1530 POPE : THE REFRACTION CONSTANTS CI. -.The Rt@uction Constunts of Crystalline Salts. By WILLIAM JACKSON POPE. THE investigation of the refi-actiou equivalents of liquids by Gladstone and others, has led to results which have so materially advanced our knowledge of moleciilar s tructuro that it is perhaps remarkable that no similar results have yet been obtained with crystalline sub- s tames. During the last 30 years, laborious determinations of the densities and refractive indices of long series of salts have been made by Topsije and Christiansen, Soret), Tutton, and others, often with the express object of obtaining a direct relationship between refracttire power and chemical coniposition ; this, however, the most important aim of such work haa not hitherto been attained. Proof is advanced in the present paper that the molecular refractions of crystalliue singly or doubly refracting salts are practically additive quantities, so that the inter-relationship of the refraction constants arid the density, on the one hand, and the composition of a salt, on the other, is of an extremely simple nature, and that on this assumption the refraction constants of a large number OE salts examined by the authors named above can be very closely correlated.The refractive index r , either of aliquid or of an isotropic solid, does not vary with the direclion, and may be a t once combined with the molecular volume in any of the usual ways in order to obtain the molecular refraction. Consequently, using the Gladstone formula,OF CRYSTALLINE SALTS. 1531 the molecular refraction of all cubic crystalline substances is obtained from the formula, V(r-1), where V is the molecular volume.If the crystalline substance be anisotropic, possessing either two or three principal indices of refraction, it is not immediately apparent in what way these several indices should be combined in order to yield a single refraction constant. Two cases must be here dis- tinguished, the one of uniaxial substances having two principal refractive indices, and the other of hiaxial crystals possessing three principal indices of refraction, A uniaxial crystalline substance has an extraordinary refractive index e and an ordinary one 0 ; the optical indicatrix of such a crystal is a spheroyd of which the principal circular section has the radius 0, and the axis of revolution has the semi-diameter e.The 40~ee7.r volume of this spherojid is --, and is equal to t,hat of a sphere of 3 radius T = $‘ox This mean refractive index, r , is a single refraction constant comparable in kind with the refractive index r of an iso- tropic or liquid substance. In a biaxial crystalline Substance, the opt,icd indicatrix is an ellipsoid, having for its three principal semi-diameters the three prin- cipal refractive indices a, p and “1 ; the mean refractive index of a biaxial substance is that radius vector ’i’ of the indicatrix which is the radius of a sphere equal involume t o the ellipso’id. The volumes of the ellipso’id and the sphere are 4ug*pr $1.7 5i- and __ 3 3 respectively ; the required mean refractive index 1- is therefore the geometric mean of the refractive indices a, /3 and “1.When a doubly refracting substance, having the principal refractive indices 01: 13, and c/, or o and e , is melted, and thus made amorphous, the wave-surface becomes a sphere of radius, r = or ,;/Z, provided no change attends the melting beyond the destruction of the regular orientation of the mass units of the crystal. Similarly, if the crystalline substance be dissolved in a solvent, if dissolution have only the purely physical effect of destroying the regular arrangement of the mass-units, the end result, so far as the specific refraction is concerned, would be the same as that of dissolving an isotropic substance again of refractive index r = q F v or TX It should therefore be possible to use the values of r thus obtained for calculatiag the molecular refractions of crystalline doubly1532 POPE : THE REFRACTION CONSTANTS refracting substances in n manner slinil~r to that used in the case of liquids, and the refractive index of an isotropic substance and the mean index T of an anisotropic one should be quantitias of the same kind, and have the same physical significance.Instea,d of calculating T as a geometric mean, it may be obtained as an arithmetic mean with sufficient accuracy f o r the experimental nurnbei-s, and much greater convenience in working ; so that The use of these approximate values of r introduces no appre- ciable error, except when substances of extremely high double refi-ac- tion are being dealt with; consequently, excepting in a few such cases, the arithmetic means will be used.Further, the results obtained by using a molecular refraction formula of the Gladstone type will alone be discussed in the present paper ; au investigation, however, 0; the Lorenz and Lorentz formula has been commenced, in order to ascertain which of the two types of expression is the more applicable to crystalline substances. On displacing T in the Gladstone formula V(r-1) by the appropriate functions of the refractive indices of the crystalline substances to be considered, the expressiou naturally takes three different forms, corresponding with the three type3 of optical indicatrix possible amongst crystalline Substances. The molecnlar refraction formula is thus .................. V(r - l)..(11, for cubic crystals ; for those belonging to the hexagonal and tetm- gonal systems it is ( 9 ) 9 v{ (+ - l} ................ 20 + e whilst for rhombic, monosymmet,ric, and anorthic crys tnls the expres- sion to be used is ............ v{(" + + y)- l} (3) * The fact that formule (2) and (3) should be for anistropic sub- stances what the ordinary Gladstone formula is for liquids, has been shown by Dufet (Bull. Xoc. franc. de Min., 1887, 10, 77), who also used the expressions for calculating the molecular refractions of a series of sodium arsenates and phosphates. Dufet, Eowever, only applied the method of calculation to a small number of salts of somewhat complcx nature, and consequently failed to obtain any general results; it is probably owing fo this circumstance that the importance of the formuh has not been recognised by those who have worked at refraction constants.O F CRYSTALLINE SALTS.1533 1 *32889 1 -33038 1 -33113 1 -33298 1 -33622 1 ‘33713 It having now been demonstrated that expressions (2) and (3) are merely expanded forms of the Gladstone formula, and that their use is necessitated by the complex optical properties of anisotropic substances, these formulse will be used without further comment, as occasion arises, in connection with the various crystalliim substances dealt with in the following pages. 5 -9304 5 ‘95’73 5 -9708 Ci -0042 6 *0445 6 *G790 It is, in the first place, of great importance to determine whether liquefaction or dissolution causes the molecular refraction of a crys- talline substance to change ; satisfactory data seem available in one, and only one, case, namely, that of water and ice.The refraction constants of water, an easily purified substarce, have been determined by many observers to a degree of accuracy far greater than is neces- sary for our purpose. In the first part of Table I, van der Willigen’s values for the refractive indices of water for various lines in the spectrum, at a, temperature of 2 0 * 2 O , and a density of 0.99885, are given ; the third column gives the molecular refractions calculated fi-om the molecular volume, and the corresponding refractive indices. The refractive indices, o and 6, oE the hexagoual uniaxial ice have been accurately determined by Pulfrich (Am. Phys. Chem., 1888, 34, 326), and are given in the second part of Table I ; the determina- tions were made at Oo, and Bunsen’s value, namely, 0.91674, for the density of ice at that temperature is used in calculating the mole- c u l s ~ refractions.The differences A between the molecular refrac- tions in the liquid and solid state, are stated in the last column of the table. TABLE 1. Water. 1- A . . . . B .. .. c .. .. D . . . . E .. .. F .. .. 1 -30496 1 *30M5 1 -30715 1 -30911 1-31140 1 -3 1335 Ice. e. 1 *30626 1 ‘3W75 1 *30861 1 *31041 1 -31276 1 * 31473 2.. - 1 -80539 1 -30688 1 -30764 1 -30954 1 -31185 1 a 31381 V(r - 1). -- 5 *98’rS 6.0255 6 *0404 6 *0778 6 -1231 6.1666 0 -0574 0 -0682 0 -06‘36 0 ‘0’736 0 9’786 0 -0876 A glance at Table I suffices to show that the molecular refraction of liquid water is not identical with that of ice, but that the differ- ences between them are of the order of 1 per cent., a quantity which cannot be accounted €or as experimental error ; in fact, calculating the value of ? a D f o r ice from the value for water, on the assumption1534 POPE : THE REFRACTION COSSTANTS that the molecular refractions are the same in the two states, we get the value 1.30579, which is smaller than that of either the ordinary or the extraordinary refractive index of ice.It follows, consequentJy, that the molecular refraction of a crystalline substance is not neces- sarily the same as that of the same substance in the liquid state. I n a recent paper by Tutton (Trans., 1896,69,507), which contains a large number of data respecting the refraction coilstants of crystals, the conclusion is drawn (p.525) that "the matter in a crystal ha^, for refraction purposes, the same average effect as the same matter uncrystallised." This conclusion evidently does not hold in the case of ice and water and, as will be presently shown, is not generally true. In the case of a salt dissolved in water, the molecnlar refraction of the dissolved matter changes more rapidly with the concentration i n concentrated than in dilute solutions ; morcover, an inspection of the curves obtained by plotting concentration against molecular refraction shows that in dilute solutions the change of curvature is not rapid, and even in strong solutions the curve deriates but little from a straight line. By continuing the experimentally obtained cuives outside the limits of the experiments, the molecular refraction of the salt in an infinitely dilute or 0 per cent., and i n an infinitely concentrated or 100 per cent., solution can be determined ; these two values would be, in terms of the electrolytic dissociation liypothesis, the molecular re- fractions of the wholly dissociated and the non-dissociated salt.Owing t o the paucity oE experimental data, such a method of calculating the inolecular refraction in an infinitely concentrated solntion only gives a very poor approximation, but the results obtained show at least that as the concentration of the solution increases, the molecular re- fraction of the dissolved salt continually approaches that of the same salt in the crystalline state, as calculated by the method described above .Thus, Gladstone and Hibbert (Trans., 1895, 67, 838) quote the numbers used in Table I1 for the molecular refractions of rubidium and caesium sulphates in aqueous solutions. The concentration of the aqueous solution is st'ated in column 2, and the corresponding molecular refraction for the C line is given in column 3 ; column 4 gives the molecular refraction in a 100 per cent. solution calculated from the values in the two solutions of highest concentration, on the assumption that the refraction-concentration curve is a straight line through these two concentrations u p to 100 per cent. Column 5 contains the molecular refract'ions of the solid salts, calculated by expression (3) from Tntton's number8 (Zoc. tit.).1534 POPE : THE REFRACTION COSSTANTS that the molecular refractions are the same in the two states, we get the value 1.30579, which is smaller than that of either the ordinary or the extraordinary refractive index of ice.It follows, consequentJy, that the molecular refraction of a crystalline substance is not neces- sarily the same as that of the same substance in the liquid state. I n a recent paper by Tutton (Trans., 1896,69,507), which contains a large number of data respecting the refraction coilstants of crystals, the conclusion is drawn (p. 525) that "the matter in a crystal ha^, for refraction purposes, the same average effect as the same matter uncrystallised." This conclusion evidently does not hold in the case of ice and water and, as will be presently shown, is not generally true.In the case of a salt dissolved in water, the molecnlar refraction of the dissolved matter changes more rapidly with the concentration i n concentrated than in dilute solutions ; morcover, an inspection of the curves obtained by plotting concentration against molecular refraction shows that in dilute solutions the change of curvature is not rapid, and even in strong solutions the curve deriates but little from a straight line. By continuing the experimentally obtained cuives outside the limits of the experiments, the molecular refraction of the salt in an infinitely dilute or 0 per cent., and i n an infinitely concentrated or 100 per cent., solution can be determined ; these two values would be, in terms of the electrolytic dissociation liypothesis, the molecular re- fractions of the wholly dissociated and the non-dissociated salt.Owing t o the paucity oE experimental data, such a method of calculating the inolecular refraction in an infinitely concentrated solntion only gives a very poor approximation, but the results obtained show at least that as the concentration of the solution increases, the molecular re- fraction of the dissolved salt continually approaches that of the same salt in the crystalline state, as calculated by the method described above . Thus, Gladstone and Hibbert (Trans., 1895, 67, 838) quote the numbers used in Table I1 for the molecular refractions of rubidium and caesium sulphates in aqueous solutions. The concentration of the aqueous solution is st'ated in column 2, and the corresponding molecular refraction for the C line is given in column 3 ; column 4 gives the molecular refraction in a 100 per cent.solution calculated from the values in the two solutions of highest concentration, on the assumption that the refraction-concentration curve is a straight line through these two concentrations u p to 100 per cent. Column 5 contains the molecular refract'ions of the solid salts, calculated by expression (3) from Tntton's number8 (Zoc. tit.).1536 POPE : THE REFRAUTION CONSTANTS conclude that it was used merely becawe, in the cages of the few salts which the author compared in the two states, i t happened to give practically the same molecular refraction f o r the crystalline salt, as was found in solution. The calculation of the mean molecular refraction of ci-ystalline substances from two of the three principal indices of refraction, thus neglecting one index which is of similar physical significance to the other two, can only be used in those cases in which the median refractive index /3, chances to be the arithmetic mean of the two extreme ones a and y.In Table 111, column 1 gives the two metals present in the double sulphate, column 2 gives Tutton's molecular refractions for the salts, and column 3 gires the molecular refractions calculated from expres- sion (3) ; columns 4 and 5 give the increase in molecular refraction for Tutton's numbers and my own, on passing from zt salt containing potassium to one containing rubidium, from the rubidium to the cesium salt, and from the potassium to the caesium salt ; these three quantities are arranged in sets of three, each corresponding to a particular dyad metal.TABLE 111. Metals in srtlt. GMg ...... Xb2Mg.e . . . CsZMg.. .... K2Zn ...... Rb2Zn ...... Cs2Zn. ...... K2Fe ....... Rb2Fe ...... KZNi ....... Rb2Ni.. .... Ca-Ni ...... K,Co ....... Rb,Co,. .... C&o. ...... I(2CU. ...... RbCUu.. .... cs,cu ...... RbzMn ..... (:Ei,J'lU. ..... Cs,Cd ...... K2SO4.. .... Rb&3OI.. ... CS,SO+, . , . . CS2Fe. ...... Rb2Cd.. .... Xolecular refrac- tion. Tutton. 92 -41 97 '73 107 '42 95-90 101 * 22 110.75 96 '92 102 -03 112.00 96 -33 101 50 111 -25 96 *63 101 -91 111'76 97-29 102 -54 111 -80 102 -95 112 -499 105 '80 114 -58 32 '30 37 -79 47 -77 Pope. 92 -08 97 -443 107 '21 95 -65 101 -07 110-69 96 -35 101 -88 111 -90 96 *16 101 -42 111 -27 96-38 101 -78 111 90 96 *87 102 -16 111 *52 102 074 112 -34 105 *61 114.41 38 -35 37 -74 47 -81 Tutton. - 5 -32 9 -69 15 '01 5-32 9 -53 14 -85 5.11 10 -07 15 *18 5 *l'r 9 9 5 14 * 92 5 -28 9 '85 15 '13 4 -25 9 '26 13 -51 9 -54 8 -78 5'39 9 -Y8 15 '37 -.- Pope. ~- 5 '443 9 -73 15 -13 5 -42 9 *62 15 *M 5.53 10 002 15 -55 5 -26 9 -85 15 -11 5 *40 9 -92 15 -32 5 -29 9 -36 14.65 9 -60 8 -83 5 4 9 10 -07 15 * 56 - - Molecular refraction xblcnlated. -- - 97 -48 107 -21 95 '63 101 '03 110.76 96 -53 101 *98 111 -66 96 -11 101 -51 111 -24 96 *a 101 '84, 111 -57 96 -68 102 -08 111 *81 102 -68 112 '41 105 '16 114 '89 - - -OF CRYSTALLINE SALTS. 1537 I(, to Rb,. The mean and limiting values of these three differences are tabulated in Table IV.Rbz to CS,. I(, to CS~. TABLE IV. Mean. Limits. I Mean. 1 Limits. . 1 Limits. Tutton.. . . Pope . . . . . I-- -- 4.25-5.39 5 *26-5- 53 4-30 4.30 4.49 4.36 -- 4-27 4-40 4.69 4-45 --- 5 -07 S *7&10 '07 9 -56 13 -51-15 *37 5 '40 8 '83-10 *07 9 -62 14 *65-15.56 I I 1 --- Mean. . . . . . . . . Mean. - 3 -55 14 97 15 -13 The limits of the differences are very much closer with my values that with Tntton's amongst the differences between corresponding potassium and rubidium salts, the mean deviation from the mean of my values is less than a quarter of that of Tutton's. A lack of uniformity amongst the latter might very naturally be expected to attend the neglect of the median refractive index p. It has now been shown tha.t within very narrow limits a constant increase i n molecular refraction occurs on changing one of the potas- sium double salts to a rubidium or cesium salt, if the dyad metal remains the same ; i t is also easy to demonstrate that on changing the dyad metal, whilst keeping the alkali metal the same, a practically constant increase occurs.The increase in molecular refraction for the ray C which occurs on passing from a magnesium salt to any of the others is given in Table V. TABLE V. Mg to 1 Zn. j 3.57 I 3.59 ' 3-48 Ni . 4 -08 3 -94 4 -06 4 -03 Co. I Fe. ~ I--( cu. -- 4 -so 4 *68 4 -31 4 -60 ,-- Xn. Cd. - 8 '13 7 -23 7 '68 ~ ~ Knowing the molecular refiaaction of one of these double salts, it is now possible t o calculate that of any of the others by merely adding or subtracting the average differences for the alkali metals (Table IV) and the dyad metals (Table V).The numbers given in the last column of Table I11 are calculated in this way from the molecular refraction of magnesium potassium sulphate ; the agree-1535 POPE : THE REFRACTION CONSTANTS ment between the found values in column 3 and the calculated values in column 6 is very close. This agreement at once suggests as highly probable that if tlle molecular refractions of other series of salts weye dealt with, these constaiits would turn out t,o be, iu the main, additive ones, and that it would be possible to calculate with fair accuracy the molecular refraction of a crystalline salt, froni a table of atomic refractions ; this view was found to be fully confirmed on examining the refrac- tive indices and molecular volumes of a large number of other salts.Amongst the double salts discinssed above, there seems but little indication that the molecular refraction is other than A purely additive property, probably because most of these salts are iso- morphous and of the same type ; dealing with salts of various con- stitutions, however, it may possibly be shown that the atomic refractions are merely average numbers and really vary with the type, just as Perkin (Trans., 1896, 69, 1025) has recently found with the molecular rotations of liquids. The molecular refractions of crystalline salts are, in t,he main, tho sums of definite increments of refraction due to the atoms or radicles contained in the molecule. By assigning definite refraction constants to the various inorganic basic and acidic radicles, it becomes possible t o calculate, with fair approximation to the founcl values, the molecular refraction of any particular crystalline salt ; the particular values of the various refraction constants are cal- culated by a process of trial and error froni the observed values of the molecular refractions of the solid salts.Table VI gives these atomic or equivalent refractioii constants for a large number of basic and acidic radicles for the D my. TABLE VI. Radicle. --- Na. ........ Li ........ K ......... Rb ........ cs.. ....... NH4 ...... Sr ........ Ba ........ Pb ........ T l . . ....... 211 ........ Xi ........ Mg ....... Refraction equivalent. 4 . 1 4 a 4 5 7 -64 10 -31 15 -25 11 ‘38 13 *95 18 *94 30 -02 22 -14 8 -81 12 -40 12 *84 Radicle.-- Go. ...... Pe” ..... Fe’” ..... cu ...... Mn.. .... Cd ...... 81. ...... Cr”’ ..... Ga ...... Cl ....... Br.. , . , , . NO,. .... r ........ Refraction equivalent. 13 -18 13 -38 23 ‘03 13 -5z 14 ’04 16 *53 14 *61 22 *25 16 ‘52 10 -99 17 -26 29 -08 13.47 Radicle. so,. ..... SeO,. .... CrO,. .... ClO, .... ErO, .... sao, ..... YIICI, .... SiB, ..... &PO, ... H2As04. . H,O (of crystal- lisation) Refraction equi d e n t . 17 -08 24 ‘11 37 ‘13 17 -86 23 ‘0 34 *30 86 -5 11 *51 21 -6 27 ‘72OF CRYSTALLINE SALTS. 3 539 Ln Table VII, these refraction equivalents are used in order to calculate the molecular refractions given in column 6 ; t’he values deduced from the observed values of the refractive indices and mole- cular volumes by the use of formuls (1), (2), and (3) are stated in column 5.Column 4 denotes the crystalline system of the salf, column 3 indicates the authority for the experimental data, and columns 7 and 8 state the real and percentage differences between the found and calculated values. I n the few cases in which data for only one salt containing a particular radicle are available, the equivalent refraction of the radicle has been calculated from the molecular refraction of that salt alone; these cases are denoted by dashes in the columns of differences. Twenty-five of the salts were examined by Tnttotl (T) ; it will be noticed that in their case the agreement between the observed and calculated values is very perfect. Another set of 45 salts was ex- amined by Topsoe and Chr.ietiansen(T and C) (Ann.C h i m Phys., 1874, [5],1, 5), in the hope that the results might lea8d to some generalisa- tion of the kind now brought forward ; the agreemeut between the found and calculated values is here not quite so good as in tlhe case where Tutton’s data were used, owing probably to greater experi- mental error. Many of the values (G) are taken froin Gladstone and Hibbert (Trans., 1895, 831), and some ( B ) are from a recent papei. by Le Blnnc and Rohland (Zeits. physikaZ. Chem., 1896, 19, 261) ; the latter seem to have been determined by Le Blanc’s method (Zeits. physilial. Chem., 1892, 10, 433), the accuracy of which has not yet been satisfactorily established. The long series of alums (S) examined by Soret (Arch. Sci. Fhys. ATat., 1884, [ 3 ] , 12, 553) is also used in the table. These salts belong t o the cubic system, and con- sequently no complication arises as in tbe case of salts possessing several refractive indices.Gladstone (Phil. Mag., 1885, 20, 162) was thus able to deal with Soret’s data, and used the refractive indices obtained for the C ray. Several of the experimental values were obtained by Dufet (D). It is to be observed that although fire different crystalline systems are fully represented, necessitating the different manipulation of the refraction constants, the agreement between the obsei~ed and calcn- lated molecular refractions is of t’he same order in each system. The differericcs between the observed and calculated values, further, are of somewhat the same order as the experimental error may be judged to be in most cases; although none of the authors whose data are employed give any indication of the magnitude OE the experimental error, the latter is in some cases undoubtedly large, as may be seen by comparing those salts of which two determina- tions, apparently of equal acc1ii’acy, are qnoled.The expelimental1540 POPE : TRE REFRACTION CONSTANTS .... _ _ ~ . .... - ........... ... h W P $ k u) 5 . . . . . - . . . . . . . . . . . . ...... .~ - .. - n .. ~~ -. . ~~. . - __ ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - ^ . . - - - " - - - ^ - - . . - . . . . . . . . . . . . . . . . . . .......... . ...... ~~ ~. .... __ - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : : : : : : Q : :t'9. 1- 9v. 2 - T I . O + 8P. 0 + 16.0 + 88.0 + €0. 8 + W.O+ 08. 8- 08.0+ 99. z + 19.0 + 80*2+ €P.O+ 98.0- 09.0- 80.0 + 92. o+ 4s. o+ 10- 0 + 92.0- &V- 1 - €1.0+ 479.0- 02.0 + v2.0 + - ................................... O'H9'913~S~H 0"H 9 '98!SnM 0zH9'gd!S% 'OzH9'9d!SUZ ' 'OzH9'9d?S!N I ' OZH9'96?Sn3 ............... 96!SZ(pHN) * a * Q~HS*O~S!N 06H9"OaS%41 OZHL"0WW OUE4"0S% ................... OzH4"OSnZ .................. O~HS'~OS!N ........................ O~EL"OS!N OaF'H tOS"s3 oszq21 OSQ O~ HP ( P ~ a ~ ) ~ 3 Z ( * ~ ~ ) .......... o~HH~';(~o~s)~o~(~HN) oZ H~'~(~o~s)!N~OHN) O ~ H 9 ' z ( ( P ~ a ~ ) a a z PHN) oZmLz ( P ~ a ~ ) ~ ~ z ( b ~ ~ ) o ~ H ~ ' ~ ( p ~ ~ ~ ) % z ( + ~ ~ ) O ~ H S ' ~ ( p ~ a ~ ) ~ ~ z ~ ~ j ................... .................. I ................. ................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .................. ................... .................... p .............................................. ......................... .......... . . p p .......... .......... .......... .......... .............. .............. 0:H 9':( '0 a S)nEf)I O6H9'"('0~S)03"H .............. .----- 'w3 V9 €9 29 T9 09 6V ' s g m LP 9P 9f w €V zv 19 OP 66 86 t 8 96 sf8 'PI SF: Z I T8 OE 62 82 0w w TABLE VIL-canbinued. cn ,,I& Difference A. Number. 61 NH4H2POJ.. ................... ti2 NaH2Y0,,2H,0 ................ 63 NaH2P04,H,0.. ................ 64 KH~ASOJ...... ................ 65 NH4H&04.. .................. 66 NaH2As0J,2H20.. .............. 6'7 N~LB~AEO~,H,O.. ............... 68 NR~AI~(SO~)~,~~H~O ............ ......... ............. 6'3 (NH4)?812(S04)2,24H20 70 K?A1,(804)1,?4H20 71 ............. 9 9 ............OF CRYSTALLINE SALTS.1543 I : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......... ....-.,..--.-.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....,........... ......... . . . . . . . . . * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I . . . . . . I . . - . . . . I d : : : . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y . . . . . . . . . . . . . . . . .ow . . . . . - . . n I ) - - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . - . - . . . - . . . . . * . . . . . . - . . . . - - . . . . .'FABLE VII-continued, i Number. Salt. 109 110 111 112 113 114 115 Mg (Br03)2,6H20 ............... Zn ( Br03) 2,6H20. ............... Ba(NO&. ..................... Sr(N03)2.. ..................... ........................ Pb(N03)s ...................... )) ...................... Obsei-r er. I I V(!r - 1). Observed. Crystalline sptem. D. T. afid C. B. T. and C. I% 9 ) Cubic.. ......... ,, ........... )) ........... ), .......... ) ) ........... ,) ........... ............. 86.88 93 -10 45.96 45 -80 40 *66 57 -14 5'7 026 Calculated. -- 89 so1 92 *60 45 -88 45 -88 40 '89 56 -96 56 -96 w crc * rp. Difference A. Real. ---- + 2 -13 -0.50 -0 S O 8 + 0 nos + 0 -23 -0.18 -0 -30 Percentage.+ 2.4% -0.54 -0 '16 + 0 -16 + 0 '57 -0 -31 -0.53OF CRFSTALLIXE SALTS. 1545 error, due probably to impurity of the salts, is in the case of the indium alums so great that no trustworthy value for the atomic refraction of indium could be calculated. The atomic and equivalent refractions given i n Table VI differ not a little from those which previous workers in this subject have deduced from observations made on solutions. This, although rather inconvenient f o r purposes of comparison, is perhaps not wholly a disadvantage, as it may assist in correcting some of the very generally prevalent fallacies re3pecting atomic refractions. These numbers are 'purely empirical values, and d3 not necessarily possess any connection with the refraction constants deduced froin observations made on the free elements themselves (compare Briihl (Zeits.physikal. Cheuz., 1891, 7, 1). It does not indeed at first sight seem a t all logical to deal with atomic constants in the case of so highly constitutivz a property as molecular refraction, although as a matter of practical convenience it is found necessary. This being premised, i t is of little moment that the atomic refrac- tions now given differ from those previously employed; those in Table VI answer well for a large number of substances of fairly similar types, namely, metallic salts, but when accurate data sha 1 have been compiled from measurements made on large numbers of compounds of widely different types, doubtless the atomic refrac- tions in Table VI whilst undergoing multiplication will also have to undergo some revision.At the same time the list is sufficiently accurate to substantiate my view that the molecular refractions of solid salts are, in the main, the sums of definite so-called atomic or equivalent refractions. It should perhaps be pointed out that Mallard (Trait6 de Cristal- lographie, 1884, 2, 490) has giren a table of refraction constants of various oxides which may be used for calculating the molecular refractions of a number of minerals, more especially of silicates. This branch of the subject has, however, apparently not been further developed. The immense progress which has been made during the past half century in organic chemistry has been almost wholly due to the comparative ease with which methods, both physical and chemical, of determining molecular constit.ution have been devised. Similarly, the fact that so little is yet known of the constitution of inorganic compounds is in great measure due to the diEiculty of attacking such substances without profoundly altering them ; the peculiar action of water, usually the only available solvent, on them, and the infusibility and sparing solubility of most inorganic compounds, also increase the difficulty of determining their constitutions. The r e d t is that amongst inorganic compounds practically no chemi-1546 LAPWORTH AND KIPPING : cal means of determining constitution are available, inasmuch a3 the substances must of necessity be examined in the solid state. Almost the only applicable methods of arriving at the constitution of inorganic compounds are thus necessarily physical ones, and, as is well known, such methods have not as yet been applied to any great extent to solid substances. The use of so highly constitutive a property as that of molecular refraction in the study of inorganic compounds may thus be expected to throw much light on the consti- tution of such complex subst'ances, for example, a8 the salts of tung- stic, molybdic and phosphoric acids. Chemical Department, Central Techizical College, South Kensington, Londost.