to be correct, the quotients PV/c should be constant so far as the gaseous laws are applicable. The table shows that even for a decinormal solution, with a pressure of 7 atmospheres the deviation is marked. It is about as great as that tor sulphur dioxide or ammonia, but in the opposite direction. Large deviation is, of course, to be expected on account of the large size of the dissolved molecules, if for no other reason. the « being Zine Sulphate. 4 Gm.-equiv. /litre. oe eae is PY. . = ORO |: 0396 39°6 24:12 01 do4 30°4 239 1 24:0 24-0 19-6 2 477 23°8 20°3 3 835 Palle: 24°95 4 137 34-2 31:0 5 196 392 36°4 6 263 43°38 It will be seen that there is a decided difference between the behaviour of the chloride and the sulphate. In the latter the values both of PV and PV/e show a well-marked minimum. The sulphate therefore follows the same rule as: the ordinary gases, deviating first on the side of less elasticity than a perfect gas ; afterwards, however, as the specific volume becomes very small, on the opposite side. (ix.) Summary. In the preceding pages an expression is obtained for the K.M.%. of a concentration-cell, with or without migration, by means of a thermodynamic cycle: the expression, which is applicable to strong as well as weak solutions, is given first, On the Graphical Treatment of Experimental Curves. 403 on the assumption of Boyle’s law, in terms of the degree of dissociation of the salt as found from the electrical vonduc- tivity ; afterwards, without that assumption, in more general terms. According to this expression the H.M.F. of a cell depends on the total osmotic pressure of the salt, not on that of the metallic ion only. Experiments are then described, both old ones recalculated, and new ones made for the occasion, in which the E.M.F. of concentration-cells of ZnCl, and ZnSO, are measured; the results being expressed by curves and tables. Finally, from the data thus provided the osmotic pressures of those salts in solutions nearly up to the point of saturation are calculated, and the analogy between those pressures and the pressures of highly compressed gases pointed out. East London Technical College, June 1900. XXXV. Noe on the Graphical Treatment of Experimental Curves. By R. A. LEHFELDT*. \ J HEN as the result of experiments a relation between two quantities y=f(2) has been found, it is sometimes desirable to calculate from it some other function of « of a kind that involves differen- tiating y. The form of the function / being unknown, it is necessary to deal directly with the numerical observations, or with the curve expressing them. ‘This is often done by finding an empirical equation for y=/(x) and differentiating it, but to find a satisfactory empirical equation is not always possible ; and if the subsequent treatment involves integration, the choice of forms is closely limited by the possibilities of the integration. There remains of course the method of differentiating the experimental curve graphically, by drawing tangents; but this should be avoided if it is in any way possible to do so, because the errors of the experimental curve are greatly exaggerated in taking its tangents; and no sub- sequent process of integration can smooth out the errors thus introduced. In certain cases the difficulty can be avoided, and a process of graphical integration, which can be satisfactorily per- formed, substituted for the graphical differentiation. Thus * Communicated by the Physical Society : read Nov. 26, 1900. 404 On the Graphical Treatment of Experimental Curves. if it be required to obtain a quantity 2 such that c=\ h(a (x) f(x) da, where ¢ is a known function, integrate this expression by parts, giving =[p@\fle)]—J ¢'@)fla) de, Here since He is bs ¢'(v) can be calenlated: the expe- | rimental values of /(#@) may then be multiplied by $’(z), and the products plotted with respect to x as abscissa, and the curve so obtained integrated by a planimeter. It wili, however, often happen that $’{(z)f(a) is not suitable for accurate plotting. In this case the independent variable must be changed to (x) =w, say. Then =[o@\fa)]—$ 9" ie = [ry] -S# ey Gee == || wy | —\ ydw. Two examples that may occur in practice are dia)=lee a. . ..) i ee Then | I= flog a di= \y log x] —\yd (log x). Ot) = 7), a eee! (i1.) free —fe) The latter is the case occurring in the preceding paper “ On EHlectromotive Force and Osmotic Pressure.” Another instance, which I did not see how to deal with at the time, occurs in my paper “On the Vapour-Pressure of Liquid Mixtures” (Phil. Mag. [5] xlvi. p. 61 (1898)), where the relation Then ook Pr 5 COS inn ae ai as, Ve pea was to be verified: here # is the molecular fractional com- position of a binary liquid mixture, p,, p2 the vapour-pressures of the two components. It is sometimes much easiér to On the Anomalous Dispersion of Carbon. 405 measure one of the vapour-pressures than the other. Sup- pose p, to be measured, then x dlogp 4, INE areas lr aera Ilence ] log m= | 1 — log | + | Ee, du, and the numerical solution becomes practicable. XXXVI. The Anomalous Dispersion of Carbon. By Prof. R: W..Woop *. 'T was suggested to me some time ago by Professor Ames that the “rapid decrease of amplitude on a wave-front, resulting from its passage through a prism of some str ongly absorbing substance, such as cyanine, might not be without influence on the direction of propag: ation of the transmitted ray. ‘In Huygens’s construction a constant amplitude is assumed over the wave-front, and it is quite conceivable that varying the amplitude might shift slightly the position of the “ effective-point.”” There are obviously two ways of attacking the problem : the mathematical and the experimental. I have been unable to treat the case by any of the geometrical methods, and the simplest way seems to be to determine the form and position of the intensity curve, treating the transmitting edge of the prism as a narrow aperture, the amplitude decreasing across its width according to some linear function, and solving by the method employed in the case of the Fraunhofer or telescopic diffraction phenomena. I have not yet attempted the solution in full, but a cursory examination leads me to anticipate that the central maximum will not be symmetrical with respect to the centre of the system. The highest point of the intensity curve will undoubtedly be at its usual place, in the line normal to the centre of the aperture, but the slope may be steeper on one side than on the other. In all deter- minations of the refractive index of strongly absorbing prisms, when working near the absorption-band, the slit image is broadened by diffraction. By setting the cross-hair of the eyepiece on the centre of this broadened image, we assume that we have determined the centre of the system. If, however, the central maximum of the pattern is unsym- * Communicated by the Physical Society. 406 Prof. R. W. Wood on the metrical, it is clear that a considerable error may be introduced in this way. For a direct experimental test we require some means of cutting down the amplitude without introducing a retardation or change of phase. In searching for a possible substance which would absorb but not retard, I tried films of smoke on glass. It seemed possible that, since the absorption is caused by very minute opaque particles of carbon, the wave might be transmitted without retardation. If this were found to be the case a wedge-shaped film of smoke would furnish the necessary conditions. Examination of the films by means of the interferometer showed, however, that a very marked retardation was introduced. This phenomenon ! subsequently found had been previously observed by Rosicky * and Stark fF. Stark’s results indicated that in the case of films deposited by coal-gas flames, we are dealing with a porous mass con- sisting of 2°28 per cent. of pure.carbon, and 97°72 per cent. of air. He considered the case as that of a turbid medium made up of air with a low, and carbon with a high refractive index, such mixtures being known to possess a refractive index intermediate between the indices of the constituent parts. He made no determinations of the dispersion. It occurred to me that the retardation in this case might be ascribed to diffraction, there being an increase of path due to the passage of the light waves around the carbon particles, the case being analogous to the passage of a sound- wave through a medium containing obstacles symmetrically distributed. I succeeded in photographing the retardation of a sound-wave resulting from its passage through several layers of glass tubes, placed side by side with spaces between. If the retardation of the light by carbon films is due to diffraction, we should expect either to find dispersion absent, which would mean that the path increase is the same for all waves, or else a greater retardation for the long waves than for the short. An attempt was at once made to determine the presence or absence of dispersion, the experiments showing conclusively that the long waves (red) were retarded more than the short ones (violet), the condition found within the absorption-band in the case of substances showing anomalous dispersion. Experiments were made with smoke-filims, and with films deposited in a vacuum on piate-glass by the filament of an incandescent lamp. ‘The average diameter of the carbon * Rosicky, Sitzb. Ber. Wien. Ak. 1878, t Stark, Wied. Anz. Ixil. p. 351, Anomalous Dispersion of Carbon. 407 particles in smoke-films is less than 0°00026 mm., while the regular reflexion at normal incidence of violet light by the deposited films indicates that the diameter of the particles must be less than one-eighth of the wave-length of violet light. (Assuming +A to be the maximum allowable phase- discrepancy.) The dispersion was first measured with a Michelson inter- ferometer, illuminated with monochromatic light of various colours obtained by prismatic analysis. The fringes were photographed and measured as described in the paper on Cyanine*, readings being obtained between wave-lengths 00040 and 00966. The results showed a steady increase of refractive index in passing from blue to red. The results obtained with the deposited films were less satisfactory, owing to the poor quality of glass. They were prepared in the following way :—An incandescent lamp bulb was cut in two and a small piece of German plate-glass introduced; the two halves of the buib were then sealed together in the blowpipe flame, and the air exhausted, after which the lamp was run for several hours at considerably above its rated candle- power. Very uniform metallic-like films were obtained in this way, which gave elliptic polarization. The poorness of the glass, however, made accurate measurements impossible, owing to the irregular curvature of the fringes, and the work will be repeated with films deposited on plane-para!lel optical glass, ‘his seems to be important, since it seems quite possible that the films may be molecular in structure ; the particles are certainly much smaller than in the case of the smoke-films, and may give a ditterent dispersion curve. As far as it was possibie to judge the deposited films showed the same anomaly as the smoke-films. No attempt was made to determine the absolute refractive index, since accurate determinations of the thickness of the smoke-films are difficult. LHven were this possible the values obtained would not mean much. Relative values only were obtained, as indicated in the following table, where n represents the fringe displacement, measured in _fringe- widths, » the wave-length, and nA the product which is proportional to the refractive index, as shown by the usual formula (u—lL)e=nd, where e is the thickness of the film. * “The Anamalous Dispersion of Cyanine,’ R. W. Wood and 0, E. Magnusson, Phil Mag. Aug. 1900, 408. Prof. R. W. Wood on the | Smoke-Film. 2. r. mr. 853 663 - 566 923 605 558 “960 566 543 1:037 520 539 1-064 479 510 1-12¢ 436 490 1-149 414 476 In the case of the films deposited by the lamp, which do not have the exceedingly porous structure of the smoke-films, we can easily determine the thickness by substituting the half-coated plate for the back mirror of the interferometer, and measuring the shift of the fringes at the edge of the reflecting carbon-film. A displacement of one third of a fringe was found with sodium light. The thickness was therefore } x 4 x 000589 or 000098 mm. The displacement. of the sodium-light fringes corresponding to four transmis- sions (two films in optical juxtaposition being used as described in the paper on cyanine) was 0°784 of a fringe, or 0°196 for one transmission. We have then, substituting in the formula (u4—1):000098 =:196 x -000589 p—1l=1-2, or the refractive index 4=2°2, not very far from that of the diamond. Fig. 1. > |GuIDE PLANE PAR PLATE } ) vf Formation of smolke-prisms. One instinctively places more reliance on determinations of refractive index made by prismatic deviation than on those based on interference methods, and an attempt was accord- ingly made to verify the results with carbon prisms. By arranging a very small pointed gas-flame close to the edge ofa glass plate, and sliding a piece of plane parallel optical. glass back and forth against a guide (the tip of the flame just: Anomalous Dispersion of Carbon. 409 touching it), very uniform prismatic deposits of smoke were secured. Viewed in reflected light the films showed Newton’s interference colours, and the prisms were judged by observing whether the coloured bands were straight and properly spaced. A suitable prism having been selected, the plate was covered with a piece of black paper perforated with two rectangular openings of equal width. One of these openings, which was several times higher than the other, was over the prism, while the other covered clear glass close to the refracting edge of the prism. The object of using diaphragms of the same width but of different heights was to secure similarity of the deviated and un- deviated images of the slit. The width of the central maximum depending on the width of the opening alone, the height could be increased to allow the passage of more light in the case of the dark prism. The plate was then placed in a large direct-vision spectro- scope (from which the prisms had been removed) and the slit uluminated alternately with red and blue light. A very intense light being necessary the electric arc was used, the slit being covered alternately with deep ruby glass and a glass trough containing a strong solution of cuprammonium combined with a cyanine film. Prismatic analysis was found to weaken the light too much. The diaphragms were covered alternately, and readings taken of the position of the slit image witha tilar micrometer. The following readings were obtained :— Red. Blue. Distance between dev. Distance between dev. and undey. image in and undev. image in divisions of micrometer. divisions of micrometer. aya) 40 60 50 a9 4] D8 48 a7 45 D8 46 D3 43 56 39 a) 44 61 40 57°2 mean. 43°6 mean. In order to see how these readings agreed with the devia- tion calculated from an interferometer determination of the Phil. Mag. 8. 6. Vol. 1. No. 4. April 1901. 2H 410 On the Anomalous Dispersion of Carbon. retardation at the base of the prism, the plate was set up in front of one of the mirrors of the instrument, a plate of equal thickness being introduced in the other optical path as a compensator. The fringes sloped abruptly down across the face of the prism, the displacement at the base being 1:7 of a fringe for the double transit of Na light, or :85 for a single passage. The retardation is therefore :00059 x °85 or °0005015 mm. The width of the prism was 2:24 mm., therefore the angle through which the wave-front should be turned 1s given by "0005105 tan 0 = a 6 = 46”. The actual deviation as observed in the spectroscope was determined as follows :— Calibration of the filar micrometer showed that one com- plete revolution of the head (160 divisions) corresponded to -248 mm.; 50 divisions, the mean between red and blue corresponding approximately to the deviation for sodium light, represents a shift of -124 mm. The focal length of the telescope was 600 mm., and the deviation is given by 2A tan 6 = 00 é= A) 5 which agrees very well with the calculated deviation of 46’. While the results obtained are what we should expect if the diffraction theory were true, they do not of course prove it; and it will not be safe to draw deductions until more accurate results have been obtained with the metallic deposits obtained from the incandescent carbon filament. A method of compensation has been devised, which will make observations with much thicker films possible. In conclusion I must thank Dr. C. E. Magnusson for much valuable assistance in photographing and measuring the fringes. Physical Laboratory of the University of Wisconsin, Madison. le saan Jt XXXVI. The Liquefaction of Hydrogen. By Morris W. Travers, D.Se., Fellow of University College, London*®. [Plate V.] [Note by Prot. Ramsay.—In the course of our researches on the gases of the atmosphere, it became evident that the only means of separating neon in a state of purity from the helium with which it was mixed, was by cooling the mixture of the two gases by aid of liquid hydrogen at its boiling- point under atmospheric pressure. In order to effect this separation, Dr. Travers undertook to design and make an apparatus which would produce liquid hydrogen in quantity ; and the following account of the experiments shows that his hopes have been justified. ] The Liquefuction of Hydrogen. d ee experiments described in this paper were carried out solely for the purpose indicated in Prof. Ramsay’s introductory note. The liquefaction of hydrogen has already been accomplished, and my experiments differ neither ih principle nor in conclusions from those of Dewar. Since, however, they show that the production of liquid hydrogen is neither so difficult nor so costly as might have been ex- pected, I have decided to publish an account of them. Without touching on controversial matter, the history of the subject may be stated in a few words. In 1884 Wroblewski (Comptes Rendus, c. p. 979) showed that when hydrogen, compressed into a capillary glass tube cooled to the temperature of liquid oxygen, was allowed to expand from 100 atmospheres to atmospheric pressure, a sudden ap- pearance of mist or spray in the tube indicated that partial liquefaction of the gas had taken place. In 1895 Olszewski (Phil. Mag. 1895 [5] xl. p. 202) confirmed these experiments by repeating them on a larger scale. Using first a glass tube of 7 mm. diameter, and afterwards a steel cylinder lined with glass, from which the gas escaped through a cock, he found that the hydrogen remained in the liquid state for a sufficient time to enable him to determine its temperature by means of a platinum resistance-coil enclosed in the apparatus. In these experiments the gas which remains in the glass tube or cylinder does work on that part of it which is escaping in overcoming the friction in the cock, the heat generated being carried away by the gas. Were the process truly * Communicated by the Physical Society : re.d Nov. 23, 1900, 2H 2 412 Dr. M. W. Travers on the adiabatic, the fall of temperature inside the apparatus might be calculated approximately from the formula where p, and p, are the initial and final pressures, T, and T, the initial and final temperatures, and / the ratio of the specific heats. The failure to produce any quantity of liquid — is chiefly to be attributed to the great ditference between the thermal capacities of the gas and of the vessel into which it is compressed. Lord Rayleigh and Kammerlingh Onnes have suggested independently that it might be possible to liquefy hydrogen by allowing the gas to do work in driving a heat-engine. The cylinder of Onnes’s engine is supposed to be constructed of a non-conducting substance of low specific heat and to be enclosed in an insulated space ; a long piston-rod transmits. the energy of the system to some mechanism placed outside the apparatus. A mixture of liquid and saturated vapour would escape from the cylinder, and this alone adds to the difficulties to be overcome in constructing the machine. Lord Rayleigh’s suggestion of applying a turbine in a similar manner could be more easily realized. By either of these processes, if conducted adiabatically, it should be possible to liquefy a perfect gas; and we now come to a method which can only be applied to gases which are imperfect and show a divergence from the simple gas law, — In the case of a “ perfect’ gas we may write the equation. Py = P22 where pv represents the total energy of the gas. If sucha gas were allowed to expand either without doing work or in doing work in such a manner that the whole of the heat generated were absorbed by the gas, no temperature-change would take place in the system. These conditions could be partially realized by allowing the gas to enter a vacuous space through a large orifice, as in Gay-Lussac’s experiment, or by forcing it through a porous plug so constructed that the velocity of the escaping gas is reduced to a minimum.. The latter method was adopted by Joule and Lord Kelvin, und the results of their experiments show that for all known oases the equation must be written Pi =Pmt® where Q is the quantity of heat absorbed or generated in Liquefaction of Hydrogen. 413 performing internal work. In these experiments the gas was compressed by a pump and escaped at constant tempera- ture and pressure through a plug of silk fibre. Work was ‘done on the gas by the pump, and the heat generated (pv+Q) was absorbed by passing it through a coil immersed in water. On its wav to the plug the gas flowed in a steady stream, doing no work. In the plug, work was done against friction and the heat generated was absorbed by the gas, so that any temperatur e-change which occurred could be con- sidered as consequent on the performance of internal workonly. If the gas were allowed to escape at a jet, instead of passing thr ough a plug, it is possible that, even in the case of a perfect gas, a fall of temperature would occur close to the jet owing to the conversion of molecular energy into kinetic energy : the effect would, however, be entirely local,and would disappear as the velocity of the stream was reduced in the formation of eddies. The results of Joule and Lord Kelvin, and of others of a more recent date, show that in the case of the commoner gases a fall of temperature takes place on free expansion. With hydrogen, however, and probably with helium also, the temperature rises; these gases being, to use Regnault’s expression, “ plus que parfait.” Tt was first sug ggested by Hampson in England and Linde in Germany, that the principle of free expansion might be applied to the liquefaction of air. In the Hampson-Iinde process the compressed air flows through a coiled copper tube, and expanding at a jet becomes cooled. The expanded gas passes back over the outside of the coil, losing any velocity it may have attained in forming eddies, so that any external work done results in the formation of heat which is absorbed directly by the gas. The effective cooling is the result of the work done against internal stresses only; and since the tem- perature of the expanded gas is lower than that of the coil, the latter together with the compressed gas it contains becomes cooled. Within the last two years Dewar has shown that at a temperature close to —200° C. hydrogen also behaves as an imperfect gas and becomes cooled when suffered to expand freely. His experiments, which are described in the ‘ Chemical News’ for March 1900, led him to apply this discovery to the liquefaction of hydrogen in quantity, and this he has successfully accomplished. The details of the method em- ployed have not however been published. Since there has been some confusion in dealing with the subject, it may be well to point out once more here that there is an essential difference between the processes employed by 414 Dr. M. W. Travers on the Olszewski and Dewar. There is no cooling of the gas in the coil of the Dewar apparatus owing to the performance of work ; this is done entirely by the pump, and the gas merely flows along the tube in a steady stream and transmits the pressure to the jet. The cooling must be attributed entirely to the performance of internal work consequent on change of volume only. In Olszewski’s experiments the pressure in the cylinder is not maintained, and work is done by the gas which it contains. The temperature at which the Joule-Thomson effect for hydrogen changes sign has yet to be determined ; it probably lies very low. I shall now proceed to describe my own experiments. In a preliminary experiment the gas, under a pressure of two hundred atmospheres, was cooled to —80° C. by passing through a coil immersed in a mixture of carbonic acid and aleohol, and was then allowed to expand at the jet of a Hampson air-liquefier, the coil of which had previously been cooled to the temperature of liquid air. Under these con- ditions it appeared that progressive cooling did not take place, and it may be concluded that at —80° C. hydrogen is still a perfect gas. Four attempts were made to liquefy hydrogen before an apparatus was constructed which gave satisfactory results. These experiments, which occupied about three months, I shall not describe ; it suffices to state that they served to show that hydrogen remains a perfect gas down to very low temperatures, The details of the structure of the apparatus finally employed in liquefying hydrogen are shown in Plate V.; text-fig. 1 indicates the general arrangement of compressor, Kc. The hydrogen from the compressor under a pressure of 200 atmospheres enters the liquefier through the tube, and passes through a coil A, which is cooled to —80° C. in a mixture of solid carbonic acid and alcohol. It then enters the coil contained in the chamber B, which is continually replenished with liquid air during an experiment. The lower portion of this coil passes into the chamber CO, which is closed and communicates through the pipe ff with an exhaust-pump; liquid air flows continuously from Bb into C through a pin- valve, controlled by a lever 6, and boiling under a pressure of 100 mm. of mercury lowers the temperature to —200° C. The gas now passes into the regenerator-coil D which is enclosed in the vacuum-vessel H, and, expanding at the valve EK, passes upwards through the interstices of the coil and the annular space F, surrounding B and GC, to the outlet G, Liquefaction of Hydrogen. 415, whence it can return through w and R and the cock 7 to the main supply-pipe N. The liquid which separates from the gas is ultimately collected in the vacuum-vessel K, which can easily be removed. In constructing the apparatus the coil D was wound on the thin steel tube ¢ which contains the valve-rod. The latter is screwed at its lower end into a perforated brass cylinder, soldered to the end of c¢, enclosing the expansion-jet. By turning the milled head a, the width of the annular space between the jet and the end of the valve-rod can be accurately adjusted and the flow of gas controlled. This valve was made for me by Brin’s Oxygen Company after the pattera of Dr. Hampson, who first applied it in his apparatus for liquefying air. To the use of this form of valve I must attribute the success of the work, for, unlike the pinhole-valve, it does not become blocked with the impurities which separate from hydrogen obtained by treating commercial zine with sul- phuric acid. The coil itself consists of 80 feet of solid drawn copper tube of 7; inch internal and @; in. external diameter ; in winding it the spirals ran alternately away from and towards the central tube, and great care was taken to pre- serve a uniform external diameter of 22 inches. The coils were carefully spaced and fixed in position with solder as each layer was wound. The length of the regenerator-coil D was 7 inches; and it must be pointed out here that in absence of all quantitative knowledge as to the behaviour of hydrogen at low tempera- tures, the choice of this dimension was a matter of guess- work ; it was found, however, to be sufficient. The next step in the construction of the apparatus was to fix the flanged plates d and e, which form the top and bottom of the chamber B, onto the tube c. The coil passes through both these plates, and e is also pierced for the passage of the exhaust-pipe f and for the liquid-air valve which is controlled by the rod b; the latter is screwed through a block fixed to the upper surface of e, so that by turning ¢ the conical point closes to a greater or less extent the hole in the plate. All these junctions were made with hard solder; the tube g, which fits exactly over d and e, was then fixed in position with soft solder. To allow of the escape of the hydrogen gas after its passage through the coils, a brass tube & of the same external diameter as the coil was fitted at the top to g by means of a collar soldered to both tubes, and supported by distance-pieces at the bottom. The annular space F so formed communicates with the escape-pipe G, as shown in the figure and section; 416 Dr. M. W. Travers on the the cold gas passing through F forms an excellent insulator for the liquid-air chambers Band C. To support the whole apparatus, and to afford a means of securing the vacuum-yessel H, a collar J is soldered to the tube & and to a tube m 4 inches in diameter, which rests on a flange n in a hole in a shelf attached to the wall of the compressor room. ‘The space between m and & is packed with animal wool, as is also the space within the containing- cylinder Q. The vacuum-vessel H is of such a diameter that when the coil B and the tube & are covered with a single layer of flannel it exactly fits over them. To make a gas-tight junction a rubber ring, which fills the space between the vacuum-vessel and the inner wall of m, is pressed between a brass ring o anda gland p. The ring o rests on three short studs on the inside of m, and the gland is forced home by three nuts and screws gg which are fixed at their upper ends into the flange n. When the gland is in position the only means by which gas or liquid can escape from the apparatus is by the tube G, or through the opening at the bottom of the vacuum-vessel H. It is, of course, intended to draw off the liquid at the latter opening, and as it is quite impossible to employ a stopcock for the purpose, the following arrangement has been adopted. The vacuum-vessels H and K are both enclosed in a glass tube LL, which is closed at the bottom and is connected at the top by a rubber sleeve s to a brass tube 2 which forms part of the gland p; a short copper tube is soldered into sand terminates in a stopcock r. When +r is closed any liquid formed at the valve E is retained in H; but when 7 is opened tue liquid can flow into K, as the gas produced by its evapora- tion can then escape. The lower part of the tube Lis enclosed in a large vacuum-vessel M, which contains a small quantity of liquid air during the experiment; it serves rather to prevent the frosting of the outside of L than to exclude heat. The hydrogen escaping from G passes through the rubber tube w into the tube R, which communicates directly with the cylinder P (text-fig.) and through the stopcock ¢ with the main supply-pipe N connecting the gasometer and the com- pressor. The cylinder P is of sheet zinc, and is soldered to the three brass tubes R, S, and T. The tube 8, which is lined with glass and has a window in front and behind, contains the nozzle of the tube leading from the cylinder w in which the water used to lubricate the cylinder of the compressor is separated; this arrangement prevents the loss of the gas which escapes each time the water is discharged. The tube T Liquefaction of. Hydrogen. ANT reaches to the bottom of a deep vessel (fig. 1, €) filled with water; it serves also as an escape for the gas issuing from G before the cock 7 is opened. ee en we me a iw ow ww bee ee es = 418 Dr. M. W. Travers on the The tube f communicates with an exhaust-pump which is not shown in either figure. Itisa simple double-action pump with a single cylinder of 3-inch bore and 6-inch stroke, and, driven by a half-horse-power gas-engine, maintains a vacuum of 100 mm. of mercury in the chamber C. The barrel and plug of the stopcock ¢ are bored so that C can be cut off from the pump and opened to the air; through the stopcock v the pipe G can be placed in communication with the pump. It is now convenient to call attention to the general system of heat-insulation in the apparatus. The coil A is surrounded with solid carbonic acid and alcohol, contained in an earthen- ware battery-jar which is unprotected; the tube between A and B is surrounded with a wrapping of animal wool and covered with baize. B and C are protected by the cold gas returning through the annular space F after passing through the regenerator-coil D; additional protection is afforded by the layer of animal wool inside the cylinder Q. The increasing steepness of the temperature-gradient at C is compensated for by the protecting influence of the upper part of the vacuum-vessel H; the vacuum-vessel M, which contains liquid air, serves as a protection to K and the lower part of the regenerator-coil D; it also prevents deposition of moisture on the tube L. The method of supporting the apparatus by the tube m answers admirably, for as the space between m and fk is packed with wool, the gland p only becomes frosted over when the experiment is at an end, showing that the influx of heat in this direction is inconsiderable. The hydrogen gas was obtained by the action of dilute sulphuric acid on commercial granulated zinc, and was stored in a gasometer over water. The gasometer consists of a cylinder of sheet iron (No. 16 gauge), 6 feet in height and 5 feet 6 inches in diameter, inverted in a cylindrical tank which was filled with water. The gas enters and escapes through a 2-inch iron pipe, passing through the bottom of the tank and terminating inside a small dome 6 inches in diameter on top of the inner cylinder. ‘This arrangement makes it possible to expel the whole of the gas from the gasometer without danger of introducing water into the supply-pipe. Before filling the gasometer the water in the tank is saturated with hydrogen by passing a stream of the gas through a tube reaching to the bottom. This operation occupies about five days. The main bulk of the hydrogen is generated in the following manner. About 40 lb. of zinc are placed in a beer-cask fitted with a tap-funnel, a delivery-tube, and an escape-pipe, which Liquefaction of Hydrogen. 419 passes into a vessel filled with water and so acts as a safety- valve; there is also a stoneware cock at the bottom for drawing off spent acid. When all the air has been expelled from the cask the gas, after passing through a wash-bottle filled with a solution of potassium permanganate, is allowed to enter the gasometer. ‘The latter is thoroughly washed out with hydrogen before the main quantity is collected. The preparation of the hydrogen occupies five hours. The general arrangement of the plant for the compression of the hydrogen, which is carried through the pipe NN to the cock and temporary communication made by means of a lead pipe o with two screw-unions, is shown in text-fig. 1. The hydrogen, or air when the latter is to be liquefied, is first of all taken into the low-pressure cylinder 6 of the compressor, which is driven by a 5-horse-power motor, and passes thence through the coil, kept cool by a current of water which circulates through the tanks surrounding the cylinders and coils, and enters the high-pressure cylinder through the tube 6 under a pressure of about 16 atmospheres. A small quantity of a mixture of glycerol and water containing 5 per cent. of caustic soda is taken into the low-pressure cylinder together with the gas. The mixture is contained in the vessel 7, and the flow is controlled by the glass stopcock and arrangement shown in the figure. In the second cylinder @ the pressure is raised to about 200 atmospheres, and the gas, after passing: through the coil @, enters the cylinder mw, in which the water used in lubricating the cylinders is separated and expelled through the cock «. This water, together with a little gas, passes along the tube wu and enters the cylinder P: the water flows into the tank ¢, and the gas, during the com- pression of the hydrogen, is allowed to return to the gasometer through the cock 7. The details of this apparatus have already been given. The gas from w passes into the cylinder >, which contains lumps of solid caustic potash to remove traces of moisture or of other impurities. This cylinder is employed in compressing both air and hydrogen, and can be connected by the tube 7 either with a Hampson air-liquefier or, as in the figure, with the coil A of the liquid-hydrogen apparatus. The tube ralso communicates with a gauge and with a cock, through which, if the pressure becomes too high, the excess of gas may be allowed to escape into the pipe NN connecting the gasometer and the compressor. The liquefier, of which the detail has already been given, does not require further description. It is sufficient to state that the gas, after passing through the coils enclosed in Q and L, expands at a valve within L 420 Dr. M. W. Travers on the controlled by the milled nut a, and finally returns by the tubes G, w, and R and the stopcock i to the tube N. ‘ed The loss of gas during each experiment amounts to about 10 per cent. of the whole; and since air and other gases of higher boiling-point separate as solids in the vacuum-vessel H, the gas becomes purer each time it is. used. During the two or three days immediately preceding an experiment, the compressor is employed in producing liquid air. For this purpose we use a Hampson liquefier, which is capable of yielding about 1°25 litres of the liquid per hour. The liquid air is stored in vacuum-vessels capable of holding altogether about 8 litres; comparatively little loss occurs through evaporation, and the vessels are usually filled up on the last morning. After preparing the liquid air it is advis- able to take the compressor to pieces and carefully inspect the valves, springs, and fibre packings. In the meantime the Hampson machine is removed, the connexions are made between the potash cylinder and the hydrogen liquefier, and the lead pipe connecting the supply-pipe NN with the intake of the compressor is placed in position. The actual experiment requires four persons. One controls the valves a and 6; the second attends to the compressor, regulates the escape of the water from the cylinder p, and opens or closes the cock # as the pressure rises or falls; the third sees that the vessel in which the coil A is immersed contains sufficient solid carbon dioxide; the fourth hands the vacuum-vessels of liquid air as they are required. The first step in the operation is to cool the liquefier to the temperature of liquid air. Liquid air is first poured into the chamber B, and thence flows into C by connecting it with the exhaust-pump through the cock ¢ and turning the valve 6; when C is partially filled and the vacuum-gauge indicates that the liquid air is not evaporating at a great rate, the valve 6 is closed and the cock ¢ is turned so as to cut off the exhaust and leave the chamber open to the atmosphere (p. 414). The vacuum-vessel M and the tube L. with the vacuum- vessel it contains are removed by rolling up the rubber sleeve s on to the tube f and lowering the cradle in which M is sus- pended. The rubber cap carrying the tap v is then fitted to the nozzle of H and connected with a rubber tube dipping into a vacuum-vyessel filled with quid air. The escape-pipe G, from which the rubber tube has already been removed and replaced by a rubber cork, is now connected with the exhaust-pump through the cock v. Liquid air is drawn into the vacuum-vessel H, and on closing the stopcock V boils under reduced pressure, cooling the regenerator-coil to Liquefaction of Hydrogen. 421 below —200° C. By closing the cock v, removing the rubber cork, and opening the stopcock V, the liquid air flows out of H. The rubber cap securing V is now removed, the tube L and the vacuum-vessels M and K are replaced in position, and the rubber sleeve s is secured to L with a single turn of copper wire. Meanwhile the assistant in charge of the compressor has removed all air from the compression-apparatus by opening the cock « (text-fig. 1), allowing the compressor to make a few revolutions and then stopping it and opening the cock p. This operation is repeated three or four times; the pressure is then allowed to rise, the valve a being closed, and the gas is allowed to escape, if necessary, through the cock «x into the pipe N. The arrangements are made so that the pressure is raised to 200 atmospheres by the time the liquefier has been cooled and the vacuum-vessels K, &e., replaced. The remaining operations may be shortly described :— Communication is once more established between the chamber Cand the exhaust-pump, and the valve 0 is carefully regulated so that the liquid air does not enter too fast; a too rapid flow is at once indicated bya fall of the mercury in the vacuum-gauge. ‘The expansion-valve is then opened by turning the milled nut d, and the gas, passing upwards through the coils, through the annular space F’, through the tubes G, w, and R, finds its way into P, and is allowed fora few moments, in order to remove air from the apparatus, to escape through the water in the tank e. The cock 7 is then opened, and the gas is allowed to circulate through the system. The chamber B and the vessel containing the coil A are continually replenished with liquid air and solid carbonic acid respectively. The whole difficulty in this part of the experiment lies in properly regulating the escape of the hydrogen. The rate of flow of the gas is roughly indicated by the height of the glycerol in the gauge z, which shows the pressure in the interior of the apparatus caused by the friction of the gas in the tubes G, w, and R. It is intended in future experiments to introduce in place of wa coil of lead pipe, and to connect the top of the glycerol gauge with a tube leading into the eylinder P,as it will then give an absolute reading of the rate of flow of the gas. The reasons for which it is necessary to carefully regulate the valve are twofold. Firstly, the hydrogen must not pass too quickly through the refrigerating-coils else the gas is insufficiently cooled; secondly, since liquid hydrogen has a very low specific gravity, the gas and liquid do not separate 422 On the Liquefaction of Hydrogen. readily at the jet, and much of the latter is lost. Further, since the efficiency of the regenerator-coil is dependent on the rate of transmission of heat through its walls—and this is proportional to their superficial area—the maximum effect is attained with a limited quantity of gas. To guard against blocking of the valve by the deposition of solid impurities, the milled nut a is turned slowly back- wards and forwards during the whole experiment. In the valve E the screw fits so tightly into the brass cylinder con- taining the jet that no gas can escape from the liquefier through the steel tube ¢, and it is necessary at times to apply some force to a. In constructing another machine 1] should either place the screw on the valve-rod in the tube ¢ about two inches above the valve, or I should ease the screw in its socket and place a gland round the valve-rod at the top of the steel tube c. There appears to be no danger of the coil becoming blocked through the deposition of solid matter inside it, even though the hydrogen contains two or three per cent. of air and perhaps traces of arseniuretted hydrogen, hydrocarbons, &e. It must be remembered that within the regenerator-coil, even very close to the jet, the temperature of the gas does not fall below its critical point or the coil would become filled with liquid, and it appears that this is not the case. Under these conditions a gas is capable of holding a considerable quantity of solids 7m solutzon, a phenomenon which has not been fully explained; this may account for the fact mentioned above. Solid impurities do, however, separate from the liquid in the vacuum-yessel H, but as the liquid on its way to the vessel K is obliged to pass through a piece of baize pressed down into the bottom of H by a spring, it can be collected perfectly clear. Almost immediately the valve E is opened the inside of the vacuum-vessel H becomes coated with a layer of white matter, which is probably solid air ; and shortly after, placing a light behind the lower part of the apparatus and opening the cock #, liquid is seen running in a fairly rapid stream from the nozzle of H and collecting in K. The flow of the gas from the jet E can then be checked, the tubes M and L lowered, and the vacuum-vessel K, which is attached to a wire, withdrawn and placed in another vessel containing a little liquid air. It would then be possible to place another vacuum-vessel in L, to restore L and M to their original positions, and to prepare a further quantity of liquid hydrogen ; this has not, however, been attempted. The apparatus which I have described, with the exception > On the Magnetic Field produced by Electric Tramways. 423 of the compressor, motor, and Hampson air-liquefier, which together cost about £200, is comparatively inexpensive. The gasometer cost £15, the material used in making the liquefier amounted to about £5, and possibly £30 was spent in the experiments in addition to the sum named. Each time liquid hydrogen is made 5 kilos of solid carbonic acid and 8 litres of liquid air are used; this involves a further cost of about £1. These figures indicate that the cost of liquid hydrogen is not excessive. Iam much indebted to Mr. Holding, lecture-assistant in the department, for assistance in constructing the liquefier and in carrying out the experiments. I also wish to express my most cordial thanks to Dr. W. Hampson for his valuable advice and for the assistance which he has so willingly © rendered. University College, London. XXXVITL. On the Magnetic Field produced by Electric Tramways. By A. W. Ricker, F.R.S.* HE following calculations were made during the inquiry which has recently taken place on the Magnetic Field produced by Electric Tramways. In the course of the dis- eussion it became evident that the gentlemen who represented the Tramway Companies had arrived at similar results ; and Mr. Parry has published in the ‘ Electrician’ for Aug. 10, 1900, a full account. of this part of the theory. I had worked out both the “source and sink” and the “ Fourier-Bar” theories, given below, before I was aware of the fact. The former is perhaps as accurate as the assumption that the earth is homogeneous will allow; and it was @ priori im- probable that the Fourier-Bar theory would represent the facts near the terminals of the line. The following results confirm this view ;. but this part of the subject was developed in consequence of a statement by the Hngineers that the “Fourier-Bar” theory agreed with the results of experiments conducted by themselves, and which are not further referred to in this paper. : '- There is no difficulty in the calculations; and my only object in publishing some account of them is to draw atten- tion to the fact, which is not, I think, generally recognized, that the leakage currents on a homogeneous earth aftect directly only the horizontal force, while the vertical dis- turbing force is due only to the difference of the effects of the currents in the trolley-wires and rails or other horizontal * Communicated by the Physical Society : read Dec. 14, 1900, 424 Prof. A. W. Riicker on the Magnetic conductors by which the current is conveyed to and from the cars. If the return conductors are insulated and parallel to the trolley-wires, the outgoing and returning horizontal currents are equal (since there is no leak), and the effects are zero at any point in the same horizontal plane as the rails, the distance of which from the line is considerable with respect to the height of the trolley-wires above the ground. The proof of these statements may be deduced directly from first principles. : ek If an electrical current flows from a source placed in the surface of an infinite uniform condactor bounded by a plane, the resulting magnetic field will have no component perpendicular to the surface. For if a plane be drawn through the source perpendicular to the surface it is evident, from the symmetry of the system, that the components parallel to this plane of the magnetic fields, produced by the currents on opposite sides of the plane, will be equal and opposite. Again, let the circuit be completed by an infinite linear conductor passing through the source and perpendicular to the surface, and let the total current flowing through this conductor and diverging from the point where it meets the surface be 1. The force due to the whole system at a point in the surface at a distance r from the foot of the per- pendicular is 2I/7, and since half of this is due to the current in the linear conductor, the other half is due to the currents diverging from its extremity. If we now place in the surface a sink equal to the source, the same statements hold good with regard to it ; and we thus arrive at the conclusion that the current system flowing from the source to the sink has no component perpendicular to the surface, and that the component parallel to the surface is the resultant of two forces I/r and —I/r’, where 7 and 7’ are the distances from the source and sink. © If we now regard the source and sink as the points at which the current passing through an electric motor enters the earth and returns to the generating station, it is evident that for points at some distance from the railway or tramway the trolley-wire may be represented by an insulated linear con- ductor joining the source and sink. The magnetic field pro- duced by this conductor will be everywhere perpendicular to the plane surface which represents the earth, and of course can be easily caiculated. : So far no attention has been paid to the rails. In reality the current flows into the soil from the.-rails or vice versa, but however complicated,the system may be it canbe broken up Field produced by Electric Tramways. 425 into pairs of sources and sinks. Hence the statement is always true, that if the earth may be regarded as a homogeneous conductor, the vertical magnetic field produced by an electric railway or tramway is due solely to the ditferential effect of horizontal currents in the trolley-wire or other feeder and in the rails, while the horizontal magnetic field is produced solely by the stray earth-currents. This conclusion, though almost obvious, is important. Experiment shows that the vertical-force instruments are generally those which are most seriously affected by the es- tablishment of an electric tramway in the neighbourhood of an observatory. The question has been raised whether the observatory might be protected by a river ; but the above discussion shows that the direct effect of the current in the trolley-wire could not be altered by any such natural feature of the district. All that can be said is that a want of sym- metry in the earth-currents might introduce a vertical component opposed to that due to the current in the trolley- wire. The simplest method of dealing with the rails is to regard them as an insulated conductor by which a fraction of the whole current returns to the generator. Ata distance from the line considerable with respect to the height of the trolley above the road, the vertical force is practically produced by the difference between the total current I and the hypo- thetical uniform rail-current, the effect of which at the point considered is equivalent to the actual rail-current, the strength of which varies from point to point. The approximate theory based on these assumptions is thus reduced to the determination of the vertical effects of a hori- zontal current 1(1—L) where L is < 1, and to the horizontal disturbances produced by a source and sink of strength LI placed in the positions of the generator and car respectively. The effects of several cars can be obtained either by dealing with each separately or by averaging. The calculations are quite simple and it is hardly necessary to set them forth at length. Other things being equal, and the tramway being assumed to be straight, the vertical force disturbance increases with the length of the tramway, and for a tramway of given length the disturbance is a maximum at points on a line perpen- dicular to and bisecting it. Under similar circumstances the horizontal force dis- turbance when the car is very distant is due only to the inflow of the earth-currents to the generating station. As the car approaches and passes the observatory the disturbance Phil. Mag. 8. 6. Vol. 1. No. 4. April 1901. 2 EF 426. Prof. A. W. Riicker on the Magnetic may increase and then diminish or vice versé, but the total range of the magnitude of the horizontal disturbing couple (supposed to be small) depends only on the current LI and the distance of the observatory from the line (y). It is equal to LI/y. In the case of a line of finite length the car may not reach one of both of the points at which the disturbance is a maxi- mum or a minimum, and the range of the disturbance may therefore be reduced. | If, now, a be the length of the line (taken as straight and as the axis of x), if y be the length of the perpendicular from the observatory on the line, 6 and b+a the distances of the ends of the line from the foot of the perpendicular from the observatory on the line, and I the total current, the disturbing forces parallel to 2, y, and z (vertical) are 2 eae 1 i F.=Dy| gy (b+ay +e? q bh b+a Hee Li+y Grarey pedbil ( b b+a ~y UVP ty V(b+artyS* Experiments were made at Stockton by placing self- registering instruments at a distance of 0-4 mile from a tramway 2 miles in length, when a current of about 150 amperes was flowing along the trolley-wire over the whole length of the line. The Vertical-force instrument showed a disturbance of Ty (y=10-° c.G.s. units of magnetic force). The calculated disturbance due to the trolley-wire was 43. Hence i= 7/43 = 16:3 pa cent. The Horizontal-force instrument gave Tie 370/22 = 19:9 p. cent: These results were in satisfactory accord, and showed that the effects produced were the same as if about 84 p. cent. of the current returned through the rails as a uniform current, and 16 p. cent. entered and left the earth at the ends of the line. 3 The current thus determined js such that if a uniform current of this magnitude (°841) flowed in the rails the disturbance produced would be equal to that actually caused © by the real current in the rails which, owing to leakage, varies from point to point. It may be called the equivalent Field produced by Electric Tranways. 427 unijorm current, and must be distinguished from the mean current in the rails. The latter may be determined in two ways : First, if ¢ is the mean current in the rails, ivae—— Ve, where R is the rail-resistance, and V the difference of potential between their extremities. The measurements of these quantities at Stockton were undertaken rather with the view of testing whether the Board of Trade regulations were fulfilled, than for determining the mean current. ‘The variations of the current and P.D. were too rapid, and the values of z deduced from them are not sufficiently in accord to command confidence. The mean of 9 observations gave 7/[=23 p. cent., but this value is not only deduced from discordant numbers but leads to too high a value of the disturbance at the observatory. In the second method of calculating the mean* we may assume that the leakage at each point is proportional to the difference of potential (v) between that point and the earth. Thus if hand & be external and internal conductivities, and 7, be the current at the point 2, dv diy —i,=k— and — —“=hv, dx da whence if p°=h/k, of which the solution is i= Ae” + Be, That is, as is shown, the problem is formally the same asx that of the Fourier-Bar. If the ends of the rails are at the points e=0 and z=a, and if the whole current (1) passes through the rails at these points pass Cram eva + J Let now the point for which #=0 be at a distance 6 from the foot of the perpendicular drawn from the observatory to a straight line, let y be the length of the perpendicular and a the length of the line, then the vertical-force disturbance * See ‘ Electrician,’ August 10, 1900, p. 595. 2F 2 428 Prof. A. W. Riicker on the Magnetic produced at the observatory by the opposing currents in the trolley-wire and rails respectively is een l=—2 7) i F Oa 2) ry == | b+a b t y UNMb+aPty VP +y? a ly a et 4 gu(a= 2) ee Leen}, {Gb +ay tye At Stockton the point of observation was opposite to the middle of the line so that b= —a/2. Therefore the disturbing force ine I 2a ly a eu (r4—a/2) = ety iy Vai+dy? til? @ Hal? F $(a—a/2)? +y$3 Hie Tf now we write c=(A+1)a/2 and y=ua/2 this becomes 41 Tu 1 quar/2 4 @—mar/2 x au V1 +? aera? + emia) ie (? Te w)s ° The first term in this expression is the disturbance due to the trolley-wire, which at Stockton was 43 y. The whole ex- pression is the actual disturbance, viz., 7 y: hence, neglecting sions and expanding the integral in terms of wa/2, we get ATw f 2 7 J/i+we+l 2 (“ay ee aS 7D —— + 5) log, ~~ y ————————_ Sapa ‘ae, Se ore i ) Gere siie rhe 5) Ua? 5/d eh ir: aauee V14+wW—-1 Vi+w/\2 It is easy to show that terms in higher powers of » are negligible, and that the expression thus obtained is more accurate than if the denominator were also expanded. Now at Stockton a=2 miles=3 2x 10’ cm., y=0'4 mile, and therefore u=O-4. Substituting these values we get I 2 (eHa/? + eq?) f1il6 + 0:7 Loa) 2) hour Neglecting the second term this gives pa/2=0°636, and substituting this value in the second term we get pa/2=0°678. If we adopt the rather less accurate but more convenient — plan adopted by Mr. Glazebrook, and expand throughout in terms of wa/2, the whole disturbance due both to trolley- Field produced by Electric Tramways. 429 wires and rails reduces to the form =i V1+u?7+1 ee es ams 4 ee en oT a Jip pe SN 2 and when I=15(c.¢.s.), w=0'4 and a=3'2x 10° cm., as at Stockton, this was equal to 7 x 10-°, whence (ya/2)=0°61. If the calculations are confined to this approximation it is Le Be use this value of ya/2, though it is probably too small. Having thus shown how to find wa/2 from the vertical- force disturbance, we may next use it to calculate the average current in the rails and the total leakage. The average current between 0 and a is Pedr 9 f= 7 OT i=) ase = ap l = jose fe (wa/2) ae 1 /pa : fer ee = || 41 3 ( ) approximately. The total leakage is the difference between the total cur- rent I and the minimum current at the central point (in). Putting «=a/2 in the expression for i,, we get i 2Qeml? 2 Ts = ty] =sech (ua/2) a= il cam = iC) approximately, > Using the more accurate (0°678) and the approximate (0°61) values of wa/2 with the accurate and approximate formule respectively, we get the following results :— —E Equivalent current ...| 83°9 p. cent. EAM CHEEME soe ecstl |) ceaceds 86°7 p. cent. | 87-4 p. cent. Minimum current : serote SUG; 8l4 ,, The leakages as deduced from the equivalent and minimum currents are 1671 p. cent., 19°4 p. cent., and 18°6 p. cent. respectively. The general result of this discussion is that if accurate 430 Prof. A. W. Riicker on the Magnetic’ values of wa/2 are required the approximation must be carried to the second term in the integral, the other terms haying their true values; but that an approximation neglecting all terms containing powers of pa/2 above the second, will give accurate values of the mean and minimum currents if the value of ja/2 used is determined to the same degree of approximation. , The evaluation of the expression ly a gf? 4 en(a-2) o eee ee ee may be proceeded with as follows :— Writing y=ual2, 2—al2=ra/2, b+a/2=Ba/2, the expression may be put in the form ITu 1 epaar/2 a Ee Maa/2 mr 5 ; ay RPGS OT hn ee a} eh! + ened?) 4s 4 (X = [Sy zi u*t = Uf we expand the integral in powers of wa/2 the general term 1s ay ny 1 27Dr pee 2 ml) me { astaeame= 2 2 Boy say. NEB) Qn ( 2*-1(A+B)dr wWLA+B) +78 ow JALAF B+ }2" Multiplying and dividing the quantity under the sign of inteyration by (A+ 8)?+w?, and writing A.» for the first term, we get : 2n u? { Ponse+ 30 Bangi + (88° + uv?) Fon oP je(ee ae 0) Bo,_1 } ; 2 or eee =e —3B Foi {3¢?+0A(1 4- =: F,,, —B(BP +2?) Bona, and when the limits are inserted fy eg a eee Beth | an In LAL Awe T {Bw ES Field produced by Electric Tramways. 4351 In the particular case under consideration, b=a/2, sothat @=0, and we get 1 1 2n+1 he = - een 2 iar) wane V1+u? 2n Bn. Also pg Os Bd 0 ne (2+ u*)8 aie Via! 2dr en =log {A+ Vd? +02} —A(A2 4-0?) —loo Vi+e41 jie ee ica 4 ey a | V itu” ul 3 foe re 2 mire he ® a ee ae &e. ZV Wey? 4 Hence approximating to the integral we get when u=O0-4 ATu 0715 i 0°758 / wa\* Vv a( eral? 4 @—Hal?) {116+ 6+ on (‘S + 41 =) + Ke. : Or, if L=150 amp., u=0'4, a=2 miles=3-2 x 10° cm., Be toc 116 pom 0:0653 (4a " r pars earl ie ak Fes a) too Se my + ee [ 6! Now the coefficients of this series are much smaller and converge more rapidly than those in the expansion of 1 1 Lf way?s ) dpa oll [a 5 et/4 1 e—pa/2 oe Wy {1- aS) ar 4 ae i= wi(S uy CR 4: Hence for a given value of wa/2 a nearer approach to the true value of the expression is obtained if we take the accurate value of the exponential term and evaluate the integral to a given power of ywa/2, than if we expand both expressions to that power of pa/2. P4324 4 XXXIX. Notes on the Practical Application of the Theory of Magnetie Disturbance by Earth-Currents. By R. T. GLAZEBROOK, D).Sc., FR.S.* HE following notes contain some appliontiont of Professor Riicker’s theory. In fig. 1 let MBA be the line, O the observatory, B the power-house, P the tram, and OM perpendicular on the line from O, Then OM=y, MB=b, BP=2, BA=e. Lei tO. OA=7,, : Fig. I. 0 M B —?P A Prof. Riicker’s expression for the vertical force at O due to an element dz is wy {fa “is } dx elk +e Sf §(b4+a)2 + 32 =h/k=exterior conductivity/ interior conductivity. Now it will be shown that for many cases as a first approxi- mation u?a?/4 may be neglected compared with unity. On expanding in powers of w and neglecting u?a?/4 in small terms, we find IP we «(a— x) oT o ((b+a)P+y?}2 and this evaluates to ov ° ? 2 1 oe eee ening rage V(a+h +7 b4- Sb? +y? or pe? (a+b)r,—bre atb+r, eo * Communicated by the Physical Society ; read Dec. 14, 1900. The Theory of Magnetic Disturbance by Earth-Currents. 433 If we take the case in which pa i — i SOP tent the arrangement (fig. 2) is as at Stockton, 2 | rte 7 F=51 == log ie th) L. \tgray <1 Fig. 2 O B M A From this equation the vertical force can be calculated. Jt is, however, somewhat complex for use. I have, therefore, examined the case in which it is supposed that the difference between flow and return current is constant along the line, the whole leak occurring at the sink. In Professor Riicker’s language, I have used the equivalent uniform current. In this case if « be the leakage coefficient, which is the same as Prof. Riicker’s 1—L, Ix fe 5” tee peel es Yy T2 ry using the same notation; or taking the above symmetrical case le a F,= == y r In this same ease Ika fe = so. Vi Now as to the value of «x. We have from the theory developed by Mr. Parry and Prof. Ricker, and from the Stockton experiments wa/2 is about ‘64 and a is 2 miles. 434 Dr. Glazebrook on the Practical Application of the | Hence expanding as far as He we find ui He 5 wa" ) K= 8 1— 12 Are ca cies he 2G? 4 ‘ or neglecting 7g 7a? in comparison with unity, > Qy2 a k= ~ 5 and | el a v7 ee Sy VY aaa It is clear that if @ is 2 miles, the value of « is about 20 per cent. too great. To compare these two formule I. and II. we may, since a/2r is less than unity, expand the logarithm in I.; we thus obtain KF pate pl a’ 1 iL ae } Oras S ry 3 r2 eee ° In the Stockton experiments a=2, y="4, r=2-04 ; 3 and the term neglected is about ‘02. A result of considerable importance may be deduced from the above formulee. It is clear that for similar circuits similarly placed the vertical foree varies as the linear dimensions of the circuit multiplied by the current. Now if thenumber of cars per mile of track is to remain constant, the current must vary as the length of the track. Hence the force is proportional to the square of the linear dimensions. F= Tig. 3. 0 oo e A’ B’ Thus if we have two parallel lines AB, A'B! (fig. 3), of which A’B! is double the length of AB and at double the distance from the source, the effect of A’B’ is four times that of AB. This is readily seen from first principles. wt Theory of Magnetic Disturbance by Earth-Currents. 48: For we have clearly F, — aL x ee ee Te) tla ok Also, since the number of cars per mile is constant | pees ov Moreover, Are, gee Hence Various interesting results may be obtained from the simple formula (II.}, which we may write 1 F = p2a?] —EEEEe (0) 4 b&b y wv (4y2 + a2) Now if the number of cars per mile be constant the current varies as the length of the line. Hence =a; a and a B=?) a\Hia y Viepae® In this expression the distance y must be measured in centimetres in order to give IF’, in absolute units. ence we must introduce in the denominator a factor 1:6 x 10’, or in the numerator *62*10-°. Thus we ‘ 10- _5 Apa* a y V(4y? +a?) where the lengths are now all in miles. 10-° is an ordinary unit in terrestrial magnetic work denoted by y. With regard to the dimensions of this expression it must ‘be remembered that p?a? is a number and da an electric eurrent. Thus «? and » both have dimensions in space, and in the values given for the two quantities it is assumed that each is referred to a mile run of line. Now according to Professor Riicker’s Stockton experiments the approximate value of pa/2 is *64, where a=2 miles, Hence p='b4, pee Al. 436 Dr Glazebrook on the Practical Application of the We may compare these figures with those given. by Mr. Parry in his paper in the ‘ Electrician’ for August 10, 1900. He takes 4 and & to refer to the exterior and interior conductivity per unit surface and unit volume respectively, and assumes one inch as his unit of length. In his formula A is the area of the cross section of the rail, and L the area of the surface in contact with the ground per inch run of rails. Thus his quantity Lh/A& corresponds to my 4/k, with this difference, that his unit of length is the inch, mine the mile; and he finds as the value of SLAJARY the AnMbee 1/180000. Multiplying this by the number of inches in a mile, we find as the value of « the quantity °35, while the leak in a line I mile long would be ‘015. Some other experiments give w="425 and. (= 8: The ratio of the leak to the inflowing current in a line a mile long, which is given by »?/8, will in these two cases be "051 and °0225 respectively. By way of illustration 1 have made some calculations on the assumption that the leak for 1 mile is 5 per cent.; so that $4?=-05 and w?="4, the value found at Stockton. In this case the term neglected in the original expansion is 3 x a’, Let us also assume that there are 8 cars in a mile each taking rather under 20 amperes, so that _ X=150 amperes=15 C.G.8, units. Hence we have hw=6, Then in this case ee Ne a = "5 : e Y yf dy? + 0°52 And if we take a line a mile Jong at a distance of 1 mile from the observatory, we have ale yal, F,="42 x y. For the values at Stockton F, is equal to 6:2y, which is rather less than the 7y actually found. Instead of working with the current we may use the P.D. at the ends, Let this be V. Then we can show that _ pa Leakage current=pk a ae ltez _ haV = ae to the same approximation. o7 Theory of Magnetic Disturbance by Earth-Currents. 434 Hence Mr HEN tcl Ay dy? + a? Now if the number of cars per mile is given V varies as a’; put V=va?, v is the potential-difference between two points 1 mile apart. 3 Hence total leak in length a= wen Aura’ fyierettle es as de ci sg, — Therefore hyv=)p?, an obvious result when the meaning of the quantities is considered, and hva* : pens See x 62 x Ke Ay VW Ay? + a? if the quantities be all in miles. Again we can eliminate a from these equations either by the use of the equation [=Aa, or by the use of the equation V=vra". And we have the following four identical equations :— 1O a if 3 pee a 0-5 ci a y V Ay a? = (RE 2 4 Bee Lee Rs a) eek . 4 AT Mis AE sh 19.28 ac AA(Ey ema) _ 62 fu Ag ae ee Nene: == TG) Winget) lf we wish to find the connexion between the length of the line and its distance from the observatory, so that when its effect is a maximum it may be less than a given quantity, 6 say, then we must have the right-hand side of the above equations less than 6. Now we have seen that Aw’/8 is the maximum leak from 1 mile of the line. Let us call this L. Then Ne = sh - 438 Dr. Glazebrook on the Practical Application of the © and our equation of condition becomes a‘ ‘ 1-24 x Tx ee y V+ +4y? From this we obtain the rule :— Calculate in absolute units the leak in a rail 1 mile long when carrying the maximum current required to drive the maximum number of cars in the mile. Let the result be Lo.g.s. units of current. Then a must not exceed the value given by the equation ee le ek ee? es a 10->=8: Y V(ae+ (a*-+ 4y?) or if L be the leak in amperes, = 101, Hence a‘ i "1241 x 10 =o yY V{a'+4y"? If we take 6=4y (a usual case in practice), this reduces to With the numbers already assumed, Ay? =60 amperes, and L=7:5 amperes=) per cent. of current. If we know the resistance of a mile of the track we can calculate the potential-ditterence required to drive the current through, for it is clear from Mr. Parry’s curves and from the theory that for a track 1 mile in length the drop required is given by the product of the current and resistance to a sufficient degree of approximation. Now for a rail weighing 92 lbs. to the mile we may be as the resistance of a mile of continuous rail the value 0°0525 ohm. ‘Thus, allowing for the bonds, the rails being in 36-feet lengths, about one-fortieth of the total resistance, we get as the resistance of a mile of single rail 0:0538 ohm. Hence the resistance of a double track will be 0:0135 ohm, and the potential-difference required to produce a current of 150 amperes will be about 2 volts. This, then, is the value of vy in the above formula.- . Theory of Magnetic Disturbance by Earth-Currents, 439 We thus obtain the following table of values of a and V. TABLE YT, pee Yy. | a. Ve | rere fe Beet ee 1 1.05 PD 2 1-45 4:25 3 1-78 6°25 | 4 2-05 8:5 | 5 2°30 10°5 | | ; Hie ee Or, if we ae wees 0225, so that the ene in 1 mile is 21 per cent., the current being 150 amperes for each mile of male and ‘he resistance of a mile of track 0°0135 ohm as before, we have :— A ASe sini debe y a. v 1 1:15 2-6 2 WSae 6:25 3 2:14 9-25 4 2-5 12°5 We may use the equation to find at what distance the Board-of-Trade potential-difference is innocuous, and what is the corresponding length of line. Substituting in the fourth equation V=7,v=2, and hv=6, I find y =3°28 miles. And since V=va’, the corresponding length of line will be W3°5, or 1°87 miles. Thus in round numbers 2 miles of track carrying a current of 300 amperes with a potential- difference of 7 volts between the ends might produce a vertical magnetic force of *5x10-° units on an observatory at a distance of 3 miles. If we remember that X is the current. sequmvea to drive the cars in a mile of line, we can put the rule thus :— Multiply the current in amperes required to drive the cars 440 Dr. Glazebrook on the Practical Application of the in a mile of line by the number j »?/8. Let the result be J amperes. Then the mae alite of a is given by se | YN (ae (@+4y) According to the figures assumed above the value of 47/8 is ‘O05. Again, we have oe ly=\ut =". Hence A=hy, as is obvious from the definitions. The value of 1/k is, as we have seen, ‘0135 ohm ; and since pe’? =h/k, we have eel hy ee Of course if a on) value be assumed for p? the value of 1/h is proportionately raised. 7 Again, for rails of similar cross-section 4 varies as the linear dimensions of the cross-section, and & as the square of the same. Hence y* varies inversely as the linear dimensions, and the leak is reduced fora giv en current by increasing the area of the rail. ='034 ohm approximately. Appendix added January 1901. An important paper was read before the German Physical Society in Berlin in June 1899 by J. Edler (Verhandl. des Deutschen physikal. Gesellsch. 1. Jahrg. No. 10), describing a series of experiments in which the magnetic disturbances due to a line at Spandau were measured at a number of stations at different distances from the line; and it occurred to me to apply the above theory to the results. The line is approximately straight, and is about 5 kilometres in length. ‘he current is said to have varied between 35 and 150 amperes. I kave assumed in the calculations a mean current ot 100 amperes, the voltage being 500 volts. I also assumed the value of the leak-coefficient for a mile of line to be ‘025, corresponding to the lesser of the two values for which tables are calculated in the paper. The value of uw? which corresponds to this leaix is, when the distances are measured in kilometres, approxi- mately equal to ‘08, and the leak in a length of a kilometres is ‘Ola?. The results for the vertical disturbance are given in Table III.,in which the first column gives the distance of the observing-station from the line in kilometres, the second Theory of Magnetic Disturbance by Earth-Currents. 441 column the calculated, and the third the observed values of the force, the unit being as usual 10-° Gauss. TABLE III. y- F calculated. F observed. 38 12°8 Bong 64 73 10°6 “79 58 56 92 4:9 4:3 301 “99 95 748 “21 24. 1-54 15 1-04 | It isclear that at the two shorter distances the formula fails to represent the facts. In the case of the next four stations, that is for a range from ‘79 to 7°48 kilometres, or from half a mile up to five miles, the agreement is practically exact. In the case of the experiment recorded in the last line the river Havel, which from a small map printed with the paper 1s apparently nearly half a kilometre in width, and another smaller stream lie between the observing-station and the line. This may possibly account for the discrepancy between theory and experiment. It is easy from Professor Riicker’s theory to calculate the horizontal resultant disturbance. Taking, as in fig. 1, A and B to be the source and sink and O the observatory, we have to find the resultant of two forces I«/OB and Ix/OA acting at right angles to OB and OA respectively, in such a way that if the one tends to increase the angle MBO, the other tends to decrease the angle MAO. This resultant is easily shown to be equal to TeRea T 1-19 i To apply this I have assumed the whole leak to take place at the ends of the line, which is clearly quite an extreme case, and have thus obtained the following table. Phil. Mag. 8. 6. Vol. 1. No. 4. April 1901, 2G AAD Dr. Beattie on Leakage of Electricity from TABLE LY. | fe | H calculated. H observed. 38 2-25 96. ane ‘64 2°15 6:09 79 2-08 4-67 ‘92 1-92 4:31 301 83 - 1:33 | 7-48 ‘21 “44 | 1-54 1:56 1-44 Tn this case the discrepancy is very marked. The observed and calculated forces are quantities of the same order ; and that is allthat can be said. Possibly this may be due to the very close proximity of the river which runs parallel to the line. The horizontal disturbance is due to the vertical com- ponent of the leakage-current. We may possibly look upon the river as an extended sink. Currents which start in a horizontal direction from the side of the rail opposite to the river may be diverted by it, gradually becoming vertical, and finally, after having the direction turned through 180°, passing horizontally, or nearly so, back under the rail and into the river ; or it may be that the water-surface under the ground is not very far below the level of the rails—the observing-stations were in most cases only 3°5 metres above the water-level,—and that in consequence of this the lines of flow are inclined ata less angle to the vertical than they would otherwise be. The presence of the river ought clearly to affect the hori- zontal disturbance more than the vertical. XL. Leakage of Electricity from Charged Bodies at Moderate Temperatures—II. By J.C. Beatriz, D.S¢., PRS LE, Professor of Applied Mathematics and Physics, South African College, Cape Town *. § 7. i a previous paper + the rate of leakage of electricity from insulated plates covered with different sub- stances was observed when the plates were charged with positive electricity to a potential of between 200 and 100 _* Communicated by the Author. Read before the Royal Society of Edinburgh, July 1900. fy Phil. Mag. ser. 5, vol. xlviii. pp. 97-106 (July 1899). Charged Bodies at Moderate Temperatures. 443 volts at a temperature between 300° C. and 400° C. The following contains the results of a number of additional ob- servations at potentials of 1 or 2 volts and with both positive and negative charges. § 8. When wires of the same metal are connected with two mutually insulated metals, and the atmosphere between these two metals is rendered conductive by Rontgen rays, uranium rays, or ultra-violet light, the wires acquire a difference of potential *. In the case of ultra-violet light this difference depends, amongst other things, as was first pointed out by Righi, on the distance apart of the two mutually insulated ‘metals. To test whether or not a similar effect was produced when the air between the plates was subjected to the effects of thorium-radiation, an arrangement of the following nature -was used. Hlectrometer. NI A cylinder of zinc, C, had an opening, O, in it. A rod of -ainc, A,in metallic connexion with the cylinder carried a zinc plate, 5. A second rod, H, of brass carried a plate of zine, D; this rod Ei passed loosely through a solid paraffin collar P. The distance between D and B could be varied. On B different metals were placed after having been covered with a thin layer ofa saltof thorium. It was found, for instance, when D was connected to the insulated terminal and B to the case of a quadrant-electrometer, that the electro- meter-reading deviated from the metallic zero t in a few * Phil. Mag. ser. 5. vol. xliii. pp. 418-440 (June 1897). + By metallic zerois meant that electrometer-reading which is obtained when the quadrants are all metallically connected to the case of the imstrument. 2G 2 444 Dr. Beattie on Leakage of Electricity from seconds to a reading at which it remained steady. When D was charged positively or negatively, the charge leaked away till this reading was reached. The difference between this reading and the metallic zero did not vary with the distance: between the two mutually insulated disks either for salts of thorium or of uranium. ; , The ditference was the same to within a small fraction of a volt, whether thorium oxide, thorium nitrate, or thorium: sulphate was used. | lt was found that the difference of potential with the zinc D connected to the insulated pair of quadrants and with polished copper covered with a thorium salt on the zinc B—this latter being of course connected to the electrometer-case—was about °5 of a volt negative. This difference was considerably increased after the copper had been oxidized by heating in air: and again used. With amalgamated zinc or aluminium used in the same manner, the difference of potential was a fraction of a volt. positive. The difference, it was found, depended very greatly on the polish of the mutually insulated metals. § 9. It has already been stated that when zine covered with salt on which iodine had been sprinkled is insulated in an iron box, and heated, a positive charge leaks away when the temperature is raised to between 300° C. and 400° C. With the arrangement described in § 2, Phil. Mag. xlviii. p- 98 (July 1899), which was again used in the experiments to be described—with a quadrant-electrometer instead of a multicellular in many cases—results of an analogous nature were obtained. These will be described more particularly in a later paragraph. 3 The insulated plates were in most instances of iron; zinc strips on which common salt sprinkled with iodine was spread were laid on these iron plates, and the latter joined to. the insulated terminal of the quadrant-electrometer, the box (of iron) surrounding these insulated plates was connected to the case of the electrometer. When heat was applied to the. outside of this box, as described in § 2, it was found that the electrometer-reading deviated from the metallic zero to a steady position, indicating a difference of potential between | the insulated plates and the surrounding disinsulated box of | about °6 of a volt negative. When the plates were charged positively, the charge leaked away till the final reading was. again ‘6 of a volt negative: a negative charge less than this increased, while one greater leaked away till the same steady reading was obtained. Charged Bodies at Moderate Temperatures. 445 The experiment was varied by placing the zinc strips on the bottom and on the shelf of the iron box, no new supplies of sait or of iodine being added. The zine was thus in metallic connexion with the case of the electrometer, while the insulated terminal was connected to the iron plates, now with nothing on. It was found that the iron plates differed in potential from the surrounding box by about ‘5 or °6 of a volt positive. A charge oiven to the plates leaked away till this steady reading was reached. It was found that no change in this potential-difference was produced by varying the distance between the zinc and the insulated iron. Experiments of an exactly similar nature were made with bromine substituted for iodine. The results obtained were the same. The difference of potential was not, as.a rule, the same in any two experiments on different days even with the same materials. This is not to be wondered at, as the iron box and the plates were thoroughly cleaned after each experiment, and a different surface state produced each time. Common salt was next sprinkled over a copper plate and iodine sprinkled on it; this was insulated in a zinc box: it was found that after heating for half an hour there was a slightly increased leak of positive electricity and practically no increased leak of negative electricity. On the other hand, when the salt was placed on the bottom of the zinc box and iodine sprinkled over it, there was a greatly increased leak of electricity from the insulated copper plate when it was charged negatively, and practically no increased leak when it was charged positively. It was also found that the steady reading showed the copper to be positive to the zine box. § 10. The following results are given to show roughly the nature of the effects observed. The insulated plate in the box was supported as described in § 2. It was connected to the insulated terminal of the quadrant-electrometer ; the sur- rounding box was joined to the case. . The insulation was first tested without flame and found good. The insulation was also good with flame and with nothing on the insulated iron plates. 446 Dr. Beattie on Leakage of Electricity from Common salt with iodine sprinkled over it placed on zine strips ; these latter placed on iron plates insulated in iron box : Plates charged positively. Blame lit spon: _ Plates charged negatively. ae! Reading in : ae. Reading in scale-divisions*. scale-divisions. 9.35 +100 9.47 —100 9.36 — 70 9.48 —125 9.37 — 95 9.48 — 125 9.39 —105 9.40 —120 9.42 —125 Plates insulated without charge. 9.44 —125 i 9.51 | 0 9.52 —J]15 9.53 —130 9.55 —130 * 100 scale-divisions=1°4 volts. The zinc strips were next placed on the bottom of the irom box so that:now they were connected with the case of the instrument ; the iron plates on which they had previously rested were again connected to the insulated terminal of the electrometer: No charge given. | ie Flame lit at 1.18. Plates charged positively. | nga | | Bre : Reading in | é Reading in Ese: Peioaitious Aa Time. | sal aitceee, 1.18 0 | 1.42 | +1380 | 1.25 Ov fe sh 1.46 | +118 | 1Zy +10 | 1.49 | +111 | 1.30 +30 | 1.50 | +109 1.39 +65 | 1.57 | + 94 1.41 +65 2.08 + 74 | 2.09 | + 73 2.10 | He: 2.14 | + 68 * 130 scale-divisions =1-4 volts. ; The above figures may be compared with the following which were obtained with a thorium salt and no flame. Charged Bodies at Moderate Temperatures. 447 Thorium oxide spread on zinc strips ; these latter placed on insulated iron plates in iron box : Insulated with no charge. | Charged positively. | Charged negatively. No flame. er. | Time. ioe Time. Reading. Time. Reading. —— -8.16 0 3.19 +120 ol —120 | 3.7 —63 3.20 | —55 || 3.22 ~78 3.18: s- 40 S0h 1 270 3.23 a58 3.19 = 70 3.21 =70 3.24 78 * 120 scale-divisions = 1-4 volts. Zine strips with thorium oxide placed on bottom of iron box: | Insulated with no charge. Charged positively. Charged negatively. wl | Time. “ime, | Reading — Reading. Time. Reading. Time. Reading. a0 || 0 3.31 +120 3.33 —120 3.29 3.32 +70 3.34 +50 3.30 3.325 +67 3.345 +67 3.91 | 3.99 +67 3.35 +67 Lithium chloride spread on zine strips, bromine poured on, zinc strips insulated on iron plates in iron box: _ Insulated with no charge. i | Bitte on al. 10.55. Charged positively. | Charged negatively. | Time. Reading *. Time. Reading. ‘Time. Reading. 10.55 0 11.23 +120 18.27 —120 11.5 — =20 11.24 —50 11.28 —60 11.12 —25 11.26 —50 11.27 —50. 11.17 50 (11.98 ee. Lae —50 | | * 120 scale-divisions = 1:4 volts, 448 Dr. Beattie on Leakage of Electricity from Same lithium chloride—with no additional bromine—placed on bottom of iron box so that it was now connected to the case of electrometer. Iron plates insulated inside box: Insulated with no charge. Blamicaeaiae) Charged positively. Charged negatively. Time. Reading. Time. | Reading. || Time. Reading. 1.48 0 2.9 £190) |) ug as 1.49 0 2.10 +60 2.134 +60 2 : +60 21 +60 2.14 +60 2.8 +60 | | With these we may compare the following figures obtained with a uranium salt, no flame being used. Uranium nitrate on zine strips insulated on iron plates in iron box, latter connected to case : Se en sy oa Charged positively. Charged negatively. Time. Reading * . Time. | Reading. | Time. Reading. 3.6 0 Peg |e ae Sy 3.18 —120 3.10 —86 3.13 +30 3.19 —~92 3.11 —90 S14 | 45 3.20 —85 3.12 —90 3.15 —75 3.20 =63, 3.16 | ~80 3.21 ~80 3.17 ~80 3.22 80 * 120 scale-divisions = 1°4 volts. Uranium nitrate on zine strips placed on bottom of iron box, iron plates insulated inside: ines ee enone: Charged positively. Charged negatively. Bari , vay a le 5 ime. Reading. Time. Reading. Time. Reading. g.25 3.40 +120 3.45 — 120. 3.26 +15 | 3.41 +75 3.46 -—15. 3.29 +20 3.42 +30 3.47 +10 3.39 +20 3.43 +20 3.48 +20 3.43 +20. 3.49 +20 a ae Charged Bodies at Moderate Temperatures. 449 § 11. Experiments of a similar nature were made with a~ number of other substances. It was found that with potas- sium chloride on which iodine had been sprinkled, spread on zine strips and insulated on the iron plates in the iron box, no ‘increased leakage of either positive or of negative charges was produced on heating. With bromine instead of iodine an increased leak was obtained, which, however, was not steady. There was no definite position to which the electro- meter-reading tended when the zine strips were insulated without charge. The electrometer-reading was sometimes on the positive side of the metallic zero, sometimes on the negative. The effect ceased after heating for about half an hour. A crack- ling noise accompanied the heating, and solid particles were thrown off the insulated zinc strips on to the iron box. With zinc chloride spread on insulated iron plates, it was found that on heating there was for each experiment a defi- nite reading, sometimes on the positive, at other times on the _ negative side of the metallic zero, to which the electrometer- _ reading deviated on heat being applied to the outside of the box. In the following list the results of the various experiments, where the quadrant-electrometer was used, are tabulated :— | | | | Difference of Outside boxy. at, Alan | | potential ob- connected | "S28" Substance — Substances _— served when no to case plates | used | laced on: charge given and Remarks. _ (made of: | 4 | P : Bes made of: | | temperature | | raised to about | | i ao0e iron. iron. | Sodium chlor- | zine strips on, None. | ide. insulated iron | plates. iron. iron. | Sodium chlor- - Negative. Steady. ide with io- | dine. | | _ iron. iron. | = zinc strips on | Positive. P disinsulated iron box. zinc, copper. . zinc strips on Positive. - disinsulated _ zine box. | iron. iron. Sodium chlor-| zine strips on, Negative. ¥ he ide with bro-| insulated iron | | mine. | plates. | iron. | iron. | Lithium chlor- |zine strips on Negative. “ ide with io-| insulated iron | dine or with plates. | _ bromine. iron. | iron. Zine chloride. | iron plates. | Negative. er | 450 Outside box connected to case made of : iron. iron. iron. iron. iron. iron. iron. iron. iron. iron. iron, iron. .Dr. Beattie on Leakage of Electricity from Insulated plates made of : | iron. iron, iron. iron. iron. iron. iron. iron. iron. iron. iron. iron. iron. ° iron. iron. Lead Substances used : with iodine. Caleium chlor- ide with io- dine. Ammonium chloride with iodine. Cuprie chlor- ide. Potassium chloride with or without iodine. Pot. chloride with bromine. Barium chlor- ide with io- dine or with bromine. Zine oxide with iodine. Barium oxide with iodine. Sodium iodide. Zine iodide. Potassium 10- - dide and man- ganese di- oxide. Potassium 10- dide and bro- mine. Potassium 10- dide and bro- mine. Potassium i0- dide and po- tassium chlor- ate. Potassium chlorate with iodine. Potassium per- manganate. chloride | zine strips on Substances placed on: iron plates. zine strips on iron plates. zine strips on iron plates. iron plates. zinc strips on iron plates. zine strips on | iron plates, iron plates or zine strips on iron plates. zinc strips «e. 99 iron plates. iron plates. iron plates. iron plates. zine strips on iron plates. iron plates. | | | zine strips on) iron plates. | | | | iron plates. Difference of potential ob- served when no charge given and temperature raised to about 350° C. Remarks, Negative. Steady. Negative. Negative. Negative. None. Sometimes po-| Unsteady. sitive, other times negs- tive. None. None. None. None. Negative, sometimes positive. Inappreciable. Unsteady. None. Negative. Unsteady. | None. | Steady. Negative. No fixed read- | Unsteady. ing _ obtain- | able. Charged Bodies at Moderate Temperatures. 451 § 12. In experiments where the quadrant-electrometer was used it was noticed that there was, in those cases where an increased leak due to heating was observed, a more rapid leak of positive or of negative electricity according as the substance experimented with was insulated or was connected to the case of the electrometer. ‘This same difference of leak depending on the nature of the charge obtains also in the case of thorium and of uranium salts. A difference, however, comes in when higher voltages are used. In the case of thorium oxide and uranium nitrate no difference in rate of leak could be observed, with the experimental arrangement used, depending on the nature of the charge. No flame was used with these two salts. On the other hand, with common salt and iodine or with lithium chloride and bromine on zine strips lying on the iron plates insulated inside the iron box, a leakage was observed on heating when the insulated substances were charged posi- tively. The leakage was such that a multicellular indicated a drop of as much as 100 volts per minute, whereas with a negative charge the leak remained the same, to within a couple of volts, as when no flame was applied. Again, when the zine strips on which the substances had been spread were placed on the bottom of the iron box so that they were in connexion with the case of the instrument, it was found that, on heating, the insulated iron plates retained a positive charge almost as well as when no heat was applied, but lost a negative one. The following figures will give some idea of the behaviour at voltages between 200 and 100 ; other figures will be found in §5. It may be noted that the substances given there as showing an increased leak show it for positive charges only with the arrangement there used. So far as negative charge goes, their behaviour when insulated is the same as that described below for salt and iodine insulated on zine strips. The iron plates were insulated in the iron box and con- nected to the insulated terminal of the multicellular, the iron box being itself in metallic connexion with the case. _It was found that on heating the apparatus for more than an hour, the leakage of electricity was the same for positive or for negative charges, the fall of potential being from 1 to 3 volts per minute, according to the day. A strip of zinc was then laid on the insulated iron plates; it was found that a positive charge leaked away a little more readily than a negative one: in one experiment the leak for a positive charge of 200 volts was 1U volts per minute, for a negative charge of 200 volts it was 4 volts per minute; in A52 Dr. Beattie on Leakage of Electricity from another experiment the respective leaks were 6°5 and 4 volts per minute. With salt spread over the zine strips the leak was the same as in the case of zine alone ; in the instance ne mentioned, 6 volts and 4 volts per minute. Finaily, when iodine was sprinkled on the common salt— femme on continuously—the following results were obtained:— +190 volts: +182 volts after $ mI ; + 58 volts lost in $ minute. — 200 volts : —195 volts after 1 minute ; — , 5 volts lost in 1 minute: Zine strips with iodined common salt were now placed on the bottom of a zinc box which was connected to case of instrument and iron plates insulated inside the box. — 206 volts negative : : 154 volts after 1 minute ; —52 volts per minute. © + 183°5 volts positive : 181 volts after 1 minute ; +2§ volts per minute. ne Hxperiments were made to determine how long the peculiarities as regards electric discharge lasted. In several instances, after a comparatively short period of heating the effect ceased. This was the case with potassium chloride and bromine, with potassium permanganate, with potassium chlorate and iodine, with potassium chlorate and manganese dioxide. In the case of salt sprinkled with iodine insulated on zine strips the effect lasts longer. In one case the strips covered. with this iodined salt; were heated till the effect was shown, and then laid aside. The same strips were heated again at the end of a week, with a similar result. Ten days later it: was again found to act. Sixteen days later the effect was still shown on heating ; on this latter occasion, however, after heating for over an hour the peculiar property was lost. A new supply of salt was then taken, sprinkled with iodine, and heated steadily ; it was found that after three or four hours’ heating the increased leak ceased. When more iodine was added the increased leak was again observed on heating. This experiment was repeated several times with the same result. With potassium bichromate and bromine sprinkled on it and placed on zinc strips, it was found that the increased leak ceased after heating for about two hours. Charged Bodies at Moderate Temperatures. 453 With zine chloride on iron plates the effect continued even after heating for three or four days. | § 14. A number of other experiments were made with the same arrangement of apparatus and with the multicellular. Those substances were chosen which were known to give off a gas on moderate heating. In the following table some of the results obtained are given. The iron box was connected to the case, and the insulated plates (of iron) to the insulated terminal of the electrometer. Potassi anate mereceiee : sium permanganat Negative. | . Substance. | MERE OE Leak. | | charge. Manganese dioxide and caustic | Positive. Normal. potash. | Manganese dioxide and sulphuric | Positive. Normal. acid. Bleaching - powder, water, and { Positive. Noel ColbaltrOxwdle i725 Jerson s cdesce aca: leeeiaee I ape EARLE OXIDE! jackie s\Sio vee dens sceet _ Positive. Normal. Manganese dioxide and potassium | { Positive. \ FAG ONS: BEM eAG rhe ence sensciden no vetoe oe s| Negative. Potassium bichromate with sul- | Positive. Normal. phuric acid. Potassium bichromate with hydro- Positive. Increased. chloric acid. | Manganese dioxide with hydro-| Positive. Increased. chloric acid. | { Positive. 1 I | { nereased. | § 15. An examination of the various results given for small voltages shows that the effect produced in the heated atmo- sphere surrounding certain insulated substances is of the same nature as the effect produced in the atmosphere surrounding bodies on which salts of thorium or of uranium are spread ; the difference of potential between the mutually insulated metals depends on the nature of the metals, but not on their distance apart. The difference observed also changes sign when the substance, instead of being on the one mutually insulated metal, is placed on the other. With potentials of 200 volts there is a one-sidedness in the discharge from certain heated substances which does not show itself in the case of thorium or of uranium salts. This peculiarity may be compared with the discharge due to ultra- violet light, which has been so thoroughly investigated by Elster and Geitel. Here, however, it is the positive charge which leaks away, while the negative is retained. It may also be compared with the behaviour of a heated metal, as observed by Guthrie, Hlster and Geitel, and others ; the 454 9 On Leakage of Electricity from Charged Bodies. substance acts as an iron body at low red-heat does, retaining negative but not retaining positive electricity. In some instances—such as potassium permanganate, potassium chlorate with manganese dioxide, potassium iodide with bromine on zinc—the phenomenon is complicated by the fact that the heating causes solid particles to fly about to such an extent as to give no steady reading on the quadrant- electrometer when these substances are insulated without charge and heat applied. These substances also, when heated, discharge negative as well as positive electricity even when the electricity is at a potential of 200 volts. For substances such as salt with iodine on zine, which are found to insulate at higher voltages for negative but not for positive charges, an explanation may be offered founded on Enright’s* and Townsend’s t experiments. Townsend shows that hydrogen given off when metal is dissolved in an acid carries off with it a positive charge. If, then, we assume that a gas is given off by these substances, and that it carries a positive charge with it, we can understand why a positive charge leaks away. In the case of salt with iodine on zine strips we have the possibility of the contemporaneous existence of common salt, sodium iodide, zine iodide, zinc chloride. It has been shown that the first two, when heated, do not give the peculiar effect observed. The second two do show this effect even in the absence of zinc ; and the fact that to restore the capability of discharging positive electricity more iodine has to be added, might lead one to explain the result by saying that zinc iodide was formed and afterwards at a higher temperature this gave off iodine which carried a positive charge with it. An attempt was made to solve the problem by chemical analysis, but the results were not promising. It is proposed to test by Kelvin’s electric-filter method whether or not the gas is charged ; and, if so, how. It may also be possible to collect sufficient of the gas to examine it directly. I have to thank one of my assistants, Mr. Michell, for much help in the laborious work of observing. Physical Laboratory, South African College, Cape Town. June 1900. * Enright, “ Electromotive Force of Contact between a Liquid and a Gas,” Phil. Mag. xxix. p. 56 (1890). + Townsend, Proceedings of the Cambridge Philosophical Society, vol. x. part 5, 1897. | [ 455 ] XLI. On the Phosphorescent Glow in Gases. By JOHN B. B. Burks, WA. (Dublin), B.A. (Res.) Cantab., Trinity College, Cambridge. [Continued from p. 356. ] Srotion IV. V On the Conductivity of the Glow. (13) A TUBE was constructed with two pairs of wire- & = gauze electrodes a b and ¢ d, occupying positions in the tube as shown in fig. 4. The wire-gauze screens were placed with their planes at right angles to the axis of the tube. The electrodes were carefully insulated, and the outside of the tube was surrounded with tinfoil which was put to earth. The distance between each pair of electrodes was 1 cm. approximately. The electrodes ab were first put to earth whilst there was a difference of potential between cd, and the Fig. 4. LARTH LARTH EARTH gas was found to conduct after the passage of each spark, even when there was no glow, but the conductivity was greatly increased as soon as the glow travelled down the tube. There was no appreciable zncrease in the conductivity when the glow was in the bulb alone. The conductivity due to the passage of the spark alone was doubtless that observed by Schuster (Proc. Roy. Soc. 1887, p. 372). The fact that the great rise in the conductivity does not occur until the glow travels down the tube shows that it is not due to radiation from the glow itself. | The method of measuring the conductivity was as follows:— The electrode ¢ was connected to one pole of four Leclanche’s batteries in series, the other pole being to earth ; whilst the electrode d was connected to one pair of quadrants of a quadrant electrometer, the other pair being to earth. Great difficulty was experienced at first in trying to screen off com- pletely ordinary electrostatic effects from the Wimshurst, the 456 Mr. J. B. B. Burke on the adjoining wires, and the bulb. But this was got over by using large screens. The connexions between cd and the electro- meter were by insulated brass rods surrounded by tubes put to earth. One volt corresponded to 50 divisions of the scale. Before sending the discharge through the bulb, the two pairs of quadrants were connected and then disconnected. As soon as the discharge passed, the electrode d gradually acquired a charge of the same sign as that on ¢, whether this was positive or negative; and on reversing the con- nexions with the electrodes, so that ¢ was insulated and connected to one pair of quadrants of the electrometer and d to one pole of the battery, a similar effect was produced. The conductivity lasts for some seconds after the discharge has stopped passing in the bulb. It is very remarkable that putting on a large H.M.F. of 320 volts between ab does not stop or diminish the con- ductivity as measured between cd. The conductivity between cd is not exactly of the same magnitude, according as the H.M.F. is along cd or de. When ¢ is the insulated electrode it always receives a negative charge; and this would affect the rate at which it would take up the ions of the opposite charge to those taken up by d. There is a maximum potential which the insulated electrode will attain in virtue of the conductivity; and if initially its potential is greater than this amount, it falls rapidly until the potential in question is reached, depending upon the potential of the other electrode. Thus with air at a pressure of 0°235 mm. and ¢ charged positively to a potential of 8 volts a positive charge is rapidly acquired by d up to 285 divisions of the scale. If now the insulated electrode d be charged to the same potential asc, the reading on the scale is 410; but when sparking com- mences and the glow reaches the electrodes, the potential of d rapidly falls to 285. When ¢ is negative, d acquires a negative charge corre- sponding to —100. If while d is at —100, cis changed from the negative to the positive pole of the battery and the sparks sent through the bulb, the positive potential corresponding to —285 divisions of the scale is rapidly obtained after a few sparks. (14) The fact that the glow can diffuse through narrow metal tubing and pass between the wire-gauze electrodes charged to a thigh potential, or between two such electrodes close together with an electromotive force between them, without having its velocity or intensity altered, nor the con- ductivity lower down the tube sensibly diminished, seems to Phosphorescent Glow in Gases. ADT show, at first sieht, that it is not the glow which conducts, and that the conductivity is in the gas itself quite distinct from the glowing particles; but the glowing particles may consist of groups of ions so close together—which Professor FitzGerald has suggested to me as a possible hypothesis— that they can protect each other in diffusing through the metal tubing, and thus enable themselves to make their way through the wire-gauzes without being finaliy broken up by the electromotive turce between these electrodes. There is, further, a difficulty in explaining the conductivity of the gas by the passage of the phosphorescent molecules through it, as their velocity is so very small; but there is no need to suppose that the conductivity is in the gas alone as distinet from the phosphorescent particles. Since the condition of the gas when the glow takes place, as has been pointed out, appears to be that of a semi-chemical mixture; and if we bear in mind the part played by oxygen, both in the after- glow and in the negative glow, in which the conductivity is likewise considerable, it seems plausible to regard the con- ductivity in the glow as being of an electrolytic natur e, due to the formation of large groups of molecules ; and this view of the matter is further strenvthened by the fact that the con- ductivity is retained after the passage of the glowing particles through the wire-gauze electrodes with an electromotive force between them, and also perhaps by the fact that the glow presents a somewhat dirty or semi-opaque appearance. The semi-opacity resembles that accompanying the pheno- menen of fluorescence of uranium glass. (See also Newall, loc. cit.) Thus we may be led to regard the phenomenon of phospho- rescence as due to the formation of large and probably com- plicated molecular groups, which are gradually broken up by molecular impacts of a certain frequency. The destruction of these molecular groups inay also be etfected, as has been shown, by negative ions of sufficient penetrating power. The radiation from the phospborescent inolecules must produce, at molecular distances, a considerable repulsion, which should diminish considerably the violence of the bombardment from other molecules, and possibly ionize the latter. (15) The capacity that, as has already been stated, a gas possesses of storing up energy from a spark which has been sent through it, and then of emitting this energy under suitable conditions in the form of phosphorescent light, is somewhat analogous to the phenomenon of thermo-lumines- cence, with this exception, that whereas in the case of the former the phosphorescence is dependent solely upon the pressure of the gas, and independent as to whether this pressure Plal. Mag. 8. 6. Vol. 1. No. 4. April 1901. POEL 458 _ Mr. J. B. B. Burke on the has been reached by compression or by rarefaction, in the latter case the phosphorescence is produced by heating the substance. But in both cases a certain amount of energy is stored up, -in the substance, from the spark. Thermo-luminescence is another instance of the part played by slight impurities in the production of phosphorescence. It is found to oceur chiefly in substances which van ’t Hoff has styled “ solid solutions,” formed when two salts, one greatly in excess of the other, are precipitated from the same solution. The connexion between them seems greater than that of an ordinary mixture. It is conceivable, as we have pointed out, that in a gas a somewhat similar semi-chemical mixture may be brouglit about under certain conditions, such, for instance, as the passage of electricity through it; and this view of the matter is strengthened by the fact that the passage of electricity through a gas is most easily effected at the pressures at which the phosphorescence appears. (16) A strong beam of sunlight when passed through a gas does not communicate to it the energy requisite for the glow (see Newall, loc. cit.); Wiedemann has shown that thermo- luminescence excited by a spark is not due to ultra-violet light ; since if a thin plate of quartz be interposed between the spark and the thermo-luminescent substance the effect does not take place. He has shown that the thermo- luminescence is excited by a radiation from the spark which he has called “Mntladungstrahlen,’ to which solid bodies are opaque. Thev are not much absorbed by gases except carbon dioxide, but they produce ionization in gases through which they pass (J. J. Thomson, ‘Camb. Phil. Soe. Proce.’ 1899). J.J. Thomson has also shown that this radiation does not proceed from the cathode or dark space, but either from the positive column of the discharge or from the negative glow. He has suggested that this radiation is analogous to Roéntgen rays. The Rontgen rays being the thin pulses produced when charged particles are stopped, and the “ Entladungstrahlen”’ the much longer pulses produced when charged particles are put into motion. There is, however, apart from the “/ntladungstrahlen,” a radiation of particles in the neighbourhood of the anode, as in the case of the cathode (see J. J. Thomson, ‘ Recent Re- searches, pp. 175-177). J.J. Thomson considers that the difference between the emission of particles from the spark and that of cathode-rays is that in the former, the pressure being greater, the molecules communicate their momentum to the surrounding gas instead of retaining it until they strike against the walls of the discharge-tube. Phosphorescent Glow in Gases. A459 This would diminish the density in the neighbourhood of the discharge and increase it, and therefore the pressure, in other parts of the tube. The experiment of Hertz already referred to indicates that the explosive effects of the discharge are more vigorous at the anode than at the cathode. Neither the glow nor the “ conductivity ’? accompanying it ean be due to “/Mnétladungstrahlen,’ since these latter must move with the velocity of light. But it is possible that the phosphorescent particles in the after-glow are forced down the tube by the explosive effects of the discharge, so that the actual velocity of the glow down the tube is not due to mere diffusion of the phosphorescent particles, but to the impulse of the explosion as well. The conductivity, so far as can be judged, is actually due to the phosphorescent particles ; since the explosion will move faster and the conductivity due to it would be detectable even when there is no glow, as its existence is independent of the presence of the glow. The same argument would hold against the “‘ntladungstrahlen.” Thus it appears from the evidenve we have adduced that the after-glow consists of a radiation or ‘ emanation ”’ from the spark of phosphorescent particles, which do not carry a charge of electricity, and which by their presence give rise to conductivity as they move through the gas. It might have been expected that the conductivity in the glow would be destructive to itself; but, as we have seen, it is only cathode-rays or negative ions when they are moving with great velocities that destroy the phosphorescence; and even then it seems possible that the effect is simply to diminish the duration considerably by increasing the brilliancy. The property which the glow thus possesses of conducting, and yet of the conductivity not being influenced by a large E.M.F. when the glow is first put under its influence, is very striking, and resembles in these respects the “ emanation ” discovered by Professor H. Rutherford (Phil. Mag. Jan. 1900) from thorium. If we view the phenomena of the conductivity of the glow from this point of view, it would appear that the glow con-ists of particles that do not carry an electric charge, but which in their passage through the gas produce ionization to which the conductivity observed is due. SECTION VY. (17) There were some properties of the glow which led me to suppose for some time that the glow itself was accompanied bya stream of charged particles which moved down the tube. A tube as in fig. 5 contained a brass plug which was con- nected to earth by a soldered wire. There were a number of Oe 2 460 Mr. J. B. B. Burke on the small holes each 1 mm. in diameter drilled through the plug. These holes were covered with a thin sheet of aluminium such as is used in the production of Lenard rays, about 0°002 mm. thickness. The aluminium lay flat upon the surface of the brass, which, however, was sunk about 1 mm. or so into the Phosphorescent Glow in Cosas. 463 (Lect. Roy. Inst. June 8th, 1888) showed that the glow contains ozone which was detected by the iodide of potassium starch test and others. Supposing then that ozone is formed at the pressures at which the variations from Boyle’s law seem to exist, it is nevertheless insufficient in itself to account for the glow which is produced at about the same pressure; since if the glow is the result of the formation of oxygen into ozone or vice versd we should expect the phosphorescence to happen whenever the pressure was altered so as to pass over this region, but such is not the case. It is only when a discharge has previously been sent through the gas that phosphorescence occurs in passing over this pressure. It is very probable, however, that the impurities upon which the phosphorescence depends are more readily acted upon in the presence of ozone. (20) We may summarise the results obtained as follows: that | (1) The glow is a volume effect. (2) It consists of unelectrified particles. (3) It is not the result of the recombination of ions liberated by the spark, as these ions travel down the long tubes away from the spark, but are molecules produced in the bulb by the spark directly. (4) An electromotive force has no effect upon the glow. (5) The glow conducts as it passes through the gas. (6) The destructive effect of sparks on the glow is due to cathode-rays or fast-moving negative ions. (7) The glow is due to impurities, but oxygen is a necessary element and most probably ozone, but they are not sufficient by themselves. (8) There is an analogy between the glow and thermolumi- nescence which is of importance. There is a certain amount of energy stored up in the gas by the passage of the spark. (9) The glowing particles resemble in some of their pro- perties the emanation from thorium. (19) The phosphorescent particles appear to be one kind of particles emanating from the spark, quite distinct from | those molecules to which the explosive pressure is due. (11) The conductivity appears to be electrolytic, depending upon the presence of impurities. (12) The phosphorescent particles appear to be large mole- cular groups formed by the spark, whose existence may be maintained for some time, notwithstanding the bombardment from the molecules of the gas; in consequence of repulsion which they must exert on molecules that approach them. 464. Prof. D. B. Brace on the Resolution of Light into In conclusion, I desire to express my hest thanks to Prof. Thomson for many useful suggestions and valuable criticisms. I also wish to thank Mr. Everett for the assistance he has afforded in the construetion of the very elaborate glass apparatus required in these researches. Cavendish Laboratory, Cambridge,. November 1900. XLII. The Observation of the Resolution of Light into its Circular Components in the Faraday “ Effect.” By VD. B. Brace, PAD. Professor of Physics, University of Nebraska*. Wee ingenious interpretation by Fresnel of the kinematical principle that two opposite circular vibrations will produce a linear vibration and wee versa, and his experimental verification in the case of quartz, has led several to investigate whether the same principle may not explain the important discovery made by Faraday in 1846 of magnetic rotary polarization. ‘This rotation, however, even under the most favourable conditions, is much less than that of quartz. This may explain why the usual explanation of the Faraday ‘‘ effect’ has remained so long without experimental veri- fication. Indirect evidence by interference methods, for example, has tended to confirm the above principle, without however conclusively establishing it. The discovery of Zeeman + (anticipated by Fievez ft) has added new interest as well as significance to the problem, and encouraged me to repeat experiments made a number of years ago. After several failures I have finally succeeded, by means of refraction, in resolving natural light into its two opposite circular components, when propagated. alone the lines of force. Various attempts had been made to obtain an arrangement of sufficient sensibility to show the double circular-refraction if it existed, and it was only through a fortunate idea that I finally succeeded. In my earlier experiments §, interference methods were first used. Two cylinders of Faraday glass were placed, one between the poles of a Ruhmkorft magnet, and the other at the further end of one of the solenoids, so that one of the two interfering rays in a Jamin Interferometer passed through each cylinder respectively. These rays could be either * Communicated by the Author: read before the American Physical Society, Oct. 27, 1900. + Phil. Mag. [5] xliii. p. 226 (1897). { Bulletin de 0 Acad. des Sciences de Belgique, [3] ix. p. 381 (1885). § Wied. Ann. xxvi. p..576 (1885). . its Circular Components in the Faraday “Efect.’? 465 circularly, elliptically, or plane polarized. When they were circularly polarized, the interference-bands from sodium light were displaced in one direction when the magnetic field was thrown on, and in an opposite direction when the field was reversed. The displacement for a reversal was *1355 of a band, while the calculated value from the total rotation of the plane of polarization of 49° 20' on the above principle | was 137. Righi, Becquerel, and Cornu had also made similar observations. ‘Their investigations, however, were confined to circular vibrations. These results admit of ditterent interpretations. The displacement may have been brought about by a relative difference in velocity of the two opposite circular rays, or the same effect may have been produced by a relative change in the phase of the two com- ponents, or both factors may together have entered into the phenomenon. ‘The observed displacement indicated that the circular vibration corresponding to the direction of the Amperian currents of the field had received a_ relative acceleration of velocity or of phase over the other component. ixperiments were further made to determine whether vibrations of varying ellipticity were also relatively accelerated in velocity and in phase. A similar displace- ment of the bands took place, but they became less and less sharply defined as the ellipticity increased. This indicated merely a rotation of the principal axes of the elliptical vibrations, and not a relative acceleration of the vibrations as a whole, since in that case the bands would have remained distinct instead of becoming partially obliterated. If the ellipticity had been increased until each ray became plane- polarized, and the relative rotation had been 90°, the bands would evidently have disappeared entirely, giving a uniformly illuminated field. These results, representing the action on light in all modes of vibration, must include that for natural light. They do not, however, settle the fact whether the medium can transmit a disturbance by circular vibrations only. It is true that there was a relative acceleration for circular vibrations, and that this would have produced the effects observed for the elliptical vibrations if we suppose them separated into their circular components, but a direct rotation of their principal axes would have produced the same thing also. It became necessary, then, to apply the direct methods of refraction to the problem. Fresnel’s combination of right- and left-handed quartz prisms could not be imitated for magnetic substances, as no two substances could be found of opposite rotary power having the same index of refraction and sufficient transparency 466 Prof. D. B. Brace on the Resolution of Light into and magnetic rotation to produce an observable resolution. Instead, an analogous system was used by inserting a half- wave plate between two prisms of Faraday glass, thus changing the respective circular components to opposite ones. But too much difficulty was experienced in obtaining the exact retardation over a sufficient surface. Refraction near the angle of total reflexion also gave imperfect resolution. In the present series of experiments different arrangements were used. Instead of refracting across a surface from one medium to another, the same thing may be attained by reflecting from a surface into the same medium, providing some of the components may be made to change their phase: by the proper amount (180°). This was attained in the following experiment. Tig. 1 is the trace parallel to the lines of force of a prism of Faraday glass placed between the bored-out poles of a powerful electromagnet. This Fig. 1. reflecting surface made angles of 66° with the polished ends: and was carefully figured and silvered. By shifting the pole- pieces, the angle of i¢idence could be varied from 65° to 75°. Under an incidence of 72° there was a relative change in phase of 90° approximately between the components in and at right angles to the plane of incidence, due to the reflecting ‘silver surface. If now natural light is sent in, it should be broken up into opposite cireular components which would be changed into linear vibrations at right angles to each other at the surface, and these should in turn be broken up into opposite circular components. ‘Those components which had the same direction of vibration as before inci- dence would be reflected at the same angle, while those oppositely circularly polarized would be deviated from the ‘ medial ray. Three lines should thus have been produced when the field was thrown on, the outer ones being oppositely circularly polarized, and the middle line being pe ea, and twice the intensity of each of the others. Although the fall resolving power of the aperture was - its Circular Components in the Faraday “Eject Abit obtained, the length of the prism (87 mm.) and consequent distance teen, the pole-pieces prevented my obtaining a suthciently intense tield to detect any resolution or widenin g of the ray. " °xX3 AVR a Oh De // oo hat eu el = ona =o 44. approximately. Assuming a resolution of 3” for an aperture of 3 centim. the resolution of the image into a triplet, the outer bands of which would be oppositely circularly polarized, could be just effected. The glass actually used was np=1°72 and w=:057’ and H<10*, so that the resolution was impossible with the constants used. In the experiments with the rectangular prism (fig. 2), with which the resolution was finally obtained, we have oy, H=-8700, np=1° 903, ey Vy Xp =O 1052; Ox 37 x 102-x 6x 10-° x 1 aie ereet 2 a5 9" PY a 0087'="5 approximately. a Fig. 4 For twenty reflexions, 67 ='52" x 20 =10!"4=:000048 x i 4 =: 0005 approximately in absolute angular units. Consider now in fig. 4 a ray a of natural homogeneous 472 Prof. D. B. Brace on the Resolution of Light into light entering the combination at right angles to the lines of force. According to Verdet’s law the Faraday “ effect” in this direction is zero. In experiments* I have found this to hold down to an angle of 0-038’ with the normal to the lines of force. JI have furthermore shown that when the Faraday “ effect ”’ 1s eliminated there is no double refraction, at least the re'ative retardation must be less than 2°8 x 107-7 per centimetre in a field of 2500 c.a.s. units for wp =0°115!. Assuming the incident ray a to be unaffected, the reflected ray a will be broken up into two opposite circular components, making an angle of -52" with each other, and equal angles with the original ray. The next total refiexion produces a relative change in phase of each of the linear components of the circular vibration, changing them into elliptical vibrations. The next total reflexion will produce a like amount. As the direction of rotation of the plane in the Faraday “ effect”’ is independent of the direction of propagation, but only depends on the absolute direction of rotation of the Amperian currents, in order that the field may impress a like change on the ray after the third reflexicn it must be circular and have the same direction of vibration relative to Amperian currents. This requires that the ray shall have a total change of phase of 4X after the third reflexion, to give it the same absolute direction of vibration in space. To effect this a mica plate, with its principal axes placed respectively parallel and at right angles to the lines of force, was carefully split and tested with two total reflexions until the entire retardation was exactly 4Ap. This must be accurate as, if there is a slight ellipticity in the ray, this residual element remaining after the subtraction of the circular component will distribute light between the two circular elements and destroy definition when examined in the telescope. After the third reflexion (or the final reflexion), the two components will be separated and form two images in the telescope, that one which has the _ greater velocity or acceleration in the magnetic field forming an image on the right, and that which has the less on the left. In the first experiment. a double slit was used whose ele- ments were each 0 06 millim. wide and 0°5 millim. apart and distant 10 metres from the prisms, the angle thus subtended being :0005 absolute unit. On account of the great absorp- tion and loss of light from so many internal passages, an intense source was necessary. All the usual methods failed, but by fusing sticks of common salt and placing them just at the bottom edge of a crucible broken in half and directing a powerful oxyhydrogen jet on the edge of the same, sufficient of * Phil. Mag. [6] xliv. p. 342 (1897). its Circular Components in the Faraday “Effect.” 473 the fluid salt passed over into the flame to produce a brilliancy comparable with the lime-light itself. Until this arrange- ment was made, it was not possible to observe the splitting of the image. All other light was carefully excluded, as non- homogeneous light produced a spectrum which prevented resolution. It is needless to say that the surfaces of the prisms should be figured to within a fraction of a wave-length, a difficult matter on account of the softness of the glass. Oxidization of the surfaces is also unavoidable, due to moisture, and they should be carefully protected and used soon atter polishing. These prisms were made originally by Messrs. Franz Schmidt & Haensch, Berlin, and later refigured and repolished by Mr. Petitdidier of Chicago, and also repolished several times in my own laboratory. The dimensions of the diagonal faces were 50 x 100 millim.; only about 65 millim. of the vertical height was used, the vertical aperture being about 10 or 11 millim. Unusual facilities for producing an intense and extensive field are also. necessary. In this experiment the air-gap was 53 millim., so that the poles could not come in contact with the prism. The terminal pole-faces were 100 millim. square, and reduced from a circular cross section of 203 millim. diameter by specially curved pole-pieces, to reduce leakage. The magnet was one of the most powerful in existence, and weighed about two tons. A description of it is given in the Phil. Mag. of October 1897. About 100,000 ampere-turns were used. The intensity of the field was measured both by a bismuth spiral and by the rotation in CS,, and gave 8700 C.G.S. units approximately for this number of ampere-turns. The magnifying powers used were 16 and 60. The best definition was obtained with the lower power. By shifting the prism the images of the double slit could be brought into: the field of view ; one or more images, corresponding to the different orders of passages within the prism, being visible at times, simultaneously. These were generally much blurred and indistinet, but certain positions were obtainable where the two images of the double slit could be definitely resolved. The effective horizontal aperture was then about 20 millim. When the circuit was closed the original double image | became first blurred, and widened, and finally, when the field had become constant, changed into a triplet thus | |], the central band being apparently double the intensity of either of the outer bands and midway between the original elements. The angle subtended by the doublet was -0005, as stated above, while the angle of separation calculated above gave the same, The predicted change hence agreed with the observed effect, Phil. Mag. 8. 6. Vol. 1. No. 4. April 1901. rae | 474 Prof. D. B. Brace on the Resolution of Light into On examining with a nicol, the central band was found not to change in intensity as the nicol was rotated, but the outer bands appeared to be plane-polarized (or nearly so), since the one was extinguished when the principal plane was 45° with the plane normal to the field, and the other when it was rotated through 90°. is In order to study better the polarization of the doublet, a single slit 0°2 millim. wide was used to obtain more light. On each side appeared diffraction-bands,—some very fine. When the circuit was made the image and all the bands, which were sufficiently fine, broke up into doublets. On referring to fig. 4, it will be seen that the rays a, and a, after the last reflexion pass through the mica plate. This, with the reflexion, produced a change of phase of slightly less than 2A, so that they were slightly elliptical, but nearly plane-polarized.. When the principal plane of the nicol was turned 45° to the left, the image on the right was cut out, and when turned 45° to the right of the vertical plane the image on the left was cut out. This indicated that the ray on the right was right-handed, and that on the left left-handed polarized after the last reflexion. Thus, the ray on the right had the same direction of vibration before the last reflexion as the Amperian currents, the direction of the lines of force being from right to left as indicated in the figure. Conse-_ quently, vibrations in the direction of the Amperian currents are accelerated (in phase or velocity), and those in the oppo- site direction are retarded by the same amount. ‘This corre- sponds to the results which I obtained by the method of inter- ference referred to at the beginning. On reversing the field the direction of polarization of a, and a, was interchanged, i. e. rotated through 90°, indicating that now a, was right- and ay left-handed. | On tilting the prism so that the number of complete passages was reduced from five to four, the image was broadened and barely resolvable into two when the current was thrown on. On tilting still farther, for three complete passages, resolution was impossible, but a blurring or broaden- ing at the edges of the image could be detected. Since the incident ray a was unpolarized, we must conclude from this experiment that only circular vibrations can be transmitted along the lines of force, any disturbance being broken up into its opposite circular components when propagated in a magnetic medium. : : Different arrangements of the prisms were used, such as sliding one over the other until the diagonal faces were exposed, and sending in the ray nearly normally to these, but ets Circular Components in the Faraday “Effect.” 475 with less perfect definition than with the auxiliary prisms. Also a single prism was used, the ray being sent in and out once, and the aperture diaphragmed down to two narrow openings, so as to resolve by the method of interferences, but with no success. Of the two assumptions (acceleration of phase and of velocity) upon which the above observed results may be explained, the former does not appear to be tenable upon dynamical grounds. Further, if there is a direct acceleration in the rotation, it is difficult to see why a plane-polarized vibration should be transmitted by its circular components to explain the rotation of the vibration, rather than without resolution and a direct rotation of the unresolved vector. The latter assumption of a change in velocity must therefore be adopted. It may also be remarked that, kinematically, it can be shown that other modes of transmission may produce a separation of the original system of rays into two opposite circular systems. Gouy*, for example, has shown that a rotary substance may produce a separation for a ray into two circular components forming equal angles with their mean position. His analysis involves essentially an integration, over the refracting surface, of the elementary Huyghenian zones, taking into account the continuous increase in orienta- tion of the ‘vector in the successive zones arising from the varying thickness of the rotating medium. When the change in orientation in absolute angular measure over unit width of the stream is a very large quantity, the resultant reduces to two opposite circular components referred to. This analysis cannot apply to quartz or any other known natural rotary substance, since in Fresnel’s experiment this orientation was not large compared with the width of the stream. In magnetic rotary substances the same condition also holds, since even in the case of iron the orientation is not a very great quantity for finite angles. We must therefore conclude that the resolution observed can only arise from the power of the medium to transmit circular vibrations, only, in the direction of the lines of force. Physical Laboratory, University of Nebraska, Lincoln, January 5, 1901. * Comptes Rendus, xc. p. 992 (1880). 22 [ 476 J XLII. The Spectra of Carbon meee By ARTHUR SMITHELLS * Introduction. HE chief object of this paper is to give an account of experiments relating to the hydrocarbon flame spectrum and to advance a new view as to its origin. The other spectrum concerned in the paper is that oma called the: carbonic oxide spectrum. The hydrocarbon flame spectrum noticed by Wollaston in 1802 was first mapped in detail by Swan in 1857, and hence it is often known as the Swan spectrum. In addition to these names the spectrum has also been called the banded, chan- nelled, or fluted spectrum of carbon, the candle spectrum, the carbon spectrum of the first order, or simply the carbon spectrum. Misunderstandings have occasionally arisen from the use of these and other names to indicate one and the same- spectrum. To avoid confusion I shall adopt the name Swan spectr ume throughout this paper. The spectra of carbon compounds have been the subject of a vast amount of research and controversy, and the literature is very voluminous. A history of the subject by Prof. Schuster will be found in the British Association Reports (1880, p. 258), and also in the text-books of Salet, Kayser, and Landauer. I do not propose to deal with the subject as a whole, but shall allude to previous work as occasion requires.. Tt will, however, be convenient to give a list of the recorded spectra of carbon compounds which I deal with in the following pages, together with the names and some of the commonest sources of the spectra. A rough diagrammatic drawing of the chief features of the spectra is given in fig. 1. 1.) THe Swan Spectrum (synonyms already given). Occurrence : (i.) The blue or greenish blue parts of hydr ocnhen flames. burning in oxygen or gases containing oxygen. (i1.) The flame of cyanogen burning in air or oxygen. (ii.) The ordinary carbon arc in air. (iv.) Many carbon compounds in the gaseous state when sub- jected to the electric discharge. a Reputed origin: (i.) Carbon as an element. (ii.) A particular hydrocarbon, especially acetylene or in general carbo-hydrogen. (iu.) Carbon as an anion. (iv.) Carbon in a molecular as distinct from an atomic state. The most general view is apparently that the spectrum is due: to carbon. * Communicated by the Author. On the Spectra of Carbon Compounds. ATT . : s = (o) =i = a Spd | = s 28 S 5 Bs So a ba Pw 3s ue o) o .) ! —SSS== $$) Q s & = = ——————>— ar) for | TN Ea | ro) aS | 2 ES 8 a So ———— > ar —— a o Ww o a -_- == 3 Er SS Q oS | = ori oO Ss _eenety = SS= i rae ee el P 8D & {il.) Tue Oxycarson Spectrum (Synonyms—the carbon mon- oxide or carbonic oxide spectrum, carbonic acid spectrum). Occurrence : (i.) Carbon dioxide and carbon monoxide with the electric dis- : charge. (ii.) Many oxygen compounds of carbon or other compounds of carbon when contaminated with oxygen and sparked. (iii.) As accidental impurity in other spectra. Reputed origin.—(i.) Carbon monoxide. 478 Prof! A. Smithelle onwhe (IIL.) Tur Cyanogen Frame SPECTRUM. Occurrence.—(i.) The flame of cyanogen in air or, generally, in oxidizing gases. Reputed origin.—The spectrum includes the Swan spectrum. This part is therefore attributed to the same origin as the Swan spectrum. The rest of the spectrum includes two distinct kinds ot groups: (i.) Those at the least refrangible end which fade in brightness towards the red. ‘These are commonly attributed to cyanogen itself. (ii.) Those at the most refrangible end which fade towards the violet. These are now attributed generally to cyanogen. (A view has been held that the Swan components plus the two most refrangible groups represent the compelte carbon spectrum.) (IV.) Tuer Cyanogen ELEcrRic SPECTRUM. Occurrence.—(i.) The electric discharge in cyanogen. (i.) The ordinary carbon arc in air. Reputed origin.—As stated above, either (4.) the spectrum of carbon plus that of cyanogen, or (ii.) carbon at high temperature. Differs from foregoing by absence of least refrangible groups (1.). (V.) THe Carson Line Specrrum (Carbon spectrum of the second order). Occurrence.—The condensed spark-discharge in gaseous eben compounds in general. heputed source : (i.) Carbon in the elementary state. | (ii.) Carbon in a simpler state of atomic aggregation than that corresponding to the Swan spectrum. Two other spectra have in the past held ground for some time as pertaining to carbon compounds. What is now generally, if not universally, admitted to be the “‘compound” or second line spectrum of hydrogen was attributed to acetylene. According to Pliicker (Pogg. Ann. cy. p. 77, 1858) carbonic acid is characterized by a red line when the discharge is first passed through it. Salet (Spectroscopie, p. 239) states that this line is one of the carbon line spectrum (v. supra), and my own observations agree with this. The present investigation had its origin in researches on the chemistry of flames, which I began to publish in 1892, ‘when I was led to consider the source of the spectrum of the inner cone of the flame of a Bunsen burner. At the same time Sir G. G. Stokes, in referring to my papers, threw out a suggestion that the Swan spectrum might be due to carbon monoxide. As this was the view to which I was myself in- clined, I was encouraged to subject the matter to a thorough investigation and to undertake a critical study of previous researches. I have accordingly, at intervals during the past eight years, continued the study and have’ accumulated Spectra of Carbon Compounds. ATO. evidence which, | think, substantiates the original hypothesis and gives a more acceptable explanation of the source of the: Swan spectrum than any hitherto advanced. I take this opportunity of acknowledging my great indebt- edness to Sir G. G. Stokes for the interest he has taken in the work, and for the invaluable criticism with which he has assisted me throughout. The Swan Spectrum from Hydrocarbon Flames. As is well known, the Swan spectrum is to be seen in all ordinary hydrocarbon flames. It the hydrocarbon is burnt without previous admixture with air, the region which gives the spectrum is visible as a bright blue sheath investing the lower part of the flame like the calyx of a flower. This part of a flame has often been confused with what is otherwise distinguished from it as the ‘“ mantle ;” but the mantle is really distinct from it. The blue calyx thins off gradually from below upwards, and is no longer visible where the bright yellow glow of the flame is intense, whilst the mantle sur- rounds the calyx and invests the whole flame. If a hydrocarbon be mixed with air before burning, as in a Bunsen burner or blow-pipe, the flame consists of two dis- tinct feebly luminous cones, which may be distinguished as the inner and outer cones. The Swan spectrum is given by the inner cone. In a paper published in 1892 (Journ. Chem. Soe. Ixi. p. 217) I showed, without any regard to spectra, that the blue calyx of a luminous flame corresponded chemically with the inner cone of a Bunsen flame. At the same time I showed that the gases arising from the inner cone of a Bunsen burner con- suming either coal-gas or a single hydrocarbon contained an abundance of carbon monoxide and free hydrogen, and I con- cluded that the combustion of a hydrocarbon with an amount of oxygen insufficient for complete oxidation resulted in a preferential oxidation of the carbon. This conclusion was opposed to the view generally held at that time, according to which hydrogen was the more oxidizable element and should, in competition with carbon for a limited supply of oxygen, be the element preferentially oxidized. Earlier and neglected observations had pointed to the same conclusions as my own, and the careful and elaborate researches of Professor H. B. Dixon (see especially ‘ The Rate of Explosions in Gases,” Bakerian Lecture, Phil. Trans. elxxxiy. A, p. 97, 1893) and Mr. Brereton Baker (Phil. Trans. clxxviii. A, p. 571, 1888). may, I think, be held to have finally proved that the first step in the oxidation of a 480 . Prof. A. Smithells on the hydrocarbon at a high temperature is the formation of carbon monoxide. abd: The fact that carbon monoxide is formed, and formed in the primary chemical act of combustion wherever the Swan spectrum is seen in a hydrocarbon flame, led me to consider whether or not the spectrum was essentially connected with carbon monoxide. Our knowledge of the genesis of spectra does not allow us to solve such a question by reasoning alone. But it is no new thing to attribute the spectra of combustion te the products of chemical action. During chemical combination the energy which is transformed can hardly be supposed to exist otherwise than in the vibrations of the nascent substance, rapidly though these vibrations may die down in consequence of radiation and molecular collisions. Thus the spectrum of a hydrogen flame is said to be the spectrum of water, and no luminous radiation from the flame can be recognized as belonging to either the hydrogen or oxygen singly. It seemed therefore prima facie that a spectrum seen in flames only in those regions where carbon monoxide was being formed might depend on the mutual action of carbon and oxygen—in other words, be essentially connected with the carbon monoxide molecule, | The Swan Spectrum and the Cyanogen Flame. The flame of cyanogen has played an important part in investigations concerning the spectra of carbon compounds. The existence of bands of the Swan spectrum in the brilliant spectrum of cyanogen was pointed out by Attfield (Phil. Trans. clil. p.221, 1862), and has been the subject of discussion by many observers. When cyanogen is burned in air the green series only of the Swan spectrum is distinctly visible, but in oxygen the Swan spectrum is completely and brilliantly developed. The cyanogen flame consists, as 1s well known, of two dis- tinct parts, a rose-ccloured inner zone and a bright-blue outer one. I found that this flame, when produced in the flame-cone separating apparatus, permitted of the ready separation of the two characteristic zones, and in a paper published in conjunction with Dr. Dent (Journ. Chem. Soc. Ixy. p. 603, 1894) I gave an account of an investigation of the interconal gases. The analysis showed that the chemical ‘change taking place in the inner cone was essentially the formation of carbon monoxide, this gas afterwards burning in the blue region of the fame to form carbon dioxide. - - Spectra of Carbon Compounds. 481 The hypothesis attributing the Swan spectrum to carbon monoxide thus receives additional support. The increased development of this spectrum when cyanogen is burnt in oxygen instead of in air is consistent with the increased con- centration of carbon monoxide that would ensue. That two distinct spectral components are contained in the spectrum of burning cyanogen is generally acknowledged, and one of these is usually considered to be incandescent cyanogen itself. The spectrum due to the undecomposed eyanogen, which includes a good deal of continuous light, no doubt exercises a considerable masking effect upon the Swan spectrum, which is the other component. When oxygen is used a higher general temperature reigns in the flame, and both components of the spectra are intensified, but as this effect is mainly towards the violet the Swan spectrum is relatively less masked by the other component than when air is used. The Spectrum of the Carbon Disulphide Flame. ~ The flame of carbon disulphide gives a continuous spectrum with no sign of the Swan bands. When carbon disulphide vapour mixed with air is burned in a Bunsen burner, carbon monoxide may be detected as a partial product, but no Swan spectrum is observed, even when a dispersion of six prisms is used to weaken the continuous light. I performed an experiment to discover whether if the Swan spectrum were potentially present it would be obliterated by the continuous spectrum of the burning sulphur. For this purpose a mixture of ethylene and hydrogen sulphide was made so as to have the same proportion of carbon and sulphur burning as in the case of carbon disulphide. No Swan spec- trum was observed in the flame of this mixture. It appears that the Swan spectrum is easily suppressed by that of simultaneously burning sulphur, so that its nonappearance in the flame of carbon disulphide is of no unfavourable significance to the hypothesis. Besides this it has been shown that carbon-oxysulphide COS is a partial product of a carbon-disulphide flame (Julius, Die Licht und Warmestrah- lung verbrannter Gase, p. 53, Berlin, Simion, 1890, also Dixon and Russell, Journ. Chem. Soc. Ixxv. p. 600, 1899), so that the amount of carbon monoxide formed may be small. I know of no other carbon compounds which yield flames specially suited to test the question of the origin of the Swan spectrum, ] 482 _ Prof. A. Smithells on the . 1 Consideration of other Hypotheses as to the Origin of the . Swan Spectrum in Flames. : | | | The evidence just recorded appears to point very aiibesh to carbon monoxide as the source of the Swan spectrum, and’ I know of no other evidence derived from flames that is | | Incompatible with this view. But it is now necessary to con- sider how far the facts are in harmony with other views that have been held as to the identity of the substance which yields | the Swan spectrum. | Swan considered that the spectrum was due to hydro- carbons ; but an investigation by Attfield, in 1662, gave currency to the view that the spectrum really belonged to carbon itself, and this view was finally adopted by Dibbits, Morren, Watts, and Salet, all of whom investigated the subject. In 1875 Angstrim and Thalen (Nov. Ket. Reg. Soc. Ups. [3], 1x. 1875) concluded that the luminous substance was a hydrocarbon—probably acetylene. It is between these two views that the opinion of investigators has from time to time been divided, and, as already stated, the amount of experimental evidence that has been recorded is most volumi- nous. The most recent investigations bearing directly on the origin of the Swan spectrum are those of Professors Liveing and Dewar (Proce. Roy. Soc. xxx. pp. 152 & 494, 1880 ; ibid. xxxill. pp. 3 & 408, 1882) and Herr Wesendonck ( Unter- suchungen tiber die Spectra der Kohlenverbindungen. Inaug. Dissert. Berlin, Schade, 1881). lLiveing and Dewar at first were strongly of opinion that the spectrum was due to a hydrocarbon, but later were led to recede from that view in consequence of their own further experiments. I will first consider the view which attributes the Swan spectrum to elementary carbon. Most observers appear to have felt the prima facie ob- jections to this hypothesis. Writing in 1880 Professors Liveing and Dewar said ‘tthe evidence that carbon uncom- bined can take the state of vapour at the temperature of the electric are is at present very imperfect. Carbon shows at such temperatures only incipient fusion, if so much as that*, and that carbon should be volatilized at the far lower tem- perature of the flame of cyanogen is so incredible an hvpothesis that it ought not to be accepted if the phenomena admit of any other probabie explanation.” Although in a later paper these authors are led to admit the existence of carbon vapour ina cyanogen flame the words * Recent researches indicate that the temperature of the positive pole is about 3500° OC. M. Moissan (Le Four Electrique, p. 159) shows that at this temperature carbon is distinctly volatile, but without fusion). Spectra of Carbon Compounds. 483 just quoted may be held to express a valuable scientific opinion in the prima facie aspect of the question. The difficulty involved in supposing carbon to exist as vapour in a hydrocarbon flame is, I am aware, an old one. The subject was dealt with by Dibbits in 1863. The explana- tion given by him has apparently been considered satistactory by many spectroscopists, but I cannot share this view. The following is a translation from the pamphlet of Dibbits (De Spectraal Analyse, p. 179) :— “ We have already shown that the flames of all hydrocarbon compounds give a common spectrum ; van der Willigen has pointed out that the spectrum is the same as that of an electric spark which passes between two electrodes of carbon; we are therefore justified in considering this the spectrum of carbon. We remark that this spectrum is only given by the lower part of the flame, that is, only in that part where the decomposition of the volatiie hydrocarbon takes place. We can give a satisfactory account of this in the following way : CrHs is dissociated as gas, C is separated, and the separated carbon atoms occur for some time free in the flame ; they are in such vibratory motion that the light emitted produces the spectrum in question. In what state of aggregation the free atoms exist in the flame at the moment of their separation cannot be determined ; solid particles they are not, still less liquid ; perhaps they are gaseous, perhaps they are in a state that is not to be likened to any of the three known states. They do not at any rate remain long in this state ; they com- bine with oxygen to form carbonic oxide or carbonic acid, or if they do not immediately burn they agglomerate to form small solid particles of charcoal, which remain for some time glowing in the flame and are the cause of the bright light ; they give then, like all solid bodies, an uninterrupted spectrum which extends the farther into the violet the higher the temperature. : “This view that the real carbon spectrum only, occurs when the carbon atoms occur in a free uncombined state gains in probability when we recollect that the carbon bands are not seen in the flame of carbonic oxide, a flame in which no free carbon atoms could occur. It is remarkable that in the spectrum of the flame of C8, we see no carbon bands but only the light of glowing CQ, and of glowing SQ.; in this flame theretore there are no free carbon atoms. The burning of CS, may be considered to occur in the following way : first, two equivalents of sulphur are replaced by two of oxygen, so that by substitution CS, passes into CQ,, and only then does the liberated sulphur burn. The spectrum of free 484 . Prof. A. Smithells on the sulphur vapour is not necessarily seen ; it is not seen even when sulphur burns alone. ‘In the flame of cyanogen the carbon atoms met for some time in the free state ; the carbon bands appear in the aT trum of this flame as already remarked.” The above reasoning involves, it will be seen, - several hypotheses. First, there is the supposition that there is an interval of freedom for carbon. atoms in a hydrocarbon flame based, presumably, upon the idea that the oxygen selects the hydrogen first. Secondly, it supposes that the liberated atoms, thou oh not part of a solid or liquid, nor yet endowed with the energy necessary to constitute a gas, are capable of emitting luminous vibrations. If this view were tenable we might expect generally to observe spectra from chemical reactions even at ordinary temperatures, The actual experimental evidence which we have commen the combustion of hydrocarbons and cyanogen would lead us rather to picture the process as involving primarily the formation of carbon monoxide. Until the affinity of the carbon and oxygen comes into play no combustion takes place, and there is thus no interval for the existence of a vapour or pseudo-vapour composed of carbon atoms in transitu. Another argument has been used to countenance the supposition that carbon vapour may exist in flames. It is to the effect that since luminous hydrocarbon flames contain solid particles of nearly pure carbon there must have been a condensation of carbon vapour or pseudo-vapour from the gaseous hydrocarbons. Now, according to Berthelot, the separation of solid soot in flames is effected by the pro- gressive coalescence of hydrocarbon molecules with elimination of hydrogen, so that the passage from the gaseous hydro- carbon to the solid soot is effected by a oradual enlargement of the molecule and not by an abrupt condensation of carbon vapour. Professors Liveing and Dewar after abandoning acetylene as the direct cause of the Swan spectrum were led to consider this gas to be the means of bringing carbon vapour into existence in flames. They point to the invariable presence of acetylene in the interior of hydrocarbon flames and to the fact that it is a highly endothermic substance. This is no doubt true, but it must be remembered that the heat of forma- tion of acetylene i is reckoned in terms of solid carbon, and there is no evidence which makes it even probable that the decomposition of acetylene in a flame, assuming such to take place, would yield carbon in the gaseous state. When acety- Spectra of Carbon Compounds. A85 lene is passed through a glass tube heated at one portion by a Bunsen burner, the gas is decomposed with emission of light and deposition of solid carbon. Wherever the decom- posing gas is luminous there is nothing but a continuous spectrum to be observed, and there is no blue base to the “flame” of decomposition. , — Some estimate of the thermal result of decomposing acety- lene into hydrogen and gaseous carbon may be obtained indirectly. The heat of combustion of carbon monoxide to carbon dioxide is 68,000 calories. No direct measurement of the heat of combustion of gaseous carbon to carbon monoxide can be made; but it is highly improbable that the heat equivalent for attachment of the first atom of oxygen to earbon is less than for the second. From solid carbon the heat of formation of carbon monoxide is 28,960 calories. The difference between 68,000 and 28,960, namely 39,040 calories, may thus be taken as the minimum amount of heat required for the vaporization of one atom of carbon. If, again, the heat of vaporization of one gramme atom of carbon be calculated by Trouton’s rule*, heat of vaporization per gramme X vapour-density _ 13 absolute temperature of boiling-point pie we have, taking 3500° as the boiling-point of carbon, and 12 as the vapour-density, DN 13 35004273” whence z (heat of vaporization of one gramme)=4086, and heat of vaporization of one gramme atom of carbon 4086 x 12=58,032 calories. ‘This value is greatly in excess of the one above used, and justifies the assumption of the latter as a minimum value. Returning now to acetylene, we have for the resolution of one gramme molecule into hydrogen and solid carbon an evo- lution of 47,700 calories. If we subtract from this the heat reckoned as above for the vaporization of 2 atoms of carbon we have 47,700—2 x 39,040 = — 30,3880 calories ; that is to say, the production of carbon vapour instead of being exothermic would be highly endothermic, or, in other words, no carbon vapour could be produced. | The ordinary flame of acetylene affords the most favourable condition known for the production from a hydrocarbon of carbon at a very high temperature. In the outer non- luminous portion of such a flame there is an extremely high. * Phil. Mag. xviii. p. 54 (1884). A86 Prof. A. Smithells on the general temperature, but this added to the heat set free within the flame by the decomposition of the gas dues not prevent solid matter separating in the flame. The acetylene flame is indeed exceptionally opaque. I think the preceding considerations show that no reliable evidence exists to warrant the supposition that the flames of carbon compounds contain carbon vapour or pseudo-vapour. On the contrary, there is much evidence against such a supposition. | The consideration of hydrocarbons as a likely source of the Swan spectrum resolves itself into a consideration of acetylene and marsh-gas, as these are the only two hydro- carbons which, in presence of carbon and hydrogen, are stable at high temperature (see Bone and Jerdan, Journ. Chem. Soci ixxn p. 4, ison). The fundamental difficulty presented to those who are inclined to regard either acetylene or marsh-gas as the source of the Swan spectrum, arises from the behaviour of the flame of cyanogen. To maintain the doctrine that acety- lene or marsh-gas is generated in the flame of cyanogen necessitates the supposition that some impurity containing hydrogen is always present. The observation of Dixon that dried carbon monoxide will not burn in dried oxygen has shown how important may be the part played by a minute quantity of water-vapour. But in the case of cyanogen experiments made by the same observer have shown that the most complete dessication attainable, both of the cyanogen and air, does not perceptibly affect the combustion. I have dried cyanogen and air for weeks over phosphorus pentoxide, but found no alteration of the spectrum of the flame, nor did the deliberate addition of moisture to the gases intensify the Swan component of the spectrum. | It is impossible therefore at present to show either by an absolute or differential method that the Swan bands of the cyanogen spectrum are dependent on the presence of some moisture which might be supposed to assist in the formation of a hydrocarbon. If the hypothesis be maintained in the face of this fact, it would necessitate the supposition that the substance to which the Swan spectrum is due must have an extraordinary degree of luminous efficiency. Though the facts of spectrum analysis will not allow us to reject such a supposition as unreasonable, it is worthy of remark that the Swan spectrum is one which includes much light, and is not like that of an alkali metal, where the luminous energy is concentrated in a few sharp lines. This is an argument against the luminous Spectra of Carbon Compounds. 487 substance being present in infinitesimal quantity in a cyanogen flame. It is also worth remarking that a flame-spectram is by no means so likely to be due to an undiscoverable or irremovable impurity as is an electric spectrum. A flame may be developed at the margin of contact of two gaseous streams, away from solid surfaces and without the intense localized temperature-effects of the electric discharge which render visible the minutest traces of matter. It appears very unlikely that so brilliant a spectrum as that of the Swan bands in the flame of cyanogen burning in oxygen can depend on an irremovable quantity of an impurity. The evidence afforded by the flame of cyanogen is so strongly opposed to the hydrocarbon view of the Swan spectrum that it is at present hardly necessary to discuss the same view as applied to hydrocarbon flames. It can scarcely be maintained that either acetylene or marsh-gas is likely to be made incandescent by the general temperature of its surroundings ina flame. If they were generated in the flame by a chemical! action involving a considerable liberation of energy there might be reason to ascribe luminosity to the newly-formed molecules, but we have no right to suppose that this isthe case. Acetylene may be formed from hydrocarbons by passing them through a heated tube, and the quantity so formed is greater than that which occurs in flame gases. I have viewed such a tube “ end-on,” but there is no sign of a spectrum. I have now discussed all the material evidence bearing on the Swan spectrum that is to be derived from a study of the flames of carbon compounds. ‘This evidence appears to be equally inconsistent with the hypothesis that the glowing substance is elementary carbon, or that it is a hydrocarbon, whilst it points directly to carbon monoxide as the source of the spectrum. So simple a view would no doubt have been long since put forward had there not been some obvious reasons opposing it. These reasons are, first that the direct formation of carbon monoxide in the combustion of carbon and its compounds was not established until recently, and secondly, the behaviour of carbon compounds under the electric discharge appeared inconsistent with such a view. T will therefore proceed to consider the electric spectra of carbon compounds. Electric Spectra of the Oxides of Carbon. The spectra of the oxides of carbon under the action of the electric discharge have been described frequently. Broadly 488 Prof. A. Smithells on the speaking, it may be said that four distinctive spectroscopic features have been noticed in connexion with these gases. Under different circumstances there may be obtained (i.) the Swan spectrum, (ii.) the oxycarbon-spectrum, (iii.) the carbon line-spectrum. The fourth feature is (iv.) in connexion with carbon dioxide a band in the red which, according to Plticker (Pogg. Ann. ev. p. 77, 1858), disappears on sparking. 1 have reinvestigated the spectra of the oxides of carbon and shall now describe the results. I will, however, preface the account by repeating that I have never been able to verify the observation of Pliicker above referred to, and that I recognize therefore only three spectra as obtainable from the oxides of carbon. It is worth remarking that the appear- ance to the naked eye of the discharge through the oxides of carbon affords an indication of which of the three spectra is predominant. Thus the Swan spectrum is associated with a greenish blue light very like that of the inner cone of a Bunsen flame burning with much air; the oxycarbon spectrum is seen when the discharge is a pale blue or white ; whilst the carbon line-spectrum is associated with a pinkish discharge. Carbon Monoaide. The gas was prepared by the action of strong sulphuric acid on recrystallized lead formate. It was allowed to rest in contact with solid potassium hydrate, and afterwards with phosphoric oxide. The Toepler pump, to which the Pliicker tube was sealed, was provided with arrangements whereby the pressure of the gas could be increased or diminished in regular stages between the limits of one atmosphere and a high vacuum. The discharge was effected by means of an induction-coil capable of giving a six-inch spark in air. A leyden-jar and a spark-gap could be introduced at will. A Steinheil spectroscope with two flint-glass prisms was used to observe the spectra. No attempts were made to improve upon existing maps of the spectra concerned—the object being rather to observe the conditions under which one or other of the spectra appeared. A comparison prism bringing into the field of view the bright Swan spectrum of a well- aerated Bunsen flame was generally used. ! The least refrangible line (516°4) of the group in the green is an excellent datum-line, since close on one side of it lies the edge of an oxycarbon band (519-7), and on the other a line of the carbon line-spectrum (515-05). The behaviour of carbon monoxide may perhaps be most clearly described by means of a table. The Plucker tube was + Spectra of Carbon Compounds. 489 filled at a moderate pressure, and then exhausted until the discharge passed. The spectrum was examined first with the ordinary discharge and then with a leyden-jar and spark-gap in the circuit. Stages of Ordinary discharge. Condensed discharge. Echaustion. (Jar and air-gap.) 1. Swan spectrum. No discharge. 2. Swan and faint oxycarbon, Swan spectrum. a". Swan and weak oxycarbon. Swan and carbon line and oxygen line. 4. Swan and oxycarbon) Carbonlineandoxygen equally. line. With a short gap the oxycarbon 5. Swan weakening, oxycar- > is seen also; witha bon strengthening. longer gap the Swan (faint) displaces the oxycarbon. Nae 6. Oxycarbon only. Later stages. The oxycarbon fades, the No discharge. mercury spectrum grows in intensity, then fades untit there is complete fluorescence in the tube. The experiment was repeated in the reverse order, that is to say, beginning with an exhausted tube and allowing carbon monoxide to enter in small instalments. The results were exactly the same. The “stages of exhaustion” used above do not represent equal decrements of pressure, but are chosen to show the main features of change undergone by the spectrum. The results above described agree perfectly with the observations of Liveing and Dewar (loc. cit.). According to the ‘experiments of Tietz (Spectrum des Kolhlenstoffs. Inaug. Dissert. Berlin, Buxenstein, 1894) the spectrum of carbon monoxide subjected to the condensed spark-discharge between platinum electrodes at ordinary atmospheric pressure contains only the lines of oxygen and carbon (line spectrum). Carbon Dioxide. The spectrum of carbon dioxide was mapped in detail by Angstrom & Thalén (loc. cit.). The variations which the spectrum undergoes with changes in pressure, changes in the character of the discharge, and with changes in the. length of the containing tubes, were described at great length by Phil, Mag. SG. Voli. No. 4 April 1901. 2K 490 Prof. A. Smithells on the Wiillner (Poge. Ann. vol. ev. vp. 77, 1858, and vor. evil. p. 533, 1859). | Wiillner gave no maps, and his readings are merely those of the scale of his instrument; it is therefore a considerable labour to follow and test his detailed verbal descriptions. The descriptions are complicated chiefly by the fact that one of the spectra involved is developed in various degrees of detail according to the pressure of the gas. This is the oxy- carbon spectrum, mapped in its fullest development by Angstrom & Thalén. Besides this spectrum there are also involved the Swan spectrum, the carbon line spectrum, and the oxygen spectrum. The oxycarbon spectrum can always be recognized at once by the edges of its principal bands, and in the following description I do not distinguish between the different degrees of its development. An ordinary Pliicker tube, sealed to the pump, was filled with carbon dioxide prepared from the liquefied gas and dried over phosphoric oxide. The pressure was reduced, and the following table marks the chief consecutive changes :— Stages of Ordinary discharge. Condensed discharge. Exhaustion. (Jar and air-gap. ) i Faint oxycarbon (linear _ Carbon line and oxygen discharge). | line. » 2. Bright oxycarbon (glow). As in previous stage. 3. srighter oxyearbon. With medium gap bright Swan; with wide gap as in pre- vious stage. A. Very bright oxycarbon. The spectrum changes from oxycarbon~ to Swan to carbon and oxygen line as the gap 1s widened. 5. Fading oxycarbon. The spectrum changes from oxycarbon ‘di- rect to carbon and oxygen line as the gap 1s widened. Later stages. The oxycarbon fades slowly. As before, fading slowly. Explanation of the Results obtained with the Oxides of Carbon. The usual explanation of the results just described is as follows:—The two oxides of carbon yield under different conditions three spectra in which carbon is involved. Two of - Spectra of Carbon Compounds. AQT these, namely the Swan spectrum and the carbon line spectrum being supposed to pertain to carbon in the ele- mentary state, there remains only one spectrum, the oxycarbon spectrum, peculiar to the two oxides. It is concluded that this orn pertains to carbon monoxide for the following reasons :—(1) carbon dioxide is known to be dissociable by heat into eit monoxide and oxygen; (2) it is the simpler oxide; (3) the flame of carbon monoxide which contains glowing carbon dioxide gives a continuous spectrum. A. complete explanation of the appearance of the different spectra under different conditions has not, so far as Iam aware, been given by anyone. Liveing and ‘Dewar infer that a low pressure is unfavourable to the stability of the mole- cular combination which gives the Swan spectrum. Wesen- donck believes that the Swan spectrum is always produced by a strong spark-discharge, though it may appear under other conditions. I think the facts admit of an altogether different explana- tion, which is at the same time simpler and more rational. J consider that the Swan spectrum is the spectrum of carbon monoxide, and the oxycarbon spectrum the spectrum of carbon dioxide—that there are in fact two spectra dependent on the association of carbon with oxygen. In support of this view I adduce the following summarized evidence :— 1. There is a striking resemblance between the Swan iii and the oxyearbon spectrum. The actual difference such as might reasonably be expected from the molecular Gaiseence of the two oxides. 2. Carbon monoxide gives the Swan spectrum predomi- nantly, except under extreme conditions. If, as is now generally believed, the conduction of a gas is electrolytic i in character, the passage of the discharge should be associated with the ‘alternate dissociation and recombination of carbon and oxygen. The process occurring in the tube has therefore a chemical feature in common with that occurring in all those flames which show the Swan spectrum. 3. Under extreme conditions of gaseous pressure or elec- trical tension, carbon monoxide gives either the oxycarbon spectrum or the carbon line spectrum, or both. Now these extreme conditions correspond also to maximum heating effects of the discharge, and it is under these circumstances that the gas may be expected to give spectra of decomposition products. Carbon monoxide is a gas easily altered by heat. Deville showed long since (Compt. Rend. lix. p. 873, 1864) that when carbon monoxide is heated in a tube to a high 2K 2 A992 Prof. A. Smithells on the temperature it undergoes dissociation into carbon dioxide and carbon. Victor Meyer (Pyrochemusche Untersuchungen, p. 61) amply confirms this observation. ‘There is good reason to foresee, therefore, that under extreme conditions carbon dioxide would he formed ina carbon monoxide tube and would exhibit the spectrum proper to it. In describing the behaviour of carbon monoxide Liveing and Dewar remark that at high exhaustion, when the oxy- carbon spectrum 1s seen, much metal is throw hemane electrodes during the discharge. J also have noticed the accumulation of a black deposit at this stage, but the deposit is formed even when aluminium electrodes are used. The deposit in my tubes was, in fact, carbon, and could always be removed by admitting air or oxygen to the tube and sparking. The behaviour of carbon monoxide under extreme conditions appears therefore to conform fully to a changed condition according to the established equation 2CO_ CO, + C. It is very noteworthy that the devosition of carbon in a sparking tube only arises when the contents are yielding the carbon line-spectram, If the Swan spectrum be due to elementary carbon it is difficult to see why a deposit of carbon is not formed in a tube even more readily when the contents are yielding the Swan spectrum. 4, Carbon dioxide gives most readily the oxycarbon spec- trum, and this remains at high exhaustions. At ordinary atmospheric pressure the gas gives only the line spectrum of carbon and oxygen. A condensed disch: arce Im a Pliicker tube boom: the formation of the Swan spectrum. This behaviour accords with the facts that carbon dioxide is relatively a good conductor, but that when the heating effect of the dischar ge is intensified the gas 1s dissociated into carbon monoxide andl oxygen. A condensed discharge in highly-rarefied carbon dioxide produces the line spectra of carbon and oxygen. I have never found the oxygen lines visible without the carbon lines being also visible, so that there is no evidence of the gas being split up easily iGO carbon monoxide and oxygen. An impression seems to prevail that carbon dioxide is an easily dissociable gas, and that carbon monoxide is relatively stable. The truth is exactly the reverse of this when’ the vases are hented statically as in a Plucker tube. Victor Mey er found (loc. cit. p. 64) that carbon dioxide has almost exactly the normal density even at 1700°, w hemes carbon Spectra of Carbon Compounds. 493 monoxide at that temperature is largely dissociated. It is true that carbon dioxide is dissociated at lower temperatures when passed through a heated tube, especially if the tube be packed with broken glass or porcelain ; but these are not the ccnditions in a Plicker tube. 5. Liveing and Dewar found that the carbon are-discharge in carbon monoxide gave the Swan spectrum with no trace of the oxycarbon spectrum, and they point to this as a remarkable fact. The non-appearance of the oxycarbon spectrum under these circumstances would indeed be remarkable if that spectrum were really due to carbon monoxide. But if, as L maintain, the true spectrum of carbon monoxide is the Swan spectrum, the observation is what would be expected. It is to be remarked also that whilst the high temperature of the discharge might favour the dissociation of the gas into carbon and carbon dioxide, and so lead to the oxyearbon spectrum, the fact that the electrodes are glowing carbon rods would act in the opposite direction, tending to conserve the carbon monoxide. This last influence appears to operate in the case of the carbon arc-discharge in carbon dioxide, for here also the Swan spectrum is brilliantly developed. 6. The spectrum of the carbon arc in air contains the Swan spectrum together with groups of lines whose origin has been traced by Liveing and Dewar, by Kayser and Runge, and by Tietz to cyanogen, or to carbon in association with | nitrogen. ‘The appearance of the Swan spectrum in this case I attribute to the formation of carbon monoxide in the arc. The generation of this gas in the are is well- known to occur, and is, indeed, a recognized source of danger to health. The appearance of the Swan spectrum in the arc, far from presenting an anomaly, removes one if we ascribe this spectrum to carbon monoxide. Ior otherwise it would be highly remarkable that the arc-spectrum should contain components attributable to the action between the carbon of the poles and the nitrogen of the air, but none attributable to the action beween carbon and the oxygen of the air with which it unites so readily. Carbon monoxide is known to be formed abundantly in the are, and according to any hypothesis readily yields a characteristic spectrum under the electric discharge. The validity of the view which I have just given is borne out in a remarkable manner by observations of Liveing and Dewar. They say: ‘‘the are in the middle of a magnesia crucible often shows no sign of the (Swan) spectrum although the cyanogen is strong. If, however, putts of air or carbon A494 ‘Prof. A. Smithells on the dioxide are passed into the are the (Swan) spectrum is pro- duced. . . the (Swan) spectrum is brought out at once in the magnesia crucible by moistening one “of the poles.” They also found that the spectrum of the are taken in water shows the Swan spectrum only. An explanation suggested by Liveing and Dewar for these remarkable facts is that possibly the introduction of cool gas or of moisture increases the resistance in the are and causes a higher temperature. It will be obvious how simple the explanation becomes if the Swan spectrum be attributed to carbon monoxide, for every condition found by Liveing and Dewar to enforce the spectrum in question is equally a condition to favour the formation of carbon monoxide. Having now summarized the evidence which supports the view [ have put forward with regard to the spectra of the oxides of carbon I will deal with facts that ene opposed to it. 1. The red line stated by Pliicker to be characteristic of carbon dioxide I have already dealt with (p. 488). I have obtained no evidence of its existence. 2. The supposed stability of carbon monoxide and insta- bility of carbon have also been with (p. 492). 3, The flame of carbon monoxide gives a continuous spectrum, and if the light of this flame is due simply to the formation of carbon dioxide, it may be asked why it does not give the oxycarbon spectrum. In answer to this question there are several important considerations to be adduced, In the first place there is no certainty that the process occurring in the combustion of carbon monoxide is the same in its chemical stages as that which accompanies the discharge of electricity through carbon dioxide. Quite apart from the part played by water in the combustion of carbon monoxide (Dixon, Phil. Trans. 1884, 11. p. 629) we are dealing there with the oxidation of ready formed carbon monoxide, whilst in the electrolytic conduction of carbon dioxide we may be dealing with the action between .carbon and two atoms of oxygen simultaneously. On the other hand, there is an observation recorded by Bureh (‘ Nature,’ xxv. p. 165, 1886) to the effect that when carbon monoxide is burned under reduced pressure the spec- trum of the flame shows signs of becoming discontinuous, and though the maxima of lieht are not well defined they are located in positions which are not incompatible with the supposition that they may be the vestiges ot the oxycarbon bands. Spectra of Curbon Compounds. 495 It is true that the two points just raised tell if at all in opposite senses. Ido not wish to lay too much stress upon them, but I think that either of them would afford an ex- planation of the fact that the flame of carbon monoxide as ordinarily produced does not give the oxycarbon spectrum. I may add that the flame of carbon monoxide burning in oxygen or in nitrous oxide still gives a continuous spectrum, and the same is true when the combustion is inverted and oxygen burnt in carbon monoxide. 4. liveing and Dewar record tbat the spark-discharge without condenser between poles of purified graphite in car- bon monoxide at atmospheric pressure gives both the oxy- carbon spectrum and the Swan spectrum. As the pressure is increased the oxycarbon spectrum fades, and the Swan spectrum becomes more intense, the carbon line-spectrum being also visible. At higher pressures the Swan spectrum predominates and is very strong. At low pressures the oxycarbon spectrum together with the line-spectra of carbon and oxygen are seen without the Swan spectrum. These observations do not appear to throw much light on the origin of the spectra. They do not in any particular degree “support the views I have put forward, nor do they contradict these views. I think it only right, however, to quote the evidence, anid for the present range ee inthe categor y of that which does not confirm my views Eiectric Spectra of Carbon Compounds not containing Oxygen. I have little doubt but that the chief difficulty which will be felt by spectroscopists in accepting the view that the Swan spectrum belongs to carbon monoxide is to be found in frequently recorded observations of the Swan spectrum under conditions which appear to exclude the presence of that gas. Thus it has been found in the electric spectrum of hydrocarbons, of carbon tetrachloride, of cyanogen, and in the spectrum produced when the electric discharge takes place between carbon points in an atmosphere of hydro- gen. In many cases the observations have been made with great care and with elaborate precautions for the removal of water vapour; less frequently, however, with equal regard to the absence of air or other oxidizing agents. I believe that at present many spectroscopists are distrustful of conclusions based upon the supposed purity of the sub- stances submitted to examination in highly exhausted Pliicker tubes. The difficulty of removing films of air or moisture from glass, the occlusion of gases by electrodes, the oxidizing character of glass itself, all can well recognised difficulties A96 Prof. A. Smithells on the quite apart from the purely chemical difficulties in obtaining pure materials. Hasselberg has observed (M/ém. de l’ Acad. de St. Péters- bourg, xxxi. No. 14, p. 7, 1883) that some kinds of glass persistently give rise to carbon and oxygen, contamination bringing to light the oxycarbon spectrum. Professors Liveing and Dewar state that ‘no chemist who remembers the extreme sensibility of the spectroscopic test, and the difficulty, reaching almost to impossibility, of re- moving from apparatus and material the last traces of air and moisture, will feel any surprise at the presence of small quantities of either hydrogen or nitrogen in any of the gases experimented on.”’ Again they say “ Photographs of the ultra-violet spectra given by such tubes tell tales of impurities as unexpected as they are difficult to avoid. Every tube of hydrogen which we have examined exhibits the water spectrum more or less, even if metallic sodium has been heated in the tube or the gas dried by prolonged contact with phosphorus pentoxide. We have expended a vast amount of time and trouble over vacuous tubes, and our later experiments do but confirm the opinion which we had previously formed that there is an un- certainty about them, their contents and condition which makes us distrustful of conclusions which depend on them.” The difficulty of obtaining carbon tetrachloride free from oxygen has been shown hy Mr. Brereton Baker (Journ. ‘Chem. Soe. Ixi. p. 728, 1892), whilst both he and Prof. J. J. Thomson (Journ. Chem. Soe. Ixv. p. 611; Phil. Mag. Oct. 1893) have shown to what an important extent the passage of the electric discharge through gases is determined by the presence of a trace of moisture. Notwithstanding the authority of these observations and the small promise they afforded of a determinate result being obtained, | have expended a great deal of time in examining the spectra mentioned above, and I now record the results. The Spectrum of the Discharge between Carbon Electrodes — wn an Atmosphere of Hydrogen. e) Angstrém and Thalén, in the paper already referred to, state that the aureole of the spark-discharge taken between carbon points in an atmosphere of hydrogen exhibits the Swan spectrum, and they regarded this as a strong confirmation of their view that the Swan spectrum was due to acetylene. No account is given in their paper of the precautions taken to purify the hydrogen. In repeating this experiment I have found that the Swan Spectra of Carbon Compounds. A97 spectrum is often to be distinctly seen under the circumstances described above, but I have also found that this ceases to be the case as the hydrogen is more and more thoroughly purified. Carbon points were prepared from gas-carbon and were heated for two hours with concentrated nitric acid, then with hydrofluoric acid. They were then washed with distilled water and heated to bright redness about an hour and a half in a platinum tube through which a current of dried hydrogen was passed. The object of this treatment was to remove as far as possible any compound containing oxygen. Hydrogen was prepared by the electrolysis of dilute sodium hydrate solution and dried by means of solid potash and phosphoric oxide. In the earlier experiments sodium amalgam was introduced into a side chamber of the sparking tube, and after the discharge had passed some time the amalgam was boiled. Though the results obtained in this case were pro- mising the method was abandoned owing to the numerous fractures that occurred. In all subsequent experiments the hydrogen was prepared either by electrolysis of dilute sodium hydrate solution or by the action of dilute hydrochloric acid on distilled zinc, a drop or two of platinum chloride being added to induce the action. The gas was passed over solid potash and then led into a short eudiometer standing in mercury and containing a stick of solid potassium hydrate. The gas was there sparked for one or two hours in order that any lingering traces of oxygen should be converted into water. It was then allowed to pass directly into the carbon electrode tube sealed to the Toepler pump and connected with phosphoric oxide tubes. The pump and tube exhausted to the highest obtainable degree to begin with were repeatedly filled with the purified hydrogen and re-exhausted. As this process was continued the discharge was from time to time allowed to pass between the carbon electrodes and the spectrum noted. Without describing in detail the numerous experiments made on this plan I may summarize the results as follows :-— In all stages of purification the discharge between the carbon poles was bright red when a jar and gap were em- _ ployed in the circuit, and the simple line-spectrum of hydrogen was very bright. With the uncondensed discharge the colour was white and the compound line spectrum of hydrogen ap- peared. In the earlier stages of purification these hydrogen spectra were accompanied to a greater or less extent by the Swan spectrum, and the red or white discharge was seen to be surrounded by the greenish aureole which, as already remarked, is always associated with the Swan spectrum. 495 Prof. A. Smithelis on the This aureole was developed most plainly at the tips of the electrodes and thinned off towards the middle of the spark. As the purification proceeded, that is, as fresh supplies of hydrogen were used, the Swan spectrum gradually faded until eventually a state was reached where the spectrum was not observed on first sparking, the discharge between the carbon points being of a pure red-colour. The Swan spec- trum, however, appeared after continued sparking. The time taken for the Swan spectrum to appear in this way was longer as the operations continued. The phenomena in fact pointed to the conclusion that something which facilitated the production of the Swan spectrum was gradually being eliminated as the purity of the hydrogen was increased. Another important observation also was made at this stage. It was found that if the discharge were stopped when the Swan spectrum had become well developed, and the whole apparatus allowed to rest a few hours, on restarting the discharge the Swan spectrum would have either wholly disappeared or have become much reduced in intensity. This disappearance or enfeeblement of the Swan spectrum was only to be noticed when the sparking tube was attached to the pump. If the tube was sealed off the fluctuation was no longer to be noticed. This points unmistakably to the conclusion that the appearance of the Swan spectrum was contingent upon the accumulation in the sparking tube of some gas which on standing diffused into the eNO Ls chambers of the pump. I attach great importance to this observation since it seems to connect in a positive way the appearance of the Swan ‘spectrum with the formation of a gaseous compound of carbon. The ultimate stage of purification of materials and apparatus reached in my experiments was such that the discharge between the carbon points in the hydrogen could be passed for twenty minutes before the Swan spectr um began to appear. If these experiments are accepted as conclusive evidence connecting the Swan spectrum with a compound of carbon there remains the further question as to what this compound of carbon really is. A decision of this question is not to be made at once. Acetylene and methane are both produced by the discharge between carbon poles in hydrogen, and as there is no spectrum known to be undoubtedly due to either of these,gases, my experiments might be held to support the view of Angstrém and Thalen that the Swan spectrum is due to acetylene or possibly to marsh-gas. Apart, however, from the other evidence already adduced in this paper to connect : 4 —— ee Fe ee a eS ee ee ee ty ee “pea se 7 eae — 6- Spectra of Carbon Compounds. A9Y the Swan spectrum with carbon monoxide, it appears to me that the phenomena just described are best explained by the gradual accumulation of this gas in the tube. Jor, if the Swan spectrum be due toa compound of carbon and hydrogen, I can see no explanation of the gradual disappearance of the spectrum as the hydrogen is purified, nor any reason why the spectrum should take tw enty minutes to appear on a par- ticular occasion. This, however, is quite consistent with the gradual accumulation of carbon ‘monoxide. How the carbon monoxide arises I am not prepared to say with certainty. The possibilities of gradual, contamination with oxygen are, however, very considerable in glass apparatus in which the electric discharge is being passed. In some cases I have found that where the Swan spectrum has appeared without obvious contamination with oxygen a modification of the dis- charge would produce the oxycarbon spectrum, which on any hypothesis points to the presence of oxygen. { have tried to detect carbon monoxide in ihe tubes by ordinary analytical tests, but the quantity of gas is very small, and in presence of acetylene it is hardly possible to work with certainty. In order to get rid of possible oxygen contamination from the glass I had sparking tubes made of copper by electro- deposition. The difficulty of getting these prov ided with electrodes and attached to the pump without leaving some small leak was, I think, eventually overcome, but the results obtained were not satisfactory. The difficulty i in getting rid of the Swan spectrum was gr eater than in glass tubes , indeed, I never succeeded in getting rid of the last traces. Futile attempts extending over many weeks led me to think that perhaps there had been some error in the experiments with the glass apparatus, but on repeating these I succeeded, as belore, in getting entirely rid of the Swan spectrum. Electric Spectra of other Carbon Compounds. It would seem at first sight as if the examination of the spectrum of the vapour of carbon tetrachloride in a Pliicker tube should afford a simple crucial test as to the connexion of the Swan spectrum with carbon monoxide. ‘This experi- ment has been performed by Watts, Lockyer, Liveing and Dewar, and by myself. According to Lockyer the electric discharge in the vapour of carbon tetrachloride gives the Swan spectrum brightly, together with the more “refrangible groups associated also according to Lockyer with alenn aaa y carbon. No sign of a hydrogen or nitrogen spectrum could be szen in the tube [ 500 Prof. A. Smithells on the even with a leyden-jar in circuit. This observation was contradicted by Liveing and Dewar so far as the more re- frangible groups were concerned, and these observers, as also Kays ser and Runge, Tietz and Hartley, assign the groups in question to carbon in association with nitrogen. Wesendonck again criticises Lockyer’s precautions for the exclusion of moisture as inadequate. According to Liveing and Dewar, though the Swan spectrum was seen in carbon tetrachloride when the tube was not much exhausted, at high exhaustions it gave a continuous spectrum. With the actual spark between close electrodes in the satu- rated vapour freed from moisture and air the candle spectrum was always “ more or less plainly seen” (elsewhere they say * brightly’). Wesendonck, on the other hand, under the circumstances iast described, observes scarcely any sign of the Swan spec- trum. At low pressure he observed both the oxyecarbon and the Swan spectrum ; at higher pres sures he gets chlorine lines and the bright green ‘“ “flame line.” I have spenta ereat deal of time in examining the spectrum of carbon tetrachloride, and have to thank Mr. Brereton Baker for supplying me with a quantity of this substance which had been treated by him for the removal of oxygen. I regret that I cannot record any very positive results. ‘The vapour is so quickly decomposed by the electric discharge that the maintenance of a steady pressure is impossible. The spectrum is preeminently that of chlorine and carbon (line- spectrum), and I have failed frequently to obtain a sign of the Swan spectrum. At other times the Swan spectrum would appear, and occasionally also the oxycarbon spectrum, showing that there was oxygen contamination. It is not improbable that the liberated chlorine attacks the glass. Dr. H. A. Wilson, a former student of the Yorkshire College, who has rendered me material assistance in this work, made a number of observations on the spectrum of chloroform vapour. ‘The results which he cbtained seemed to show unmistakably that a tube containing this substance did not yield the Swan spectrum when adequate precautions had been taken to remove oxygen. The presence of a little air or oxygen led to the development of the spectrum. I have not abandoned hope of obtaining more unequivocal results from the examination of carbon tetrachloride. For the present I cannot claim more than that the observations hitherto recorded by spectroscopists with this substance are incapable of furnishing a decision in one sense or the other as to the origin of the Swan spectrum. Spectra of Carbon Compounds. d01 The observations which have been made on the spectra of rarefied cyanogen and hydrocarbon gases are no more sa2tis- factory. Wesendonck makes the highly significant observa- tion in special reference to hydrocarbons that the pure sub- stances do not give good spectra. The admission of a little air, he remarks, g oreatly i improves ‘the spectrum, and hydrogen also improves the spectrum without accentuating its own. From many carbon compounds he could observe little else than a continuous spectrum. The difficulty of freeing cyanogen from moisture may be overcome, but the difficulties of freeing it from other oxygen compounds have appeared to me insuperable, and have de- terred me from undertaking any lengthened experiments with this gas. Whilst fully conscious of the importance of observations on the electric spectra of the compounds of carbon with chlorine, hydrogen, and nitrogen, I can only repeat that the difficulties of obtaining and “maintaining these compounds free from oxygen are roe the most commndelble kind, and I believe that the recorded observations go so far at least as to show that when oxygen is known to be present the Swan spectrum is correspondingly enforced. The Experiments of Prof. J. J. Thomson. In a paper read before the Royal Society (Proc. R. 8. xlv, p. 244) in 1895 Prof. J. J. Thomson describes some highly interesting observations on the spectra of carbon compounds, which he summarizes as follows :—“ The view which seems most in accordance with the results of observations on the discharge through these vapours is that the candle spectrum (1. é. Swan spectrum) is the spectrum of carbon when the atom is charged with negative electricity or of some com- pound of carbon in which its atom is negatively charged, while the carbonic oxide spectrum is the spectram of carbon when the atom is charged with positive electricity or some compound in which the carbon atom is positively charged.” I do not propose at present to enter upon a discussion of _these results, for they are not only in the nature of a pre- liminary communication, but they scarcely invelve the main question dealt with in this paper, and in any case I cannot tind that they present any serious obstacle to the view which I have advanced concerning the origin of the Swan spectrum. The experiments, however, are so important that 1 am bound to mention them, and it may well be that their further pro- secution will throw much light on the immediate subject of this paper. 502 On the Spectra of Carbon Compounds. Evidence from the General Character i: the Swan Spectrum. It is a remarkable fact that Angstrom and Thalén, who ascribed the Swan spectrum to a hydrocarbon, should have been led to do so, in the first instance, by its general resem- blance to the spectrum of the oxides of alkaline earth metals, After describing the Swan spectrum they say “‘ cette descrip- tion de Vaspect des raies est tout-a-fait identique a celle donnée auparavant par rapport aux rales des oxydes métal- liques, et nous pensons que cette analogie remarquable ne peut ¢tre entierement fortuite.’ They insist further that carbon in the elementary state is characterized by a line spectrum, and that the Swan spectrum is conditioned by the atmosphere in which the discharge takes place, it being found only in the aureole and not in the line of spark. Although they ascribe the spectrum to a hydrocarbon the general argument is equally cogent for the doctrine advanced in this paper. It is also important to remember that it was the inherent probability of the correctness of the above views that led Professors Liveing and Dewar to their exhaustive and elabo- rate researches on the spectrum of carbon. At the outset of their experiments and for long afterwards these investigators inclined most strongly to the view that the Swan spectrum was due to a hydrocarbon, and they found an additional argument in the resemblance of the Swan spectrum to that of a compound of hydrogen and magnesium. Although so many investigators have found themselves Pompolled to ascribe the Swan spectrum to elementary carbon, I am not aware that any rational explanation has been given of the relation of this spectrum to the line spectrum of carbon. Cases are not uncommon of an element giving more than one spectrum, but the conditions for transition are in most cases known and, i in a sense, intelligible. In the case of carbon no such conditions are known; the line spectrum of carbon is sometimes but not always obtained simultaneously with the. Swan spectrum, and the dependence of the Swan spectrum on the nature of the atmosphere in which the discharge takes place is certain. If it could be shown that the development of the Swan spectrum from the discharge between carbon poles in different atmospheres followed the conductivity or some other physical property it might be maintained that both it and the line spectrum were due to the element carbon. But this has not been shown, and, I believe, cannot be shown; on the other hand, there is the strongest evidence that the a ee a t we a a a ee DEFENDANT'S EXHIBIT D~31 On the Absorption of (ias in a Cubbies ae 503 development of the Swan spectrum depends upon the che- mical nature of the atmosphere in which the discharge takes place. Tn concluding this paper I wish to say that for the sake of brevity I have refrained from alluding at all fully to the literature of the carbon spectra, and have confined my re- ferences to previous researches which bear most directly on the matter under investigation. I say this lest it might | de thought that I had not given due attention to the work of previous observers. As a matter of fact I have made a careful critical study of all the papers to which I could find references. I have not discussed the astrophysical bearing of the origin of the Swan spectrum as I do not feel qualified to deal with the subject, but so far as I can judge, the view which I have advanced does not conflict with any established astrophysical theory. During the progress of this investigation I have received eonsiderable assistance from students ne the Yorkshire College, notably Dr: Gathrie, Dr. Dent, and Dr. H. A. Wilson, nl to them my thanks are due. I am especially indebted to Dr. Wilson and to my assistant Mr. A. Dickson for their skilful assistance in the constr uction and manipulation of apparatus employed in the electrical experiments. The Yorkshire College, Leeds. XLIV. On the Absorption of Gas in a Crookes Tube. By R. 8. Wittows, B.A., D.Se., Trinity College, Cambridge, 1851 Eahilition Scholar * Introduction. T has been observed by different experimenters that the continued passage of a dischar ge through rarefied gas contained in a sealed tube introduces a difference in the appearance of the discharge. Thus Pliicker f found that on many occasions strize only appeared in a Geissler tube after the discharge from a Ruhmkorff’s coil had been passing for some time, ‘and that a continuance of the dischar ge served to make the striee better defined. Miiller and De la Rue found that the continuous discharge from their large batter vi as distinguished from the intermittent discharge from an * Communicated by Prof. J. J. Thomson, F.R.S., T Plucker, Poge. Annal. 1858, vol. ciii. p. 91. ~~) 5 4. Dr. R. S. Willows on the induction-coil, produced similar changes. For example%, they found that on first passing the discharge through tubes supplied by Geissler, the appearance of the luminosity was totally altered after the current had been passing for a few minutes only, and hence they had to discontinue the use of tubes sealed off from the pump. More recently it is known by all who have had experience with Réntgen-ray bulbs, that a tube giving out soft rays, of little use in surgical applications, may, by continuous use, be made to emit rays of the most penetrating kind, and that finally the tube requires heating in order to admit of the discharge passing at all. When this stage is reached in the life of a bulb, the only way to restore it to its original condition is to let in fresh gas and re-pump it. By an examination of the spectrum of the discharge, Hutchins + found that if a trace of foreign gas or vapour be admitted into a tube in which the pressure is very lew, the spectral lines of this gas disappeared after a few seconds, leaving only the hydrogen lines visible. The latter are no doubt due to the water-vapour, from which it is so difficult to free the tube. . While working on the striated positive column by the help of a large battery of small storage-cells, I noticed that the pressure was liable to undergo variation if the current was kept on for many minutes, and that if the tube had been in use for some time there was always an apparent absorption of gas. 5 eee Prof. J. J. Thomson informed me that he had carried out some experiments on the subject with an induction-coil as the source of current, and suggested that I should continue the investigation, especially as a battery lends itself much better to quantitative results than the intermittent and irregular supply froma coil. Qualitatively the results are the same whether a coil or a battery be used. The experiments have had for their object ghe investigation of the conditions influencing the absorption of gas in a Crookes tube, and if possible to throw light on its desti- nation. 1. The apparatus used was that shown in fig. 1. A Toepier pump could be put in communication with the remainder of the apparatus by a tap B. Next comes the tube N to be experimented on. C is a large bulb containing PO; ; it can be put in communication with the exterior by means of a three-way tap F, and with N through two taps * Phil. Trans. Part 1. 1878, p. 155. + Wutchius, Amer. Journ. of Science, vol. vil. 1899, p. 61. Absorption of Gas in a Crookes Tube. 505 D, E. C served as a reservoir in which gas could be dried at a pressure of a few centimetres and kept ready for use ; this was necessary, as it was found that unless well-dried gas was worked with, consistent results could not be obtained. 6 ES Small charges of gas could be admitted to the tube N by alternately opening and closing first D and then H. F was useful in the admission of prepared gases to the bulb C, and in allowing the partial exhaustion of the apparatus by a water-pump. H leads to a Fe gauge; J is another drying-bulb containing P,O;, and serves to dry the whole of the space shut off from C.” By this means, if necessary, N could be co hie by another experimental tube and dry gas still kept mC. The mode of conducting an experiment was as follows :— A suitable pressure, about 1 mm., was established in N, and a current of known value from a large battery was passed for half an hour. A few minutes were allowed for cooling, and then a second reading of the pressure was taken. The current could be measured by means of an insulated galvanometer, and it could be brought to any desired value Phil. Mag. 8. 6. Vol. 1. No. 4. April 1901. 21. 506 Dr. R. S. Willows on the by means of a liquid rheostat placed in the circuit and shown in fig. 2. Fig. 2. This consisted of two fairly wide capillary : tubes having platinum wires fused into their closed lower ends; both limbs were nearly filled with distilled water to which had been added a small amount of impurity such as KHO. Another platinum wire, bent twice at right angles, could be moved up and down by means of an insulating handle. The whole was suitably supported and insulated on paraffin blocks. In order to make the change in pressure produced by the action of the discharge as large as possible, the volume in communi- cation with N must be reduced as much as it can be; hence, at the time of making an experiment, taps B and E were closed and J was cut off from N by means of a mercury trap L. 2. To give some idea of the magnitude of the effects, the following numbers are given:—The volume of the tube N, auge and connexions was in most cases about 100 c.c., and 223 divisions on the gauge represented a millimetre pressure. Witha current of about 10°8 x 10~* amperes passing for half an hour, a decrease in pressure of from 10 to 40 gauge- divisions took place, the amount depending on the pressure. Thus in a case where the volume was 108 c.c. and pressure about 1 mm., a current of 10°83 x 10~* amperes running for thirty minutes produced an alteration in pressure of twenty scale-divisions, or a reduction of 7; mm. nearly. From this it can be found that in this case the passage of 3°888 coulombs of electricity causes ‘013 ¢.¢. of gas reduced to 760 mm. pressure to disappear. When different currents were tried, it was found that the amount of gas that disappeared increased more rapidly than the current. | | | The chief difficulty met with was the trouble experienced in getting the electrodes quite clear of gas. In most cases in which aluminium-wire electrodes were used, it was found necessary _ to pass a strong current for at least twenty hours before regular measurements could be obtained ; in several cases the tube near the cathode was too hot to be touched with the fingers, and it was kept in this state for several hours at a time. In one case in which hydrogen was used, thirty hours of this treatment was insuthcient to gjectall the gas from the electrodes. In the earlier experiments it was found that, ‘starting from Absorption of Gas in a Crookes Tube. 507 a pressure of 1 mm., the mass of air which was absorbed increased as the pressure was diminished down to about *) mm., when the rate of absorption gradually decreased. This presence of a maximam effect was, however, proved to be due to the electrodes not being clear of gas, and this being given off masked the effect it was desired to measure. The later experiments always showed that the lower the pressure the quicker the rate at which gas was absorbed, the current being the same in every case. 20). 460° 60 80 100 ~—-: 120 140 160 180 200 220 FPPRESSURE Fig. 3 shows the effect of a constant current at different pressures. The abscissee are pressures ; the ordinates are proportional to the mass of gas absorbed in thirty minutes when the mean pressure has a value given by the corre- sponding abscissa. : 3. A cylindrical tube of soda-glass provided with aluminium- wire electrodes was first used. From an extensive series of readings, the rate at which it ran down™ was determined for pressures varying from 1 mm. downwards. In doing this a considerable quantity of gas was caused to disappear. The tube was then strongly heated for several hours by a Bunsen burner: only a very small fraction of the gas reappeared. (This was found to be the case afterwards when a still stronger heating was applied to the broken tube enclosed in combustion- tubing.) If this was again absorbed by means of the current and the heating again performed, still less came off ; and by repeating this several times scarcely any could be driven off at last, but on admitting fresh gas it was found that the * T have used the term “ running down ”’ to denote the lessening of the pressure due to the continued passage of the discharge. 212 508 . Dr. R. 8. Willows on the heating had slightly increased the rate of absorption. Prob-- ably most of the increase of pressure produced by heating was - due to water-vapour driven off the walls of the tube. ; 4. The previous tube was replaced by one of lead-glass - similar to it in all other respects. This ran down at a slower rate- (about 10 per cent. less), the gas being air in both cases. The effect for nitrogen was exactly the same as for air in both tubes.. The lead-glass tube was next filled with hy drogen. Although — a strong current was passed for about 35 hours, no decrease in pressure was obtained, but on the contrary it increased, although only very slowly, about one division in several hours: finally. The whole apparatus was pumped down to a very small fraction of a millim., and nitrogen again admitted into: reservoir C (fig. 1). By means of taps D, E a small amount was let into N, and so the tube was filled with nitrogen and: the electrodes had had no opportunity of re-absorbing gas.. On passing a current the nitrogen disappeared as before. It would seem from this exper iment that either hydrogen is not absorbed by lead-glass, or is absorbed so slowly that the small. amount of gas ejected from the electrodes, even after long use,’ is sufficient to overshadow the decrease in pressure resulting therefrom. | The latter alternative was proved to be the true one. A bulb of lead-glass was filled with hydrogen and an electrode- less discharge passed for some days, the bulb being cut off from the rest of the apparatus, w hich was made of soda-glass.. It was found that the pressure slowly decreased. In a soda- glass bulb the electrodeless discharge caused a much quicker absorption of gas. The fact that absorption takes place with: the electrodeless discharge, proves that the gas is not occluded by the metal of the electrodes as is sometimes assumed. The- absorption is much slower for the electrodeless discharge than for one in which electrodes are used, but this may be- ne to the difference in the currents through the gas. ; . To test whether the distance of the discharge from the es made any difference, a tube like the one shown in fig. 4 was used. Very regular readings could not be obtained with this tube. I attribute this to the difficulty of getting the gas out of the electrodes, the length of the latter rendering this: troublesome. At the higher pressures (1 mm.) the gas disappeared at a slower rate than was the case when a cylindrical tube of smaller diameter was used. At pressures below °5 mm., the shape of the tube made little difference. The appearance of the tube at the low pressures was as shown in the figure. The negative glow filled nearly the: whole of the bulb, the positive light was only visible at the: Absorption of Gas in a Croakes Tube. 509 -end of the anode nearest the glass. The relative amounts of negative glow and positive light in this bulb and in an ordinary cylindrical tube are therefore very different in the ‘two cases, without, as has been shown, influencing the rate -at which the tube runs down. Fie. 4. baal +ve Glow +E In order to compare the results obtained in the last ex- periment with those obtained from previous ones, it was necessary to reduce by calculation the volumes of the appa- ratus to the same value in each case, so that the gauge- readings may always represent the same mass of gas absorbed. The length of the electrodes was also a disadvantage, In order to test further the effect of allowing the negative glow to develop or of confining it to a small volume, and Fig. 5. generally of producing a dissymmetry between the two electrodes, a tube like that shown in fig. 5 was used. The rate at which the pressure de- creased was determined first when A was cathode, and secondly when the current was reversed. This rate was found to be the same in the two cases, although the appearance of the discharge was very different. When A was cathode there was scarcely any positive light to be seen except just on the tip of the anode, and another small plate of it where the tube opened out into a bulb; with A as anode the cylin- drical part was filled with positive light, while the bulb was nearly filled with negative glow. [t appears from this that the amount of luminosity developed has no effect on the absorption of the gas. B+ive 6. The tube shown in fig. 5 was silvered 510 Dr. R. 8S. Willows on the on the inside by precipitating silver from silver nitrate and its rate of running down again determined. In order to prevent the discharge from passing along the silver, either directly or by means of platinum sputtered from the wires passing through the glass, these wires were enclosed in the soft glass used to fasten them into the tube. The rate at which the pressure decreased was the same as before the silver was deposited on the surface. It was found that air, nitrogen, and hydrogen all gave the same rate of running down. Another tube was lined with mica, but this produced no difference in the rate of absorpticn. 7. The effect of keeping the discharge from striking directly on the glass composing the tube Fic. 6 was investigated by means of the tube oe shown in fig. 6. It consisted of a tube about 3°5 cm. diameter, having an aluminium-wire elec- trode A sealed into the closed end. This electrode was entirely surrounded by the other electrode B, which consisted of a cylinder of thin sheet aluminium, the upper end of this cylinder being closed by another flat, circular piece. In order to make the discharge take place well inside the cylinder, the bottom of the electrode A was fused into a thin covering of soft glass. When this was done the discharge passed directly from metal to metal. The tube had to be run hard for several weeks before regular readings could be obtained. When this stage was at last reached, the following results were obtained. It was found that when A was the anode there was hardly any absorption of air, but when A was cathode the pressure decreased as before. At pressures near 1 mm. the absorption was appreciably quicker with this tube than with those pre- viously used; probably, had the regularity of the readings permitted a close comparison, it would have been found that this held throughout the whole range. | When B was cathode the whole tube was hot during the passage of the current, considerably more so than when the current passed in the opposite direction. To show that the fall in pressure is not altogether due to oxidation of the metal, the experiment was repeated with Absorption of Gas in a Crookes Tube. Sit nitrogen. The change of gas produced no appreciable effect in the rate of running down. It was found with nearly every tube that, when the elec- trodes had been cleared of gas, the fall of pressure was abnormally great when a fresh charge of gas had been newly admitted from C (fig. 1) to the experimental tube, and this took place although it had been drying for some days. The difference between the rates of running down accord- ing as A was cathode or the reverse was very marked at pressures above *5 mm.; in some cases the current could be passed for several hours with A anode, and the pressure did not alter by more than one division on the gauge; while if it were reversed and kept at the same value, there was a de- crease of about 25 divisions per half-hour. At pressures below :2 mm. the alteration amounted to four divisions per half-hour with A the anode, a reversal of the current raising this to 60 or 70 divisions in the same time. The resistance of the tube was very much greater when A was cathode than when it was anode. The measurements were very irregular with hydrogen gas, notwithstanding some interesting results were obtained. The pressure did not decrease so quickly as with air and nitrogen when A was cathode, but with a reverse current the hydrogen disappeared much faster than did the other gases under similar circumstances. With hydrogen as with the others, the absorption was always more marked when A was cathode than when it was anode. Hydrogen further differed from air and nitrogen in that when the apparatus was allowed to stand most of the gas reappeared. Thus, after running for several hours and then allowing to stand, the pressure generally rose during the first half-hour by about ten divisions on the gauge; it then re- appeared more and more slowly, after a couple of hours rising about two divisions per hour; after several hours’ standing it was found that about two-thirds of the gas had again appeared, and this gradual reappearance went on for several days. Other peculiarities also showed themselves with hydrogen. “When B was cathode, the voltage required to maintain (not start) the discharge gradually decreased as the pressure de- creased down to about °6 mm., after which it rose again. This is in general agreement with the results obtained with other tubes and gases; but when A was cathode the voltage required increased as the pressure was lowered from 1°25 mm. The resistance of the tube when A was cathode was also 512 . Dr. R. 8S. Willows on the much greater with hydrogen than with other gases; generally the opposite was the case. With B cathode, the resistance was not very different whether the tube was filled with hydrogen, nitrogen, or air. The appearance of the discharge was also peculiar. When B was anode the discharge was bright green next to the outer cylinder, and gradually shaded away until midway between the electrodes the luminosity was very weak, finally next to the cathode it was red. The cathode hydrogen spectrum generally gives a large number of lines: in this case it only gave the red, blue, and green. The difference between the rates of running down, accord- ing to the direction of the discharge, although distinct, was not so well marked when an induction-coil was used as the source of current. This is probably what we should expect, for with this means of producing the discharge the current is not easily measured, and so it 1s very likely that the currents in the two directions are very unequal, that from B to A being the less, since it has been noticed that the resistance is greater when this is its direction. The apparatus was refilled several times with hydrogen, but the same peculiarities always showed themselves. On taking the tube to pieces, it was found that the outer cylinder had become covered with a thin white film in some parts, probably oxide of aluminium; while other places were marked by the presence of sputtered aluminium, giving rise to brilliant bands of different colours. : 8. So far no suggestion has been made as to what becomes of the gas that disappears. As a raison d’étre for some of the experiments which follow, I will briefly notice some possibie explanations. Hither the gas combines chemically with the glass, the mercury vapour, or the electrodes, or the carriers or ions are shot at the sides of the tube where they are held either elec- trically, if they do not lose their charge, or mechanically by penetrating into the walls of the tube*. With reference to the first of these alternatives, the mercury vapour may be left out of account since it was found that gas disappeared even when care was taken to ‘exclude it from the tube. A cylindrical tube was pumped down by means of a mechanical pump to about ‘75 mm., as * According to W. Rollins (Elec. Rev. April 11th, 1900, p. 358) it appears that it has been thought that the gas escapes through the walls of the tube, a not altogether impossible idea at first sight when we remember that the carriers in Lenard rays can be shot through thin layers of aluminium. Absorption of Gas in a Crookes Tube. 513 judged from the distance apart of the strie, and an induction- coil discharge was passed for two days, at the end of which it was giving out Rontgen rays. The absorption cannot be ‘accounted for by supposing the electrodes to combine with or occlude the gas, for, as has already been shown, an electrodeless discharge also brings it about. An experiment of Prof. J. J. Thomson’s, which he is good enough to allow me to use, shows further that the gas ‘does not leak out either through the walls or along the electrodes. A tube was used which communicated with the exterior through two taps, the volume between the taps being known; it was exhausted to about *5 mm., cut off from the pump, and weighed. A discharge from a eal was passed for some days, ea amounts of gas being admitted when necessary. By repeated weighings ‘it was shown that the weight of the tube increased by ‘amounts equal to the weights of air that had been admitted, although after admission the discharge had caused the pressure to fall so much that Rontgen rays were given out by the tube. Difficulties in accepting either of the alternatives advanced above are not wanting. Thus against the chemical view it may be noted that air, nitrogen, and hydrogen give nearly the same rates of absorption in a soda- -glass tube; that throughout the experiments no differences in the behaviour of the first two were noticed ; and that punaces of soda-glass, lead-glass, mica, silver, or aluminium showed little differ- ence, ‘at least when nitrog en and air were used. ' Tf the view be adopted that the ions are shot into the glass and held there, from their greater velocity the negative | ions are the more important. In that case differences in the rate of running down might be expected, according as facilities were or were not afforded the negative lons of ‘reaching the glass. The experiments in Sec. 5 show that this is not the ease. This view would, however, explain the result of Sec. 7, that the rate of absorption was much faster when the cathode was surrounded by the anode than when the current runs in the opposite direction; for in the former case the negative ions have a greater chance of being shot into the walls (in this case the anode) than in the latter. To test this view other experiments were performed. 9. Since negative ions are shot off from the cathode at right angles to its surface, the shape of the electrode will influence the number which reach the walls. With a disk most of them will be shot up the tube, while with simple wire electrodes more will be sent to the sides. 514 Dr. R. S. Willows on the A tube like the one shown in fig. 7 was used ; it was found. that when A was cathode, the rate of absorption was about fifteen times greater than when it was Fig.7. anode. If this be really due to more ions being A shot into the glass in the first case, it should be possible to increase the rate of running down when B is cathode, by deflecting the negative ions on to the glass by means ot a magnetic field. Although a strong electromagnet was used for the purpose, no increase was found. The difference in the rates of absorption accord- ing to the direction of the current may be ex- plained by the difficulty of freeing a disk electrode trom occluded gas, as it cannot be made thoroughly hot. This gas is given off in greater quantity when B is cathode, on account of the greater heating, and so masks the effect it is desired to B measure. This might also explain some of the results of Section 7. 10. It has been shown in Sees. 6, 7 that replacing a soda- glass surface by one of silver or aluminium entails no differ- ence in the rate of absorption: this would seem to show that the gas penetrates the Jast two substances. That this pene- tration was not due to cathode rays was shown as follows :— Between the anode B (see fig. 6) and the glass was placed some dry common salt, and a discharge was passed for some days using A as cathode. It is known from the experiments of Wiedemann and Schmidt and others that cathode rays colour the salt blue, but no blue coloration was found after several days, although in the meantime a large amount of gas was absorbed. That some of the gas penetrates the walls is proved by an observation of Gouy’s*. It was noticed after bombarding a piece of glass for some time with cathode rays, that when it was strongly heated small bubbles of gas made their appear- ance just in the surface, and when the glass was nearly molten these escaped. The amount that can be driven off in this manner does not, however, nearly account for the large amount that can be absorbed ; several tubes were heated till they were on the point of collapsing, and only small quantities of gas were evolved. 11. In order further to insure that the electrodes did not produce the fall in pressure by combining with the gas, a tube was used having platinum wire for electrodes. It was * Compt. Rend. vol. exxii. 1896, p. 775. Absorption of Gas in a Crookes Tube. 515 noticed that the amount of gas they contained was consider- ably less than for similar aluminium wires: when this gas had been driven off, the rate of absorption was equal to that found in a similar tube with aluminium electrodes. After using the same end as cathode for several days, a curious effect was noticed. The resistance of the tube suddenly decreased, as did also its rate of running down, the positive column doubled its length, and the heating at the cathode was less marked. This was not due to the discharge passing along the glass, for, on reversing the current, the resistance and rate of absorption rose to their original values. It is likely that some of the sputtered platinum close to the cathode acted as electrode, when the latter would be a disk rather than a point; this would lessen the resistance and also the heating effect. If the absorption is due to a chemical action, the latter effect might be expected to reduce it also, since it would depend on the temperature of the gas. 12. It has been frequently noticed that Réntgen-ray bulbs after prolonged use show a bluish-violet coloration; this is not merely a surface coloration but extends also to the volume of the glass. Villard* believes this is due to Réntgen rather than cathode rays. M. and Mme. Curie + have noticed the same effects in glass flasks containing radio-active substances. This coloration did not appear in my experiments except in tubes that had been run down very low with an induction- coil, so that the chemical action producing it does not have any appreciable effect on the absorption of gas. It was thought that this coloration might be due to alkali salts in the glass. Some common salt placed in a tube in which the pressure was a mm. was coloured the whole distance between the electrodes after a few days’ passage of a discharge; no change could be seen in the glass. It was noticed when the salt was exposed to the discharge and was cut off from the mercury pump, that the rate of running down was extremely slow ; when the salt was shielded from the discharge (see Sec. 10) it was found not to influence the absorption. If the coloration is due to a physical modification of the salt, this result would not be expected; so that it must be looked on as supporting Wiede- mann and Schmidt’s view of a chemical action. 13. Since the results of the experiments seemed to point to a chemical combination between the gas and the glass, various samples of the lattes were made into tubes and the rate of absorption tested. * Phil. Mag. Feb. 1900, p. 244. + Ibid. p. 242. 216 On the Absorption of Gas in a Crookes Tube. One sample, bought as soft Jena from the dealers, ran down. very quickly the first time it was used, until about 120 c.c. at a pressure of 1 mm. had been absorbed, when no further fall in pressure occurred although the discharge passed for several days. The tube was then left exposed to atmospheric pressure for several weeks. When the discharge was again passed a further quantity of gas disappeared, but this was considerably less than in the first case. That a tube can be ‘made which shows a limited capacity for absorption, seems to point clearly to the action being a chemical one. Tubes made of soda- and Jena-glass were treated with hot acids, but this was not found to influence the absorption. Mylius * has shown that if glass be soaked in water for ‘several days and then heated to 300°--400° C., it is rendered less liable to be acted on chemically. This treatment applied to soda-glass produced no difference in the rate of running down; but a soft Jena-glass tube was made to run down much more slowly, although the quantity of gas that it finally absorbed was unaltered. Jena-glass further differed from soda-glass in that hydrogen was scarcely absorbed at all. If a Jena-glass tube which refused to absorb more gas was heated, a small quantity came otf, but this could not be reabsorbed as in the case of soda- lass. , To summarize: It appears from the experiments that most, if not all, of the gas absorbed is to be accounted for bya chemical combination with the glass; that if tubes are desired in which the pressure remains constant they should be made of Jena-glass in preference to lead-glass, and of lead-glass rather than of soda-glass; and finally, that in the first two cases hydrogen is absorbed to a far less extent than air or nitrogen, the last two gases showing little difference. . 14. One or two effects noticed during the experiments may ‘be added here. It was frequently noticed that when a battery of voltage just insufficient to start the discharge was connected to a ‘tube, a double reversal by means of a commutator frequently enabled the discharge to pass. When running tubes with a striated positive column con- tinuously with a battery, I have often observed the following : at a distance of two or three striz away from the anode a well-defined dark deposit (aluminium ?) appears round the whole circumference of the tube, just opposite the bright part of a striation, to which it is equal in width. This gradually * Chem. Soc. Abses 1889, p. 549. Notices respecting New Books. a We disappears only to reappear opposite another stria generally nearer the cathode. ‘Two or sometimes three of these bands may be visible at the same time ; they at length disappear altogether, being most frequent in tubes recently made. In conclusion I offer my best thanks to Prof. Thomson for the great help I have derived from his valuable suggestions, and also to Mr. E. Everett for his assistance with some of the glass-work. Cavendish Lrtboratory. XLV. Notices respecting New Books. Annuaire pour Tan 1901, publié par le Bureau des Longitudes. Avec des Notices scientifiques. Paris: Gauthier- Villars. Ae usual, this handy little annual contains a mass of useful infor— mation, and will be welcomed by the engineer and the man of pure science alike. Among the specially contributed articles for the present year we notice “ The Electric Transmission of Energy,” by M. A. Cornu; “The Projected Revision of the Meridional Are of Quito,” by M. H. Poincaré; and the historical notice re- garding the ‘“‘ Establishment of the Metric System,” by M. Bassot.. At the modest price of 1 fr. 50 ¢., the volume, which contains close on 800 pages 8vo, is a marvel of cheapness. The klectro-Chenist and Metallurgist. A monthly journal devoted to Electro-Chemistry and Metallurgy. Vol. I. No.1. January 1901. London: Messrs. Sherard Cowper-Coles & Co., Ltd. We heartily welcome the appearance of this new journal, which will undoubtedly fill a gap in English technical literature. The rapid strides which electro-chemistry and electro-metallurgy have been making within recent years are sufficiently remarkable to justify the assumption that before very long a number of the older chemical processes will be superseded by electro-chemical ones. In view of the importance of the subject, it seemed somewhat strange that there should in the English language have been no. periodical devoted to electro-chemistry. The journal under review makes a very good start: it contains a number of highly interesting articles by well-known specialists, and, as an extremely important feature, we may note the illustrated abstracts from contemporary foreign journals. If the ‘ Hlectro-Chemist and Metallurgist’ “maintains the remarkable combination of high-class contributions and extremely moderate price with which it starts, we have no doubt that it will achieve the success which it certainly deserves. The Periodic Classification and the Problem of Chemical Evolution. By Guorce Ruporr, B.Sc. London: Whittaker & Co., 1900. Messrs. Whittaker have recently been publishing a series of small text-books devoted to special scientific and technical problems, and the book before us forms the latest addition to the 518 Notices respecting New Books. series. It is a most readable and interesting account of a subject which has always had a powerful fascination for most men of science, and seems particularly opportune at the present moment, when the ultimate constitution of matter is one of the outstanding problems in physical science to which particular attention is being devoted. A clear historical account is given in the first chapter of the various attempts at classification of the elements, and is then followed by an account of the laws of Avogadro, Dulong and Petit, and Mitscherlich. Next comes avery full discussion of the Periodic Law, followed by an account of its applications. In Part II. the problem of chemical evolution is dealt with, the concluding chapter giving a brief résumé of the various speculations which have been put forward from time to time regarding the constitution of matter. Here it seems a pity that the Author did not bring his work up to date by giving an account of Professor J. J. Thomson’s researches ; these are only briefly alluded to on one of the introductory pages to the book. A number of appendices are given containing various ° useful tables and notes. In dealing with the bibliography of the kinetic theory of gases, the Author might well have added to his list the recently published translation by Mr. Baynes of Dr. Meyer’s book on the subject. Inorganic Chemistry. By RapHann Munpona, F.C.S. Revised to date by J. Castenn Evans, F.C. Fifth Edition. London: Thomas Murby. ) WHEN a text-book has run through several editions, it has, zpso facto, established its right to exist; at the same time, unless the work of revision is carefully carried out for each consecutive edition, it is liable to be displaced by more recent publications. The revision of the latest edition of Professor Meldola’s highly successful text-book has been carried out by Mr. Castell Evans, who, in a prefatory note, expresses the hope that he has “suc- ceeded in bringing the book quite up to date.” We feel compelled to state that we cannot share this view. One or two examples will serve to illustrate how imperfectly the work of revision has been carried out. Although argon appears in the table of elements on p- 6, it is not even mentioned in the chapter on the chemistry of the atmosphere. On p. 222 we read the following amazing state- ment: ‘The metal aluminium is now prepared on a large scale by reducing the double chloride of aluminium and sodium with metallic sodium.” As it would be hardly fair to credit Mr. Castell Evans with the colossal ignorance of recent developments in electro- metallurgy which is evinced by the above sentence, we prefer to suppose that somehow or other he simply omitted to read it. Language which is at the present time decidedly archaic has, in many instances, been allowed to remain unaltered. Misprints are exceedingly numerous, and it is difficult to believe that the proof- sheets were read with anything like ordinary care. Altogether, we are unable to bestow much praise on the manner in which the work of revision has been carried out. Notices respecting New Books. 519 The Theory of Commutation. By C. C. Hawkins, M.A. Pp. 1-82. London: ‘The Electrician’ Printing & Publishing Co. Ltd., 1900. Tue sparkless running of dynamos and motors is one of those extremely complicated problems in which theory has considerably lagged behind practice. It is only quite recently that the vague- ness which characterized all the earlier attempts to deal with this matter theoretically has disappeared, and has given place to a treatment characterized by lucidity and precision. The pamphlet before us is an attempt to expound the present condition of the problem, and is largely based on the valuable work of Arnold and Mie. Although most practical men will be unable to follow the somewhat complicated mathematical treatment, they will find a good deal of interest in the numerous diagrams which graphically exhibit the results of laborious calculations. The discussion of the energy-changes which take place during commutation should prove particularly interesting. The pamphlet is an excellent summary of our present knowledge of this difficult subject. The omission of brackets in connexion with the solidus notation leads to a good deal of ambiguity in some instances, and we hope that this defect will be remedied by the author should another edition be called for. Theoretische Betrachtungen uber die Ergebnisse der Wissenschaftlichen Luftfahrten des Deutschen Vereins zur Forderung der Luftschif- fahrt in Berlin. Von WitnEtm von Brzoup. Braunschweig : F. Vieweg und Sohn, 1900. Pp. 1-381. Tus pamphlet-is an extract from a large and elaborate treatise giving a full description of the work done by the Deutscher Verein zur Forderung der Luftschiffahrt in Berlin. The pamphlet deals with the scientific value of the data obtained during the various balloon ascents, with the distribution of temperature in a vertical direction, and with the periodic fluctuations of pressure, tempera- ture, and humidity. Mémoires Originauey sur la Circulation Générale de lV Atmosphere. Annotés et Commentés par Marcen BrinLouiIn. Paris: Georges Carré et C. Naud, 1900. Pp. xx +163. Tis book is a collection of the more important original memoirs relating to the great problem of the circulation of the atmosphere, and includes papers by Halley (1686), Hadley (1735), Maury (1855), Ferrel (1856-1861), Werner Siemens (1886), M. Moller (1887), Oberbeck (1888), and H. von Helmholtz (1888 & 1889). Some of these memoirs are translated in their entirety, while of others only abstracts are given. M. Brillouin has contributed a most interesting introduction, in which the historical development of the subject and the present state of the problem are clearly set forth. The book is beautifully printed and tastefully bound. 520 Geological Society. Die Erdstrome vm Deutschen Reichstelegraphengebiet und ihr Zusam- menhang mit den Lrdmagnetischen Erschenungun. Im Auftrage des Erdstrom-Comites des Elektrotechnischen Vereins Bearbeitet und Herausgegeben von Dr. B. WeinsteIn. Mit einem Atlas Ent- haltend 19 Lithographirte Tafeln. Braunschweig: F. Vignes und Sohn, 1900. Pp. vi+ 78. In 1881 the Hlektrotechnischer Verein appointed a committee to investigate the phenomenon of earth-currents. After the necessary preliminary investigations, a regular series of observations was commenced in 1883 on two underground cables, whose directions were roughly north-and-south and east-and-west respectively. The first cable was one connecting Berlin with Dresden, the second ran from Berlin eastwards as far as Thorn. The cables were placed at the disposal of the committee by the postal authorities. In the circuit of each cable was included a registering apparatus, the ends of each cable being earthed. The observations were con- tinued until 1821, when the cables could no longer be spared. The mass of observations accumulated during that period has been subjected to a careful analysis by Dr. Weinstein, and the present pamphlet and atlas are the outcome of his labours. Besides an account of the various periodic changes which earth-currents under- go, and which appear to be chiefly influenced by the position of the sun, Dr. Weinstein gives an account of the corresponding periodic changes i in the intensity of the earth’s magnetic field, and discusses the connexion between the two. He states it as his opinion that almost the whole of the diurnal variations in the earth’s magnetism are really due to the magnetic effect of earth-currents. At a time when the attention of physicists is centred on the subject of magnetic records in connexion with the somewhat heated dis- cussion which is now being carried on between the advocates of magnetic observatories and those of electric-traction systems with uninsulated rail-return, the present account of a series of simul- taneous magnetic and earth-current observations should prove of considerable interest. XLVI. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 168. | June 20th, 1900.—J. J. H. Teall, Hsq., M.A., F.R.S.. President, in the Chair. Nie following communications were read :— 1. ‘On the Skeleton of a Theriodont Reptile from the Baviaans River we Colony).’ By Prof. H. G. Seeley, E-Ris.) PF aiiss VPGes 2. ‘Fossils in the Oxford University Museum.—lY.: Notes on some Undescribed Trilobites.’ By H. H. Thomas, Esq., B.A., F.G.8. 3. §On Radiolaria from the Upper Chalk at Coulsdon (Surrey). By W. Murton Holmes, Esq. Phil. Mag. 8. 6. Vol. 1. Pl. V. 73To exhaust es »o MO & wy MM OY Alla aie lll, ih SSS — 2 eae aaa a on tty Try UU Suu it aa ia ay HH AVAURINIGT RUGITTARVANANG BcneS = >) “'t buhdb bb bbb ubdbb bb bode b bbw (00000000000000000 tafetefetetsteteteretsy Y i / 5 an —— NE ees el ; THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES.] vf MAY 1901\ 4 = XLVII. The Striated Hlectrical Discharge. By J. H. Jeans, B.A., Scholar of Trinity College, and Isaac Newton Student in the University of Cambridge *. \ (Continued from Ser. 5, vol. xlix. p. 262.] N Fam i: § 12. 5 ee first part of this paper contained an exami- nation of the differential equation which, upon Prof. Thomson’s theory of conduction by ions, is satisfied by the intensity of electric force at any point of an electrical discharge. With a view to simplifying the discussion of this equation, the assumption has been made that the quantities g and a depend only upon the electric intensity at the point at which they are measured. | But a simple calculation will show that this electric in- tensity is not, in itself, sufficiently strong to effect ionization f, and the causes which seem most likely to account for ioni- zation{t are not such that qg will satisfy the condition which has been imposed upon it. We must, therefore, examine to what extent the results which were obtained only upon this assumption will remain valid if the assumption is not com- plied with. : At the outset it may be noticed that differential coefficients of g do not occur in the equation for the intensity. Hence * Communicated by Prof. J. J. Thomson, F.R.S. + J. J. Thomson, ‘ Recent Researches,’ § 218, p. 192. { The causes of ionization have recently been discussed by Prof. Thomson, Phil. Mag. 1. p. 278. Phil. Mag. 8. 6. Vol. 1. No. 5. May 1901. 2M 522 Mr. J. H. Jeans on the this equation will, at any specified point of the discharge, remain unaltered if we suppose that g has the same value at every point of the discharge as it has at the point in question. Using this value for g, we can draw a diagram similar to fig. 1 (Part I. p. 251), and at the point in this diagram corresponding to that point of the discharge which we are considering, the value of - will have the same sign as has dp the value of a for a point moving with the shading at this oint. : But q¢ varies from point to point of the discharge, and as g varies the vertex of the parabola in fig. 1 will move up and down the axis of symmetry, while the parabola will always pass through the two points A and B. ‘The vertex can never — pass to infinity along this axis, since g can never actually vanish* (equation 10, Part IJ.), and the vertex can never pass on to the axis y=0, since g can never become infinite. Hence the points at which ad vanishes will no longer (as in Pp ay s § 5) lie on a single parabola, but they will all lie within a certain region which is bounded by two parabolas, both of which pass through the two points A, B; and are concave to the line joining them. From this it follows that there must be curves of the four types shown in fig. 2, which will satisfy the differential equation, and therefore there must be two curves similar to those shown in fig. 5, which will satisfy the differential equation together with the boundary conditions. Under the present conditions it would be useless to attempt to discover under what circumstances these two forms of solution will be the only possible forms. In what follows it will be assumed that we are dealing with a solution of the type which is represented by the discontinuous line in fig. 5. § 13. Reference has already been made to the variety which is observed in the appearance of the discharge near to the anode. The theory has been found to be capable of accounting for the phenomena observed near the cathode, and also for the striated column in the middle of the tube, — but it has not, so far, accounted for the apparent difference in the behaviour of the two electrodes. The considerations put forward in the next two sections are meant to suggest a way in which this difference may arise, although no attempt * For instance, if we regard dissociation as the result of collision, we must remember that all velocities are posszble at every point. Hence however small the chances of dissociation may be, the “ expectation” of the number of dissociations (and therefore the value of g) will never absolutely vanish. Striated Electrical Discharge. 923 has been made to supply a formal proof of the principle upon which the argument rests. The curved line in fig. 7 is the graph which was found to represent the distribution of intensity along the line of dis- charge which is predicted by theory. The anode is repre- sented by A, the cathode by HE, and the ordinate at any Fig. 7. A Ze B C D a E intermediate pointis equal to y, the semi-square of the electric intensity at that point. The linelmn... is the line (y=) below which. the differential equation with which we have been working ceases to hold. The value of p (y= 2) at a point m at which the graph meets this line will be slightly different from the value of p at the adjacent point B in which the ideal mathematical graph meets the axis y=0. Let this small difference be denoted by a,,,, the difference being taken so that @,, is positive. Thus we shall have = Ame aa ko ais Aq Oo = > — Pas n ky Adri ED p kes Pr and so on, the suffixes m,n, p...- referring to the points n,n, p«..in fig. 7 Fig. 8 represents the plane of p, y (¢. fig. 2), and STU is the line y=n. In this plane the graph for y will be repre- sented by a single curve, and each striation will correspond 2M 2 524 Mr. J. H. Jeans on the toa single convolution of this curve about the point T, the curve being confined within the area AbGcBOA. The range of possible values for @,, it is easy to see, will be the line Tc, the limiting values being Uc and UT. Similarly the Fig. 8. range of possible values for @p will be UT, and so on. Now the ratio of Tc to /T depends on, and is roughly of the same: order as, the ratio of TU to TS, and therefore of hk, to hy; and direct experiment shows that this ratio is large. As we pass along the graph away from the anode, the curve in fig. 8 will revolve about T in a left-handed direction. All the curves which meet STU within the range Tc must, by the time they reach TS, be compressed into a smaller range Tb. Hence if 60,, dap, ... are the variations which occur in passing from any one curve to an adjacent curve, we may reasonably expect that ee will be large. P Passing beyond p the curve enters the region y=——, we E : V ke obtain [i : 27° Aqr* 167*C?u? ney US Lad & tay LAs by ee rT at 72 ) 167*C?u ” Se eee vail is ies The solution (3) is imaginary, but two such solutions properly combined give, as a real solution of (2), f=Aé® .cos & +z ). The factor e gives the amplitude of the wave; and 27 nL Whence =V, the velocity of propagation. ee ive tC 7? When (©? is negligible in comparison with C (z. e. when the conductivity is small), this expression expanded gives 5(N2,, 22 Westin tte WA oo, EER CAN and similarly, C= SATO (2 te ley ya) SL The units here used are the electromagnetic system; hence V,, from its definition EA » 1s the velocity with which the wave would move in the given medium if its conductivity were acces let D, =the maximum amplitude of a wave on entering a sheet of the dielectric of thickness 2; D =maximum amplitude of wave on emerging. Then D =Dvpe®*, Orn 2 eee Digan | Then log g= E29 = —27CKV 923 whence C2? log? g a DON a Am’ V 972 550 On the Double Refraction. of Electric Waves. This value substituted in (4) gives V,° I? log? ¢ 2, 2 8772 V=Vo— (6) Equation (6) is the relation between the velocity of the waves in a given weakly-conducting dielectric and their absorption by the dielectric. Weare supposing here that the medium is not crystalline in the sense of having different dielectric constants along different axes, but that it is merely heterogeneous in that it has different conductivities along different axes. In a medium of this kind, Vo is constant for a given specimen, while the absorption-coefficient pes 0 depends upon the direction of the electric force in the specimen. In that orientation of electric force in which absorption is greatest, V is smallest, and therefore index of refraction is greatest. This agrees with the results of my experiments on woods. With all the specimens tested, when the wood is so oriented that its grain is parallel to the electric displacement, the index of refraction is greater than with the grain perpendicular. In the former orientation also the absorption is greater than in the latter. | Returning now to the experimental data, let V; and g, be the values found for V and gq with the first orientation; V, and gg the corresponding values with the second orientation. When these values are substituted in (6) we have two new equations which combined give Vira ol alogs W. Vi— Vo log? de Dividing numerator and denominator of the left-hand member by v the velocity of the waves in air, we obtain 1/m,—1/N wi log? n (7) Vns—i/n, log? 4, - ae 3 The right-hand member can be calculated from the ab- sorption data. Call it R’, then 1/ny= R?/ng— (R?—1) | e ° ° e (8) where »,=index of refraction in the first orientation, Ny=index of refraction in the second orientation, and = mg=V yb. Production of a Spectrum by Anomalous Dispersion. 551 Hence the sufficiency of the bare assumption of hetero- geneous conductivity to explain the double refraction of electric waves by a medium like wood can be tested by comparing the value of y, obtained by calculation from equation (8), with the dielectric constant of the medium measured by some static method. The latter data I have not at hand. However, without such a comparison, it is still seen that heterogeneous conductivity plays an important part in the phenomenon of double refraction of electric waves. Universitat Leipzig. January, 1901. LIT. On the Production of a Bright-Line Spectrum by Ano- malous Dispersion and its Application the “ Flash-Spectrum.”’ ais WwW. Woop *. N a communication published in the Proceedings of the Royal Academy of Sciences, Amsterdam, W. H. Julius makes the very brilliant suggestion that the “ flash-spectrum,” seen immediately at totality, may be due to photosphere-light abnormally refracted in the atmosphere of metallic vapours surrounding the sun: in other words, the light of the flash- spectrum does not come from the reversing layer at all, but from the photosphere. The author shows that the light which will be thus abnormally refracted will be of wave-lengths almost identical with the wave-lengths which the metallic vapours are.themselves capable of radiating. This beautiful theory not only explains the apparent shallowness of the reversing layer, a thing that has always puzzled astro- physicists, but it accounts for the extraordinary brilliancy of the lines. I have succeeded in producing such a flash-spectrum by an arrangement in which I have endeavoured to imitate as closely as possible the conditions supposed to exist at the surface of the sun: in brief, I have obtained a spectrum of bright lines, with light from a source showing a continuous spectrum, by means of anomalous dispersion in an incan- descent metallic vapour. The theory of Julius supposes the sun to be surrounded by an atmosphere of metallic vapours, the refractive index of which decreases with increasing distance from the surface. In this atmosphere the rays of light coming from the photo- sphere will move in curved paths similar to rays in our own atmosphere. The refractive index is, however, very small except for * Communicated by the Physical Society : read April 26, 1901. 552 Prof. R. W. Wood on the Production of wave-lengths very near those which are absorbed by the vapour; consequently the light most strongly refracted, if it could be sorted out and examined with the spectroscope, would resemble very closely the light emitted by the vapours. Julius shows how this sorting out of the more refrangible rays may account for the bright-line spectrum usually attri- buted to the reversing layer, these rays moving in curved paths in the solar atmosphere, thus reaching us after the photosphere has been hidden by the moon. For the reproduction of this phenomenon in the laboratory it is necessary to form an atmosphere of metallic vapour in which the refractive index changes rapidly from layer to layer. This I succeeded in accomplishing by allowing the flame of a Bunsen-burner, fed with metallic sodium, to play against the under side of a white plaster plate. On looking along the surface of the plate, it was seen that a dark space existed between the flame and the cold surface, resembling somewhat the dark space surrounding the cathode of a Crookes’s tube. It seemed highly probable that, inasmuch as the temperature of the flame was lowered to such a degree by contact with the plate, the density of the sodium vapour would increase very rapidly from the surface of the plate downwards. The change may of course be abrupt instead of progressive, though I am inclined ‘to favour the latter supposition. In either case the action will be practically the same, the case being similar to the transition from a curved. ray to a broken-tine ray, as the change of the index of the medium becomes less gradual. Having covered the under surface of the plaster plate with a non-homogeneous layer of sodium vapour, a spot at the edge of the Hame was illuminated with sunlight concentrated by.a large mirror. This spot radiated white light in every direction and corresponded to the incandescent photosphere of the sun. A telescope, pro- vided with an objective direct-vision prism, was directed towards the white spot and moved into such a position that, owing to the reduction in the width of the source of light by foreshortening, the Fraunhofer lines appeared in the spec- trum (fig. 1). This represents the stage of an eclipse when only the thin crescent of the sun is visible. The sodium- flame appeared superposed on the spectrum of course. On moving the spectroscope until it was well inside of the plane of the illuminated surface and feeding the flame with fresh sodium, the solar spectrum vanished, and there suddenly blazed out two narrow bright yellow lines almost exactly in the place of the sodium lines. Fig. 2 shows the inverted sodium-flame, the faint continuous spectrum and the “ flash.” a Bright-Line Spectrum by Anomalous Dispersion. 993 Cutting off the sunlight with a screen caused the instant disappearance of the bright lines. Figs I. PLASTER FLATE & \G Wi gut” 7 ‘ ( D,= §896-2 ) &, = 5890-2 Fig. 2.—Ilash Spectrum of Sodium produced by Anomalous Dispersion. Repeating the experiment, I found that the bright lines eame into view on the sides of the sodium lines towards the blue ; that is to say, it is light for which the medium has an abnormally low refractive index that is bent around the edge of the plate and enters the instrument. This is precisely what we should expect, for sodium vapour has a refractive index of less than 1 for waves slightly shorter than D, and D,, as was shown by Julius in his paper*. The rays then will be concave upward in a medium in which the refractive index yaries, as | have supposed it to vary in the present case. If * [ have since found that the refractive index is less than 1 for the entire yellow, green, and blue portion of the spectrum, and greater than 1 for the entire red, orange, yellow end. In other words, I have obtained a complete anomalous spectrum with sodium vapour. Phil. Mag. S. 6. Vol. 1. No. 5. May 1901. ria 554 Production of a Spectrum by Anomalous Dispersion. the sodium vapour is very dense, we see only a single bright line bordering D,, owing to the complete absorption of the light between the lines. I next instituted a search for the light of a wave-length slightly greater than that of the sodium lines. For these waves the vapour has a refractive index greater than 1, conse- quently the rays will be concave downward in the layer of vapour. (The paths are indicated on an exaggerated scale in fig. 1.) If we move our prismatic telescope ‘down in a search for these rays, the solar spectrum will appear and drown out everything, but if we set up a screen (shown in fig. 3) in Fig. 35. e METERS mae Bis ane? Ailes eee FosITION FOR A= 5889 is ae ee ee wwe ew ewe wm ewww wwe ; Z if | bal a 566 Prof. Morton on the aes of Polyphase if n is odd it is. Qar n—l1 (si = aa sin = n Zz If n=2 we have the two-wire case and 7=1. In general, the distance of the equivalent pair of wires 1s n Xx the diameter of the circumscribing circle. 5). The following table gives the values of » for the different modes, from n=2 to n=12 :-— N= 2 3 4 5 oy =~] (@2) io) — (=) pan a 12 ——S | | —————— | | | SO g=1 | 1:00) 0:866) 1:00 | 1-28 | 1-73 | 2°43 | 3°48 |508 |7:50 | 11-2 | 169 2 0500] 0437) 0-433) 0-457] 0500] 0-561) 0-640) 0-741) 0-866 : 0333) 0:299] 0-288) 0-289 0-298) 0°313 0-333 4 | 0-250] 0-228) 0-218) 0-215) 0-217 5 0-200) 0-186) 0-177 6 0-167 In fig. 1 these values of » are plotted against the number of wires. Points which correspond to modes of the same order are joined by a curve—of course the intermediate points on these curves have no physical meaning. 6. Inspection of the diagram or of the table brings out the following points. The values for the first mode, ¢ or that in which there is the smallest phase-difference between consecu- tive wires, become rapidly much greater than the values for the other modes. We shall see that this means a smaller value for the attenuation-constant of the waves. The new mode which makes its appearance at each even value of n corresponds to phase-difterence a between successive wires. This case was worked out in the former paper, and has 7= 5. The same value of 7 reappears when the number — of wires is doubled—the magnitude, for intermediate numbers, first decreasing and thenincreasing. The physical reason for this repetition of the same speed and attenuation is obvious. With the doubled number of wires the corresponding mode T : ; has phase -difference 3° and the arrangement admits of being broken up into halves. .. Hach half has phase-difterence a and, from symmetry, they have no inductive influence on each other. It is only when n is a multiple of 4 that this division into independent nalf-systems is possible. Ratio of equivalent distance for pair of wires to diameter of circle. Currents along a Number of Parallel Wires. 567 eee ST ee eget ee Phe be babel Number of wires. 568 Prof. Morton on the Propagution of Polyphase 7. Effective Resistance, Capacity, and Inductance of the Leads.—For slow oscillations along a line of resistance R, inductance L, capacity C, and leakage conductance 8, all per unit length, we have m= —(R+ pL) (S+ipC). With no leakage, as in the present case, ie = —ipC (R + wpL) Zi ee =(= ic) If the attenuation is small we get from this R ZINE Kez If we throw into the above form the m? found for a poly- phase system, we can find the R, L, and C of a lead which would produce on slow oscillations the same diminution of speed and the same attenuation. In separating out the constants we are guided by the fact that, when p vanishes, R must become the ordinary steady-current resistance. We have ip 2rn loo ‘=) m= k?—Ce=kh?— f= wk, *Jo( (koa) kad (koa) A ise Gye ky?a? ie: 1 ky‘a* 1 kya % x [ Dba ee te : Atrpa*ip Aiup aD ee lb gp tess) Set Ped so) as (? Ry ’ writing R, for eo the steady-current resistance of unit length of wire. m= —ipC(R+ipL) aes fe (9 4 (HR, Le) ee V2 io cen OR, 6 Ry 2 a a o Currents along a Number of Parallel Wires. 569 , 1 : i ; Put V?= K and the right-hand side may be written K 1 u2p? See teP ) —ip =| Ges Re 2 log—— ° +ip (2 log = i ea Thus the effective capacity is The effective inductance, when p is small, approaches the value lip log + atu 2 the general value being for small frequencies ye 1 pip? L —— lo A8 R,? eee as in Lord Rayleigh’s formula. With high frequencies, using the appropriate approxima- tions for the J functions, we get the corresponding expression pe Ro approaching the limit te ,= loo ce n The resistance agrees with Lord Rayleigh’s well-known expression. 8. It is easy to extend these results to take leakage into account. If the dielectric be supposed to have a finite resistance p’ it can be shown * that the constant ,? is altered to p> _ duip V2 A This leads to the value S= ae a a) Beara: * Cf. J.J. Thomson, ‘ Recent Researches,’ p. 262; Sommerfield, Wied. Ann. Ixvii. p. 233 (1899) ; Gray & Mathews, ‘ Bessel Functions,’ chap. 13. Phil. Mag. 8. 6. Vol. 1. No. 5. AZay 1901, 2P Attenuation-Constant. 5970 ~~ Prof. Morton on the Propagation of Polyphase GG. Mie * has used the above method in his accurate treat- ment of the two-wire problem. Fig. 2. OP e Se SG 7 Orn TS. lO: Number of wires. * Mie, Ann. d. Phys. ii. p. 202 (1900). Currents along a Number of Parallel Wires. 571 9. In the case of the last mode of an even number of wires, as discussed in §6, we have the 2nd, 4th, 6th ... wires acting as returns to the Ist, 3rd, 5th.... The inductance Ly can then be obtained directly by the method used by Maxwell (Treatise, vol. ii. p. 318). Also the capacity can. be found on the lines followed in Heaviside’s paper on the Capacity. of Suspended Wires (Electrical Papers, vol. i. p. 42). The analysis used will be found to lead to equations similar to those used in the present paper. 10. Numerical results for a particular case.—To se an idea of the effect produced by the variation in the mag- nitude of 7 on the circumstances of propagation, I have worked out numerically the case of = = 100. The alan x tion alone was considered. The results are shown on fig. 2, where the ordinates give the ratios of the attenuations caused by the different arrangements to that for two wires, the wires being supposed spaced round a circle of constant size. The value L, was used for the mnie ee applying to slow alternations. If we keep to a given mode and increase the number of wires, the attenuation first increases slightly and then steadily diminishes. For example, the attenuation for three wires with phase-difference 120° is greater than for two wires, that for four wires with difference 90° is equal to the two-wire value, that for five with difference 72° is less. The smallest values of the attenuation are got when the phase-difference is the least possible. For six wires the ratio of greatest attenuation (phase-difference 77) to least (phase-differ- ence 60°) is about 1°3: 0°8. For twelve wires it is 1°58 : 0°64. If, instead of the low-frequency limit for L, the high-fre- quency limit had been used, the only difference would have been a slight widening of the extreme values, leaving the general form of the curves unchanged. For example, the end values for twelve wires now come out 1°64 and 0°63 for the 6th and 1st modes respectively. : ae ; site Increasing the ratio — has the opposite effect, bringing co) a , the values slightly closer together. For = = 500 the values for twelve wires are 1°38 and 0°70. Queen’s College, Belfast. 22nd Febru: ary, 1901. [Bae LV. On the Change of the Colours of Cloudy Condensation with the Number of Available Nuclei, and on the Effect of an Electric Field. By C. Barus*. 1. 7JNHE steam-tubef in which an ordinary jet is used to produce the colours of cloudy condensation has two disadvantages, inasmuch as in the first place the quantity of steam issuing at a given pressure cannot be varied, and in the second place the manner in which the nuclei are brought into the jet is not easily understood. One is not sure that the whole of the “ dust’ f is active in producing condensation when the charged air comes in contact with the jet from without. Again, the colours of a relatively high order are best seen at relatively low temperature and pressure, and require a large volume of steam if they are not to be too faint for recognition. Both desiderata are met in the follow- ing device, in which the steam flux is annular, the air influx axial, and which has the final advantage of making the jet more easily accessible ; for the saturation of colours even of high order is now such that the lower window and lateral influx of charged air may be dispensed with. The body of the jet (fig. 1) is of a bullet-shaped pattern, Fig. 1.—Section of Steam-Jet, Scale 1/2. iN N . q OTOL LLL LO NN (ZL SD TOUANGANA sce ctetssanas NQDo N * Communicated by the Author. + The present paper is a continuation of my earlier experiments given in’ this Magazine [5] xxxviii. pp. 19-35 (1894). The old apparatus referred to- is there described, together with the conditions under which colours are- obtained. The new series of researches with the steam-jet (a brief account of which will be given in this and subsequent papers) were made possible by a grant from the Smithsonian Institution, and are published by permission of the Secretary. t I shall continue to use the antiquated term “ dust” for convenience.. On Change of the Colours of Cloudy Condensation. 573 AA being a hollow conoid about 5 centims. long and 9 centims. internal diameter, provided with a side tubulure, T, conveying the steam from the steam-box. The body being open above and below, receives the hollow spindle, BC, axially, the latter being secured in any position by the snugly-fitting screw at C. The top, B, of the spindle is ground into the upper aperture of the body like an ordinary screw-valve, so that steam may be quite shut off or supplied in any reasonable quantity, at any pressure, by turning the head of the spindle at C. The bottom of the spindle receives the T-tube G EF, the joint being ground so as to admit of rotation of the spindle around the tube. Air charged with nuclei is conveyed through this tube, entering at F’, from an aspirating train presently to be described. To obviate the danger of steam entering the tube EK F and quenching the “duster,” a hollow nozzle, D, is ground into the top of the spindle and removable at pleasure. This introduces the nuclei at about one centim. above the annular opening in the jet where the pressure-excess has practically vanished. The nozzle does not otherwise interfere (tests made) with the action. Should water enter the tube H, it may usually be removed by opening the stopper G. Very little difficulty is thus occasioned from this cause. The colour-tube is now modified as shown at C (fig. 2), the jet, J, playing directly into the open bottom of the tube, and as this is telescoped (not shown) the lower section may be raised to facilitate access to the jet. The mirror which throws up daylight is shown at m, n being the observation window cleaned with caustic potash applied with a probang through a. The escape steam-pipe is at e. The bottom of the spindle is joined by a thin tube%, ¢, about one millim. in diameter, to the phosphorus “ duster,” P, which here consists of a glass tube about 30 centims. long and 1 centim. in diameter, containing a succession of thin pellets of phosphorus secured between strips of wire gauze and kept at a temperature of 25°-30°. F is a fine screw stopcock, admitting the compressed air of the gasometer train, of which D is the desiccator, U the pressure-gauge, V the volume-flask (capacity, 8 litres), graduated on the side in litres, and M a large Mariotte flask of copper raised or depressed by the pulley p. It will be seen that on closing the cocks ¢ and d, of V, the water enters the flask V by the * This tube will usually be called the “absorption ” tube, because a great number of the nuclei are unavoidably lost here. Cf. ‘ Science,’ xi. pp. 201-206, 1900; Am. Journ. Sci., March 1901. Prof. QC. Barus on the Change of the ol4 Fig. 2.—Diagram of Colour-Tube C, and Appurtenances. Scale 1/10. Colours of Cloudy Condensation. 575 side tube at a constant head. To empty V (M depressed), ce, d (communicating with the atmosphere), and / are opened. _ With this apparatus any desired colour may be shown in the colour-tube by adjusting the valve F, and maintained for any reasonable length of time. There is usually little danger of exhausting the phosphorus. 2. In the following Table I have given several series of results obtained on different days. Different (absorption) tubes, t, were used, and hence the results can only be com- pared by putting the volume of charged air producing blue as 1 litre/minute*. Variations between the series naturally remain because it is impossible at different times to select the same shade of blue from a continuous series. The pressure of the steam-jet is given under p, @ is the temperature of the air, and oP the pressure-excess of the volume-flask in centims. of mercury. It is superfluous to reduce to standard pressure and temperature, TaBLE.—Colour seen in the Steam-Tube and relative number. of Particles entering in case of the Annular Jet. “Blue ’=1. | Volume Volume Colour. per ae Colour. per P Ps ; | minute. | _ minute. | Crimson- | Crimson ...| 28 IO, =... “30 p=6em. | Yellow ...... 38 Yellow- _ | 0=27°C. || Green ...... D3 crimson... ‘45 |0P=5'5em.|! Blue-green .. ‘69 Green ..:... ‘70 | Blue (light) | 83 Blue (light) | "83 | Blue (full)...| 1:00 Blue (light) | “95 iiviiolete so... I 1-25 Violet ...... pe St | Blue (full)... 1:10 Carne Se | Blue (light) | P| | Crimson...... ‘17 Green ...... | ‘78 | \| Yellow- ce | erimson... 26 | Yellow- In this series large volumes of air | green...... 37 _ relatively poor in nuclei were used. | Green ...... ‘D1 | In the following series the volumes | Blue-green ,. 63 are smaller but richer. The curves | Blue (light) Eh a and 6 of the chart are probably | Blue (full)...) 1:00 not identical even for the same | standard blue. || 1 | These observations are reproduced in the chart (p. 578) by representing the thickness of an air-plate which would on * This is the case for air entering the colour-tube in nearly the saturated state. . / 576 Prof. C. Barus on the Change of the transmission give the same colour by Newton’s interferences, as no better method is immediately available. The ordinates are the volumes per minute of charged air (blue=1 litre/min.) producing the colour given by the abscissa in the tube. (Cf. Bulletin U.S. Weather Bureau, No. 12, 1895.) If these series are examined individually as far as blue, they will be found to le on lines with but slight concavity upward. Beyond the blue the upward trend is marked and rapid. The regularity throughout is as good as may be expected when colour criteria, sometimes faint, are made the basis of measurement. The curvature suggested is probably real: it is possible, however, that the emanating intensity of phosphorus is being overtaxed in proportion as the air-current velocities are increased. This would be particularly the case near and beyond the opaque region, which lies on the left side of the diagram. Curves a and 0 are referred to in the Table. It is interesting to compare with these results the data obtained with the earlier form of tube in which the “ dust ” comes in contact with a simple jet laterally from without. I will make selections of mean values from a large number of my earlier data as follows :—The numbers denote the litres per minute of air saturated with phosphorus emanation, needed to produce the colour in the steam-tube, if full blue requires | litre/min. : Faint crimson, °25 ; faint yellow, °35; green, °55; blue- green, ‘60 ; light blue, -90; full blue, 1°00; violet, 1:50; opaque, 2°00. | These data are necessarily irregular as they show the mean positions of a large number of observations for each colour under varying conditions. Compared with the present experiments, however, they lie quite within a common group of values*. Indeed the series of values when the jet is “dusted” in a great variety of ways from without, the nuclei being borne into the tube by a convection-current of air often travelling many feet to reach the jet, and the results of the present paper, where active air is at once introduced into the jet from within, are indistinguishable provided the same “‘dust ”’ value be given to one of the colours (blue), and the charged air be not too much exhausted of nuclei. This result will appear more clearly in subsequent papers. Here I will add an immediate application. 3. Having in an earlier paper shown that the volume of * The old data are marked X in the chart. In their saturation they correspond to the curve 6. Results to the left of the violet must be left in abeyance till I can construct a duster giving the necessary saturation without explosion. Colours of Cloudy Condensation. 577 air charged with phosphorus nuclei passing per second longi- tudinally through a slender tubular condenser K (fig. 3), ’ Fig. 3.—Tubular Electrical Condenser. Scale 1/10. + + LE / il | bears a constant ratio to the electrical current passing for a constant potential-difference radially between its surfaces, and that therefore both currents correspond to a definite colour in the’colour-tube, the latter becomes, to some extent, a gal- vanometer. In other words the colour obtained is, under proper graduation, a measure of the current in the condenser. We have thus a new method of estimating to what extent the nuclei take part in the conduction of electric current, for the question is yet an open one whether condensation may not be promoted by a distinct set of nuclei from those which convey electric current. Both, however, must occur pro- portionally to each other; the former, for instance, being later stages of growth of the latter, or produced in other ways from the other. The present experiment admits of an easy modification which will throw some light on the inquiry. In fig. 2, let the tube ¢ be replaced by the slender tubular condenser K (fig. 3), 50 centims. long effectively, internal radius *159 centim., external radius °300 centim., so that the air-space is about ‘141 centim. thick. Through this cylin- drical shell air saturated with phosphorus emanation is passed at various speeds from the gasometer, entering at a, and leaving, to enter the jet, at b. The external shell of the con- denser is permanently put to earth, the internal shell charged ‘to as high potential-differences as the apparatus warrants, and alternately discharged. The observations were made by looking down the tube C through the window n after adjust- ment for a given colour had been made at F’, to ascertain the effect of successively charging and discharging the condenser. - For potential-differences of 60, 150, and 300 volts between the shells and for all available colours, not a trace of colour- fluctuation in the steam-tube was to be observed, due to charging and discharging the condenser; whereas the slightest turn of the stopcock F immediately changes the colour perceptibly. One concludes therefore that the number of nuclei removed by current is insignificant as compared with the total number present, if, indeed, different nuclei may not respond to the BI8 = On Change of the Colours of Cloudy Condensation. different functions of promoting electrical conduction and condensation. : CuHart showing the litres per minute of air nearly saturated with phosphorus emanation, corresponding to the colours given as inter- ferences by the abscissas. Cf. Table. Early observations with simple jet marked x. Cr, denotes crimson (second order); Y%, yellow; Bl, blue; Gr, green; V, violet; Op, opaque, &c. The minus sign denotes light blue; the plus sign deep blue. OMB) BL BG. Ge XG The result admits of a quantitative expression as follows : From the chart it appears that colour-differences correspond- ing to °06 litre/minute (blue equivalent to 1 litre/minute) can certainly be detected. This amounts in the blue region to about 6 per cent. of the total number of nuclei entering. The potential gradient would be 2100 volts per radial centim. | Hence even in this strong field the total number of nuclei is iN still overwhelmingly large as compared with the number conveying current, a result which agrees with data which I found in the case of spherical condensers, and is indicative of the strong ionizing potency of phosphorus. Brown University, Providence, R.I. fe SRo0 J LVI. A Note on van der Waals’ Equation. By Haroup Hitton*. i. RING in mind the great importance of van der Waals’ equation, it seems worth while to collect the various mathematical properties of the family of curves w hich is the graphical representation of the equation, together with some accurate tracings of several members of the family. The form of van der Waals’ equation we sha.l consider is 86 3 bs Yeme Tose a2? Bi arie 0 ceeee Gola em (@) or, as it may be written, dyx2?— (y+ 86) a?+9x2—3=0, where 2, y, and @ are Scape the “ reduced ”’ volume, pressure, and temperature; 2. the volume, pressure, and temperature expressed with Te critical volume, pressure, and temperature respectively as units. The equation (z) may be considered as representing a family of curves of the fourth degree, of which 6 is the parameter. The curve (a) cuts the axis of w in finite points, where 80x? —9x7+ 3=0; Hi roots of this equation are ee if O>z; — equal to = if == 323 both positive and >5, if @ lies between = and 0; ane root is infinite if @=0 ; al Hoots are real, one ie Rowen —« and 0, and the other between 0 and , if @ is negative. The curve cuts the axis of y in no finite point. The curve has the axis of w as an ordinary asymptote, and a triple fo at infinity in the direction of the axis of y, at which «=; is the tangent to one branch, and the tangents to the other ee branches coincide in «=0. Hence to every value of # there can be at most one finite value of y; and to every value of y there can be at most three finite values of x of which two may be imaginary. If @ is positive, the curve has a branch between «=x and a= ;, touching y=0 and a=; at infinity ; so that y is in each case positive; a branch lying between w=; ald e—0- and touching these lines at infinity, so that y is in each case negative (in ‘fact for most positive values of @ this branch lies altogether so far on the negative side of y=0 that it cannot well be drawn on any diagram, and hence does not appear in fig. 1); and a branch on the negative side of e=0 touching * Communicated by the Author. 580 Mr. H. Hilton on van der Waals’ Equation. z=0 and y=0 at infinity, so that w and y for the branch are always negative. If 0=0, the curve breaks up into the ee line e=; and the curve vee 3=(0; these two branches meet at the point = —27). If 9 is negative, there is a branch between w=co and x=, touching y=0 and «=4 at infinity, y for this branch 3 being always negative; a branch between ws and #=0. fonchine these lines at infinity, so that near «=; he ordinate of the curve is positive and near #=0 negative (the branch crosses the axis of a and has an inflexion, but cannot ina diagram be well distinguished from a straight line); and a branch on the negative side of z=0 for which y is negative near «=( and positive near e=— (the branch crosses the axis of #, has a tangent parallel to this axis, and an inflexion). Any member of the family can be readily traced by taking a series of values for « and calculating the corresponding values of y. Fig. 1 shows as much of the curves 9= ; and §=—1 as can be conveniently put on a diagram. Fig. 2 shows the part of the curves lying between x= and w=5 (which is the part interesting from a physical point of view) for 19 positive values of 0. The tables given below show the values of 2 y ealenon to three places of decimals from which the figures were drawn. Any member of the family is of degree 4, of class 5, and of deficiency zero; it has two double points and one cusp (coinciding in the multiple point at infinity) ; two bitangents; and four inflexions (of which two are always imaginary, and 2187 2048 The area included between any curve of the family and the lines y=0, 2, =0, z,=0, is 80 |, 3a = Se 3 98; Jay Regictat The orthogonal trajectory of ae system is x*(32—1)= 2 (3a°y—9Iuxv +6). the other two are also imaginary if 0> =—— The radius of curvature at any point is 40° (Be —1)?+ (2402 —6 8a—12)?18 182? (32—1)*[8@x2*—(32—1)?] 3 if the tangent at the point is parallel to y=0, this simplifies into x*(3x—1) a) Mr. H. Hilton on van der Waals’ [quation. 581. GRE ee, Bee Soe07 04008) 220e05e00 SRE HSS EEC PEPE SECC CCC BERR CCH cere SECC CSS eT SECC CCPC eee a J See eee eee ee aes Tes MEGeseoo tae hee mes wa (SE) OS 1a ane || Sa ee "> ee | €| LEL-G | 99T-G G69-6 | G¢0-€ | GIFS 9GT-F GFP-E | GEL-G |GI8-F OL6-§ | LET-€ | L99-¢ | 199.F | L99-€ C89-G | SPP-P bation QC9.¢ 816-9 eeeeee | Coe eee GGG: GLG: 1&9: 90L- GOL: FOG: OG0-T F80-1 6LL-T LGT-T 961-1 ee [86-1 8G&-T 6LE-1 VEF-T 004-1 069-1 LT 198-1 090-4 GLE-G L16-G 666-6 000-9 "9g Jo Son[wA JuoIoyIcE Loy / Jo sonTeA.. GE: Zee: gag. 168: LaF Chr: OCF: OFF: QGP. GcF- i0F- 18: 18: 6G: uzG: Ost: 000: GLI. | GOP: G&G. L99- C8L 6&8: 989: 000-0 86E-G 9 000-ST | OG6-TT LEG: GUC: L9G: CRG: COG: 686: OGG: G&G: OIG: G8I- VFI: 960- T&0- vO: — USM ios Oe. — 00¢.— COL a NG] 686-1 — LLG-. — 868-T— ‘J ATav yy, 000: 1— LET le Té8-1 — 6E1-6- I8P-G-- 068-6 — 6EE-6 — 691-6 — 000-4 — 986-6 — OCG: T OGI- SFI- I8T- 1¥G:- Ss: OSPF: OGL. [Es G5. 860-1 GLI-T ESET 1é¢-1 CLL-T 80-6 OLF-G 000-8 FOL-E S89-P €&E-G GGL-9 1OT-L §EE-8 L166 000-Z1 C18-FI OGL-8T et a Se tt IGN GC) CD). HI SHI SHANNA Odo HH HE te) SHAH O69 DAID 0 iq 2 ~ Ken) SSI~MDADAADH HOM NHARONSNSSS —_— 584 Mr. H. Hilton on van der Waals? Equation. TABLE II. ‘ Values of y for Different oe BAL. ee Values of 8 @. cs 80=4. 86=—8. 3 =" il 33°383 | — 73333 46°667 “25 — 25 | 48000 | — 64000 | — 16-000 2 —4 75000 | — 85-000 — 59°000 15 —'5d | 133°333 | —140-606 —118-788 “i all 300:000 | —305°814 —288°571 = & — 29 12-000 | — 13-600 — 8-800 —10-/| — 40 3°000 — 4-000 — 1-000 —1°5 — 55 1:333 — 2°060 "121 —2:-0 = (0 ‘750 —1:321 393 — 25 — 85 “480 — ‘951 “461 —3:0 —10-0 333 — 733 “467 =o —115 “241 — 589 ‘455 —4-0 —13-0 187 - 495 “428 —4°5 —14:5 148 — 424 404 —5:0 —16°0 "120 — 370 ‘380 | Differentiating («) we have OG BY i 6 da (Gr) ir .. The tangent is parallel to y=0 when (8a—1)? =42°9. Eliminating @ between this equation and (a), we have (3@—2) S92", > 6 Uae eee as the curve through the points where y has a maximum or minimum value. Differentiating (8) we have dy 6(l—2) d’y _ 6(8x—A4) da eae and die i ear ae . (8) has a tangent parallel to the axis of x at point (1, 1) and an inflexion at the point (5 »)- This curve cuts y=0 where «= 5 has a triple point at infinity at which tangents coincide with a=0, and has an inflexion at infinity at which the tangent is y=0. It is of degree 4, class 4, and deficiency zero; has 1 double point and 2 cusps (coinciding in the multiple point at infinity), 1 double tangent and 2 inflexions (one at infinity). It passes through the points (—6; ‘093) (—5; °136) (—4; °169) (—8; °407) (—2; 1) (—1°5; 1:926) (—1; 5) (—°5; 28) (1; —1700) (2; -—175) (3; —40°741) om Mr. H. Hilton on van der Waals’ Equation. 585 (333; —27) C4; —12°5) (5; —4) (667; 0) (85; °781) es ty (1333 ; 844) (13; -741).. 3 b>}, G03. 7392) (3; 259) (4; :156) (5; °104), and is shown in fig. 1. Differentiating («) again twice we have Oye) 14d). 18 > By 212968. 2 ae (oe 1). at? be (Sr Dea ae .. At a point of inflexion (3e—1)?=862*. Hliminating @ between this equation and (a) we have yea Or Or ET ea as the curve through the inflexions of the family. For a point where the tangent has 4-point contact we must have GUA yo de de aa 4 2187 2 and hence we have «=3; @=i93; hence we see that the curve (y) touches the member of the family for which G= aoe at the point G; ot) ; it also touches the branch yx*=—3 of the curve of the family for which 0=0, at the point (5 ; —27) (but elsewhere lies wholly above the branch), but touches no other member of the family at a finite point. Differentiating (y) we have = — (60-9242), T4 = it has therefore tangents parallel to y=0 where v=:271 and *,(8e—5) (3e—1) ; 1-229 (approximately), and inflexions at the points (5; —27) (2-3 9936). It passes through the points (—5; ‘290) (—4; °519) Pauls (2 527312) (—1; 13) Cl; 46000) (2; 25) (211; 0) (25; —68)(°38; —41:975) (333; —27) (4; —17°188) ieee Gos 3.0), Cl 3.1) (2; 1178) (17333 3 1-160) (1667 ; *994) (2 ; *312) (8; °457) (45 °285) (5; °194), and is shown (as far as possible) in fig. 1. — It is of degree 5, class 5, and deficiency zero; it has 3 doubie points and 3 cusps (coinciding in the multiple point at infinity) ; 3 bitangents (two of which are imaginary) ; and 3 inflexions (all real, one at infinity). It has a quadruple point at infinity at which the tangents coincide with «=O, and an inflexion at infinity at which the tangent is y=0. It meets the curves of the family (a) for which 6= 2 (+ V3—1)[°824 and —3 074 approx.] in the axis of a. Phil. Mag. 8. 6. Vol. 1. No. 5. May 1901. ym Oe 586 Mr. H. Hilton on van der Waals’ Equation.. The curves (8) and (y) only meet in 2 finite pein namely (1; 1) (5; —27). Their nent of ¢ that at the point whose abscissa is « are respectively 4a +36(1—2)? 53 oe {9 +4 (Ca?—9@ +2)212 6.x'(3a—A4) 4x*(3a—5)(382—-1) Tf ACE is astraight line parallel to y=0, such that for a certain value of 6 the areas ABC, EDC are equal (see fig. 3); then the ordinate of A (or E) represents the pressure Fig. 3. at which the substance boils for that particular value of @. The curve through all such points as A and E we will call the “ border” curve. (Cf Memoirs of Phys. Soc. London, vol. i. part 3, p. 453.) Let 2, x, «3 be the abscisse of A, E, and C respectively, and y their ordinate. Then 5) s 80 BLy—1 os (y + Bin ) (%#,—21)= 3 log else on: 7 ie Ge) [See Nernst’s ‘ Theoretical idee’ ] Now &j, %», 3; are the roots of 3ya? —(y+80)a2 4+.92x—3=0, 1 and therefore Uj2y + Hoy + Uli = — 5 Ly Lots = LO] BO *, eliminating #3, yx)°xo? +#,+ x#.—321%=0, and therefore 3a,—1+ VJ (82, —1)?—Ayx,? 2yx? f Ly = the positive sign being taken, for y is positive in the region considered, sat Lo > Ba. 2 9 (oe oe Substituting this value for x, and (yar ae z Lig Mr. H. Hilton on van der Waals’ Equation. 587 86 in (i.) we have (writing « for x,) (222y + 9u—38-3V1—6x 4 9x? —4y2*) (V1 —6et 9x2 —4yx3—14 3x —2ya*) : 3V1—62 + 9a*—4ya?—3 + 92 —2yx* = 4yx* (yz? + 3)(38x%—1) x log ( ee 5 ) (9) as the equation of the border curve between e=4and «=1. Similar reasoning shows that the equation of the border curve between e=1] and c= is found by changing the sign of the radical in (6). “To trace the curve (6) directly is not easy, but we can readily determine a number of points on it with fair accuracy when once a number of curves of the family (a) are carefully drawn. We have in fact to choose the points A, Ei (fig. 3) so that the areas ABC, EDC are equal, and this may be done by help of a planimeter ; or, more simply, by ensuring the equality of the number of millimetre squares in these two areas when the curves («) are plotted out on paper ruled in square millimetres. The curve (6) evidently passes through the points (1; 1) and (; 0) [as may be verified also from its equation]. The tangent at each point is parallel to the axis of «: this is evident in the case of the former point, we may prove it in the case of the latter, thus :—A tangent to (a) parallel to the axis: of « is ee — - where (80—1)=40u* ; if @ is small, « must be large cae 3v—140], and we have appr oximately 46z=9. Then the tangent becomes (sub- stituting 10 oe x, and neglecting higher powers of @ than the second) y = oe Hence the ordinate of the point on the border curve BR ics to this value of 6 is < ae, Now the curve (a) cuts y=0, where 9-9 ef He Me A 2 ibd ie Z (if @ is small), and makes an angle 1 tnt { =1)3 aoe : por tan—1 ae +2} or — when @ is small, with the axis of w; hence the abscissa 2 2Q2 588 Mr. H. Hilton on van der Waals’ Equation. of the point on (68) CEE to this value of @ is j tal hence the tangent to (6) i point (4; 0) makes an angle iis | + \o | | 0 bie Aloe 0 with the axis of & ; 7. e., it touches the axis of x at this point. The curve (6) is shown in iiejandlls The relation between the reduced temperature and volume at the boiling-point is found by eliminating y between (a) and (6) ; it 1s :— 3 a (160 +27)a®?—362 +9 Ha (27 —326@) 2° + 92? —-—30—-1 Ae Rip Il | sf SEE ns ( (27-160) ®@—3+3(30—1)4 / 0 (—32 A) + Ya a ae 3u—1L ( (3x —1)(160x?— 182 +6) between w=} and =1; and the same with the sign of the radical changed between v=1 and x=x When y is so large that the equation dyx? —(y +88)? +9x—3=0 has only one real root, this root is (cf. Works on Theory of Eee put 1. all + 31 vy 10) + 5 “(y+ 86) sg: tee =f eR 54 (y? — 20y0 — 867) + We +80)" sf as { 18y(y—49) + J (y+ 80) —2y a 729y + 54(y? —20y0— 80") + (y +80) } | If we assume that this expression, which is the real root of ® x when y is large, by the principle of continuity represents the smallest root of the equation when y becomes so small that the equation has three real roots, we obtain the relation be- On the Propagation of Cusped Waves. 589 tween the reduced pressure and temperature by substituting this expression for z in the equation (68). Tt should be noted that we have confined ourselves to a strictly mathematical treatment without taking physical con- siderations into account. The equation (@) can hardly be considered to have any physical application when @ is negative, and ceases to represent necessarily the relation between the volume, pressure, and temperature of a substance when «<4, for then doubly central impacts between the molecules become impossible (cf. Memoirs of Phys. Soc. of London, vol. i. part 3, page 384). Teferences in the Figures, Reference | nuonber... 1/2 3/4| 5 |6) 7 |8 9 10 Bea Talay ia | Geel | Tee) ton Ron Pe 04 5/6 6707 7-58 92 16 | 24 | 32 | 40 | 48 | 56 | G4 | 79 80 |-8 All the curves in fig. 2 (except 6) should run up to the asymptote a= 5; but, for the sake of clearness, they are dis- continued before they approach each other so closely as to be mutually indistinguishable. Figs. 1 and 2 are ruled into reference squares whose sides are half the unit of length. Note. Since I wrote the above I have heard from Mr. R. E. Baynes, M.A., Christchurch, Oxford, that he obtained an identical result for the equation of the border-curve many years ago. LVU. Onthe Propagation of Cusped Waves and their Relation to the Primary and Secondary Focal Lines. Bye Erol. R. W. Woop *. ia a previous paper (Phil. Mag. July 1900, p. 148) I have shown the forms of the wave-fronts reflected from spherical surfaces, by means of geometrical constructions, _ and photographs of the actual waves. In the present paper I shall discuss somewhat more fully the case of the reflexion of a plane wave by a hemispherical mirror, where we have a reflected wave of a form which I have likened to a voleanic cone. A superficial examination of the forms might lead one to imagine that the bowl of the crater collapsed to a point at the principal focus of the mirror. This can of course only be ~ Communicated by the Physical Society, 590 | Prof. R. W. Wood on the true in the case of a concave spherical wave, which is only given by a parabolic mirror. We shall find as a matter of fact, if we examine the geometrical construction, that the cusp of the wave, or the rim of the crater, which traces the caustic as I have shown, is continuously passing througha focus. In other words, the curvature of the crater increases as we go from the bottom to the rim, at which point the radius becomes zero. ‘The inner edge is then continually passing through a focus and appearing on the outside, building up, as it were, the sides of the cone. These wave-fronts were drawn by constructing the orthogonal surface, which was shown to be in section an epicycloid formed by rolling a circle whose diameter was equal to the radius of curvature of the mirror, around the outside of the mirror. The evolute of this curve is the caustic, itself an epicycloid, and the reflected wave-fronts form a family of parallel curves, which are the involutes of the caustic. Though the caustic and orthogonal surface (evolute and involute) are similar epicycloids, the reflected wave-fronts, or parallels to the orthogonal surface, are not epicycloids. It may be well to point out here an error that sometimes appears in text-books on Optics, namely, the assumption that the wave- front (say in the case of a spherical wave refracted at a plane surface) is an hyperboloid in the second medium, because the caustic is the evolute of an hyperboloid. An hyperboloid wave will not propagate itself as an hyperboloid, nor an ellipsoidal wave as an ellipsoid (except in an anisotropic medium), the parallels to a conic being in general curves of the eighth degree. In the case above cited, we should speak of the wave-ironts after refraction as the parallels to an hyperboloid. Fie. 1, oe] Wave Front Let us suppose the wave to be just entering the mirror. The form of the portion which has already suffered reflexion is a cusp extending around the upper edge of the hemisphere Propagation of Cusped Waves. 591 (fig. 1). The upper branch of the cusp is concave upward, and is the portion of the wave which left the redecting surface first and has passed through a focus. The lower branch is concave downward, or in the direction of pro- pagation, and represents the portion of the wave which has just left the surface and is on the way to its focus. The radius of curvature increases from zero as we go away from the cusp-point along either branch, as I have said before. This cusped wave moves down the mirror, the lower branch being continually replenished by consecutive portions of the incident wave as it encounters the mirror, the upper branch being continually added to by elements of the lower branch as they pass through their foci at the cusp. As I have said in a previous paper, the cusp traces the caustic surface ; and since the wave is always coming to a focus on the cusp, the increased illumination along the caustic is accounted for. Let us now examine the relation of these reflected wave- fronts to the primary and secondary focal lines. If we inspect the diagram usually given to illustrate the formation of focal lines (Winkelmann, p. 33, for example), it is at once apparent that the wave-tront between the two focal lines is expanding along one meridian, and contracting along a meridian at right angles to it; in other words, the wave is convex along one meridian and concave along the other. The form of the surface is not unlike a small bit on the inside of an anchor- ring. be edor now the diagram shown in fig. 2, remembering that the complete wave-tront at this stage is formed by the rotation of this figure around the axis of the mirror. The bow! of the crater is concave along every meridian, but it is at once apparent that any portion of the outer slope has the required saddle-shape, being concave in horizontal planes and convex in'vertical planes. From this it is evident that the outer wall of the volcanic cone, before it crosses the axis of the mirror, always represents the portions of the wave-front between the primary and secondary focal lines. That this is true is evident, when we recollect that the first - focal line is formed by the intersection of rays on the caustic surface, or, regarded from the wave point of view, by the passage through their foci on the cusp of the wave of adjacent elements of the wave-front. The second focal line lies on the axis of the mirror ; consequently the wave-front between the lines is that portion of the surface which has passed through a focus on the cusp, but which has not crossed the axis. [ have found that a small glass model of the wave-front, 592 On the Propagation of Cusped Waves. shown in cross section in fig. 2, is extremely useful in making the whole matter clear. It can be made by drawing down a large thin tube, melting the end down flat, and then sucking it in a little. | oo . purr or Another useful piece of apparatus can be made by silvering the outside of a hemispherical glass evaporating-dish or half of a large round-bottomed flask. The concave mirror thus formed should be mounted on a stand, and a two-candle power ‘pea ” electric lamp arranged so that it can be moved along the axis of the mirror. In my second paper on the photography of sound-waves it was shown that a spherical > On Mixtures of Hydrochloric Acid and Methylether. 593 wave, starting in the principal focus of a hemispherical mirror, is reflected as a saucer-shaped wave, the curved sides of the saucer coming to a focus in a ring surrounding the nearly flat circular bottom. If we place the lamp in the focus of the mirror, and hold a sheet of ground-glass in front of it at the proper distance, we can show the luminous ring and the uni- formly illuminated circular area within it. JI£ we move the lamp to a point midway between the principal focus and the surface of the mirror, we get a ring of intense brilliancy, with but very little light within it. The wave-front constructions for this condition are shown in fig. 3, the distribution of energy being roughly shown by shading the reflected wave-fronts. While I have brought out nothing but what would be apparent to anyone on a very cursory examination of the constructions, some of the points may be of use to those engaged in teaching elementary optics. University of Wisconsin. ss LVI. Miatures of Hydrochloric Acid and Methylether. By J. P. KuENEN*, [ 1875 Friedel} discovered that methylether (B. P. —23°5 C.) and hydrochloric acid when brought together below zero produce a liquid which boils at 2° C.; this liquid was not a chemical compound in the usual sense: the pro- portion in which the two substances are present in the liquid was not always the same, and, moreover, did not correspond to a simple molecular composition (about 6 parts of ether against 5 parts of acid). At the same time the formation of liquid at temperatures far above the boiling-point of the ether and the strong contraction of the vapour-mixture above the boiling-point which he observed proved that the two substances display a strong mutual affinity. He therefore concluded that the molecules of the acid and the ether unite to form a dissociable molecular compound: these double molecules occur in the vapour—hence the abnormally high vapour-density—and especially in the liquid. Both phases are mixtures of double molecules and single molecules of the components. From Friedel’s observations it follows that mixtures of the * Communicated by the Author; being extracted from the Archives Néerlandaises des Sciences exactes et naturelles, + Compt. Rend. 1xxxi. p. 182. 594 Prof, J. P. Kuenen on Mixtures of substances in question have the comparatively rare peculiarity. ofa maximum in their boiling-points, and therefore a minimum in their vapour-pressures. The object of the investigation described in this paper was to trace this minimum up to the critical region and to obtain a complete pressure-temperature diagram for these mixtures. The theory of mixtures developed by van der Waals* makes it very probable that mixtures with a minimum vapour-pressure combine this with a maximum in the critical temperatures. They belong therefore to a type which so far has not been fully investigated. | It was of first importance during the investigation to keep in view the possibility of irreversible chemical action, as this would naturally entirely alter the character of the mixtures. Friedel had not observed chemical action, but this did not. give any warrant with regard to the behaviour of the mix- tures at higher temperatures. In the course of the work it was found that even below 100° C. a chemical action takes place which increases in rapidity as the temperature rises. The chief products of the - action are methylchloride and water. As the critical tem- peratures of the majority of the mixtures lie above 100° an important part of the research became impossible, and it appeared that the combination of methylether and hydrochloric acid is unsuitable for the purpose of exploring the complete . diagram for the type to which it belongs. At the same time there are so very few representatives ot this type which lend themselves to an investigation in the critical region, that one cannot afford to reject the combination altogether. It 1s pro- posed shortly to undertake the investigation of mixtures of acetone and chloroform. At first no chemical action had been noticed: it is possible that the action depends upon the presence of moisture or other impurities which happened to be present in smaller quantity in the first experiments than in the later ones. It is more probable, however, that the difference is due to the first mixtures containing little acid, the later mixtures gradually more and more. The velocity of the chemical action must have been correspondingly smaller, and the results above 100° obtained with these mixtures need not therefore be com- pletely rejected, although no great value must be attached to the actual numbers. It is possible that the existence of chemical action at high temperatures may give rise to some doubts as to whether the phenomena observed by * Kuenen, Phil. Mag. xliv. p. 199. Hydrochloric Acid and Methylether. 595 Friedel and myself far below 100° may be ascribed to pure mixing, or whether these too are influenced by the same forces. I believe these doubts to be unfounded. Whatever we may think the molecular condition of the mixtures to be— whether we assume the formation of double molecules or not— the essential difference between the progressive chemical reaction which gradually changes the condition and the character of the mixtures on the one side, and the forces which bring about the immediate equilibrium on the other, cannot be denied. An equally distinct contrast exists between formation of liquid in a single substance, even with association of molecules, and irreversible polymerization. At the same time it is possible that there may be some connexion between the strong affinity at low and the action at high temperatures. The chief results arrived at are the following :— 1°. The mixtures have a minimum vapour-pressure i accordance with what could be derived from Friedel’s experi- ments. This minimum exists up to the critical condition. 2°. Addition of hydrochloric acid raises the critical tem- perature of methylether. For the reasons explained above, the complete relation between critical temperature and pres- sure could not be obtained. The results are represented in the figure, page 596. The curves were completed in the part of the diagram where observations were impossible by hypothetical pieces. The general character of the diagram seems beyond doubt. It shows how the mixtures as expected combine a maximum critical temperature (at A) with the minimum vapour-pressure and in what manner the minimum curve meets the plaitpoint curve at 6. As was proved by van der Waals*, the two eurves touch each other at 4, and the plaitpoint curve is continuous at A. According to principles laid down by me before + the mixtures will have retrograde condensation of the first kind between C, and #, of the second kind between B and A, and of the first kind between A and C,. The diagram agrees generally with one obtained a priors for a mixture with minimum vapour-pressure by Hartman {. It bears to a high degree the internal evidence of correctness, and it can hardly be doubted will be confirmed when a different representative of the type without chemical action is examined. Another peculiarity of the figure worth noticing is the * Van der Waals, Kon. Ak. Amsterdam, Mei 25, 1895. + Kuenen, Communications, Leiden, no. xiii, 1894; Phil. Mag. xl. p. 189. ; { Hartman, Dissertatie, Leiden, 1899, Prof. J. P. Kuenén on Miztures of 596 SALI SOUL] i Hydrochloric Acid and Methylether. 597 broadness of some of the condensation loops of which the loop in the figure for a mixture of 7 per cent. ether to 93 per cent. acid shows a striking example. Near the minimum the loops are necessarily very narrow, and therefore also between Band C,: this is not the case with the mixtures between 6 and C,, at least not with those some distance away from B. For a mixture like the one in the figure the two critica! points P and & must be far apart from each other and from the critical point (not shown in the figure) which the mixture would have if it did not separate into two phases of different composition, but behaved like a single substance*. With. mixtures of maximum vapour-pressure and minimum critical temperature, such as ethane+ nitrous oxide, which were dis- covered some time ago, the loops between B and the critical point of ethane were “broader than the other s, but even there remained relatively narrow ; and it was natural then to suppose that this fact had greater generality than now appears to be the case. The shape of the plaitpoint curve and the great distance between 6 and C;, in this case might have suggested the probability of broader loops, even without the confirmation by experiment. It is unnecessary to indicate the shape and changes of the plait on the W-surface for mixtures of hydrochloric acid and methylether, as we can refer the reader to Hartman’s thesis quoted above. As regards the experiments themselves, I will only mention that the methylether was prepared from pure methylalcohol and sulphuric acid, and absorbed in sulphuric acid from which it was afterwards liberated by water. Il refrain from com- municating all the numerical data obtained, as no value can be attached to the results except qualitative value. Mr. W. G. Robson assisted me during the whole of the investigation. The “question what is the molecular condition of the mix- tures seems as yet hardly capable of satisfactory solution. The criteria which are applied for this purpose with regard to single substances fail with mixtures. It was lately pointed out by Kamerlingh Onnes + that the law of corresponding states cannot without further consideration be applied to mixtures; and van der Waals’s equation deviates too much from * Compare van der Waals, Kon. Ak. Amsterdam, 27th November, 1897, + Kamerlingh Onnes, Kon. dk. van Wet. 30 June, 1900. In this paper mixtures without mutual association are called “ deal ” mixtures: ‘‘normal ” mixtures seems more in accordance with the common use of the two words. 598 Geological Society : the truth for us to be able to use it as a test for the existence of double molecules. The formation of liquid above the boiling-point of methylether does not prove that association has taken place: a somewhat high value of the mutual attraction-constant aj, in van der Waals’s equation will give a minimum in the vapour-pressures, and the phenomenon may therefore occur with normal mixtures. The abnormal vapour- density naturally suggests the formation of double molecules in the vapour, and therefore a fortéort in the liquid (compare the case of acetic acid), but again we need a trustworthy criterion to decide between high attraction and association. However probable the association in Friedel’s mixtures may appear, one cannot decide between the two possibilities with the same sharpness as for single substances. University College, Dundee. LIX. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p, 520. ] November 7th, 1900.—J.J. H. Teall, Esq., M.A., F.R.S., President, in the Chair. HE following communications were read :— 1. ‘ Additional Notes on the Drifts of the Baltic Coast of Germany.’ By Prof. T. G. Bonney, D.Sc., LL.D., F.R.S., F.GS., and the Rev. E. Hill, M.A., F.G.S. The authors, prior to revisiting Riigen, examined sections of the Drift to the west of Warnemiinde, with a view of comparing it with that of the Cromer coast. Where the cliffs reach their greatest elevation, 2 or 3 miles from that town, they are com- posed of a stony clay, which occasionally becomes sandy. At intervals, however, sand interbanded with clay occurs, filling what appear to be small valleys in the Drift. A layer of grit and stones, occasionally associated with a boulder, occurs once or twice between these sands and clays. The valleys are excavated in the great mass of stony clay which extendsfor 4 or 5 miles to the west of Warneminde; and the synclinal slope of the layers and the contortion of the under- lying bedded sands indicate that the mass filling them has been let down as a whole, either by solution of the Chalk beneath the prift or by the melting of underlying ice. Of these two hypotheses the authors view the latter with the more favour, but it also has its difficulties. In Rigen, Arkona was visited ; here Chalk occurs, apparently as >. On Altered Rocks from Bastogne. 599 a sort of island in the Drift. At the well-known locality by the lighthouse it seems to overlie a drift, but on closer examination the latter appears more probably to have filled a cavity excavated in the Chalk: this apparent inlier of Drift probably being only a remnant of a much larger mass; therefore it is likely that this part of the coast nearly corresponds with a pre-Glacial chalk-cliff against which the Drift was deposited. In the Jasmund district the authors lay special arataeis on three points :—(1) The ‘inliers’ of Drift appear to occupy valleys excavated in the Chalk; (2) these valleys can be traced for some distance inland; (3) the steep walls of Chalk towards which the Drift dips sharply, and against which it ends abruptly (usually on the southern side), often trend gradually inland, as if the present coast-line had passed obliquely across an old valley. In one or two instances the Drift is slightly twisted up against this steep face of Chalk. The authors call attention to cases where the Drift clearly rests against old surfaces and cliffs of Chalk; and to one in particular, which was not visible in 1898, where (a) clay, (6) sand, and (c) clay occupy a shallow valley, and have assumed a synclinal form. The authors give reasons to show that neither solution of the Chalk, nor ice-thrust, nor folding, nor even faulting, can satisfactorily explain the peculiar relations of the Drift and Chalk in Riigen; and they can find no better explanation than that offered in their previous paper. 2. ‘On certain Altered Rocks from near Bastogne and their Relations to others in the District.’ By Catherine A. Raisin, D.Sc. Prof. Renard, from the petrographical study of specimens, and Prof. Gosselet, after description of the district and its stratigraphy, have attributed the changes in these rocks to mechanical dis- turbances. Dumont had previously described many examples and inclined to the view of contact-alteration, which was favoured by Von Lasaulx’s discovery of a granite in the Hohe Venn, and M. Dupont’s identification of chiastolite from Libramont. The present paper treats especially of the garnetiferous and hornblendic rocks, giving the full petrographical and field-details of a few examples. It points out that the effects of pressure are evident over the whole district, while mineral modifications re- sembling the results of slight contact-action are found in certain areas. In a few cases these modifications are more marked, and ‘sometimes increase as we approach veins composed of quartz, felspar, and mica, such as might be connected with a concealed granite. The peculiar. garnetiferous and hornblendic rocks, although occurring within the zone of alteration, are extremely limited; often forming patches or bands a few feet across, They differ, as described in the paper, from ordinary contact-altered rocks. The evidence, in the authoress’s opinion, is in favour of Prof. Bonney’s suggestion that they are due to some form of hot-spring action. 600 7 Geological Society. November 21st.—J. J. Teall, Esq., M.A., F.R.S., President, in the Chair. The following communication was read :— 1. ‘A Monchiquite from Mount Girnar,.Junagarh (Kathiawar),’ By John William Evans, D.Sc., LL.B., F.G.S. After a brief account of the rocks of the monchiquite-type, in which ferromagnesian silicates are embedded in an isotropic matrix with the chemical constitution of analcime, the author describes an example from Mount Girnar, where it is associated with a nepheline-syenite intrusive in a mica-augite-diorite. The most striking feature of this rock is the occurrence of colourless spheres uf various sizes up to about 1 mm. in diameter. The rest of the rock is mainly composed of a hornblende of the barkevikite-type ; a pale green augite is also present. Both the spherical spaces and the interstices between the ferromagnesian silicates are usually filled with an isotropic material which has the composition and most of the physical properties of analcime. This material does not, however, show the anomalous double-refraction which is characteristic of that mineral, nor has it any crystalline outlines, being simply an allotriomorphic glass-like groundmass. It contains a large number of acicular inclusions, most of which do not affect polarized light: they exhibit a parallel arrangement in one or more directions, and appear to indicate a high degree of symmetry. Cleavage-cracks with similar orientation may be occasionally observed. As it is clearly a crystalline body, its isotropic nature refers it to the cubic system, and its identity with analcime may be considered proved. It is evident that this mineral, growing outward from different centres, has formed the spherical spaces by pushing aside the previously crystallized minerals until they came into contact one with the other, and has afterwards crystallized in the interstices between them. The presence of a groundmass of analcime (or one having the same composition) in all the members of the widely distributed monchiquite-group of rocks implies the occurrence in different localities of a residuary magma of uniform composition, which remains liquid after the other constituents of the rock have crystallized out. Analcime must, therefore, represent an eutectic compound. If the cooling were sufficiently rapid the magma would consolidate as a glass, as may be the case with some monchiquites. On the other hand, where such a magma has separated and cooled slowly enough, a nepheline-syenite will be formed. | At some points the analcime in the spheres and in the interstices has become decomposed into alkali-felspars and nepheline, as in the pseudo-leucites of Dr. Hussak, so that in these places the rock might be described as a hornblende-tinguaite. In other parts much of the analcime has passed into cancrinite. The presence of a mineral of the eudialyte-eucolite group is also noticed. = * TUE LONDON, EDINBURGH, axp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. ee Rea s 2 e Q) [SIXTH SERIES.] SY ma Le ——_———— /1, JUN171901 §& i 4 JUNE 1901. \ ~E: # A 4 N =~ eG \O me a. 1K. ‘The Magnetic Properties of the Alloys ys se Aluminium.—Part If, By 8. W. Ricuarpson, D.Se., Principal and Professor of Physics at the Hartley College, Southampton, and Louis Lownps, B.Sc., 1851 Exhibition Research Scholar, University College, Nottingham*. [Plate VI.] CONTENTS. Page Sey SLETROOG EGHTIONS Lees oe Bie igi Cdk OA nn 601 § II. The Magnetic Measurements ...........000.000e 603 § IIL. The Measurement of Temperature ................ 606 Sele ele vElear imo Cineuiies aces oa clot o/s oe + 3,4 ole Lae «os 607 § V. Connexion between Hysteresis Loss and Temperature 603 § VI. Changes in the Magnetic Properties produced by repeated ea pines a eNO. 8,6! sR Os: 615 § VIL. Experiments near the Temperature of Minimum eee TMU Vi re cpa gaeh Syaithn cbscnsaraisy bs Ses Neda sade 620 § VIII. Connexion between Temperature of Minimum Per- meability and Percentage of Aluminium ........ 625 § 1X. The Microstructure of the Alloys .............00. 624 § I. Introduction. Ae account of a series of experiments performed by one of us on the magnetic properties of certain impure alloys of iron and aluminium is given in the Philosophical Magazine for January 1900. As the results obtained from these experi- ments were of a very interesting character, the authors * Communicated by the Physical Society: read June 8, 1900. Phil. Mag. 8. 6. Vol. 1. No. 6. June 1901. 2K 602 Prof. Richardson and Mr. Lownds on the Magnetic thought it desirable to undertake further experiments on the magnetic behaviour of these specimens. [ixperiments were accordingly made in the first Instance to ascertain in what way the hysteresis-loss, between given limits of the field strength, was connected with the temperature for the specimen containing 3°64 per cent. of aluminium. As will be seen later, these experiments show that the hysteresis-loss attains a maximum value at a temperature con- siderably higher than the temperature of maximum induction, An account is also given of some experiments on the changes produced in the magnetic properties of the alloy by heating to a high temperature and subsequently cooling. It is shown that the magnetic properties depend largely on the previous history of the specimen; successive curves connecting the maximum induction obtained for any given value of the field- strength and the temperature differing from one another to some extent when the heating has been carried to a high temperature. ‘This difference has been found to be greater for weak than for strong fields. There does not, however, appear to be any essential differ- ence between the behaviour of this alloy during heating and cooling (except near the temperature of minimum permea- bility, e. g. critical temperature). Similar results have been obtained for the specimen containing 5°44 per cent. of aluminium. For the speci- men containing 9°89 per cent. of aluminium, however, no change in the magnetic properties could be detected due to heating and cooling unless the heating was continued to about 670° C., which temperature is about 220° higher than the temperature of minimum permeability for this specimen (e.g. 450° C.). In addition an account Is given of some experiments on the abrupt change in the permeability that takes place at a temperature of 652°C. (vide p. 139, Phil. Mag. Jan. 1900). : The Ballistic method was used for determining the hysteresis- loss; and the Balance method (wide Part I.) for obtaining the smaller values of the induction when the specimen was near the temperature of minimum permeability. The specimen in the form of a ring was wrapped round with asbestos-paper. Next to this was twisted the ther- mometer-wire which consisted of platinum wire of ‘2 millim. diameter. This wire was connected to platinum leads of 5) millim. diameter. Compensating leads, cut from the same specimen of wire, passed out along with these between the primary and secondary winds. Properties of the Alloys of Cast-Iron and Aluminium. 603 The primary and secondary coils, which were of copper wire and insulated with asbestos-paper, came next, and externally a well-insulated platinum wire (diam. *5 millim.) was wound non-inductively round the ring. The specimen was heated electrically, this non-inductively wound platinum wire being used as a heating circuit. The specimen, with the surrounding coils, was packed in asbestos waste and placed in a sand-bath. Experiments were made at temperatures ranging from 15° C. to 800° C. The conclusions arrived at from these experiments are as follows :— (1) The hysteresis-loss at first diminishes as the temperature rises. It then increases and reaches a maximum value at about 550° C., which temperature is about 80° higher than the temperature of maximum induction. On further heating it falls off rapidly and becomes negligible at about 700° C. (2) The magnetic properties of the specimen depend largely on its previous history. (5) There is no essential difference between the behaviour of this specimen during heating and cooling* (except near the temperature of minimum permeability ). (4) An abrupt increase in the permeability takes place at 652° C. (during heating) followed by an equally abrupt diminution on further heating. (5) This abrupt change in the permeability is more marked with falling than with rising temperatures. (6) Continued heating and cooling diminish the permeability of this specimen (probably due to disintegration) *. (7) The curve connecting the temperature of minimum per- meability and the percentage of aluminium for the speci- mens investigated is a straight line. (8) The microscopic examination of the specimens shows the presence of crystals. § IL. The Magnetic Measurements. The first series of experiments was made with a view to ascertaluing in what way the hysteresis-loss between given limits of the field-strength was connected with the temperature of the specimen. The ballistic method of measuring the induction was made use of in this set of experiments. The experimental arrangement was roughly as follows :— * This statement does not hold for specimens containing only a small quantity of impurity, as will be shown in a subsequent communication. 2R2 604 Prof. Richardson and Mr. Lownds on the Magnetic The secondary of the ring was joined up in series with the secondary of a standard mutual inductance-coil and a D’Arsonval ballistic galvanometer. A known standardizing current was then sent through the primary of the mutual inductance-coil and the throw of a spot of light (reflected from the mirror of the galvanometer on to a transparent scale) on reversing the current was noted. Then if . M = the value in ¢.c.s. units of the standard mutual inductance ; ry = the value of the standardizing current ; d = the throw of the spot of light ; k = some constant ; we have My=hkd - 2"... The primary of the standard mutual inductance-coil was then disconnected, and a current was sent through the primary of the ring and an adjustable resistance. This current was then varied ‘ by steps,’ and the throw corresponding to any change éy in the current strength was noted. Then if | N = the number of turns in the secondary of the ring ; S = the mean sectional area of the ring ; 5B = the change in the induction in the ring correspond- ing to a change dy in the current strength ; d’ = the throw of the spot of light ; we have oB.8.N=kd or d : oB=h ex. Ma |) Combining (1) and (2) we obtain the equation = ila al ee ae CE The Primary Circuit. The ring was wound with a primary coil of 42 turns of copper wire insulated with asbestos-paper. ‘The primary was connected to the two mercury cups 1 & 2 of the rocker D (vide fig. 1). To the cups 3 & 4 of this rocker were connected the ter- minals of the primary of the mutual inductance-coil M. Properties of the Alloys of Cast-Iron and Aluminium. 605 This rocker enabled the battery B to be connected at will to either the primary of the ring R or the primary of the standard mutual inductance-coil M. E oe F The rocker D was directly connected to a variable resistance C and a reversing-key K. To K was connected a battery of five storage-cells B and a Weston’s voltmeter V, to the terminals of which was attached a resistance 7. The value of this resistance was one ohm, and hence the reading of the voltmeter in volts was numerically equal to the primary current in amperes. This resistance was composed of thick platinoid wire twisted spirally and suspended by threads in a box with perforated sides and cover to allow the free circulation of air round the wire. It was found by trial that the resistance of this coil was not appreciably changed by the passage of the greatest current used in the experiments. The adjustable resistance C consisted of a number of coils of platinoid wire attached to a brass frame. ‘The free ends of these coils were connected to a series of stops on the upper circle. Contact was made by means of a T-shaped brass arm revolving round the axis of the frame, and of such dimen- sions as to enable the resistance to be varied without breakiug the circuit. This arrangement of coils was found very con- venient for varying the current ‘ by steps.’ The Secondary Circuit. The secondary of the ring and the secondary of the mutual inductance-coil were connected permanently to one another on ae er = SS ie a SSS ee Sete Do ae SS ee 606 .Prof. Richardson and Mr. Lownds on the Magnetic throughout the experiments. This circuit could be connected when desired to the galvanometer terminals by means of the rocker Q. The galvanometer was a Crompton Midget D’Arsonval, and was suitable for ballistic or deflective zero work. This instrument consists of a circular coil suspended bifilarly between the poles of a permanent magnet. ‘The suspending fibres, which are of bronze, serve to carry the current. The valvanometer was very dead-beat and consequently the throws could be read with considerable ease. The secondary circuit was kept closed throughout a series of readings, and the throws were always taken in the same direction. The kind of accuracy obtainable with this instrument can be seen from the following observations. The primary of the standard mutual inductance-coil was connected to the battery, and three successive readings of the kick obtained on reversing the current in the primary were taken for currents of different strengths. The following set of readings were obtained :— Throws. Current in Throw Amperes. + current. 1 2 33 Mean 1°42 152 149 151 150°7 106-1 1:0 n4:5 113 115 114:2 106°2 0-782 83 83 82'5 82:8 105°9 0:27 28°5 29 28°5 28-7 106°3 It will be seen from this table that the instrument is suit- able for ballistic work. The value of the standard mutual inductance-coil was 533,626 o.a.s. units. Its value was obtained by Mr. C. G. Lamb by comparison with a standard coil kept in the Engineering Laboratory at Cambridge. § ITI. The Measurement of Temperature. The method used for measuring the resistance of the ther- mometer-wire was the same, in all essentials, as that described Properties of the Alloys of Cast-Iron and Aluminium. 607 in Part I. (Phil. Mag. Jan. 1900). The four arms of the bridge consisted of (1) The thermometer-wire and leads. (2) The compensating leads, a resistance 7, and a portion of the bridge-wire EH. (3) A resistance of 275 ohms. (4) A resistance of (275—p) ohms + portion of bridge- wire HE. (p being equal to the resistance of HF to within J, of an ohm. | When a balance is obtained, the resistance 7 of the ther- mometer-wire is given by T,=7,+ resistance of HH. The temperature was deduced from 7; by means of the formula — pee Gea, 7% me The values of 7,, 7100, and 6 for the given specimen of wire were determined from observations of its resistance in ice, steam, and the vapour of boiling sulphur. This specimen of wire was obtained from Johnson & Matthey, and was of the quality prepared by this firm for thermometer work. For this wire bl 7 and T1009 =?,(1+0°377). S1V. The Heating Circuit. The heating circuit consisted of a platinum wire, of dia- meter 0°5 mm., well insulated with asbestos-paper, and wound non-inductively round the ring outside the other coils. This wire was connected with an ammeter A (vide fig. 1), an adjustable resistance N of thick platinoid wire, and the terminals of the town mains (100 volts) P, L. By altering the value of the resistance N the heating current could be varied at will, and thus any required temperature (within the limits of the experiments) could be obtained. With this arrangement a current of 7 amperes raised the temperature of the ring above 800° C. The insulation resistance between the various coils was tested from time to time during the experiments. In no case (after the first heating) was it less than 1,000,000 ohms, and in genera! it probably was much greater than this, 608 Prof. Richardson and Mr. Lownds on the Magnetic 8 V. Connexion between Hysteresis Loss and Temperature. It had been observed in the earlier experiments that the curve connecting the maximum induction reached at each reversal and the temperature for a given value of the field- strength altered to some extent after the specimen had been heated to a high temperature. ‘This was also found to be the case with the specimen containing 5°44 per cent. of aluminium. In the case of the other two specimens investigated, how- ever (the one containing 9°89 and the other 18°47 per cent. of aluminium), this was not the case, unless the temperature reached was much higher than the temperature of minimum permeability. For the alloy containing 9°89 per cent. of aluminium the curve was quite constant under all conditions, unless the specimen was raised to a temperature of 670°C. (4. e. 220° above the temperature of minimum permeability), in which case a new curve of the same general shape as the original curve was obtained. The change in this case may be due to the specimen reaching the melting-point of aluminium. That conclusion, however, is not borne out by the experiments on other specimens, as in general a noticeable change takes place at a temperature considerably lower than this. In order to obtain comparable results, the loops were taken in the order of increasing temperature: the temperature on any day on which an experiment was made being higher than that reached in the preceding experiment. The experiments were conducted under the following conditions :— At about 10 a.m. the heating current necessary to produce the required temperature was started in the heating circuit. A steady temperature was, in general, reached at about 3 P.M. The specimen was kept at this temperature till about 5 P.m., to ensure a uniformity of temperature when a loop was taken. - ie specimen was then allowed to cool, and the process of e-heating was commenced on the following day *. ee some cases several loops were taken in one day. When this was so, the higher temperatures were obtained without first cooling the specimen to the temperature of the room. The standardising throw was taken before and after the observations for each hysteresis-loop. The loops obtained are shown on Plate VI. * This method is spoken of as the method of successive heatings. Properties of the Alloys of Cast-Iron and Aluminium. 609 Data. Temp. 24°C. || Temp.159°C. | Temp. 226°C. || Temp. 311°C. a. B. | 15k B. lal B. H. Be €.G.s. |lines per|| C.G.s. |linesper|) c.c.s. |lines per|| o.«.s. | lines per units. | sq. cm. ||- units. | sq.cm. || units. | sq. cm. |, units. | sq. cm. 8:20 3089 || 8:20 3108 | = 8:20 3147 8:20 3309 6°64 2956 || 6:64 2956 6°64 2994 6°64 3156 aol el: 26D 4°81 2727 asoill 2784 4-8] 2027 3°36 2575 || | 3°36 2517 || 3°36 2574 3°36 2736 2°18 W36o7 Ne | 218 2327 || 2°18 2546 2°18 2526 1-06 2155 1-06 2098 || 1:06 2098 || 1-06 2260 cae 2021 47 1964 |. ‘47 1983 || At 2107 0 1850 | 0 1793 || 0 1812 0 1936 — ‘47 1754 | — “47 1659 | — ‘47 1678 || — °47 1764 — 1:06 1487 | —1-06 1392 | —1-06 1374 || —1-06 1402 —218 648 | —2:18 362 | —2°18 133 || —2:18 | — 372 —3'35 | — 820; —336 | —1120 |) —33 —1363 || —3°36 | —1785 —481 | —1983 | —48: | —2117 | —481 | —2250 || —481 | —2507 —664 | —2708 | —6°6) | —2746 | —664 | —2822 | —6:64 | —3022 —820 | —3089 | —o20 | —3108 | —820 | —3147 || —820 | —3509 July 21. July 21. July 24. July 25. Temp. 361° C. Temp. 370°C. || ‘Temp. 381°C. || Temp. 392°C. H. B. H. B. |), ORL. B. H. B. 8:20 3318 8:20 3318 | 6°64 3185 6°64 3185 | 664 3080 || 6°64 2772 4°81 2994 4°81 2975 || 481 2889 481 2595 3°36 2784 3°36 2765 3°36 2698 || - “33 2418 218 25595 2°18 2498 218 2D) Mh Gal's 2241 1-06 2307 1 06 2288) ||) 1:06 2241 1:06 2005 “47 2155 “47 2136 | “Asif 2088 "47 1868 0) 1926 0 1983 | Q 1878 0 1691 — 47 1812 || — ‘47 1792 || — *47 1745 || — :47 1514 | —1:06 1392 || —1:06 1373 | —1:06 1306 || —1-06 1081 —2'18 | — 839 || —2:18 | — 972 || —2:18 | —1020 || —2:18 | — 983 —3°36 | —2040 || —3°36 | —2136 | —3°36 | —2069 | —336 | —1868 —481 | —2651 || —4°81 | —2689 | —481 | —2603 | —4:31 | — 2339 —664 | —3070 || —6-64 | —38070 | —6:64 | —29384 | —664 | —2693 —820 | —3318 || —8:20 | —3318 || —820 | —38213 || —820 | —2890 July 26. July 26. July 26. July 28. Insulation tested. R >10® ohms. 610 Prof. Richardson and Mr. Lownds on the Magnetic R=>16° ohms. Insulation tested. Insulation tested. R> 10° ohms. Data. Temp. 416° C. Temp. 449° C. Temp. 460° C. Temp. 502° C, ED, B | H. B. H. B. H. B. 8:20 2625 8:20 2487 8:20 2389 8:29 2239 6°64 2507 6°64 2398 6:64 2301 6°64 2181 4°81 2349 4°81 2257 4°81 Zein 4°81] 2027 © 3°36 DUN 3 36 2124 3°36 2053 3°36 1903 2:18 2074 | 218 1991 2:18 1929 2:18 ioe 1-06 1897 | 1:06 1832 1:06 1770 1:06 1673 ‘47 779 | ‘47 1726 “Ai 1681 “47 1602 6 1602 O 1584 0) 1487 0) 1478 — °47 eas | cal 1460 || — °47 WAYS | 047 1407 —1:06 1150 1:06 1106 || —1:06 1168 |} —1:06 1195 —2:18 | — 875 || —2-18 | —. 858 | —2918 |) — 584 eS eas a eee --3:36 | —1701 || —3:36 | —1637 || —3:36 | —1487 || —3°36 | —1519 | —4°81 | —2133 || —4-81 | —2044 || —4:81 | —1912 || —4:8F | —i779) —6'64 | —2448 || —6:64 | —2328 || —664 | —2212 || —6:64 | —2080 —820 | —2625 || —8:20 | —2487 || —8:20 | —2389 || —820 | —2239 July 28. Aug. 15. Aug. 18. Aug. 16. Insulation tested. Insulation tested. R>1C® ohms. R> 10° ohms. Temp. 569° C. Temp. 582° C. Temp. 602° C. Temp. 642° C. H. B. 180 B dale B H. 7B. 8:20 1690 8:20 1354 8:20 637 8:20 271 6:64 1620 6°64 1301 6:70 584 6°64 203 4°81 1513 4-81 1A) 4°93 LS 4°81 168 3°36 1425 3°36 1124 3°45 460 3°36 142 2°18 1319 2:18 1053 2°30 389 2:18 124 1:06 1230 1:06 965 ie 33 1:06 Q7 “47 Wee 47 912 DS 301 ‘47 80 ®) 1106 || 0) 841 || ) 283 0 62 aS lil TOSS wee 788 || — °d53 230 = 04 44 — 1:06 929 || —1:06 664 || —1:12 159 —1:06 9 SING 593 || —2:18 BO I OO) | = ils SDV —3°36 | — 27 || —3°36 SON) oa 4a =159 —3°36 | —115 —4:81 | — 929 || —4-81 | — 558 || —4°93 | —336 —4-81 | —150 —6:64 | —1460 ||.—6°64 | —1124 || —670 | —513 || —6°64 | —186 8:99 | 1690 | =820 | 1854 || —8:20 | =637) aits8-20n een Aug. 18. Aug. 24 Aug. 25 Aug. 30 Properties of the Alloys of Cast-Iron and Aluminium. 611 It has been stated that the Band T curves (H =a constant) change to some extent after the specimen has been raised to a high temperature. It was hence thought desirable to obtain a set of hysteresis-loops while the alloy cooled, to see whether there was any essential difference between its behaviour during the processes of heating and cooling. Fig. 2. ss! 26 Re eee eae eee _| eo ee areas Bees See | Ee LS ae: eae ae nee __ SERRE 242 ee eee Accordingly the specimen was heated to 800°C., and allowed to cool by stages down to the temperature of the room. Double reversal throws and loops were taken at intervals when the temperature was steady. his series of experiments lasted 26 hours, both the authors being present throughout the experiments. The curves of double reversals will be seen to be different from those obtained by successive heatings (wde fig. 3), though, as will be seen later, the curves obtained from con- secutive heatings and coolings approximate much more nearly to one another. | As a check on the results, the ring was unwound and then re-wound with cotton-covered copper wire soaked in melted paraffin, and again tested. The values obtained in the two cases were found to confirm one another. The loops obtained are shown on Plate VI. The hysteresis loss was calculated in each case and curves connecting the hysteresis loss and the temperature for the given limits of field-strength are shown as fig. 2. 612 Prof. Richardson and Mr. Lownds on the Magnetic Fig. 3. ABS Se ate ES Hie || | TASS co a SE Ee Data. 583° C.| 544°C. | 501°C. | 471°C. | 454°C. | 428°C. Properties of the Alloys of Cast-Iron and Aluminium. 613 Data. | 394° C. S88o Cai 370° CG, | 354°C.) 3002 C: | Baie Os Te | a aa SON Tene B. ‘Ee B. B. ie ibe 8:20 2690 2912 | 3151 3221 3195 3055 6°90 2602 2805 | 3045 3115 3089 2947 5°25 2460 2646 | 2886 2956 2929 2788 384 2301 2487 | 2727 2779 2752 2593 2°60 2142 2257 | 2515 2602 2598 2416 | 1:33 1929 2062 | 2320 2372 2328 2186 ‘D9 1788 1938 | 2178 2213 2186 2044 a0) 1646 1798 | 1965 2018 2009 1850 — o9 1434 1620 | 1805 1859 1832 1708 —1°33 1062 1230 | 1381 1451 1445 1389 —2-60 — 796 | — 805 |— 885 |— 796 |— 646 |— 443 —3°84 | —1752 | —1920 |—2106 |—2071 |—2009 |—1d584 —525 | —2212 | —2416 |-2637 |—-2655 |—2628 |—2345 —6-90 | —2496 | —2735 |-2974 |—3027 |—3000 |—2805 =e) |) 2690 | 9919 |=3151 |= 3221 13195 |—3053 | 151° C 1 151° C. 21° C. 21° ©, H | B H B. H B isl B 820 | 2982 || — -59 1602 820 | 2951 || — -59 1582 690 | 2876 -|| —1:33 1301 6-78 | 2840 || —1-30 1304 5:25 | 2717 || —2:°60 168 5-13 | 2674 || —2-54 379 384 | 2540 || —3:84 | —1319 3-78 | 2489 || —3-78 | —1008 2-60 | 2363 || —5:25 | —2186 254 | 2286 || —5:13 | —2026 1:33 | 2115 || —6-90 | —2700 1:30 | 2064 || —6-78 | —2636 59 | 1956 || —820 | —2982 59 | 1916 || —8:20 | —2951 0 1832 0 1804 The observations obtained from the experiments with rising temperatures are indicated thus x, and those obtained from the experiments with falling temperatures (-). _ It will be seen that the curves develop maxima at the tem- peratures 570° and 530° C. respectively. If these curves be compared with the corresponding double reversal curves fig. 3, it will be seen that the hysteresis loss falls off as the induction increases, reaches a minimum value at a temperature about 100° higher than the temperature of maximum induction, and attains a second maximum when the induction has about half its maximum value. 614 The relation between the Coercive Force and the Tem- perature is shown on Pl. VI., and was obtained from the Prof. Richardson and Mr. Lownds on the Magnetic Variation of Hysteresis Loss with Temperature. Limits of Field-strength + 8-2 and —8-2. Experiments with rising Temperatures. Experiments with falling Temperatures. in degrees cent. 24 159 226 311 361 370 J8l 392 416 441 449 460 502 O27 569 582 587 602 642 Temperature} Hysteresis Loss in ergs per C.c. 2132 2019 1989 1733 1550 1526 1447 1272 1240 1161 1177 1240 1224 1178 1399 1178 1082 do4 D7 Temperature in degrees cent. Hysteresis Loss in ergs per Cie: 2092 2035 1940 1892 1892 1795 1700 1502 1478 1383 1520 1335 1400 1368 588 iollowing readings .— With rising Temperatures. Data. With falling Temperatures. Temperature. Coercive Force. : | | | | 24° C, 159 226 dll 361 370 381 392 416 441 449 460 502 527 569 582 587 602 SS CCS CEH GS es ga ie ee ee LL WAL WNOMINMMAGNIRMOW AA Temperature. 31° ©, | 151 234 284 330 304 370 388 394 428 454 471 501 544 583 Coercive Force. Wiley tyrwhywnytyw HC Or ed> bo CO DS Rt Co CEE Properties of the Alloys of Cast-Iron and Aluminium. 615 § VI. Experiments on the Changes in the B and T curves due to successive Heatings and Coolings. The magnetic properties of the specimen change to some extent after heating to a high temperature. The difference between two successive B and T curves (H=a constant) is much smaller for strong than for weak fields. In all the cases tried the characteristic form of the curve was maintained. ‘The nature of this change can be seen from a consideration of the curves shown on fig. 3. The curves A and B were obtained from double reversal throws taken simultaneously with the hysteresis loops for rising temperatures. They were plotted from readings which are indicated on the diagram thus x In the figures T stands for the temperature in degrees centigrade, B for the maximum induction reached at each reversal, and H for the field-strength in c.G.s. units. H=8:2 c.c.s. units. | H=3-8 c.e.s. units. uh B iT B 24 Ola 24 1364 159 aloe 146 1468 226 3223 Nay/ 1487 alt boot 165 oso 361 3376 204 1621 370 3376 228 1697 381 38261 307 1955 392 2939 312 2021 416 2644 370 229 449 2584 382 2741 502 2381 392 2035 527 2195 415 1858 569 1708 500 MS) 582 1389 970 442 587 1257 594 248 602 628 640 106 642 Dol The specimen was then heated to 800° C., and. double reversal throws were taken for fields of 8:2 and 3°48 units during cooling. The values obtained are indicated thus x in fig. 3. It will be seen that the magnetic properties have changed considerably owing to the repeated heatings and coolings. 616 Prof. Richardson and Mr. Lownds on the Magnetic = 3"2, H=3-48. He B. Ae B 696 168 696 106 638 274 638 112 582 1027 58) 292 O64 1567 o+4 637 541 1910 500 1123 900 2195 477 1291 474. 2319 450 1397 452 2380 428 1451 428 2425 408 1520 408 2495 394 1647 Bt 2780 383 1813 386 3035 369 1990 309 3269 360 1990 360 3320 oo4 1990 oot 3320 326 1902 330 3328 293 1795 291 3293 235 1505 235 3185 152 1274 152 3062 20 1045 20 3015 The specimen was next slowly heated to 434° C. and then slowly cooled, double-revesal throws being taken at intervals; the readings (not given) were found to lie on the last curve obtained. The specimen was then unwound and rewound with cotton- covered copper wire soaked in melted parattin, and double- reversal throws were taken at ordinary temperatures. The values obtained confirmed the preceding observations. The ring was now wound with asbestos-insulated copper wire, the number of turns in the primary and secondary being the same as in the previous experiments with asbestos insulation. The specimen was then heated by stages to 720° C. and cooled, double reversals being taken at each stage when the temperature was steady. This experiment lasted 36 hours. These values are indicated on the diagram thus :— (-) for observations during heating, | 5 ‘ : a for observations during cooling. Properties of the Alloys of Cast-Iron and Aluminium. Observations during heating, indicated on fig. 3 thus, (-). 617 1a l=tep) H=3°48. iP: B. i B. 16°5 2988 165 1054 114 3015 ayy 1175 186 3117 184 1369 251 3200 254 1516 280 3302 280) 1720 307 3398 309 1877 334 3367 332 1942 360 331 362 1998 377 2951 378 1797 387 2664 389 1583 398 2554 398 1517 436 2405 44] 1452 487 2220 481 1249 55d 1683 559 416 660 268 657 139 669 250 67 148 684 166 683 Th 700 65 703 37 71 37 711 is) 7] - : a ae: ! ‘ Observations during cooling indicated thus —;—on fig. 3. He=82 | H=3-48 | a B. ith B. 688 igi 683 102 630 240 630 129 628 222 628 120 614 250 614 129 593 407 590 194 577 758 578 240 560 1406 560 361 528 1952 427 740 500 2201 502 1045 444 2442 444 1443 401 2034 402 1489 o9t 2553 dot 1535 385 2682 387 1554 | 376 3062 376 1813 360 3311 360 1970 309 3340 298 1767 298 3067 | The curves obtained from these last two sets of readings approximate closely to one another throughout the oreater Phil. Mag. 8. 6. ‘Vol. 1. No. 6. June 1901. 28 618 Prof. Richardson Gn We Lownds on the Magnetic part of their length. The authors have been ied to the con- clusion thai the heating- and cooling-curves for this alloy are coincident only when the highest temperature reached in the experiments is considerably less than the temperature of minimum permeability. When the temperature approaches this value the magnetic properties of the specimen change, and a new curve connecting the induction and temperature is obtained. 3 Table of Values of H and B at Atmospheric Temperatures. ih. ie. f ane : = From Observations in From Observations in 1897. March 1900. Jah B. H. B. 0-94 216 0-6 93 1°55 469 1-04 208 2°20 675 eres aie) 3°45 1674 2°88 853 4-40 2200 4-03 1435 5°39 2614 5°76 2187 6:59 2990 6-91 2540 7:82 3294 8°63 2980 8:99 3540 W530), 3480 940 3630 12°65 3620 11-49 3906 14°38 3835 13°19 4180 Wey 7 4125 14°87 4394 20:93 4415 18°36 4720 23°85 4620 27°20 5310 26°72 4785 32°70 5680 £9°60 49795 33:00 5670 32°47 5145. In the accompanying table is given a series of values of the induction and field strength at ordinary temperatures, ob- tained (i.) in the summer of 1897, and (ii.) in March 1900. The two curves connecting them are shown as I and II on fig. 4. It will be seen from these curves that the effect of repeated heating and cooling is to diminish the permeability of the specimen. Let us seek for an explanation of this unexpected result. It is known that impure specimens of iron containing large amounts of aluminium disintegrate in course of time. It is hence not unlikely that the same process is at work in spe- cimens containing less aluminium, though in a less: marked degree. The microscopic examination of the specimens shows the presence of crystals. Properties of the Alloys of Cast-Iron and Aluminum. 619 The coefficients of expansion of these crystals are probably different from the coefficient of expansion of the surrounding matrix; and since solidification takes place at a high tempe- rature, the material of the specimens would, ab ordinary temperatures, be in a strained condition. Fig. 4 ee ee es | 10 20 30 The effect of repeated heating and cooling would gradually produce disintegration. Let us assume that the change in the magnetic condition due to this breaking down of the material of the specimen Is, to a first approximation, equivalent to the introduction of an air-gap in the magnetic circuit. If this were the case, the actual magnetic force in the spe- cimen would be les s than that due to the magnetizing-current alone. Let us assume that, after a certain number of heatings, the only change going on is due to disintegration, and that the actual force in the specimen can be represented apprexi- mately by the expr ession (H—KB) (as would be the case with a split ring), where H= the magnetic force due to the spiral alone, and K is some constant depending upon the number and size of the gaps in the specimen (due to disinte- gration). If then H,, H, be the values of H on the two curves I and [I (fig 4) corresponding to a given value of 5, we should, on the above assumption, have the relation ic? — K,B= H,—K,P, Z5 2 620 Prof. Richardson and Mr. Lownds on the Magnetic where K,, K, are the two values of K for the two curves con- sidered, or a =(K,—K,)=constant. Hence, on the above assumption, the curve connecting (H,—H,) and B should be a straight line. This curve is shown as III on fig. 4. | It will be seen that this curve differs considerably from a straight line. It is interesting, however, to compare these curves with some obtained by Mr. ©. G. Lamb (Phil. Mag. Sept. 1899). Mr. Lamb experimented on a piece of iron first in the form of a bar, and secondly in the form of a ring. The B and H curves for the ring and bar are shown in Mr. Lamb’s paper on fig. V. as R and P respectively. If now H,, H, are the field-strengths corresponding to a eee given value of B for these two curves, then —1,— should B theoretically be a constant, and the curve connecting (H,— H,) and B should be a straight line. : If, however, a curve connecting (H,—H,) and B be plotted from ine two sets of obser one in question, it will be found to differ from a straight line, and to be very similar in general form to curve III above. Hence it is concluded that the assumption made to explain the change in the per- meability of the alloy due to repeated heating and cooling is probably much nearer the truth than the form of curve TL would at first sight seem to indicate. § VIL. Experiments near the Temperature of Minimum Permeability. A third set of experiments were undertaken to trace the changes in the induction (with a constant field) with change of temperature in the neighbourhood of the aa ae “of minimum permeability. As mentioned in Part J., an abrupt change in the per- “meability is observed at a temperature somewhat less than this. This abrupt change was more marked during cooling than during heating. It attained its maximum value at a tempe- rature of 652° C. with rising temperatures, and at a tempera- ture of 645° C. with falling temperatures. This small difference of 7° C. might be due to the tempe- rature of the ring lagging behind the temperature of the Properties of the Alloys of Cast-Iron and Aluminium. 621 thermometer. As, however, the heating and cooling were conducted very slowly, the authors believe it to be a true temperature hysteresis effect. The balance method (described in Part I.) was used in these experiments. This method, which is inapplicable when the permeability is large (except in the case of laminated rings), enables small permeabilities to be determined with ease and accuracy. The curves obtained are shown on fig. 5 and were plotted from the tollowing readings. First Series : with rising Temperatures. H=82 H=3-48 | T B. T B 584 496 DAT 360 601 294 580 197 606 262 594 152 619 227 600 136 636 227 604 122 644 258 614 112 | 650 319 619 1U8 | 653 324 626 112 654 303 630 115 656 275 635 116 663 222 63 120 683 Q7 638 123 697 48 640 130 643 134 | 644 136 646 147 | 648 165 649 i174 650 179 ADD 172 657 162 | 660 148 | 665 131 | | 683 dd | 703 16-9 708 13-0 | 722 7:3 73d Feat | | TAL 6-4 622 Prof. Richardson and Mr. Lownds on the Magnetic Second Series: with falling Temperatures. how, H=3-48 Alt B. T B 721 19-1 741 6-4 719 19:7 728 7-4 700 380 702 16°6 671 168 691 32°8 666 218 675 80°5 655 314 667 127°5 652 362 656 187 630 383 655 195 649 411 653 203 648 427 652°5 2t1 647 439 645 iP, 644 At2 644 250) 641 044 643°5 236 635 270 643 220 614 242, 642 205 609 943 639 164 617 129 610 131 597 148 O73 230 Noy7 y 274 550 308 Fig. 5 Properties of the Alloys of Cast-Iron and Aluminium. 623 § VIII. The Relation between the Temperature of Minimum Permeability and the Percentage of Aluminium in_ the Specimens. It is not possible to say, with any degree of precision, at what temperature the permeability of a specimen attains its minimum value, as the change of permeability with tempe- rature is very gradual in the neighbourhood of the temperature of minimum permeability. It also appears to depend to some extent on the strength of the field considered, being higher for strong than for weak fields. For the specimens so far investigated the following approxi- mate values of the temperature of minimum permeability have been obtained. Temperature of r cent. of Aluminium. has ee ~ ot Minimum Permeability. 3°64 790° C. 544 650 9°89 450 18-47 29 A curve connecting these values is shown as fi This curve will be seen to be a straight line. Fig. 6. POS lene Besenseeeel OL NE Bom cdl lot ot She boss a aaa Se Per cent. of Aluminium. Temperature of Minimum Permeability. 624 Prof. R. W. Wood on Cyanine Prisms and a § IX. Lhe Microstructure of the Alloys. It has been suggested in Part I. that the general behaviour of the alloys might be explained on the assumption that they consisted of crystals surrounded by a solidified mother-liquid. With a view to ascertaining if this was the case the spe- cimens, after grinding and polishing, were etched with dilute nitric acid and examined microscopically. ‘The eyepiece of the microscope was then removed, and the adjustment was altered until the image fell on the screen of a camera. When as clear an image as possible was obtained on the screen, a slow plate was exposed for about 15 minutes. In this way photographs (Pl. VI.) were obtained showing the forms of the crystals in the specimens containing 9°44, 9°89, and 18°47 per cent. of aluminium respectively. Photograph A. (Specimen containing 5:44 per cent. of Al.) Crystals can be seen in the form of Maltese crosses. Photograph B. (Specimen containing 9°89 per cent. of Al.) In places crystals having the appearance of a number of rods placed side by side can be seen. Generally the rows are arranged in pairs, the distribution being not unbke that of the bones of a herring. | Photograph C. (Specimen containing 16:47 per cent. of Al.) The crystals are similar to those shown in photo- graph B; but are larger in size. The magnification of A and C is about 25 diameters. The magnification of B is about 50 diameters. An investigation on the magnetic properties of pure alloys of iron and aluminium is now in progress, and we hope very shortly to publish an account of some of the earlier experiments cn these purer specimens*, University College, Nottingham, June 7th, 1900. LXI. On Cyanine Prisms and a New Method of exhibiting Anomalous Dispersion. By R. W. Woop ft. HAVE already described a inethod of making prisms of solid cyanine by pressing the fused dye between plates of glass, which are far superior to liquid prisms or the solid prisms made by Wernicke for the purpose of exhibiting anomalous dispersion. Until quite recently I considered that twenty or thirty minutes was about as large an angle as could be used to advantage. With such large angles very little green light * Vide Phil, Mag. March 1901. + Communicated by the Physical Society: read Feb. 22, 1901, New Method of exhibiting Anomalous Dispersion. 625 gets through the prism, and on viewing a source of light through the refracting edge we see merely a red and a blue image, the former being deviated more than the latter. With a new supply of the dye which we have just received Ihave, however, been able to make prisms of over one degree, which transmit an abundance of green light. Viewing the incandescent loop of an electric lamp through one of these prisms, we see a most beautiful anomalous spectrum—a broad band of light with the colours arranged in the order green, blue, violet, red, and orange. When it is remembered that the largest angle which Pfliger was able to obtain by Wernicke’s method was of but two minutes, the advantage of the fusion-method is apparent. While engaged in some experiments on the dispersion of selenium, from which most beautiful prisms can be made by the same method, I was led to try the experiment of crossing one of these prisms with a small diffraction-grating. Selenium has an extraordinarily high refractive index, over 3 for certain colours, and the prisms are quite transparent for the red and orange. The deviation produced by one of these prisms is about double the angle of the prism, and I was led to try the experiment of crossing one of them with a diffraction-grating. On viewing an arc-lamp through the combination, the dif- fraction-spectra were most distinctly seen ou each side of the central image, each one with its tail nicely curled up at the edge of the absorption-band, which begins in the yellow and stretches to the extreme ultra-violet. Having such excellent cyanine prisms at my disposal, it occurred to me to try crossing one of these with a diffraction-grating, for the purpose of showing the dispersion- eurve. I have usually used a spectrometer and low-dispersion prism for this purpose. The grating mounted with the cyanine prism was found to be equally efficient. One has only to view an arc-light through the combination. The diffraction-spectra are deviated by the prism, the red ends being turned up, while the blue-green ends are turned down in a most beautiful manner. I used a photographic copy of a 2000-line-to-the- inch grating, about 5 mm. square, fastened over the refracting edge with sealing-wax. The curved spectra can also be seen when the sun is viewed through the combination, though less perfectly, owing to its size. In conclusion, some hints regarding the construction of cyanine prisms may be of use to any wishing to repeat the experiment. The cyanine was obtained from Gribler of Leipzig, and is 626 On Cyanine Prisms and Anomalous Dispersion. in the form of lumps cf quite minute crystals. The old sample had a different appearance, consisting of long needle-shaped crystals not caked together. A certain amount of dexterity is required to make good prisms, which can only be acquired by practice. Small rectangular pieces of thin German plate glass are prepared (measuring about 2 x 3cm.),and a thin strip cut from a visiting-card glued along the short side of one. A piece of cyanine about the size of a coarse shot is placed near the opposite side, and the edge of the plate heated over a small flame until the dye fuses, holding another cover-strip in the flame at the same time, in order to have both at about the same temperature. ‘The hot edge of the cover is now to be brought down into the cyanine, and the plate gently lowered until the edge rests on the strip of card. The plates must be at once placed under pressure in a small clamp, where they are to remain until cold. I find that the flat-jawed metal clamp of one of Gaertner’s laboratory supports gives the best results. The pressure is to be applied close to the refracting edge of the prism only, as shown in the figure. This is very important. Hxperience is the only guide to the degree of pressure required. With the new sample of cyanine the removal of one of the glass plates, when this is desired, is much GY ZA) j easier than with the old. For most purposes, however, I prefer to leave the cover on, cementing the two plates together with sealing-wax. , It will be found that there is a very narrow strip of clear glass at the refracting edge, where the glass plates have come into optical contact. This produces a diffraction-band super- posed on the anomalous spectrum, but it is so faint that it 1s not troublesome. it is usually necessary to turn the prism slightly to get the green part of the spectrum ; that is, the incidence should not be normal. (Hxamples exhibited.) The cyanine prism should be held with the label-side towards the eye, and an incandescent lamp or gas-flame turned edgewise viewed through the slit. The refracting edge (which is to the left) should be turned away from the eye a little, though the eye must be brought close up to the aperture. The same thing On a Mica Echelon Grating. 627 applies when using the prism in connexion with the spectro- meter. ‘To see the dispersion curve by means of the grating and prism, one has only to view a naked arc-lamp through the y small rectangular aperture. | University of Wisconsin. SSS \, LXIL A Mica itieten Graeng. ie peer R. awe Woon. AVING experienced some difficulty, when discussing Michelson’s remarkable retardation-grating, in making students understand how it is possible for the sodium lines to be separated by a distance fifteen or twenty times as great as the distance between the spectra, it struck me that an echelon, built up of very thin films instead of thick plates, coming midway between the ordinary grating and the echelon as commonly constructed, would be useful in demonstrating the theory. Such a grating I have made of mica. By it lines, which with an ordinary grating of the same number of grooves would appear single, can be resolved and still not be farther apart than the spectra. It shows spectra of the same general appearance as in the more powerful instruments, can be set for single and double order, and though useless as a tool for research, is almost as satisfactory for purposes of demonstration as the costly batteries of thick plates. A number of thin sheets of mica were examined with the interferometer, and one selected over a considerable portion of which the fringes appeared straight and unbroken. This area was roughly outlined with a ‘pin-scratch, and cut up inte a dozen small rectangles with a print-trimmer. The retardation of one of cnese = was measured with the interfero- meter, and found to be fifty wave-lengths for sodium-light. Lhe grating would therefore yield spectra of about the 50th order : I say “about,” for the order varies with the wave- length of the light aul the inclination of the grating. A * Communicated by the Physical Society: read February 8, 1901. ee De 628 Prof. R. W. Wood on a grating-space of 0°5 mm. was determined upon, and astrip of glass was accordingly ruled with this spacing on a dividing- engine. Qn this scale the echelon was built up, the plates being put in position under the microscope, and cemented at the edges by means of small bits of sealing-wax and a hot wire. Considerable difficulty was found in attaching each plate without disturbing the spacing of the others. The first two or three gratings that were made were not very satisfactory; but some experience having been obtained by practice, an excellent one was finally obtained. Only nine plates were used owing to the opacity of the mica in thicker layers. The battery was mounted on a square of cardboard over a rect- angular opening of the same size, a clear space 05 mm. wide being left to serve as the first grating-line of zero retardation. The whole number of lines was therefore ten. The resolving-power, represented by the product of the number of lines and the order of the spectrum, would accord- ingly be about 500. Obviously the sodium lines,*requiring a product of at least 1000 for resolution, were beyond the power of the instrument; but the two yellow mercury lines, sepa- rated by 2°5 times the distance between the Na lines and requiring a product of only 280, seemed suitable. The hight from an ‘‘ end-on” mercury-tube, after passing through a collimating-lens and prism, was focussed on the. collimator of a spectrometer, the green (monochromatic) image of the tube being brought on the slit. On placing the echelon on the table of the instrument the spectra showed clear and sharp, and by turning the grating a little could be brought into either single or double position (see Lord Blythswood and Dr. Marchant’s paper, Phil. Mag. Apr. 1900). Faint secondary maxima appeared between the principal maxima, owing to the small number of grating elements. By slightly shifting the position of the lens, the yellow light from the tube was now focussed on the slit, when the principal maxima immediately doubled in a most beautiful manner and the faint secondary maxima disappeared owing to overlapping. The distance between the components was about one third of the distance between the spectra. For the sake of comparison, a grating of the same spacing and number of lines was ruled on a piece of smoked glass. (‘T'o prevent the film from tearing it should be first wetted with alcohol and dried.) The slit was illuminated with white light, and a cyanine film placed before it. This cut off all but the extreme red and blue; and it was found that in the first order the grating was unable to separate the extrerne red and blue of the Mica Echelon Grating. 629 spectrum, while the echelon easily resolved the Hg lines, showing the effect of the introduction of retardation. The constants of the grating were as follows :— ¢ the Thickness of plates 0°05 mm. Width of space 0°5 mm. Retardation of each plate, 50 waves. Calculating the separation of the Hg lines by Michelson’s formula, we have oe = - . ot where & =0°'05 mm. | teen. > = 280, bes =. a Si ar or the distance between the Hg lines is 3 of the distance between the snectra. It will be found instructive to illuminate the slit-plate of the spectrometer with a focussed continuous spectrum, and observe the way the different orders of echelon spectra file by when the continuous spectrum is moved across the slit, showing the dependence of order on wave-length. If the slit be illuminated with white light and a continuous spectrum be formed in the telescope by means of a prism, this spectrum will be found to be crossed by heavy dark bands when the echelon is placed in front of the prism. ‘The explanation of these bands makes a good problem for advanced students. A clew may be found by repeating the experiment with the slit-plate illuminated with the continuous spectrum instead of white light, and moving this spectrum very slowly. It may be of interest to some to know that the Zeeman effect can be shown with an echelon made of four interfero- meter-plates, the light being the green rays from a mercury- tube. Physical Laboratory of the Uuiversity of Wisconsin, Madison. Ei s68000 7 LXIIL. Conductivity produced in Hydrogen and Carbonic Acid Gas by the Motion of Negatively Charged Ions. By JOHN S. Townsend, M.A., Wykeham Professor of Physics, Ouford, and P. J. Kirxpy, I.A., Fellow of New College, Oxford *. 1 | wae experiments described in this paper are a con- tinuation of those which have been published in ‘Nature,’ 9th August, 1900, p. 840, and in the ‘ Philosophical Magazine,’ February 1901, p. 198. These papers contain an account of experiments which were made at the Cavendish Laboratory, about a year ago, on the conductivity produced in air at low pressures. The current between two parallel plates was found to depend upon the distance between the plates, the pressure, and the electric force in a manner quite different from the current at high pressures. The conduc- tivity was obtained by allowing Réntgen rays to pass through the gas; and it was found that the accompanying phenomena could be explained by supposing that the negative ions produced by the action of the rays generated others by collisions with neutral molecules, the new negative ions thus generated having the same properties as those produced by the rays. The proof of this theory rested, in the first place, on the connexion between the current and electric force for various distances between the plates. The number of ions, a, gener- ated by a single ion in going through a distance of one centimetre was found from the experiments. The values of a thus found experimentally depended on the pressure, p, of the air and the electric force, X, acting between the plates. The relation connecting the three variables a, p, and X was found to be of the form “=7f(—)s which shows that a is proportional to p when ~~ is constant. Further evidence in support of the theory was thus ob- tained, since from the kinetic theory of gases it 1s easy to show that a, p, and X should be connected in the above manner, The application of this theory led to the conclusion that an ion makes 21 collisions with molecules in going through one centimetre of air at one millimetre pressure. When the force acting on the ion is sufficiently great, two new ions (one positive and one negative) are produced at each collision. For smaller forces new ions are not produced at each collision. * Communieated by the Authors. On Conductivity produced by Moving Ions. 631 It was found that on some occasions new ions were produced when the velocity of the colliding ion is equal to the velocity acquired in moving freely between two points differing in potential by 5 volts. From this it was concluded that the energy required to ionize a molecule is not greater than xe 300? being the charge on an ion in electrostatic units. It was also shown that the collision theory explained the results obtained by Stoletow with ultra-violet light *. Experiments have recently been made by Prof. E. Ruther- ford and Mr. R. K. McClung+ to determine the energy reyuired to produce an ion. It was concluded that the amount of energy necessary to ionize a molecu!e was equal to the energy acquired by an ion in travelling freely between two points differing in potential by 175 volts. If the energy were as large as ine there would be no appreciable number of new ions produced by collisions, unless the potential- difference between the electrodes in the gas considerably exceeded 175 volts. In the experiments with Réntgen rays, to which we have referred, and also in Stoletow’s s experiments with ultra-violet light, lar ge increases 1n conductivity were obtained when the potential-difference was as low as 60 volts. It would therefore be impossible to explain these experiments by a collision theory if the value of the energy required to 175 xe S000 In order to avoid this difficulty we might have attributed the increases in conductivity at low pressures to a surface- effect, and have adopted the theory of surface-layers, which was given by Prof. J. J. Thomson f as an explanation of Stoletow’s results. We do not, however, consider that this theory gives a good explanation of the phenomena, since it does not explain the effects obtained by separating the plates. The method em- ployed by Prof. KE. Rutherford and Mr. R. K. McClung for finding the energy necessary to produce an ion consisted in determining the total energy of a beam of rays, the rate of absorption of the rays by a gas, and the conductivity of the gas. When the energy absorbed by the gas was thus found, and the corresponding ‘number of ions, the amount of energy required to produce one ion was deduced. We are of opinion that an estimation of the energy required to produce an ion by this method is not wholly trustworthy. There * Stoletow, Journ. de Fhys. ser. 2, vol. ix. + E. Rutherford and R. K, McClung, Phil. Trans. 1901. { Phil. Mag. Dee. 1899. ionize a molecule were as great as 632 Prof.Townsend and Mr. Kirkby on Conductivity produced seems to be no means of determining how much of the energy of Roéntgen rays absorbed by the gas goes to produce ions, and how much is spent in heating the gas. In the case of ordinary light traversing a gas, une energy which is absorbed is converted into heat without the genesis of ions. - Prof. Rutherford and Mr. McClung’s results cannot therefore be keld to invalidate the Collieion! theory. 2. We have found that the phenomena which characterize the conductivity of air at low pressures are also to be met with in hydrogen and carbonic acid gas. The experiments with these gases were made in the same manner as those which were previously made with air. Particular care was taken to make the apparatus air-tight. The pressure of the gas as shown by a McLeod gauge did not alter perceptibly during a week. Some of the experiments were repeated with fresh gas, and the same conductivities were obtained. The method of conducting the experiments has already been described in the previous papers. When the electric force was reversed a small difference in the conductivity was obtained, which, as has already been explained, arises from the secondary rays emanating from one of the Bisete odes. The currents were obtained for various electric forces, while the pressure of the gas and the strength of the radiation were kept constant. Several sets of obser- vations were thus made with ditterent pressures. The fol- lowing tables give:the mean currents obtained by reversing the force. ‘The pressure of the gas in millimetres of mercury is given at the head of each column. The difference of potential between the electrodes is given in the first column. The sets of observations given in the different columns are numbered for future reference. Experiments were made with different strengths of radia- tion, and it was found that when the pressure was constant the ratios of the currents corresponding to the various forces did not depend upon the intensity of the Rontgen rays. No precautions were therefore taken to have the different sets of observations made with the same intensity of radiation. In these experiments the current was practically constant for forces in the neighbourhood of 72 volts per centimetre. Experiments 3 and £ at pressures of 14°5 and 9°5 mms. were not continued for the higher forces in order to avoid taking observations near the sparking potential. The rays used in the experiments at 9° mm. pressure were stronger than those used in the other three sets. Jf we had maintained the same strength of rays throughout, the first numbers in the fourth column would have been very small and difficult to in Gases by the Motion of Negatively Charged Tons. 633. determine accurately. On the other hand, the bulbs which give the strongest rays are as a rule less ‘constant, so that in order to arrive at the same degree of accuracy at the lower pressures the observations had to be repeated several times. Taste 1.—Currents in Hydrogen between plates 5:3 milli- metres apart. The electric force X acting on the gas being given in volts per centimetre. Pressures. p. 34 23:5 14:5 95 72 19-1 ils 6:25 12-5 Pils - ss 13:5 287 ae = 16:1 358 : jen 21:2 430 ue ak 3l) 502 bes on aD 574 ; 14 aye 103 665 a Ba, lee bag 39°7 234 789 24:7 23°09 80°5 843 ae 191 897 31 41 951 36 58 if 2 Oo: 4 In the above experiments the current which is obtained with a force of 72 volts per centimetre represents the number of ions produced in the gas by the rays. This current remains constant until new ions are produced by collisions. The electric force required to produce an appreciable number of ions diminishes as the pressure is lowered. For pressures lower than 9-5 millimetres, the ions can be detected when the difference of potential between the plates is as low as a volts. This is shown by the results given in Table II. (p. 6384 Tt will be seen from the last set of experiments cr the current reaches a constant value. When this stage is reached, the force is large enough to produce new ions at every collision. Phil. Mag. 8. 6. Vol. 1. No. 6. June 1901. 27 634 Prof. Townsend and Mr. Kirkby on Conductivity produced TasiE I1.—Currents in Hydrogen. Plates 5°5 millims. apart. Pressures. | Xi rd 4°7 eTi7E "84 3096 69 7 5-43 bi 138 8:2 91 92 6°4 207 11 15°5 126 276 18 25:5 Vrfeo} 345 32°5 40:5 20°8 aes a) 68 66°5 25:5 11:2 484 153 119 316 TE 558 490 See 40 11-2 5. 6. thes 8. The following experiments were made with the plates farther apart in order to obtain experimental results in support of equation (1) (section 3) :— TasiE IL1.—Currents in Hydrogen. Plates 10°3 millims. apart. Pressures. X. 14:5 9:5 4:7 37 131 247 |) eee 185 ae 27°5 Be Da avd ee 32°5 295 151 42 109 332 oH see 280 369 a: 73:5 406 20:1 119 435 ie 194 464 29°8 325 493 ase 670 At pressures of about 30 millimetres the presence of new ions in hydrogen can easily be detected by a potential-differ- ence of 500 volts between the electrodes 5 millimetres apart. With carbonic acid gas at 30 millimetres pressure, a much higher voltage would be necessary to obtain an appreciable number of new ions. With plates 5 millimetres apart very large conductivities can be obtained at a pressure of about 4 millimetres. In some cases the conductivities were so great that they could not conveniently be measured by a sensitive electrometer. in Gases by the Motion of Negatively Charged Ions. 635 When this point was reached, the determinations of current were first made for the smaller forces with a suitable strength of rays. The set of determinations at the fixed pressure was continued for higher forces with the rays reduced to a fraction of their original strength. The first observation in the second series was made with the same force as the last observation in the first series, in order to find the amount by which the rays were reduced. The numbers tabulated are the observed currents multiplied by a factor, and represent the currents which would have been obtained if the rays had been left at the same strength throughout. ‘The last six numbers in experiment 3 in the following table were obtained in this way. TasLe [V.—Currents in Carbonic Acid Gas. Plates 5 millimetres apart. Pressures. X. 18°3 88 3°95 1:4 68 25 | 097 76 140 35 19°6 76 5:25 Die 152 141 ao is 10°8 SJ] 78 298 tee = 86 ; aS 13:6 304 cts 33 30°8 20 380 48 54:4 29°3 456 a as 95°7 40-2 14:1 19°5 532 153: 64 126 162 52-9 608 88 216 250 72 16-2 684 abe 129 420 411 99 760 198 195 778 660 161 19 836 232 302 1460 912 286 530 2830 21°3 23°93 972 337 8950 4330 1032 395 1290 8300 : 1 De 3 4, 5 6 if 3. We have found from these observations the number of ions, a, that a single ion generates in going one centimetre in a gas at pressure p under an electric force X. When the temperature is constant @ is a function of X and p. ‘e If no negative ions are distributed uniformly between two plates, and a force X perpendicular to the plates acts on them, ° the total number which reach the positive plate is eet—_ ] * re Rg! GO ae > 1 being the distance between the plates. * J.S. Townsend, ‘ Nature,’ 9th Aug. 1900. 2T 2 636 Prof. Townsend and Mr. Kirkby on Conductivity produced The equation takes into account the fact that each negative ion generated by collision produces a ions per centimetre as well as the original 7» ions. In our experiments the number m) is easily found for the larger pressures, being proportional to the smallest current given in the tables. In these cases the force acting on the gas is insufficient to cause new ions to be produced by collisions, and is large enough to collect all the ions generated by the rays on the plates. This is obvious from the fact that the current is practically constant for a large range of forces of the order oH 80 volts per centimetre. The ratio -- for any other force X is the ratio of the 19 current produced by X to the current obtained with the smallest force given in the tables. These ratios can therefore be obtained by experiment, and by means of equation (1) the values of a corresponding to the different values of X and p can be calculated. The values of a obtained by equation (1) for a fixed pressure and force were the same for different values of J. This point was examined very caretully with air ; and it will be seen from the experiments given in the two previous papers, that when @ is constant the effects produced by changing the distance 7 are in accordance with the formula. At lower pressures, when new ions are generated with forces less than 80 volts per centimetre, the current corresponding to n, was found by an application of the theory to which we have already alluded, and of which we shall give a simple expla- nation. In section 5 of the paper in the Phil. Mag. to which we have referred, it was shown that an ion travelling freely be- tween two points differing in potential by 4 volts acquires a velocity ten times as great as its mean velocity of agitation. If we assume for the present that the mass of a negative ion is smaller than the mass of a molecule of a gas, then the velocities acquired by the negative ions under small electro- motive forces will be so great in comparison with the velocities of agitation of the molecules, that the latter may be considered to be at rest. In travelling under an electric force through the gas, an icon makes a number of collisions with the molecules, the velocities of impact depending upon the free paths. The circumstances attending the collisions will vary im many ways, and the impacts may be considered to be of various types. On some occasions, when the velocity of the colliding ion is sufficiently great, the effect of the collision will be to produce two new in Gases by the Motion of Negatively Charged Ions. 637 ions, one positive and one negative. Let us consider the eftect of increasing the pressure and force in the same pro- portion on the value of a, which we shall consider to be an unknown function ef p and X. When p is increased to zx p, the total number of collisions per centimetre will be inereased in the ratio z, and all the free paths will be diminished in the same ratio ; a force zx X acting along these shortened paths will have the same effect as the torce X acting on the longer free paths. Hence the types of collision will not be altered, and the only effect of increasing p and X will be to increase the number of collisions per centimetre of any specified type by the factor z. In particular, those types of impact which produce new ions will be increased by the factor z. The connexion between the three variables «, p, and X must therefore be such that when p and X are altered in the same proportion, a similar alteration takes place in a In general, let a=(X, p) ; therefore e2= O(2X,2p) and zp(X,p) = (2X, zp). Hence ¢ is of the form fs and <= /(;) ale ERR aan HT This equation does not involve any assumption as to the velocities of the ions before or after impact. If we take the values of a for a fixed pressure and plot a curve having Xx é as coordinates — and =, its equation would be y=/(z), the same forall pressures. In fig. 1 we have marked the positions of the points determining the curves for the various pressures for the smaller values of the variables. The curves in fig. 2 are on a different scale and correspond to tie larger values of = and — Each point is numbered to indicate the experi- — in the tables from which the value of a was determined ; the points bearing the same number belong to observations at the same pressure. It is obvious that the curve through one set of points goes through some of the other sets. It was impossible to get points belonging to one set to cover the whole range of the curves, as a discharge takes place in some cases for rather small values of X. The curves overlap sufficiently to justify us in regarding this coincidence as a confirmation of the collision-theory. The point of contact of the tangent from the origin deter- 638 Prof. Townsend and Mr. Kirkby on Conductivity produced ! xX : : mines the value of —, which gives the pressure for which ais a maximum when the force is constant. This result is easily obtained by differentiating with respect to p in equation 1. The points corresponding to experiments 8 with hydrogen and 6 and 7 with carbonic acid gas are not repre- sented in the diagrams, as the scale would have to be greatly reduced in order to take in points corresponding to such large values of = The determination of the constant m) for experiments 6 and 7 with hydrogen and experiments 5 and 6 with carbonic acid were determined from the curves. The value of — x : was found from the curve for the value of — corresponding 4, to the smallest current found experimentally. The value of ny) was then deduced from the equation et —] al ? and the number so found was used to obtain the values of — for the larger forces. Instead of having recourse 0 to this method, we might have made a series of experiments with forces smaller than 80 volts per centimetre, and thus have determined 7). This would have involved a good deal of experimental work, as the electrometer-deflexions were very small. We therefore considered it best to calculate ny from the determinations of current with 80 volts per centi- metre. The last experiments serve to determine the maximum valuesof —. The value of - obtained from experiment 8 with hydrogen was 11:5. In carbonic acid gas, the largest ot ‘ ; z z. value of - obtained from experiment 6 was 23, corresponding xX to ne ae from experiment 7 it was found that - reached the value 29 when x was 9120, P 4, The results at which we have thus arrived enable us to compare the mean free paths of ions with those of molecules. We have found that a negative ion makes 11:5 collisions per centimetre in hydrogen at 1 mm, pressure, and 29 collisions in Gases by the Motion of Negatively Charged Ions. 639 per centimetre in carbonic acid gas at the same pressure. The mean free paths at that pressure are therefore the reciprocals of these numbers. The mean free paths of molecules of gases at 760 mm. pressure and 0° centigrade, as deduced from experiments on viscosity, are* 1°78x10~-° centimetre for hydrogen and °65 x 10-° for carbonic acid gas. At one millimetre pressure and 12° centigrade the mean free paths would be ‘0141 and ‘0051 for the two gases respectively. (The temperature at which our experiments were made was about 12° centigrade.) The number of collisions per centimetre would consequently be 78 for hydrogen and 196 for carbonic acid gas. The collisions of a single molecule A with other molecules of the gas arise partly from the motion of the molecule in question, and partly from the general motion of thé gas, If the molecule were travelling so fast that the motion of trans- lation of the rest of the gas was inappreciable in comparison with it, the number of collisions per centimetre would be less than the numbers given above in the ratio of 1 tol-41. (See Maxwell, Phil. Mag. xix. 1860.) We therefore see that a molecule of hydrogen travelling very fast through the other hydrogen molecules would make 55 collisions per centimetre, and a molecule of carbonic acid would make 1388 collisions per centimetre in an atmosphere of carbonic acid gas. The corresponding number for air is 91. From these numbers we find that the mean free path of an ion is longer than the mean free path of a molecule in the following ratios :— 4°8: 1 in hydrogen, 4-6: 1 in carbonic acid gas, 4-3 flo air: If we suppose that the material of a molecule extends to a distance R from the centre, then according to our theory new ions are generated when the colliding ion, moving with a sufficient velocity, comes within a distance R of the centre of the molecule. If the linear dimensions of a negative ion are small compared with those of a molecule, we see from the above ratios that the centres of molecules are about 2R apart when collisions occur. If the above ratios were exactly 4:1, we should have concluded that molecules actually touch on collision. We hope to obtain more accurate determinations of the mean free path of ions by means of other experiments. In * Meyer, ‘ Kinetic Theory of Gases.’ 640 Prof. Townsend and Mr. Kirkby on Conductivity produced the experiments which we have given for low pressures the electrometer-deflexions were too small to allow of very aecu- rate measurement, but we do not think that experimental errors would account for the differences between the above ratios and the ratio 4:1. ttt ta ENPRREAeSS PN eee Pt A a EE N\-]-- Poe ee mi eee Be COLLIN 2 RERSEREES BERESABRES Ee Rea 20 “I 2 From the curves given in figs. 1 and 2 an estimation can be made ot the number of new ions generated by a single ion in Gases by the Motion of Negatively Charged Ions. 641 moving with a fixed velocity through the gas. For this purpose it would be necessary to find the equations of the curyes ; but we do not intend to investigate this poiut until Bie 2. ae BECHER ee kh eel £00 700 600 500 400 metry Sona on aaa Ne ae “a Been) “di — 2 some other experiments are made at lower pressures, which e, a may give the larger values of — more accurately. For values of = less than 800, the curve for carbonic acid almost coincides with the curve for air. We may conclude that for smali velocities of the colliding ion the ratio of the number of new ions generated to the total number of collisions is nearly the same for carbonic acid as for air. — ae ee | See eee as _ Dae —_ SS RR ss Fac am = 642 Mr. R. Beattie on the (Hysteresis of Nickel and Jjonsequently, the energy necessary to ionize a molecule of carbonic acid would be of the same order as the energy necessary to ionize a molecule of air. It would appear from the relative shapes of the curves for hydrogen and carbonic acid, that it requires less energy to ionize hydrogen than air or carbonic acid. Experiments are at present being made on the conductivity between electrodes of various shapes. These investigations are important, as they enable us to find out whether the increased conductivity is due to the motion of the positive or negative ions. The results obtained with air led to the con- clusion that the genesis of ions is to be attributed to the motion of the negative ions, and that apparently the positive ions take no part in producing new ions. The experiments described in this paper were made at the University Observatory, Oxford ; and we must express our thanks to Professor Turner for having placed some of his rooms at our disposal. LXIV. The Hysteresis of Nickel and Cobalt in a Rotating Magnetic Field. By R. Buarriz, B.Sc. * Ge far, the few who have worked at the subject of magnetic hysteresis in a rotating magnetic field have been content to experiment with iron and steel, without seeking to extend their investigations to other magnetic substances exhibiting hysteresis. ‘To repair to some extent this omission, the experiments about to be described were made on the hysteresis in a rotating magnetic field of nickel and cobalt, the two metals which, next to iron, most deserve attention. The method employed was similar to that previously used by the writer in conjunction with Mr. R. C. Clinkert. A cylindrical wooden box, B (fig. 1), with a tightly fitting lid, L, was suspended by a steel wire, W, between the poles, N, S, of an electromagnet which could be rotated round the vertical axis OW. A brass pin driven axially into the lid of the box passed loosely through a hole ina Hxed support at O, and served to prevent lateral motion. The material to be examined, in the form of a thin circular disk seen edgeways at D, was placed in the. box and held in position by the pressure against it of the lid. When the magnet was rotated slowly so as to avoid the pro- duction of eddy-currents, the suspended system experienced * Communicated by the Author. t See ‘ The Electrician,’ Oct. 2nd, 1896, Cobalt in a Rotating Magnetic Freld. 643 a couple and was, in consequence, twisted through an angle proportional to the hysteresis loss, the two quantities being connected by the formula ed aK Woy OP ane a sre) where W is the hysteresis loss per cubic centimetre per cycle, V is the volume of the disk, K is the couple required to give the suspended system a twist of one radian, and @ is the Biex ie deflexion in degrees. Since (1) does not contain the speed of rotation, the method was essentially a staticai one. Theoretically, therefore, with everything quite symmetrical about the axis of rotation, a single observation of 6 made after 644 Mr. R. Beattie on the Hysteresis of Nickel and the magnet had been brought to a standstill, combined with a knowledge of K and V, ought to have been sufficient to determine W. But, practically, perfect symmetry was, of course, unattainable, and @ varied considerably during a rotation so that a mean value had to be taken. The plan actually followed was to rotate the magnet clockwise 15° at a time, the position of the pointer P being read off on a circular scale at each halting-place; then to rotate the magnet counter-clockwise, taking readings every 15° as before. Half the difference between the means of the two sets of readings gave the proper value of 9. The constant K was obtained by loading the suspended system with a mass of known moment of inertia, and observing its periodic time when making torsional oscillations about OW (1) in the loaded, (2) in the unloaded condition. In determining the intensity of magnetization it was assumed that the disk, closely similar in form to a flattened ellipsoid of revolution, and placed in an approximately uni- form field, would be pretty uniformly magnetized, and that its demagnetizing factor might, in these circumstances, be taken as Y ea 9) S Na ss where ¢ is the thickness and a the diameter of the disk. To obtain the intensity two distinct experiments were needed. One of these was made by removing the disk and rotating between the poles of the magnet an exploring coil connected with a ballistic galvanometer. This gave the strength, H, of the applied field. or the other experiment a few turns of wire were wound diametrically round the disk and connected with the ballistic galvanometer. The disk thus over-wound was then placed in the field with its plane horizontal and quickly turned through 180°, the diameter of winding placed perpendicular to the lines of force. The resulting galvano- meter-throw measured the total magnetic flux, I’, through the coil, and the intensity of magnetization, I, was readily deduced from the equation Ghote in which A, is the area included within the coil wound dia- metrically round the disk, and A, is the area of a diametrical cross-section of the disk taken perpendicular to its plane. The experiments on nickel were carried out with a disk ‘0525 em. thick and 3°97 cms. in diameter. The results are Cobalt in a Rotating Magnetic Field. 645 Hysteresis Loss in Ergs per cub. centim. per Cycle. _ Le) je) a @ So LS aS) S > S i=) i=) j=) S S S S S Oo Oo i=) Oo = 006 MW Ge) 0 00F ‘PPL Mjousvyy oarpezoy ut uoay pue 4jeqog ‘pexory Jo stsetaqysC pp -—~"g 008 009 ‘S}IUN "G'O 1H Ul UOL}EZYoUsePT Jo AjIsuJUT OOOT ° 008T COST given in Table I., and exhibited graphically in the curve marked “ Nickel” in fig. 2.. From this curve it is seen that for an intensity of about 340 C.G.S. units, the hysteresis loss reaches a maximum value of nearly 10,000 ergs per cubic 646 On the Hysteresis of Nickel and Cobalt. centimetre per cycle. As the intensity is increased from this point to the highest value attained—viz , 475 C.G.S. units produced by an applied field of 460 C.GS. units—the hys- teresis loss rapidly falls off. The latter portion of the curve is sensibly a straight line, and if it were to retain this character over the unexplored region, the hysteresis would disappear entirely at an intensity of 500 C.G.S. units, which is about equal to the saturation-intensity of nickel. TABLE I.—Nickel. Intensity of Magnetization | Hysteresis Loss in Ergs in C.G.S. units. per cub. centim. per Cycle. 46. 675 125 3,120 165 5,060 200 6,940 264 9,300 296: 9,710 342 9,920 370 9,440 412 8,300 436 7,220 460 4,550 475 . 2,700 TABLE Th =*Gorale Intensity of Magnetization | Hysteresis Loss in Ergs in C.G.S. units. per cub. centim. per Cycle. 80: 2,780 160) 6,950 2F0) 11,100: 340 18,100) 430 22,200 526: 28,500 — 650) 35,400 725 35,400: 800; 34,000 865 29,900 910 24,300 945 17,400 970 13,900 980: 11,800 In Table II. and the “ Cobalt” curve of fig. 2 are shown the results of experiments on a disk of rolled cobalt °0815 cm. thick and 3:96 cms. in diameter. The maximum hysteresis loss for this material (86,000 ergs per cubic centimetre per cycle) occurs at an intensity of 700 C.G.S. units, and is very On a Theory of Colloidal Solution. 647 much greater than for nickel. The tail-end of the curve— like the corresponding portion of the nickel curve—is ap- proximately a straight line ; its continuance as such would lead to the hysteresis loss vanishing at an intensity (1050 C.G.S. units) not far removed from the saturation-intensity for cobalt. The third curve in fig. 2, with the same general character as the others, has been plotted from data derived from the paper already alluded to. It refers to a moderately soft specimen of iron, and has been added for the sake of comparison. Owens College, Manchester. LXV. A Theory of Colloidal Solution. By F. G. Donnan, M.A., Ph.D., Junior Fellow, Royal University of Ireland *. THNHE main fact concerning “ colloidal”’ solutions, a fact which has been established by experiment and thermo- dynamical reasoning, appears to be that such “solutions ” are in reality complexes of two phases, of which one exists in a state of extremely fine division, interspersed throughout the other. It must be observed, however, that it is not a sufficient description to call such complexes mere “ suspen- sions,’ for what we have here to deal with is not so much a certain sort of mixture or pseudo-solution, as rather a peculiar condition of matter, namely the ‘‘ colloidal” state. This fundamental point was clearly emphasized by Graham, but seems to have been somewhat lost sight of by some modern writers. Thus Krafft + has proposed a theory of colloidal solutions in which it is supposed that the molecules of col- loidally-dissolved substances rotate round each other in closed paths. Apart from the consideration that such a theory is invalid, inasmuch as it gives no explanation why these orbital systems should not possess translatory motion, it is evident that such a theory must, in any case, be highly unsatisfactory, for the really essential point would be the explanation of how such a state of affairs came about. What we have to account for, in fact, is the following. A solid substance C, when brought in contact with certain liquid media, breaks up or disintegrates into these media, but in such a manner that the disintegration process does not proceed to the molecular limit. The liquid medium appears then to be interspersed with minute aggregates of C, which are still so much larger than molecular magnitudes that they * Communicated by the Physical Society: read March 8, 1901. + Ber. d. d. Chem. Ges. vol. xxix. p. 1354 (1896). SSS — SSS SSS 648 Dr. F. G. Donnan on a are subjected to a statistically almost uniform molecular bombardment, and hence possess only very small quasi- molecular motions. These complexes, moreover, are such that changes of temperature, or the addition of comparatiy ely small quantities of other substances, frequently cause the sudden precipitation in mass of the substance C. In what follows an attempt is made to show that all these phenomena can be explained by the application of a well-. known hypothesis, namely by means of Laplace’s theory of intermolecular attractive forces. In doing this it is necessary, and in the present case essential, to carefully distinguish between the kinetic molecular equilibrium and the statical.* (mechanical) equilébriwm at the interface of solid and liquid. — Let us consider first the state of affairs between a crystal- line solid and a liquid medium which dissolves it. Here we have, at any given temperature, a definite con- centration of the dissolved solid. This equilibrium is a. molecular-statistical one, and consists in the balancing of two statistically equal and oppositely directed molecular fluxes. At the same time, owing to the fact that a definite interface exists between the solid and the liquid, it is clear that any small volume-element of the solid lying near the interface is in statical equilibrium. The resultant of all the inter- molecular forces is, in fact, an inwardly-directed force urging this volume-element towards the inner part of the solid. Thus a crystalline solid immersed in its saturated solution is (a) in statical equilibrium under a compressive stress ; (6) in kinetic-molecular equilibrium under equal and opposite molecular fluxes. Hence, during the process of solution of a crystalline solid, although there is a net outward flux of molecules, we must suppose that the resultant mechanical force acting on any. small volume-element of the solid in the immediate neighbour- hood of the solid-hquid interface remains inwardly directed, so that the “molar” integrity of the mass is preserved, although ‘‘ molecular” disintegration is taking place. The theory which is here proposed for the pseudo- solution of colloidal matter regards this phenomenon as a process of molar or mechanical disintegration due to the non-existence of statical equilibrium in the thin surface-layers of the solid when the latter is in contact with certain liquid media. Consider the solid, I, bounded by the planes AB, CD, and surrounded by the liquid medium O (it is sufficient to con- sider the problem in two dimensions). Let de be any small volume-element of I situated just at the bounding interface * Jn this connexion see Larmor, ‘ Aither and Matter’ (1900), passem. Theory of Colloidal Solution. 649 AB. Then de is acted on by two forces r and J, as indicated in the diagram, J being due to the attraction of Iand » to that of O. For crystalline solids l>r; for “colloidal ” matter in contact with certain liquids we assume that >. D It follows then that the solid I will begin to disintegrate into the liquid medium O. It is difficult to form an accurate mental picture of what exactly happens in this case. Probably the solid “ mixes”? into O in the form of excessively thin sheets or extremely fine and branching filaments. It must be observed that the colloidal solid is not in an “explo- sive’ state, for the disintegration only affects at any moment the excessively thin surface-layers. The question now arises as to how far this process will continue ; for if it be supposed to go on until the limit of molecular intermixture be arrived at, it is evident that a true solution must result. But as we understand by colloidal matter that condition of matter which gives “colloidal solutions” (defined by certain peculiar properties), it is clear that there exists something which arrests the disintegration-process before the molecular limit is arrived at, and yet at a point where the resulting “ grain ”’ is exceedingly fine. The essence of the theory here proposed lies in the nature of the assumptions whereby this stoppage of the process of disintegration or intermixture is accounted for. Let the attraction of the matter contained in the semicircle PQR be a very large percentage of the attraction due to the infinite (or practically infinite) mass of O lying to the right ofde. Let similarly the attraction due to LMN be the same very large percentage of the total attractive force exerted on Phil. Mag. 8. 6. Vol. 1. No. 6. June 1901. 2U 650 Dr. F. G. Donnan on a de by the practically infinite mass of I. These circles corre- spond in fact to the so-called “ spheres of molecular action.” We assume that not only is r>J/, but that also semicircle PQR>semicircle LMN. The physical significance of these assumptions may he stated as follows :—It is assumed that the molecular “ adhesion”’ between I and O is greater than the molecular “ cohesion” of the colloid I, and that the intermolecular attractive forces fall off more rapidly with increasing distance in the case of the molecular cohesion of | than in the case of the adhesion hetween Land O. It is easy to express these conditions in i precise mathematical form by choosing a suitable law of force with two constants, but considering our present want of knowledge such a formulation could only serve the purposes of illustration. _ With the assumptions made, it now becomes possible to explain why the process of intermixture is arrested before the molecular limit. Suppose that the sheets, filaments, or particles have become so thin that the plane CD occupies a position C’D’ within the semicircle PVR (see fig. 1). Then it is evident that the value of 7 will be diminished since there now exists an effective component due to O acting on the lefé of de. In fact, the resultant attraction due to O bears a ratio to its former value equal to the ratio of PRST to semicirele PQR. At the same time, so long as the plane O’D’ lies within the semicircle PVR but outside LMN the value of the force { will not be sensibly altered. Accordingly there exists a critical thickness of I such that the forces 7 and r just balance. When this state of division is reached the process of disintegration ceases, and there results a two-phase medium consisting of the medium I dis- tributed throughout the medium O in some state of extremely fine division. Such a medium corresponds on the present theory to a colloidal solution. Fig. 2, which requires no further explanation, applies to the case of spherical particles of I immersed in O. If the medium O be continuousiy removed by evaporation or otherwise, or if sufficient of I be colloidally dissolved, there results an interlacing network of I distributed through O, and a more or less elastic jelly is produced (c/. the views of van Bemmelen). For thicknesses of I greater than the critical, the medium T has a tendency to ¢ncrease its common surface with QO, .e., it possesses an effectively negative surface-tension. For thick- nesses less than the critical, however, there will be a postteve surface-tension. Hence if the substance I be produced in the Theory of Colloidal Solution. GOL medium QO by chemical means, its aggregates will grow to this critical size and stop there, z.e., will remain in colloidal solution. Bias 2. If a colloid be defined as a substance which forms those pseudo-solutions termed colloidal, it follows from the above that this description is not sufficient unless the other medium, 2.e. the pseudo-solvent, be specified. This point is well illus- trated by the result obtained by Krafft * with the soaps ; these substances give true solutions with alcohol, and colloidal solutions with water. There is nothing to prevent a substance being partly colloidally distributed throughout a given medium and partly in true molecular solutiony. Hence all gradations may occur. The foregoing considerations render intelligible many of the peculiarities exhibited by colloidal solutions, namely, their small diffusibility and small osmotic pressure, their frequent want of optical transparency, their “ solidifica- tion ” to jellies, their precipitation by changes of temperature or by the addition of comparatively small quantities of certain substances, &c., &c. It is necessary, however, to remark that only reversible changes admit of explanation on the above theory. The zrreversible phenomena so frequently exhibited by organic colloids can only be explained by intra-molecular changes. As regards the nature of the “ colloidal” state, as distinct from a colloidal solution, the present theory lends support to the view that in matter in the colloidal state the intermolecular forces are in general smaller than in the case * Ber d. d. chem. Ges. xxvii. p. 1747 ; xxviii. p. 2556; xxix. p. 1328. + So far as I am aware, this possibility was first mentioned by Mr. W. B. Hardy. U2 652 Mr. C. G. Barkla on the Velocity of ot crystalline matter, and fall off comparatively rapidly with increasing distance. This view is in harmony with the fact that substances which tend to assume the colloidal condition are in general those which possess feeble powers of erystalliza- tion. A solid colloid is in fact an amorphous body possessing only an exceedingly minute velocity of crystallization. Whether, however, a colloid body is quite analogous to a highly supercooled viscous liquid with excessively small velocity of crystallization, such as “solid” glass, is not a question which I shall attempt to consider here. Some colour, is, however, given to this view by the recent work of Barus, who considers he has obtained colloidal solutions of glass in water. The whole question is intimately connected with the hitherto unsolved problem as to the real nature of the solid state. Chemical Laboratory, University College, London, W., Christmas, 1900. LXVI. The Velocity of Electric Waves along Wires. By CHarRLes G. Barks, B.Sc., 1851 Lhibition Scholar, Trinity College, Cambridge*. HE theory of the propagation of electric waves along a wire, when a hollow surrounding cylinder serves as the return circuit, was given by J. J. Thomson in ‘ Recent Researches ’f. More recently Sommerfeld discussed the problem of the propagation of waves along a single wire isolated in space. By the consideration of several examples, the conditions of which may be realized in practice, he showed the velocity of propagation along fine wires to be considerably less than the velocity through free space. The propagation of electric oscillations along parallel wires has recently been discussed by Mie§ and Morton |. Experimentally, Trowbridge and Duane{] found that “ the velocity of short electric waves along two parallel wires differs from the velocity of light by less than 2 per cent. of its vaiue.” (The copper wire used was of diameter *215 cm.) #* Communicated by Prof. J. J. Thomson. + J. J. Thomson, ‘ Recent Researches,’ p. 262 (1895). t A. Sommerfeld, Wied. Ann. xvii. p. 258 (1899). § Mie, Ann. d. Phys. i1. p. 202 (1900). || Morton, Phil. Mae. [5] vol. 1. p. 605 (1900). 4, Trowbridge & Duane, Am. J. Sc. ser. 3, vol. 1. p. 104 (1895). Electric Waves along Wires. 653 More recently Gutton *, in comparing the velocities of electric wayes along wires (diam. ‘11 em.) and in air, found within the errors of observation (about 1 in 20) that the velocities are the same. St. Johnf showed the dependence of the velocity on the magnetic permeability of the substance of the wire by using iron and copper wires of the same diameter, and measuring the wave-lengths, corresponding to a certain frequency, along the wires. His resulis verified what had previously been demonstrated by J. J. Thomson, that the magnetic properties of iron are called into play under extremely rapid alternations of the magnetizing forces. St. John also used copper wireg of different diameters, and found, for oscillations of the same period, the wave-length along wire of diameter ‘03915 cm. to be moze than 4 per cent. less than that along °1201 cm. wire. The half wave-lengths which he obtained for the same frequency along different wires were as follows :— Copper (1201 centim. diameter) 255°8 centim. (0884 3 | OE ee COGSdG= =; ee oli Gp hats (OES EES seer pp yc ee The parallel wires were 30 centim. apart. Prof. J. J. Thomson suggested the use of the Rutherford detector { in a measurement of the velocities along wires of various diaméters and materials, and it was with this object in view that the following experiments were made. Preparatory to attempting the measurement of the relative velocities of the waves aleng wires of different diameters, Lecher’s system of wires was set up, and the exhausted tube, as used by by him, replaced by a wire bridge with a loop at the middle tor the reception of the detector-needle§. The system then consisted of two large rectangular zine plates, to which were attached by rods the brass balls between which sparking occurred. Parallel to and distant 5 or 6 centimetres from these plates were two smaller ones S and W! (fig. 1). To the centres of these were attached the two ends of a copper wire SKK’S’, the two portions AK and A’K’ of the wire being parallel and about 7:8 centimetres apart. Connecting corresponding points of the parallel wires was a movable bridge BB! of the same material as the wires. * Gutton, Comptes Rendus, cxxviil. p. 1508 (1899). + St. John, Phil. Mag. |5] vol. xxxviil. p. 425 (1894). { Rutherford, Phil. Trans. 189, p. 1 (1897). § Rutherford, Phil. Trans. 1897. 654 Mr. C. G. Barkla on the Velocity of At the middle of the terminal bridge KK’ was a loop of one turn, in which was fixed a glass tube closed at one end. The detector-needle consisted of a bundle of fine iron wires, fixed by paraffin-wax in the end of a glass tube, which was just wide enough to slide inside the fixed. tube. Fig. 1. ia : In order to compare the intensities of the oscillations at the loop under different conditions, it was of course necessary to have the detector-needle in exactly the same position for each observation. Accordingly, the inner tube was pushed home in the fixed tube (in which position the loop passed round the middle of the detector-needle), and turned round its own axis till a fine pointer attached to the outer end came into a position indicated on the stand. To obtain a measure of the intensity of the oscillations at R during the different observations, the needle was first magnetized to saturation. When placed ina given position near the magnetometer, the deflexion of the magnetometer- needle was not absolutely the same after each magnetizing process, so that for the earliest observations the detector needle was frequently demagnetized and remagnetized again, to make this initial reading as nearly as possible a constant quantity. This, however, was found to be unnecessary, as the final value of the deflexion, after the occurrence of the oscillations whose intensity the detector indicated, appeared to be independent of these slight initial variations of the saturation reading (see Table I.). When saturated, the needle was placed m position at R, and sparking between the knobs N and N’ was set up for a fixed period, by an induction-coil whose terminals were connected to the large plates. After the demagnetizing process, the detector-needle was placed in a definite position near the magnetometer, and the © Electric Waves along Wires. 65 deflexion of the magnetomer-needle observed. The difference between this and the standard saturation deflexion was a measure of the intensity of the oscillations at R. It was necessary to allow the sparking to continue for some definite time, for the amount of demagnetization of the de- tector-needle depends not only on the intensity of the oscil- lations of certain period producing the variable magnetic field, but also on the number of those oscillations™. In these experiments, the dependence of the demagnetization on the period of sparking was appreciable as shown by fig. 2, which Fig. 2. 190 180 Magnetometer Deflexions. 10 15 20 25 Time in seconds. j=) i) | was obtained by plotting magnetometer deflexions as ordi- nates, and times from the commencement of oscillation as abscisse. The first second in this case produced about 89 per cent. of the total demagnetization; after this the rate of change rapidly fell off. The period of sparking chosen for the following experiments was 15 and sometimes 20 seconds. A small error in the time observation did not then appreciably affect the result. The greatest trouble experienced throughout these experi- ments was that occasioned by the irregularity of the sparking, many long series of observations being entirely useless for exact determinations. It appeared that long periods of sparking were productive * See Rutherford. 656 Mr. C. G. Barkla on the Velocity of of the most consistent results, temporary diminutions of in- tensity being then inappreciable in the result of the wuole period. The spark-gap was 3 or 4 millimetres in length, so that the discharges were not of the most violent nature, and hence not so liable to produce sudden changes on the surfaces between which sparking occurred. It was found, however, that im- mediately after these surfaces were repolished there was a rapid change in their character during sparking, and the effect on the detector-needle of two consecutive periods was altogether different, though everything else remained unchanged. Platinized balls were not an obvious improvement. The ordinary hammer interrupter also was replaced by the Wehnelt interrupter, but for these long periods of sparking the results were not so good. The only satisfactory readings were obtained after sparks had been passing for a considerable time, and the faces of the knobs had lost their polish, so that further sparking pro- duced little or no change on them. The constancy of the detector’s indications during some of these occasional steady states was remarkable, as the following example shows. During a series of observations made with the bridge in different positions, alternate readings were taken with the bridge in a standard position, so that corrections might be made for changes in the intensity of sparking. These standard readings, which are given below, were taken as closely as possible to tenths of a millimetre on the magnetometer-scale. As will be seen, the variations, with one exception, were almost imperceptible. The table also shows the final read- ings to be independent of the small variations in the saturation values. TABLE [, Position of , Saturation Final bridge. See) SOY, deflexion. deflexion. Standard 0. 203°1 mm. 156°3 mm. os 20285 ,, GO 22guaes i if 2023 ;, | 1561 5, i ms 202; anes E562 ae us pm 203°1 5 15605, ¥ ~ 203°3 ESOS Gigs i 202-05) =a) 15G;05) 0, a | ZO es) fotnes 4155 de ni 5 ZOD ee 15605, m " 201585 aa, 156 a6 i os 200 + 156 ate | ous of detector-needle, shown on magnetometer scale, Demagnetizati Electric Waves alung Wires. 657 The amount of demagnetization of the detector-needle was observed for different positions of the bridge along the parallel wires. Alternate readings were taken hou a bridge, so that any variation in the intensity of sparking could be cor- rected for. The corrections were, however, very small. Fig. 3 shows the curve obtained by plotting positions of the movable bridge measured from A and A’ as ‘abscisse, and amounts of demagnetization of the detector-needle for those positions of the bridge as ordinates. Fig. 3. 60 USeerartaeet 15 CREAR ot ee 1v0 200 300 400 500 Distances of the bridge from A (fig. 1) in ee a It was found that there was a maximum of demagnetiza- tion when the bridge BB’ was in such a position that the lengths of the two circuits SABB’A’S’ and BKRK’B’ (giving the capacities at S and §’ and the portions of wire SA and S’A’ an equivalent length along the parallel wires) were in the ratios of small odd to even numbers. The movable bridge BB! was included in both circuits. _ The equivalent length of the capacity and wires SA and S'A' was obtained from the observation of the position of the most sharply-defined maximum which corresponded to the simplest possible ratio 1: 2. The total length of the circuit BKRK’B’ being known, that of the circuit equivalent to SABB/A'S’ was determined by this ratio of the lengths, and hence the equivalent value of the capacity and curved portion of the wire was obtained. 658 Mr. C. G. Barkla on the Velocity of From this the positions of the bridge dividing the circuits in the other simple ratios given below were calculated. The positions of the bridge giving the five principal maxima as shown on fig. 3 were approximately determined. In this experiment the distance from A to the mid point of KK’ was 750°3 cm., the length of BB’ 8 cm., and the equiva- lent length of AS (including the capacity) 158-9 em. Tase II. Ratio of equiva- Calculated Distance of bridge lent lengths of distance of from A, experi- circuits. bridge from A. mentally determined. 1:4 20°95 ems. 23°35 cms. 1:2 145) 1415, 3:4 2302, 226-0, 3:2 387-4, 388-5 ,, O32 AQ2Z a5 ADdeS igs More careful determinations were made with a system of different dimensions. The distance from A to the mid point of KK’ was 806°5 em., the length of the movable bridge 29 cm., and the equivalent length of the portion AS was taken as 143 cm. The agreement in this case was very close, though shorter bridges give better definition of the maxima. TApnealial: Calculated distance of Ratio of equiva- lent lengths of Distance of bridge from A, experi- circuits. bridge from A. mentally determined. 1:4 ao°2 cms. as'4 cms. 1:2 168°65 ,, 168°63 ,, 3:4 2619 2600 ,, 3:2 4296, 4302, 5:2 BALA, Fett or: The other positions of the bridge giving maxima of de- magnetization could not be experimentally determined with such accuracy as that in which the circuits were divided in the simple ratio 1: 2. It was also found, as might be expected, that a shorter bridge gave more cusp-like and better defined maxima. In Rubens’s experiments, in which KBB’K’ was an open circuit, the maxima were given for positions of the bridge Hlectric Waves along Wires. 659 which divided the circuits so that their equivalent lengths were approximately in the ratio of odd to odd numbers. In that case the two ends of a circuit were in opposite electrical conditions, and therefore the length of each circuit was an odd number of half wave-lengths; but with the closed end KK’ the length of the whole circuit BB'/KK’ must be that of an even number of half wave-lengths, and resonance between the two circuits occurs only when their equivalent lengths contain an odd and an even number of half wave-lengths respectively, which is only possible when these lengths are in the ratios of odd to even numbers. When the two circuits are tuned so that their lengths are in the ratio 1: 2, SBB’S’ (giving equivalent lengths for capacities, &c.) is half a wave-length, and the total length of the circuit KBB’K’ a complete wave-length *. If now the circuits are entirely separated by making BB’ a terminal bridge of the first circuit and placing a similar bridge B,B,’ very close to BB’, while the parallel wires are cut between the two, there is no conducting connexion between them, and the osciilations in B,KK’B,’ are caused entirely by induction f. In this form resonance occurs as before without the inter- ference from other systems of waves, the oscillations having a maximum intensity when the two circuits SBB/S' and KB,B,'K’ are tuned. This arrangement, as shown in fig. 4, was used in the following determinations. The wire used for the primary eircuit had a diameter ‘076 cm. and was supported by light ebonite pegs at A, B, B’, and A’. Similar pegs also held the ends B,B,’ of the secondary circuit in position just beyond sparking distance from BB’, while the bridge KK’ with the loop and detector-needle were movable along the parallel wires B,Z and B,’Z’, whose ends were held in position by silk threads attached to Z and Z!. To compare the velocities of the waves along different wires, the obvious method was to keep the frequency constant and to measure the wave-length corresponding to that fre- quency along the various wires. Tirst the arrangement shown in fig. 1 was set up and the position of the bridge, at which resonance between the two circuits occurred when their equivalent lengths were in the ratio 1 : 2, was noted. * See Rutherford’s paper, Phil. Trans. 1897. t+ Lecher showed that if a double bridge was used and the parallel wires were cut between the ends of the bridge, the intensity of oscillation round the circuit KBB’K’ was very slightly changed, showing the oscillations in that circuit to be due to induction. 660 Mr. C. G. Barkla on the Velocity of Then the primary and secondary circuits, as shown in fig. 4, were made of approximately the same dimensions as those of Fig. 4. the first arrangement when tuned as described. The exact length of the secondary circuit giving the maximum intensity of oscillation was finally obtained by the method of moving - the end bridge KK’. As the position of KK’ was obtained more accurately the wires were cut down, so that when the final adjustments were made there was neither disturbing capacity nor a third circuit whose oscillations would interfere with those of the secondary. ‘the circuit KB,B,'K’ then possessed the same natural period as that of the circuit SBB’N’, its length being exactly one wave-length. As the only change made in the system throughout a series of experiments was that of changing the wires of the secondary circuit KB,B,’/K’, it was necessary to ascertain the magnitude of its effect on the period of the primary, and if at all appreciable to measure and allow for it. To do this another circuit was placed near the primary with the terminal bridge B,B,’ on the side of BB’ away from B,B,’ and with the parallel wires leading in another direction. A rough experiment showed that the presence of this circuit did not affect the tuning of the initial secondary by an amount that could be detected. The effect was also shown to be quite negligible by altering the distance between the bridges BB’ and B,B,’ of the two circuits. At about ‘4 cm. apart sparking just did not occur across from one bridge to the other, while at 8 cm. apart the intensity of the induced oscillations was just sufficient to enable one to tune with accuracy. This variation in the distance between the circuits was made several times, and Electric Waves along Wires. 661 each change seemed to show that the frequency of the primary was slightly less when the bridges were very near than when at a considerable distance from each other, but the change in the position of the bridge KK’ for syntony only amounted to 2 or 8 mm., and as this was within the limits of possible error, absolute certainty on the point was impossible. It was, however, too small to affect the results obtained. It should be noticed that the proximity of the wires of the primary to the secondary circuit would affect the period of the secondary in the same way as the secondary wires would affect the primary, but the alteration in the period of the primary would be double that of the secondary, and conse- quently would make itself felt by the change in the length of the secondary necessary to give perfect resonance. The conclusion from these two experiments is that the period remained practically constant throughout the changes in the secondary. Another question which arose was whether or not the position of the bridge giving the maximum intensity of oscillation was the position in each case which made the circuit KB,B,'K’ an exact wave-length corresponding to the period of the primary. In the case of stout wires a wave traverses the circuit with very slight diminution of intensity ; consequently increasing or decreasing the length of that circuit by a small amount has very little effect on the intensity of the wave after once traversing the circuit. When wires of high resistance are used, a small change in the length of the circuit may alter the intensity of the wave after completing the circuit by an appreciable amount, i.e. by the amount due to the damping by that length of wire by which the circuit is lengthened or shortened. Let a be the amplitude of a wave starting at the end B,B,’, AL ae its amplitude when at R, BAT ae ® its amplitude when at R again, and so on; where a is the length of a double circuit of parallel wires necessary to produce the diminu- tion of intensity which the wave experiences in once traversing the circuit. When the secondary is in tune with the primary, if we take the amplitude of oscillation at any instant as the sum of the amplitudes of the damped pulses which would be induced separately by the various oscillations in the primary, the expression for this amplitude, n complete periods after the 662 Mr. C. G. Barkla on the Velocity of first pulse reaches R, may be written ve ae Bae 2 +- ab" e).? bo. 2). G6 Om ree in which 6 is the damping factor for the primary corre- sponding to e~*" in the secondary. This expression may be written OWA ae 2 (Ort) — e~@+)az) eae = say.) ©, 1. ees The oscillations at R reach a maximum of intensity when nm is such that prt! e7(@+l)ar > pnt? — eo (M+2)Ax and >b"—e7—™, 1. e. when i lb) Seno tea and, b"1—b)*, Then nt 1 — et I)rx a) ee Cet ies ° ° ° ° ° (4) Considering the extreme case in which the damping in the secondary was greatest, 27. e. with a secondary circuit of platinum of diameter °0025 cm., by taking b=1 in (4), an inferior limit to. the value of e~*” is obtained. The slope of the damping curve is, in this case, less than the value given by Cees Are A tam 0={ ~ Foray fh As an approximation we write age eee tan @ tet—1 9 hg, (1—6) being small in comparison with (l1—e-™) ; or 2k—1 i! 2 tan O= | oF log, (1-,) oth estes) The position of the bridge for resonance is approximately that in which the slope of the demagnetization curve is given by this expression. With this wire, however, exact measurements were impossible, and only an attempt at the order of result was made ™*, * In these experiments the demagretization was not accurately pro- portional to the amplitude of oscillation for vibrations of the same frequency, as a uniform fell was not produced by the few turns round the cetec‘or-needle. 664 Mr. C. G. Barkla on the Velocity of The maximum occurred when the length of the secondary circuit was about 600 centimetres ; a gradient in the curve of about —‘04 millimetre scale-divisions per centimetre dis- placement of the bridge (which was the slope given by (5) when #=half the complete length of the circuit) was given with a length of circuit 8 or 10 cm. greater than that for the maximum, where the gradient was zero. This gave for the length of the circuit about 610 em., which was the wave-length for a frequency of oscillation whose wave-length along ‘074 cm. copper was 663°4 em., showing the velocity along ‘0025 cm. platinum in the cireuit used to be about 92 per cent. of the velocity along *074 cm. copper. The damping was so enormous that the position could not be determined without a possible error of 2 per cent. or more; the example is given as one in which an approxi- mate correction for damping was applied. The greatest possible fractional change in intensity (due to damping) per unit displacement of the bridge, as calculated from (3) for the other wires used, would not displace the maxima from true positions of resonance by an amount that could be measured, any such displacement being well within the limits of possible error ; so that in these cases the damping effect has been entirely neglected. 1t is possible to eliminate the displacement due to damping in the fine wires by making the ends of the parallel wires over which KK’! moves of stout copper, though the reflexions at the junctions are liable to disturb the true reading. — Such an experiment gave, when correction was made for the copper in the circuit, a wave-length along the fine platinum wire of about 614 cm., which is in fair agreement with the previous result. The first series of experiments was made on copper wires of different diameters. The primary circuit was unchanged while copper wires of diameters ‘076, 0377, -0149, -0038 centimetres in succession constituted the secondary circuit. In each case the distance between the parallel wires and the length of the bridge B, B,' was 7:3 cm. The movable bridge had four turns round the detector-needle, and was of approximately the same length for each of the wires. The correction for the length of the bridges was neglected, as it was a small quantity of practically the same magnitude in each case. The total length of the secondary circuit, when -076 cm. wire was used and the two circuits were tuned, was 1298:95 cm. ‘The position of the bridge giving maximum intensity of oscillation was obtainable with great accuracy, Electric Waves along Wires. 665 the final position being determined only by the results of observations taken when the sparking was in one of its most regular states. An approximate result was obtained in a few minutes, but frequently the observations continued for several days before the sparking was sufficiently reliable to give results on which to base the final adjustments. Not till the position of the bridge was finally settled were the measurements of the circuit made, so that these are here given as exactly as it was possible to take them, with the bridge in the definite position previously decided upon, though this position was not deter- minable with the accuracy w ith which the measurements were taken. The possible error in the result given for the stoutest copper (diam. ‘076 cm.) does not exceed about °05 per cent. After each of the wires had in turn formed the secondary, a second determination was made with the :076 cm. copper, and when the measurements were taken the length was found to be 1299°05 cm., differing by 1 cm. from the previous result. No pretence is made to this degree of accuracy; in fact it was found later that small irregularities in the wire (such as probably were present in the first instance) increased the length to 1299°35 ems. ‘This is, however, sufficient to show the reliability of the results. The average ‘of the two readings is given in the table. With the finer wires the maxima were not sc well marked because of the greater damping, and the determinations were not so accurate, the possible error for the finest copper wire amounting to about *2 per cent. To demonstrate the dependence of the velocity on the wave- length, the same wires were used in the secondary when the primary had a frequency almost twice that in the previous series. The results are tabulated on p. 666, and show the dimi- nution of velocity in the finer wires to be greater with the higher frequency. The difference in the wave-lengths measured along wires of different diameters, the parallel wires being 7°8 cm. apart, is considerably g oreater than that calculated as “by Sommerfeld for isolate wires. Fig. 5 shows the relation between the velocity along copper wires and the diameter of the wires (the parallel wires in this experiment being 7°8 em. apart). The curves were obtained by plottine the variations from the velocity along ‘076 em. copper wire as ordinates and the diameters of the wires as abscissee, the wave-lengths along ‘076 cm. wire being Phil. Mag. 8. 6. Vol. 1. No. 6. June 1901. DX 666 On the Velocity of Electric Waves along Wires. 1299°2 cm. and 663:4 cm. for the lower and upper curves respectively. Diameter of Wire *. Wave-length. Woe Ae ge. UE Anois 1299-20. - ||) uO 0377 ,, (vIB ,, ) 12956, 99°73 0149 ,, (006 ,, ) 1289-1, Nigar 0038 5, (0015, ) 1280°5 ,, 98-6 0740 em. (03. inch) 663-4 om. 100 O37 (Ol 6608. ,, 99-6 0148 ,, (006 ,, ) 6576 99-1 0036 ,, (0015 ,, ) 6516, 98-2 Fig. 5. Percentage Variation of Velocity from that, along ‘076 em. Wire. 0 “0075 015 0225 03 Diameter of Wire in inches. The effect of increasing the specific resistance of the material of the wire was shown by comparing the wave-lengths, cor- responding to the same frequency, along wires of the same diameter but of different material. The comparison was made between platinum and copper, the specific resistances of which are in the ratio of 7: 1 approximately. The fre- quency was about the same as the higher of the two given for the copper wires of various diameters. There was a decided difference between the two wave-lengths, the mea- surements of which are given below. In the determination * The diameters given in inches were the origmal diameters of the wires; these were slightly changed by stretching. | Geological Society. 667 of the wave-length along °0158 cm. platinum two measure- ments were taken. In the first the bridge was placed at the end of the region of possible maximum intensity giving as great a wave-length as possible. In the second the measure- ment was taken with the bridge at the other end of the uncertain region in which a maximum of demagnetization was obtained. ‘Thus the two readings given are the two extremes of the possible true position of the bridge. The positions of the extremes were based on two entirely different sets of readings between the taking of which the wire of the secondary was rearranged, The position midway between the two is given:— Wave-length. Proportional Wavye-length. ‘015 em. copper 651 100 0158 om. platinum fy7y bO4S6 99°63 eK 647°4 | : Thus the velocity of electric waves along platinum wire of diameter ‘0158 cm. was less than the velocity along copper wire of the same diameter by about °4 per cent., the wave- length along -015 em. copper being 651 cm.,and the distance apart of the parallel wires being 7°8 cm. The possible error in this is necessarily great ; for a more exact determination the average of a number of such results must be taken. This, however, is of the order that might be expected from the results of the calculations of Sommerfeld and Mie. I hope ina subsequent paper to compare these experimental results with those obtained by a theoretical treatment of the subject. My thanks are due to Prof. J. J. Thomson for suggestions and advice relative to this work. i Cavendish Laboratory. LXVII. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 600. | November 21st, 1901 (cont.).—J. J. H. Teall, Esq., M.A., F.R.S., President, in the Chair. : The following communications were read :— 2 ‘The Geology of Mynydd-y-Garn (Anglesey).’ By Charles A. Matley, Esq., B.Sc., F.G.S. Mynydd-y-Garn, a hill of less than 600 feet elevation, stands above the village of Llanfair-y’nghornwy in North-west Anglesey. The mass of the hill is an inlier of sericitic and chloritic phyllites (Garn Phyllites), surmounted by a massive conglomerate (Garn Conglomerate), and surrounded by black slates and shales of 668 Geological Society :— apparently Upper Llandeilo age. The general dip of all the rocks is northerly and north-easterly. The Garn Phyllites are usually green altered shales and fine gritty rocks, and are intensely contorted near their southern boundary. Even where not contorted they show under the micro- scope evidence of powerful earth-movement. They are considered by the author to be part of the ‘Green Series’ of Northern Anglesey. They are cut off to the west and south by a curved fault, probably a thrust, which brings them against Llandeilo slates and breccias. The Garn Conglomerate, Grit, and Breccia, a formation perhaps 400 feet thick, rests upon the Garn Phyllites and contains fragments derived from them, as well as pebbles of quartz, grit, gneissose and granitic rocks, etc. It passes up gradually into black slates, from which a few Upper Llandeilo fossils have been collected. In the black slates an oolitic ironstone or ferruginous mudstone has been found, which may perhaps be on the same horizon as the similar rock recorded by the author in Northern Anglesey. On the eastern side of Mynydd-y-Garn is another group of rocks, the Llanfair-y’nghornwy Beds, which the author correlates with the basal part of his Llanbadrig Series. They consist of phyllites resembling those below the Garn Conglomerate, but they contain also beds and masses of quartzite, grit, and limestone. They are much broken, and partly in the condition of crush-con- glomerates. They have been thrust over the Llandeilo black slates, and the thrust-plane has been traced to the coast at Porth yr Hbol. This thrust is continuous with that which forms the southern boundary of the ‘ Green Series’ of Northern Anglesey. The district around Mynydd-y-Garn has been affected since Llandeilo times by two powerful earth-movements, acting one from the north, the other from the north-east. The first-mentioned prevailed in the area west and north-west of the hill, where the pre-Llandeilo rocks are frequently shattered to crush-conglomerates. Around Mynydd-y-Garn itself and east of it the principal direction of movement has been from the north-east; south of the hill the structure is perhaps the result of the interference of these two movements. 3. ‘On some Altered Tufaceous Rhyolitic Rocks from Dufton Pike (Westmorland). By Frank Rutley, Esq., F.G.S. With Analyses by Philip Holland, Esq., F.1.C., F.C:S. The specimens described were collected by the late Prof. Green and Mr. G. J. Goodchild from the Borrowdale volcanic series which constitutes the central mass of Dufton Pike, and the chief interest attaching to them is their alteration, probably as the result ot solfataric action. One of the rocks, which has the composition of a soda-rhyolite, contains felspar, augite, magnetite, and possibly spinel or garnet, scapolite, and ilmenite. The porphyritic crystals of felspar are much corroded, and are sometimes mere spongy masses 10 which mica and opal-silica have been developed, together with small quantities of carbonates, In a second example, felspar-fragments On the Unconformity of the Upper Coal Measures. 669 appear as a meshwork of rods which extinguish simultaneously, and are embedded in an isotropic groundmass crowded with globu- lites and little rods. A faint streakiness which cannot be fluxion- structure passes through the matrix of the rock and the meshwork of the felspar-fragments without deflection. Analyses of the rocks and diagrams constructed from their molecular ratios correspond closely with those of soda-rhyolite and potash-rhyolite respectively. December 5th.—J. J. H. Teall, Esq., M.A., F.R.S., President, in the Chair. The following communications were read :— 1. ‘On the Corallian Rocks of St. Ives (Hunts) and Elsworth.’ By C. B. Wedd, Esq., B.A., F.G.S. Starting 24 miles south-west of Elsworth, the author traces the Elsworth Rock at intervals through Croxton, Yelling, Papworth Eyerard, etc. to Elsworth, and thence towards Fen Drayton and near Swavesey. The Oxford Clay is found to the west of it, and the Ampthill Clay to the east. Frequent fossil lists are given, and the character of the rock is described at the different exposures. Again, from Haughton Hall, west of St. Ives, the ‘St. Ives Rock ’ is traced through that town and towards Holywell. The actual connexion with the Elsworth Rock cannot be seen owing to an area of fen. But that the two rocks are identical the author considers is proved by the consistency of the two rocks, the absence of any other rock-bed, the dip of the strata, and the presence of Ampthil Clay above. The Corallian strata of the area appear to have been deposited more slowly than the Oxfordian strata. Of the two zonal ammonites of the Corallian, the dominant form in the Elsworth Rock and in the stone-bands of the Ampthill Clay is of the plicatils and not the perarmatus-type. 2. ‘The Unconformity of the Upper (red) Coal Measures to the Middle (grey) Coal Measures of the Shropshire Coalfields, and its Bearing upon the Extension of the Latter under the Triassic Rocks.’ By William James Clarke, Esq. The Upper Red Measures have a much greater extension in the Shropshire Coalfields than the productive Measures below. In the Shrewsbury field they are the only Carboniferous rocks present, and rest on pre-Carboniferous rocks, When the sections of collieries at and near Madeley are plotted on the assumption that the base of the Upper Carboniferous rocks is horizontal, the Lower Measures are found to be bent into a | syncline rising sharply to the north-north-west and more gently to the south-south-east. A second syncline, broader and deeper, extends from Stirchly towards Hadley, but the westerly rise is often hidden by the boundary-fault of the coaltield. This pheno- menon is known locally as the ‘Symon Fault’; and instead of taking Scott’s view that it represents a hollow denuded in the Lower Coal Measures, the author considers it due to folding before late Car- boniferous times. A third little syncline occurs at the Inett and Caughley. Similar phenomena are exhibited in the Forest of Wyre 670 Intelligence and Miscellaneous Articles. Coalfield, where a series of unproductive measures come in between the Lower and Upper Coal Measures. The axis of the folds runs east-north-eastward, and their amplitude and length diminish in proceeding from north-west to south-east. Inter-Carboniferous folds also occur in the North Wales and North Staffordshire fields. 3. ‘ Bajocian and Contiguous Deposits in the Northern Cottes- wolds: the Main Hill-Mass.’ By 8. 8. Buckman, Esq., F.G.S. After giving comparative sections at Cleeve, Leckhampton Hull, and Birdlip, to show the disappearance of three horizons at the second locality and five more at the third, the author interprets the absence of the beds as due to ‘ pene-contemporaneous erosion ’ brought about by the elevation of rocks, due to small earth- movements along a main south-west to north-east axis and sub- sidiary axes north-west to south-east. In the Northern Cotteswolds the beds which come in at Cleeve disappear, while there is a development of the Harford Sands, the Tilestone, and the Snowshill Clay above the Lower 7’rigonza-Grit. A series of detailed sections along the main hill-mass is given. On tracing the rocks from west to east across the Northern Cotteswolds, the whole of the Inferior Oolite disappears, except quite the upper portion which rests directly on Upper Lias, and the Upper Lias itself undergoes denudation ; eastward the latter thickens again, and basal beds of Inferior Oolite reappear. Thus the axis of an important anticline is along the Vale of Moreton. The general result of the observations does not confirm Prof. Hull’s view that these members of the Jurassic are thinning and disappearing eastward. The observed phenomena were really brought about by contemporaneous erosions ; whereof the principal one occurred before the deposition of the Upper Trigowa-Grit. A revised map of Bajocian denudation is given, and itis shown that, owing to anticlinal axes along the Vales of Bourton and Moreton, pene-contemporaneous erosion must have had considerable influence in determining the position of these valleys. Such erosion is likely to have taken place along similar lines at different times, and therefore may be connected with folds in Paleozoic rocks and may have a bearing on the thickness of rocks overlying the Coal Measures. <. ey eee oa SC ATENT OFFICA Sree Barus (Dr. C.) on the change of the colours of cloudy condensation, 572. Beattie (Prof. J. ©.) on leakage of electricity from charged bodies, 449, Beattie (R.) on the hysteresis of nickel and cobalt in a rotating magnetic field, 642. Bonney (Prof. T. G.) on the drifts of the Baltic coast of Germany, 598. Books, new :— Weber’s Die partiellen Ditferential-Gleichungen der ma thematischen Physik, 166; Ball’s Treatise on the Theory of Screws, 260; Annuaire du Bureau des Longitudes pour Van 1901, 517 ; The Electro-Chemist and Metal- lurgist, 517; Rudorf’s The Peri- odic Classification and the Problem of Chemical Evolution, 517 ; Mel- dola’s Inorganic Chemistry, 518; Hawkins’ Theory of Commutation, 519; von Bezold’s Theoretische Betrachtungen uber die Ergeb- nisse der Wissenschaftlichen Luft- fahrten des Deutschen Vereins zur Forderung der Luftschiffahrt in Berlin, 519; Brillouin’s Mémoires Originaux sur la Circulation Géné- rale de VAtmosphére, 519; Wein- stein’s Die Erdstrome im Deuts- chen Reichsteleeraphengebiet,520, Bottomley (Dr. J. T.) on the ex- pansibility of a hard Jena glass, 125, Brace (Prof. D. B.) on the resolution of light into its circular com- ponents in the Faraday effect, 464; on the determination of the order of crystal-plates, 546. INDEX. Buchanan (J.) on magnetic induc- tion in iron and other metals, 330. Buckman (S.8.) on Bajocian deposits in Northern Cotteswolds, 670. Burke (J. B. B.) on the phospho- rescent glow in gases, 342, 455. Carbon, on the anomalous dispersion of, 405; on the spectra of com- pounds of, 476. Carbon dioxide, on the specific ionic velocities in, 81; on the spectrum of, 489; on the conductivity pro- duced in, by the motion of nega- tively charged ions, 630. Cathode-rays, on radiation produced by, 361. Chance, applications of the theory of, to racial differentiation, 110. Chapman (F.) on the eolian sands of Kathiawar, 167. Chattock (Prof. A. P.) on the specific velocities of ions in the discharge from points, 79. Clarke (W. J.) on the unconformity of the Coal-Measures, 669. Cobalt, on the hysteresis of, in a rotating magnetic field, 642. Coherer, on the simple, 265. Colloidal solution, on a theory of, 647. Colours, on the change of the, of cloudy condensation, 572. Concentration at the electrodes in a solution, on the, 45. Condensation, on the change of the colours of cloudy, 572. Conductivity produced in gases by the motion of ions, on the, 198, 630. Coomara-Swamy (A. K.) on Ceylon rocks and graphite, 168. Crémieu’s experiment, on, 325. Crookes tube, on the absorption of oas in a, 503, 671. Crystal plates, on the determination of the order of, 546. —— symmetry, on the thirty-two classes of, l. Crystals, on differential double re- fraction in, 539. Currents, on the propagation of polyphase, 563. Curves, on the graphical treatment of experimental, 403; on the family of, representing van der Phil. Mag. 8. 6. Vol. 1. No. 6. June 1901. 673 Waals’ equation, 579 ; of errors, on the normal, 669. Cusped waves, on the propagation of, 589. Cyanin, on the anomalous dispersion of, 56; on prisms of, 624. Dark space, theory of the, 361. Dielectric, on the elongation of a, in an electrostatic field, 357. Dixon (EK. H.) on the specific ve- locities of ions in the discharge from points, 79. Donnan (Dr. F. G.) on a theory of colloidal solution, 647, Double refraction, on, due to un- equal heating, 169; on differential, 539; on the, of electric waves, 548. Earhart (R. F.) on the sparking distances between plates, 147. Earth-currents, on the theory of magnetic disturbance by, 432. Echelon grating, on a mica, 627. Electric conductivity produced in gases by the motion of ions, on the, 198, 630. —— convection, on the inertia of, 227. discharge, on the specific velo- cities of ions in the, from points, 79; on the effect of a magnetic field on the, through a gas, 250; on the striated, 521. field, on the effect of an, on cloudy condensation, 572. inertia, on, 227, —-— spectra of carbon compounds, 495, tramways, on the magnetic field produced by, 423, 432. waves, on indices of refraction for, 179 ; on the double refraction of, 548; on the velocity of, along wires, 6, Electricity, on leakage of, from charged bodies, 442; on the pro- duction of, by air subjected to v-Yays, 939. Electrodes, on the concentration at the, in a solution, 45. Electrodynamics, on the mental equations of, 325, Electrolysis, on the liberation of hydrogen by, 45. Electromotive force pressure, 377. funda- and osmotic 2Y 674 Kivans (Dr. J. W.) on a monchiquite from Junagarh, 600. Evans (W. T.) on the expansibility of a hard Jena glass, 125. laraday effect, on the, 464. Field, on the effect of an electric, on cloudy condensation, 572. FitzGerald (Prof. G. F.), obituary notice of, 360. Flash spectrum, on the, 551. Gases, spectroscopic notes concerning the, of the atmosphere, 100; on the conductivity produced in, by the motion of negatively charged ions, 198, 630; on the effect of a magnetic field on the discharge through, 250; on the phospho- rescent glow in, 342, 455; on the absorption of, in a Crookes tube, 503, 670. Geological Society, proceedings of the, 167, 520, 598, 667. Glass, on the expansibility of a hard Jena, 125; on double refraction in, 169. Glazebrook (Dr. R. T.) on the theory of magnetic disturbance by earth- currents, 452. Glow, on the phosphorescent, in gases, 342, 455; on a theory of the negative, 361. Grating, on a mica echelon, 627. Gwyther (R. F.) on progressive long waves in shallow water, 106. Heating, on the stresses in solid bodies due to unequal, 169. Helium, on the concentration of, from the atmosphere, 105. Hill (Rev. E.) on the drifts of the Baltic coast of Germany, 598. Hilton (H.) on van der Waals’ equation, 579. Hydrochloric acid and methylether, on mixtures of, 595. Hydrogen, on the liberation of, by electrolysis, 45; on the specific ionic velocities in, 79; on the visibility of, in air, 100; on the liquefaction of, 411; on the con- ductivity produced in, by the motion of negatively charged ions, 630. Hysteresis of nickel and cobalt in a rotating magnetic field, on the, 642. Induction, on magnetic, in iron and other metals, 330. INDEX. Inertia, on electric, 227. Interruptor, on the function of self- induction in Wehnelt’s, 246. Tons, on the specific velocities of, in the discharge from points, 79; on the conductivity produced in gases by the motion of negatively charged, 198, 630. Tron, on the magnetic properties of alloys of, and aluminium, 296 ; on magnetic induction in, 320, Jeans (J. HI.) on the striated elec- trical discharge, 521. Jena glass, on the expansibility of a hard, 125. Kirkby (P. J.) on the conductivity produced in gases by the motion of negatively charged ions, 630. Kuenen (Dr. J. P.) on mixtures of hydrochloric acid and meth vlether, 595. Laws (S. C.) on changes in the magnetic condition of an alloy of iron and aluminium, 296. Leakage of electricity from charged bodies, on, 442. Lees (Dr. C. H.) on the viscosities . of mixtures of liquids and solutions, 128. : Lehfeldt (Dr. R. A.) on electro- motive force and osmotic pressure, 377; on the graphical treatment of experimental curves, 403. Lenses, on astigmatic, 239. Light, on the resolution of, into its circular components in the Faraday effect, 464. Liquids, on the viscosities of mix- tures of, and solutions, 128. Lownds (L.) on the magnetic pro- perties of alloys of iron and alu- minium, 601. Luminous intensities of sun and sky, on the relative, 555. Magnetic disturbance by earth- currents, on the theory of, 432. field, on the effect of a, on the discharge through a gas, 250; on the, produced by electric tram- ways, 423, 432; on the hysteresis of nickel and cobalt in a rotating, 642, induction in iron and other metals, on, 530. precession, on, 314. properties of the alloys of iron and aluminium, on the, 296, 601. INDEX. Magnusson (C. E.) on the anomalous dispersion of cyanin, 36. Majorana (Dr. Q.) on the relative luminous intensities of sun and sky, 555. Matley (C. A.) on the geology of Anglesey, 667. Metals, on magnetic induction in, 330. Methylether and hydrochloric acid, on mixtures of, 593. Mica echelon grating, on a, 627. Mizuno (T.) on the function of self- induction in Webhnelt’s inter- ruptor, 246. Morton (Prof. W. B.) on the pro- pagation of polyphase currents along a number of parallel wires, 563. Nickel, on the hysteresis of, in a rotating magnetic field, 642. Osmotic pressure, on electromotive force and, 377. Oxygen, on the specific ionic velo- cities in, 82. Pearson (Prof. K.) on applications of the theory of chance to racial differentiation, 110 ; on the normal curve of errors, 670. Phosphorescent glow in gases, on the, 342, 455. Photometer, on a new sky-, 597. Pierce (G.) on indices of refraction for electric waves, 179; on the double refraction of electric waves, 548. Pocklington (Dr. H. C.) on the equations of electro-dynamics and Crémieu’s experiment, 525. Points, on the specific velocities of ions in the discharge from, 79. Polyphase currents, on the pro- pagation of, 563, Positive column, theory of 361. Precession, on magnetic, 314. Pressure-gauge, on a sensitive, 96. Projectiles, on the resistance of the air to, 530. Racial differentiation, applications of the theory of chance to, 110. Radiation and absorption, on Balfour Stewart's theory of the connexion between, 98; on, produced by cathode-rays, 361. Radio-micrometer, on a new, 179. the, 675 Raisin (Dr. C. A.) on altered rocks from Bastogne, 599. a. Rayleigh (Lord) on Balfour Stewart's theory of the connexion between radiation and absorption, 98; on the visibility of hydrogen in air, 100; on the demonstration at atmospheric pressure of argou from very small quantities of air, 103; on the concentration of helium from the atmosphere, 105 ; on the stresses in solid bodies due to unequal heating, 169; on the propagation of sound between parallel walls, 301. Refraction of sound by wind, on the, 159; on double, due to unequal heating, 169; on indices of, for electric waves, 179; on differ- ential double, 539; on the double, of electric waves, 548. Rendtorff (E. J.) on differential double refraction, 539. Resistance of the air at speeds below 1000 feet a second, on the, 530. Richardson (Prof. S. W.) on the magnetic properties of alloys of iron and aluminium, 296, 601. Rollins (W.) on the absorption of gas in a Crookes tube, 671. Rucker (Prof. A. W.) on the mag- netic field produced by electric tramways, 423. Rutley (F.) on rhyolitic rocks from Westmorland, 668. Sacerdote (Dr. P.) on the elongation of a dielectric in an electrostatic field, 357. Sand (Dr. H. J. S.) on the con- centration at the electrodes in a solution, 45. Schuster (Prof. A.) on electric inertia and the inertia of electric convection, 227; on magnetic precession, 314. Self-induction, on the function of, in Wehnelt’s interruptor, 246. ee (P. E.) on the simple coherer, Sky, on the relative luminous inten- sities of sun and, 555. Smithells (Prof. A.) on the spectra of carbon compounds, 476. Solutions, on the concentration at the electrodes in, 45; on the vis- 676 cosities of mixtures of liquids and, 128; on a theory of colloidal, 647. Sound, on the refraction of, by wind, © 159; on the propagation of, between parallel walls, 301. Sowter (R. J.) on astigmatic lenses, 239. Sparking distances between plates, on the, 147. Spectra of carbon compounds, on the, 476. Spectroscopic notes concerning the gases of the atmosphere, 100. Spectrum, on the production of a bright-line, by anomalous dis- persion, 551. Stresses in solid bodies due to unequal heating, on the, 169. Striated electrical discharge, on the, 521. Strutt (Hon. R. J.) on the tendency of the atomic weights to approx- imate to whole numbers, 311. Swan spectrum, on the, 476. Symmetry, on crystal, 1. Thomson (Prof. J. J.) on radiation produced by cathode-rays, together with a theory of the negative glow, the dark space, and the positive column, 361. Townsend (Prof. J. 5.) on the con- ductivity produced in gases by the motion of negatively charged ions, 198, 630. Tramways, on the magnetic field produced by electric, 423, 432. Travers (Dr. M. W.) on the lique- faction of hydrogen, 41]. Turpentine, on the specific ionic velocities in, 85. Van der Waals’ equation, note on, 579. Villari (Prof. E.), how air subjected to «x-rays loses its discharging property, 5395. INDEX. Viscosities of mixtures of liquids and solutions, on the, 128. oe Walker (W. E.) on the specific velocities of ions in the discharge from points, 79. Warrington (A. W.) on hydro- meters of total immersion, 360. Waves, on progressive long, in shallow water, 106; on indices of refraction for electric, 179; on the double refraction of electric, 548 ; on the propagation of cusped, 589; on the velocity of electric, along wires, 6. Wedd (C. B.) on Corallian rocks of Elsworth, 669. Wehnelt’s interruptor, on the func- tion of self-induction in, 246. Willows (Dr. R. 8.) on the effect of a magnetic field on the discharge through a gas, 250; on the ab- sorption of gas in a Crookes tube, 503. ‘Wind, on the refraction of sound by, 159. Wires, on the propagation of poly- phase currents along parallel, 563 ; on the velocity of electric waves along, 6. | Wood (Prof. R. W.) on the ano- malous dispersion of cyanin, 36 ; on the anomalous dispersion of carbon, 405 ; on the production of a bright-line spectrum by ano- malous dispersion and its appli- cation the flash-spectrum, 551 ; onthe propagation of cusped waves, 589; on cyanin prisms and a new method of exhibiting anomalous dispersion, 624; on a mica echelon grating, 627. x-rays, on air subjected to, 535. Zahm (Dr. A. F.) on the resistance of the air at speeds below 1000 feet a second, 530. END OF THE FIRST VOLUME. ° Printed by Taytor and Francis, Red Lion Court, Fleet Street. Phil. Mag.5.6 Voll PIV X git VIRUS 22 afi PENS ec hls 'e, ‘e \ *? Neat Mimtexrm Bros. lth. U7 Phil. Mag 5.6 Vol.1.PL.VI. 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