TUTTON : THE REFRACTJON CONSTANTS, &C. 235 XIX.-The Refraction Constants o f Cyystalliue Salts. BY ALFRED EDWIN TUTTON. IN a recent issue of this Journal (Trans., 1896, 69, 1530), there appears a contribution by Mr. Pope on the above subject, containing a criticism of certain results published by the author of the present communication earlier in the past year (Trans., 1896, 69, 502) con- cerning the molecular refraction constants of the sulphates and double sulphates containing potassium, rubidium, and cmium. I n the paper referred to, which includes no new experimental data, Mr. Pope advances a claim to originality with regard to the additive nature of the molecular refractions of crystallised compounds, to which, it appears, he is not entitled. It was clearly sbomn in the author’s memoir that this rule of additive moleculnr refraction held good in the cases of the whole of the 22 double sulphates of the series R2M(S04)2 + 6H,O, the results of the investigation of which were then presented, and i t was thereby established that the same refraction equivalents which were observed in the case of the simple alkali sulphates apply also to those salts when combined with the sulphates of magnesium, zinc, iron, nickel, cobalt, copper, manganese, and cadmium.The author did not, however, lay claim t o the discovery of the rule that the molecular refraction of a crystallised compound is the sum of the re- fractions of its components, for the reason that he considered that the valuable work of previous observers, notably that of Gladstone, in which he utilised the data of Topsoe and Christiansen andof Soret, and more recently that of Perrot (A~chiv.cles Sciences pJqs. et nut. G e n h e , 1891, 26 and 669, and 1893,3), after allowing for the fact that the experimental data were not in every case all that could be desired, had already led t o that conclusion. The author consequently only presented his results from more accurate experimental data in further confirmation of the rule, and based upon its acceptance the whole argument for the similarity of the refractive power of the simple alkali sulphates when alone and when forming part of the double sulphates. Hence, when Mr. Pope speaks of the rule as ‘‘ my view that the molecular refractions of solid salts are . . . the sums of , . . atomic or equivalent refractions,” and further states on tlie first page that ‘‘ proof is advanced in the present paper that the molecular refractions of crystalline salts are practically additive quantities,” he is not contributing anything original, such proof having alreatly been advanced.Mr. Pope further draws attention t o the fact that the author, in arriving at his values for the general molecular refractions of his salts,236 TUTTON : REFRACTION CONSTANTS OF CRYSTALLINE SALTS. all of which crystallised in systems involving biaxial optical properties, took the mean of the values corresponding to the two extreme indices, a and y, rather than the mean of those corresponding to all three, a, p, and 7, and, apparently, he considers the author to be unaware of the mathematical nature of the problem.His conclusion that this course was pursued ‘‘ merely because, in the cases of the few salts which the author compared in the two states, it happened to give practically the same molecular refraction for the crystalline salt as was found in solution ” is unfounded. The author carefully considered the question during the preparation of his memoir, and decided that i t was amply sufficient for the purpose in view (that of ascertaining whether the same refraction equivalents applied to the alkali sulphates when contained in the double sulphates as when alone) to take the mean of the two extreme values, because all the salts under considera- tion exhibited extremely feeble double refractions-that is, the two extreme values were exceptionally close together, so close, indeed, that it was evident that the differences between the results so ob- tained and those derived by taking the mean of all three values would come within the limits of experimental error, although the utmost care had been taken to reduce the latter to a minimum, and there would be no gain in accuracy in return for the extra labour entailed.I n seeking confirmation of his contention that this extra labour ought to have been incurred, Mr. Pope presents a number of tables purporting to exhibit the results, recalculated in accordance with his view, from the author’s experimental data, and also comparing the recalculated values thus obtained with the author’s values. From the comparison (Table IV, p. 1537), i t would appear that the course con- tended for by Mr.Pope leads to results which differ from the author’s values by amounts far exceeding the experimental error. The author has taken the trouble to check Mr. Pope’s recalculations, with the result that no less than thirteen mistakes were found in the first three columns of figures in Table I11 for which Mr. Pope is responsible, and a similar number in the last column consequent on the others. I n two cases, the arithmetical errors are in the whole numbers, and not in decimal places, and one of them amounts to a fifth of the whole value and is three times the amount of the real difference due to the two methods of procedure. These two cases occur in the third column of figures in Table I11 ; that opposite K,Cu should be 5.25, instead of 4-25, and that opposite Cs,Cu should be 14.51, instead of 13.51.Both these inaccurate values appear as the inferior limits in Table IV, for the increment corresponding t o the passage from potassium to rubi- dium and to cmium respectively, hence, there is no wonder that, to quote Mr. Pope’s statement following the table, ‘‘ the differences areTUTTON : REFRACTION CONSTANTS OF CRYSTALLINE SALTS. 237 Rb, t o Cs,. very much closer with my values than with Tutton’s.” When the arithmetical errors are corrected, Table IV naturally assumes a very different aspect. I n its correct form, it is as follows. K, t o cs,. Increase in rnolccular refraction in passing from ! Limits. K, to Rb,. Diff. IMoan. ! Limits. Diff. Mcan. I I Limits. ~ Diff. IMean. 1 0’91 15’15 It is obvious that the differences between the extreme values found experimentaIIy in different cases of the same chemical replacement, which are due, in part a t least, t o experimental error, are much larger than is the variation in these differences according as the experimental values have been calculated from two refractive indices or from three. Mr.Pope seeks to contro- vert the author’s statement that “the matter in a crystal has, for refraction purposes, the same average effect as the same matter uncrystallised,” and in order to do so he first quotes the case of water and ice, wherein it is observed that the molecular refraction of water, calculated from the determinations of van der Willigen for 20°, appears to be slightly lower than that of ice as calculated from the determination of Pulfrich for 0”. He then extends the dis- cussion to the sulphates of rubidium and czsium, as determined with the same material by Dr.Gladstone in solution and theauthor in the crystallised condition, and states that “just as in the case of ice and water, the molecular refraction in the crystalline state is greater than that calculated for the solution.” It appears to have escaped Mr. Pope’s notice that this is so only for caesium sulphate, and that in the case of rubidium sulphate the opposite is the fact. Both differences, however, are well within the region of experimental error as regards the numbers for solutions. Moreover, water is notEa good test substance, behaving exceptionally, as it does, in so many respects, and particularly when the comparison is made between the one at 0” and the other a t 20”. Such difference as there may in reality be between the refraction effect of a substance when dissolved and when crystallised, due to change of state, is very minute, and from the broad standpoint from which the author was regarding the matter his statement was correct. It remains to notice one further point.