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Chemists have been trying to determine the atomic weights of the chemical elements for now fully a century. Dalton introduced the idea in 1804, while Berzelius made the first reliable determina- tions as far back as 1814 and for a third of a century kept ahead of all others in this work. - While the laboratory work required for atomic weight determi- nations has been greatly improved since the time of Berzelius, the methods of reduction of the same by mathematical calculation have remained almost the same as those used by Berzelius a century ago. The work I have done in this line has hardly become known in this country, where the work done in one of the scientific departments at Washington, published by the Smithsonian Institution and dis- seminated under the official frank, continues to be upheld as the standard through the Committee on Atomic Weights of the Amer- ican Chemical Society. But at the opening of the volume for the present year it is declared that “there is confusion and uncertainty throughout the table of atomic weights.” It therefore seems desirable that this question be considered independent of the dominant chemical school by those who, like electricians and physicists, come in contact with the broad question of the constitution of matter which involves that of the atomic weights of the chemical elements. - In the old Berzelian calculations the atomic weight of oxygen is assumed as a fixed constant (IOO by Berzelius, 16 at present) and all other atomic weights are referred to this standard. This system has led to the now “official” value IO7.88 for silver, a value which I have repeatedly shown to be in conflict with the most renowned *Journal Am. Chem. Soc., 1910, p. 4. Keprinted from Proceedings American Philosophical Society, Vol. x/ix., 19/o. Ól) , () | H 66 360 HINRICHS-THE TRUE ATOMIC WEIGHTS [December 2, recent determinations to the extent of over one tenth of one per cent. This is not the place for renewing the discussion in detail; the publications in question are accessible to all. We would rather take up the question in the broadest way and try to decide it by a sort of crucial test. We will show that the evidence on which the value I6 for 04:ygen rests is evactly the same as that which gives the value 108 for silver. It is a fact that all chemical reactions are approximately exact only and that all laboratory work is subject to the same limitation. It is therefore incorrect to assume that in the reactions and in the laboratory work there is involved no error whatever on the part of the oxygen and that all errors are due to the other elements asso- ciated with oxygen. It seems sufficient to state this to have it admitted. - But if oxygen be supposed free from all material imperfections, as is assumed in the common calculations, its actual shortcomings are not blotted out thereby—they are simply placed to the account of the other elements which are unfortunate enough to be in reaction With the supposedly perfect element, assumed to be immune from error by the school. Hence the errors of the associated elements will be correspondingly magnified. In this way, the dominant school now has arrived at the value Io.7.88 for silver. Let us try to see how this has been brought about and how the question may be put in the above crucial form for decision. It is agreed by all and not even denied by the American School that the atomic weight, for O = 16, is very near the round numbers: Ag IoS, C1 35.5, C I2, N I4, etc. These values we have called the absolute atomic weights. - Accordingly, the true atomic weights can differ from these abso- lute values by small fractions only ; this we call the departure and designate by the letter epsilon (e). Hence the real mathematical problem is the determination of the departure for each element in every reaction used. We determine the departure in thousandths of the unit. Thus, if the American Chemical School be right in declaring that the atomic weight of silver is 107.88, the departure for silver would have the enormous value 1910. J OF OXYGEN AND SILVER. - 361 — I2O, while for the element oxygen in all reactions and in all determinations made by all chemists at all times and under all con- ditions the departure was zero always. But is this introduction of the departure for the entire atomic weight not merely a formal matter? Not to the man versed in higher mathematics; for he knows that even the most complex func- tions permit a simple solution by proportional parts for all cases in which the increment of the variable is sufficiently small. Thus this solution would even hold true, with fair approximation, for the departure of I2O thousandths of a unit, above indicated. We may therefore express the difference between the Berzelian reduction maintained to the present day by the dominant school of chemistry and our own as corresponding to the difference between common algebra and higher mathematics. While we have worked with the departures instead of the entire atomic weight for Over twenty years, we had not been able to deter- mine the relation between the different departures of the different elements in a given chemical reaction until we discovered the equa- tion of condition in 1907. Since then we have determined the depar- tures for each element in all the three hundred chemical reactions that have been used for the determination of atomic weights during the entire century. The results have been put into five tables, each giving sixty reactions. The first two of these tables have been pub- lished, the other three have been ready for publication since the close of IQ09. Now we may return to the point at issue, the value of the atomic weight of silver: is it 107.88 or is it 108, on the scale of 16 for Oxygen P Our tables show that oxygen occurs in I58 of the reactions used for the determination of atomic weights, while silver occurs 115 times. Consequently the atomic weight of oxygen has been deter- mined I58 times and that of silver II.5 times. Of course, the domi- nant school will declare that they have done no such thing; but that will not prevent us from using the data they have published although we will accept their declaration as made in good faith. The following table gives the results obtained, as stated repeat- 362 HINRICHS THE TRUE ATOMIC WEIGHTS [December 2, edly: departures (expressed in thousandths of the unit) from the absolute values I6 and IO8. TABLE OF DEPARTURES e (IN THOUSANDTHS). Departures. O-IO II-2C 2I–IOO O-2O 2I-40 || 4I—IOO O-IOO IOI- OxYGEN. No. of cases 89 3O 33 I Ig 17 I6 152 6 Mean e I 5 — I 2 I4 — I 7 I SILVER. No. of cases 39 22 36 6 I 22 I4. 97 I8 Mean e — I —5 —23 —2 —5 -—54 — IO No. per cent. Oxygen 58 2O 22 78 I I I I I IOO 4. . Silver 4O , 23 37 63 23 I4 IOO I8 Mean 49 2 I 3O 7o 17 I3 IOO --- All 656 Determ. for all elements 49 2 I 3O 7o I8 I 2 IOO 7 An extended study of this table would be most instructive, but a brief summary must answer here. It is noted that we have given two distinct sets of returns: by intervals of IO and of 20 thousandths of the departure. In each set we have given only the first two intervals, putting all the others into a third column. The table itself shows the reason for these modes of record in the great predominance of the small departures. This very predominance of the small departures means that the real departures are minute and the actual departures here tabulated as the results of the experimental work done during the century prove the absolute atomic weights to be the real atomic weights of nature. The question of a minute weight of the chemical valence, touched upon in our recent publications, does not come under con- sideration here. The table shows that 50 per cent. of all cases give departures below IO thousandths (O.OI) and 70 per cent. below 20 thousandths (O.O2) on all the 656 atomic weight determinations made by all the 3OO reactions employed. This proves that the determinations have for their limit the absolute atomic weights themselves and that the departures represent mainly the imperfections of the experimental work. • The relatively few larger departures (only about 12 per cent.) 1910.] OF OXYGEN AND SILVER. 363 above 40 thousandths (O.O4) are mainly due to the fact that we have taken all reactions used without excluding those known to be imperfect and which are generally excluded by others. It will also be noticed that the mean departure for the greatest number of cases is only one or a few thousandths; it is without sig- nificance in the question here considered. This question can now be fully answered. Bearing in mind that increased atomic weight necessarily brings a slight increase in the departures for experimental reasons, we must admit that the depar- tures for orygen and for silver are essentially alike, so that the values O = 16 and Ag = 108 stand and fall together. If oxygen is 16, then silver is IO8, with nearly the same degree of precision. Again, if the value Io8 is denied for silver, then the value I6 for oxygen is equally untenable. Finally, it appears to me that it has been fully demonstrated that the assumption of immunity from error for oxygen is as false in fact as it is absurd in philosophy; possibly that accounts for the tenacity with which the school has clung to the same. ST. LOUIs, Mo. 3 9015 06728 9762 2 L- O Ō 0 C Ll] > 2 D DD NOT REMOVE 0R MUTILATE CARD |||||||||||||| Binder Makers Syracuse, N.Y Pamphlet Gaylord Bros., Inc. PAI. JAN 21, 1908 Photomount --）Ķ= ！= |------~--~：·№， ſº،， * … 7 … （ … * · * （ . ）~：-…--~：،ae ：№ º：§§§§§§§ • • •~--~--~----••：،•ſ ºſ ºrº • Pºr Cae-rºsae: