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CHEMICAL NEWS,
June 10, 1910

Atomic Weight and Ideal Space-symmetry Ratios.

265

THE CHEMICAL NEWS. present studied, yield with strict accuracy to formulæ of

VOL. CI., No. 2637.

Now the entire weights of the elements so far as at the same order as that of hydrogen, like formulæ being applicable to like elements, the rule being that the indices of the crystalline symmetries are high, the others low, e.g.,— Ca (40-136) (Richards, &c.) =

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ATOMIC WEIGHT ACCURATELY A FUNCTION | Hexa? [ = (Icosa x H)*] Hexa x Dodeca2 x Hexa xH
OF THE VOLUTION OF
IDEAL SPACE SYMMETRY RATIOS.

By NEWMAN HOWARD.

A CORRESPONDENT referring to my articles in the CHEMICAL NEWS (ci., 181 and 205), finds his attention arrested by two formulæ expressed in terms of the line ratios of the five ideal symmetries, or so-called regular solids. He has not perceived that all the numerical expressions stand for similar line ratios. Lest other readers are in similar case, let me further explain.

The ruling formulæ of the volutional interconversion of the numbers 3, 4, and 5-a principle which, in reply to my correspondent, permit me to say, has not, so far as I know, been before discovered-may be thus stated :

Sr (87.586) (Committee)

=

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3 x 4 dodeca2) +

icosa +

(subject to HO deviation)

Octa, tetra, hexa, icosa, and dodeca here as before stand for the ratios between the edge and centripetal lines, severally of the regular octahedron, tetrahedron, cube, icosahedron, and dodecahedron. H, the value of hydrogen (0 = 16), is not in all cases precisely the same. But it differs by o o0001 and 0'00004, exactly as by Morley and the four corroborating experimenters it is found to differ. Obviously the equation remains true if x be affixed to the indices. Of several consequences we may instance the following, found true when x=7:

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=

hexa & icosa x H

1.54 Icosa x H

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Tetrax octax x hexa; and this equation presumably facilitates that compound of those three geometric configurations which has been proved by Retgers and Barlow and Pope to be the central principle in elemental crystals. But in the change from the crystalline to other phases, an acceleration takes place, and if our hypothesis be true an expression of this acceleration is found in the change of the equal indices of x in the last equation to the indices 42, 3, &c. The effect of this change is to substitute for the crystalline equilibrium the non-crystalline icosadodecahedral equilibrium, subject precisely to the weight of hydrogen.

Gravitation is an affair of position, and operative only where positions are not equililrial. It is, in electric terminology, the disturbance of equipotential; but of an in-flow, not of a surface round-flow. It may be remarked that the change of volume in the contraction of ice to water is of such an order as we should expect by this hypothesis.

Tetra

Hexa x H max.

=

hexa or

:)

octa" hexa x dodeca icosa x octa

Octalex Tetra x Icosa3
Hexao x Dodeca x H1

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THE PRESERVATIVE MATERIALS USED BY THE | heat. Hence further evidence is necessary before it can ANCIENT EGYPTIANS IN EMBALMING.

By A. LUCAS, F.I.C.

IN a recent number of the CHEMICAL NEWS (vol. c., p. 296) there is a short Note by Dr. Paul Haas on the Inorganic Constituents of Two Egyptian Mummies. These mummies, which are stated to be of the Twelfth Dynasty, were both found in the same rock tomb though in separate coffins, and the remains are described as those of two brothers. There was such a marked difference, however, in the appearance of the mummies as to suggest that two different methods of preservation had been used, and a chemical analysis of portions of the bodies proves that such was the case.

In connection with the analysis of one of the mummies, Dr. Haas draws attention to three special points, namely, (1) the presence of calcium carbonate, (2) the presence of an aluminium compound, and (3) the absence of sodium compounds in more than the normal amount ordinarily found in the human body.

Dr. Haas suggests that since the calcium carbonate can have served no useful purpose in the embalming process, it may have originated in the use of quicklime which in the course of time has become converted into carbonate, and he adduces the extraordinary dryness of the body as a possible proof of this.

However, when it is considered that in all probability the rock tomb in which the bodies were found was in a limestone cliff, the presence of calcium carbonate is not remarkable. Possibly, too, the coffins were opened in the first instance at or near the place where they were discovered, and whether this took place inside or outside the tomb, contamination with limestone dust might readily occur. It is well known, too, that in many instances the body cavities, as also the limbs themselves, were packed with various materials, including Nile mud, and if the mummy in question had been treated in this manner, calcium carbonate, which is normally present in Nile mud, would naturally be found with the body-tissues.

About two years ago, through the kindness of Dr. Elliot Smith, F.R.S., I was enabled to examine fragments of three mummies from the tomb of Amenhotep II., and obtained the following results:

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(a) Sand, calcium carbonate, oxide of iron, and alumina. (b) Chiefly calcium carbonate, but contains also small amounts of oxide of iron and alumina.

It will be seen that calcium carbonate was found in each of these three cases, in two of which it was present in considerable amount. Knowing, however, that these mummies came from the Valley of the Kings, where the tombs are excavated in a limestone hill, I concluded that the calcium carbonate was an accidental impurity.

be said that the aluminium cannot have been originally present as a silicate, and before it can be accepted that the Egyptians made use of aluminium salts in embalming on account of their astringent properties.

The conclusion that the sodium salts found are only in such amount as is normal in the human body is noteeither salt or natron, whether as a bath or in the solid worthy, and seems to preclude the use in this instance of state.

In the case of the second mummy, however, the results of the analysis were entirely different, and comparatively large amounts of sodium salts were found to be present, and the conclusion is drawn by Dr. Haas that "the use of some mixture such as natron would appear probable." (The total amount of soda was 9:03 per cent calculated as oxide, the sulphuric anhydride amounted to 2'99 per cent, and the chlorine to 1.89 per cent). This supports the views expressed by myself some two years ago as the result of work on mummy preservative materials (Cairo Scientific Journal, April, 1908, August, 1908, and December, 1908), namely, that in some cases at least the body before burial was soaked in a solution of natural soda or natron, as it is termed, and that this was the substance described by Herodotus as natrum, about the composition of which there is such a difference of opinion.-The Cairo Scientific Journal, iv., No. 42.

DETERMINATION OF CARBON IN IRON AND STEEL.

By MAX. R. TREMBOUR.

THE following method of determining carbon in iron and steel by direct combustion may perhaps prove to be of some interest, especially in cases where the results obtained by the solution of the steel in ammonium or potassium cupric chloride and following combustion of the separated carbon are rather doubtful, as is the case with many special steels.

The method consists in burning the steel drillings in a current of oxygen by aid of ferric oxide Fe2O3, and, if the drillings are very coarse, after addition of a small amount of powdered iron, which serves to start the ignition of the coarse sample by generating the required heat.

If in making the drillings care is taken to obtain them as thin and flat as possible, and the drillings so obtained are then sifted between a 20 and 40-mesh sieve, they will burn readily, in most cases without the addition of powdered iron. To obtain such drillings in large quantity the author uses a drill the edges of which are notched in such a manner that the notches of the one edge correspond to the cogs of the other. However, almost any size of drillings can be completely burned by using a corresponding amount of powdered iron.

The apparatus used in the determination is the ordinary combustion furnace and train. A fused silica tube is preferably used, as this stands the high heat caused by the rapid combustion of the steel much better than a porcelain tube.

The iron oxide required can be easily obtained in satisfactory purity by heating and igniting iron chloride (FeCl3). The powdered iron when used has to be standardised before use to determine its carbon content. The author preferably uses iron reduced by hydrogen, which can be obtained perfectly free from carbon by reducing the iron oxide manufactured as above in a stream of hydrogen. The lower the temperature is kept during the reduction, the more readily the iron powder obtained will burn. Most of the iron by hydrogen on the market contains carbon up to several tenths of I per cent.

With regard to the presence of an aluminium compound in the ash of the mummy examined by Dr. Haas, this seems quite a usual occurrence, and the ash of the three samples above-mentioned all contained aluminium, which is also a common ingredient in the ash of the resinous materials used by the ancient Egyptians as preservatives. Dr. Haas concludes that the aluminium could not have been originally present as a silicate because it "dissolved out of the ash of the incinerated material by dilute hydrochloric acid," and hence that it was possibly employed by the ancient Egyptians in the form of a soluble aluminium salt on account of its astringent property. It should not be forgotten, however, that kaolin and many silicates con- The procedure is as follows:- From 1 to 3 grms. of the taining aluminium, although almost insoluble in strong steel (the factor weights of 1.3635 grms. or 2.7270 grms. hydrochloric acid in their natural state, become readily are a suitable amount) are weighed out and well mixed soluble in even dilute acid after calcination at a dull red-with about 1 to 4 grms. of Fe2O3, and (if the sample is

CHEMICAL NEws, June 10, 1910

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Determination of Sulphur in Pyrite and Marcasite.

coarse) with 1 to 2 grms. of powdered iron.

The mixture is spread out in a porcelain boat upon a thin layer of Fe2O3, and care is taken that no pieces of the steel are much raised above the surface of the mixture. Then the boat is pushed into the combustion tube, all burners of which are lighted before to full heat with the exception of the three or four directly under the place where the boat is to be placed. After closing the tube and turning the stream of oxygen on, the last three burners also are lighted. The oxidation takes place in from one to two minutes, whereupon the oxygen is run through the apparatus for about Then the potash bulb is weighed twenty minutes more. as usual.

During the oxidation care must be taken that enough oxygen is introduced into the tube. As soon as the three burners under the boat are lighted, the bubbling in the potash bulb will cease, and at the same time the tube will become very hot and light around the rear end of the boat, At this time the volume of where the oxidation starts. oxygen introduced into the tube must be so increased as to keep up the bubbling in the potash bulb, and must again be slowly diminished as the oxidation ceases.

If the operation has been performed all right the material in the boat will be thoroughly fused with the exception of A simple test some Fe2O3, which was added in excess. for the complete combustion is to grind the mass in an agate mortar, and then pour some acid upon it, when no effervescence should show up.

The layer of Fe2O3 is to prevent the material from sticking fast to the bottom of the boat, which when carefully handled will last for a large number of determinations. Instead of the porcelain boat a platinum boat of large size can be used with much advantage.

The following results obtained show that the method gives very satisfactory checks with other methods, which are much more troublesome and protracted :

Solution in potassium cupric chloride and combustion of residue.

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0.802

0.805

0.822

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0'768

0.687

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0.676

0.686

0.687

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Volatilisation of the

Fe in Cl

and combustion of residue. 0'350 0'928

THE EXACT DETERMINATION OF SULPHUR
IN PYRITE AND MARCASITE.
By E. T. ALLEN and JOHN JOHNSTON.
(Concluded from p. 260).

Corrected Analyses by Fresenius's Method.-It is com-
monly directed in this method to pulverise the sulphide
But since we have
before fusing with sodium carbonate.
shown that this operation may involve a considerable error,
the following analyses were made on the 20-mesh material.
Only in details was there any change in the ordinary pro-
cedure. For the sake of certainty in correction we fused
with a mixture of 4 pts. sodium carbonate and 1 pt. sodium
nitrate (instead of nitre). (The correction constants were
determined on precipitates of barium sulphate which were
thrown down in solutions containing only sodium salts).
Six grms. of the mixture were used. The fusion was heated

267

in a platinum crucible, first over a burner and finally for a
few minutes over the blast; meanwhile it was protected
from the sulphur of the flame by a good-fitting asbestos
board. The cooled fusion was extracted with water, and
the precipitate well washed. The iron was re-dissolved
and re-precipitated as described under the first method.
Both filtrates were brought to about 350 cc., and acidified
as there described; the remainder of the procedure is also
In correcting the weight of the
the same in every way.
precipitate it must be remembered that the sulphate was
precipitated from a solution containing close to 6 grms. of
sodium chloride, the amount yielded by 6 grms. of the
above fusion mixture. The presence of this salt makes a
considerable difference in the composition of the precipi-
The occluded sodium sulphate amounts
tated barium sulphate, and therefore in the corrections to
be applied to it.

on the average to 17.4 mgrms. (for 2 grms. precipitate),
and the correction for it (after an allowance of 10 per cent
for incomplete extraction) 12.2 mgrms.; the average vola-
The sum of these corrections is
tility loss is 5'9 mgrms., while the solubility loss remains
unchanged, 2.0 mgrms.

20.1 mgrms. (The correction constants were determined on precipitates formed in the presence of 5 grms. and 10 grms. NaCl respectively. The occlusion number is practically identical for both. The volatility losses are 5.2 mgrms. and 8.8 mgrms. respectively; by interpolation we obtain 5'9 mgrms. for 6 grms. NaCl).

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Corrected Results by Lunge's Method. The weighed quantity of sulphide crushed to 20-mesh size was allowed to stand over night in the cold with 10 cc. of a mixture of 3 vol. conc. nitric acid and 1 vol. conc. hydrochloric acid. The solution was then evaporated on the steam-bath, first without, then several times with hydrochloric acid to remove the nitric acid. The remainder of the analysis was exactly like the method proposed and described above. The concordance in the duplicates given above shows that the determinations were carefully done. We ascribe the lower results by Fresenius's and Lunge's methods to a loss of sulphur during oxidation. (The possibility that a loss of SO4 may be caused by the contamination of the precipitate by iron should also be considered. In Fresenius's method a little iron is dissolved when the fused mass is This iron would probably be carried leached by water. down by the barium sulphate as ferric sulphate, which would lose sulphur on ignition. See Jannasch and Richards, Journ. Prakt. Chem., xxxix., 321; E. A. Schneider, Zeit. Phys. Chem., 1892, x., 425). In the last determination of the sulphur in marcasite a little unoxidised sulphur was, in fact, noticed. The loss probably would not have occurred had the material been finely ground, but if fine grinding is resorted to another error is introduced. The Carius method of oxidation avoids both errors.

Control of Sulphur Determinations.-For the sake of control, 5-grm. portions of both pyrite and marcasite were As subjected to qualitative analysis. Except for a trace of copper in the marcasite, only silica was found; 0.04 per cent in the pyrite, and o 20 per cent in the marcasite. a final check on the accuracy of the sulphur determination it seemed desirable to determine also the amount of iron in portions of the same purified pyrite and marcasite.

268

Determination of Sulphur in Pyrite and Marcasite.

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Grms.

1.9659 BaSO4 0'0084

2'0417 BaSO4 0'0084

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The percentage of iron from these three analyses is 46.63, 46'49, and 46°54; the mean value is 46.55 per cent Fe.

2. Gravimetric.-The first determinations of the iron were made by the gravimetric method. To our surprise 1*9743=51*18% S they were all unaccountably high. As a result of some study it may be said that determinations by this method are invariably too high if certain precautions are not taken, and in view of the importance of the method our experience 2*0501=52.99% S is here included. 1'9722 BaSO4 0.0084

Marcasite. 53°33

c. 05127 grm. marcasite gave Corrections as above

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53°13

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Determination of the Iron.

If the precipitation is done in platinum by pure ammonia the results leave little to be desired. In the following determinations the sulphide was dissolved in aqua regia, 19806=53.07% S the excess of acid removed by evaporation, the residue dissolved and filtered into platinum, and twice precipitated by pure ammonia. In this precipitation the details given by Lunge were followed, viz., the liquid was heated to a temperature of 40-50°, the ammonia added, and the whole then heated to boiling. In the second precipitation macerated filter-paper was added to the solution to make the ignited precipitate more porous and to insure the complete re-oxidation of any magnetite formed in the burning (W. F. Hillebrand, Bull. U. S. G. S., cccv., p. 88). The second precipitate was thoroughly washed by the aid of the pump. The ammonia used was purified by distillation, the washed vapours being absorbed by water in a ceresin bottle; 25 cc. of this ammonia gave no weighable residue. Pyrite (a) 05272 grm. gave 03504 grm. Fe2O3 ; Fe=46 46 per cent. (b) o'5344 grm. gave 0.3557 grm. Fe2O3; Fe=46'53 per cent.

1. Volumetric.-About 0.25 grm. substance was decomposed in the usual way with 10 cc. of a mixture of 3 parts conc. HNO3 to 1 part conc. HCl. The excess of acid was gotten rid of by evaporating with sulphuric acid, first on the water-bath and finally over a free flame, until voluminous white fumes appeared. The residue was dissolved and diluted with water to about 200 cc., nearly neutralised with ammonia,* reduced with sulphur dioxide,† and titrated as usual with permanganate solution in the presence of sufficient added sulphuric acid. A weight burette was used throughout. The permanganate solution was standardised by means of sodium oxalate ("nach Sörensen," obtained from Merck), which had been previously heated for an hour at 240°. (This heated salt, as was afterwards observed, reacted very slightly alkaline, due to the formation of a trace of sodium carbonate, but cannot account for the fact that the volumetric results are somewhat higher than the final results obtained by precipitation with ammonia. Any other impurity in the oxalate, if neutral to permanganate, would of course make the percentage of iron too high). As a result of several closely agreeing determinations, 1 grm. KMnO4 solution =0.002633 grms. Fe. A number of blank experiments were performed, and the amount of permanganate used up in them, varying from 0.05 to 0'07 grm., was subtracted from the quantity used in titration. The amounts given below have been corrected in this way.

(a) 0.2682 grm. pyrite required—(1) 47·62 grms. ; (2) 47:54 grms. permanganate.

(b) 0.2682 grm. pyrite required—(1) 47'53 grms.; (2) 47·63

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The mean value, 46'49, agrees very closely with the theoretical number for FeS2, viz., 46.55 per cent Fe. Marcasite (a) 0.5028 grm. gave o'3344 grm. Fe2O3;

Fe-46 49 per cent. (b) o'5209 grm. gave 0.3471 grm. Fe2O3; Fe=46 57 per cent.

The mean value is 46 53 per cent Fe.

A Common Error in the Gravimetric Determination of Iron.-From several private communications, as well as from our own experience, it appears that the results obtained from gravimetric determinations of iron are generally too high, and by an amount which may well be 2 per cent of the total iron present. Nevertheless, there appear to be no specific references to this fact in the literature. The first two analyses of pyrite made by us gave identical results, 47'45 per cent Fe, which are certainly much in excess of the true value. These analyses were performed exactly as described above, except that the iron was precipitated in beakers of Jena glass by means of ammonia, the purity of which had not been recently controlled. This was confirmed by a number of analyses of a solution of ferrous ammonium sulphate, in which the conditions of oxidation and precipitation were varied; the results, however, varied only from o'004590 to 0'004623 grm. Fe per grm. solution, as compared with 0.004524 obtained volumetrically.

It was now found by evaporation in platinum that the ammonia left a residue; this ammonia had been re-distilled not long before; nevertheless, from 25 cc. of it (about the amount used in a double precipitation), insoluble residues weighing 30 to 3.2 mgrms., were obtained. Now, since the usual weight of a precipitate of Fe2O3 is from 300 to 350 mgrms., it is evident that this source alone may be responsible for an error of as much as 1 per cent of the total iron. The ammonia was therefore subjected to re-disbottles of (1) ordinary glass, (2) Jena glass, and (3) ceresin tillation, and the washed vapours absorbed by water in (such as are used for hydrofluoric acid).

Direct tests made one month later showed the amount of residue from 25 cc. ammonia from each of these to be respectively :- (1) 0.7 mgrm.,* (2) 0'4 mgrm., (3) o'o mgrm.

The distillation of this ammonia was conducted with very great care. The much larger amount of impurity given above is not to be referred to any special lack of care during the distillation, and that such an amount is not exceptional is shown by the uniformly high results of a number of analyses in which other samples of ammonia

CHEMICAL NEWS

June 10, 1910

Determination of Sulphur in Pyrite and Marcasite.

The ceresin bottle is thus entirely satisfactory; the others have been attacked by the ammonia to a slight extent, but sufficient to produce an error in the determination of iron which is not negligible.

That impurity in the ammonia is not responsible for the whole error is evident from the following analyses, in which the iron was precipitated twice in Jena glass beakers by means of pure ammonia :-(a) 0'5048 grm. pyrite gave 03383 grm. precipitate, whence Fe=46 85 grms. per cent. (b) o 5239 grm. marcasite gave 03514 grm. precipitate, whence Fe-46.89 per cent.

Thus the error is still fully o'6 per cent of the total iron. Further, special experiments undertaken with the purpose of tracing down this source of error showed that the use of glass beakers was responsible, and that by discarding glass entirely, and by making the precipitations in platinum vessels, satisfactory results are obtained.

269

grinding of sulphides, the method of oxidation and the corrections for barium sulphate precipitates would appear to be of perfectly general application. In the case of sulphides like those of antimony and bismuth, in which not all the sulphur would be in soluble form after oxidation, an excess of sodium carbonate would be required to transform it all into sodium sulphate, and the excess of sodium carbonate, of course, would have to be subsequently changed into sodium chloride, which, as we have seen, increases the errors due to occlusion and volatility. The method, however, is still applicable, though the errors would have to be determined for each special case.

Summary.

It has been shown that when the sulphides of iron are ground for analysis they suffer partial oxidation to sulphur dioxide and ferrous sulphate. If they are finely pulverised this error is not negligible; it may be reduced to 0.05 per cent by gentle crushing to 20-mesh size, which is sufficiently fine for the proposed method of analysis. Inhomowork, would have to be pulverised for the purpose of accurate sampling. In that case the error could be determined by washing a weighed portion of the powder with boiled water in an atmosphere of carbon dioxide, and determining the iron in the washings; the operation is rather exacting on account of the readiness with which the moist sulphide oxidises.

The definitive determinations of iron in pyrite and marcasite were made under these conditions, and, as we have seen, correct results were obtained. It is evident that it is necessary to guard against these sources of error when-geneous material, such as would be met with in commercial ever ammonia is used as a precipitant; they may exert a specially large influence in the determination of aluminium on account of its low atomic weight, and of the fact that it is frequently determined by difference.

If it is necessary to determine both iron and sulphur in the same sample, the use of sodium carbonate for the precipitation of the iron is advisable on account of larger errors otherwise involved. Experience has shown that it is safer to add the sodium carbonate slowly, and in dilute solution (in order to diminish occlusion), and that it may sometimes be necessary to make more than one subsequent precipitation with ammonia in order to obtain precipitates free from all foreign material.

Complete Analyses of Pyrite and Marcasite.

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Assistant I.

48.25
48.62

Assistant II.

48.15 48.41

The variations in the work of each analyst are:-I., 0.37 per cent, and II., o 26 per cent of the pyrite, or o'7 per cent and o'5 per cent of the total sulphur. Our own results show variations of o'07 per cent and o'05 per cent of the sulphide, 0.13 per cent and o'10 per cent of the total sulphur. These are the results obtained by using Carius's method in the oxidation; the results of the other methods, although they indicate a loss of sulphur, show equal uniformity in the determination of the sulphur present. Application of the Method to other Insoluble Sulphides. -Although we have not tried the method proposed in this paper in the analysis of other sulphides, the principles which we have discussed, viz., the error involved in the

were used. However that may be, the figures represent real amounts, which may be encountered by any one who does not specially control the purity of the ammonia he uses.

Such bottles are used to some extent for this purpose. The mag

In the proposed method the sample is oxidised in sealed tubes according to Carius; this avoids all possible loss of sulphur. Lunge's and even Fresenius's method gave in our hands lower results, a fact which we attributed to a loss of sulphur during oxidation, occasioned by the use of coarse material, or perhaps, in Fresenius's method, to the presence of iron in the barium sulphate.

The iron is removed by two precipitations with sodium carbonate. The object of this is to avoid ammonium salts, which cause much larger losses of sulphur. In precipi. tating the barium sulphate several conditions must be carefully followed, viz., the free acid must be reduced to a small measured quantity, and the precipitation must be made at a measured rate. These two conditions are necessary because they determine the composition of the precipitate, which is not pure barium sulphate, while the first determines also the loss by solubility.

In every case three corrections must be made on the weight of the barium sulphate precipitate :-(1) A correction for solubility of the precipitate, which depends on the volume of the solution and the quantity of free acid it contains; (2) a correction for the occlusion of sodium sulphate by the precipitate, which depends on many conditions, but chiefly on the quantity of alkali chloride originally present in the solution; (3) a correction for a certain amount of free sulphuric acid lost on ignition. This is not due to any sort of decomposition of the barium sulphate, but to the presence in the precipitate of "free" sulphuric acid, probably in the form of sodium acid sulphate. The most important conditions affecting this error solution, and the rate at which the precipitation is made; are the quantity of free acid and of sodium chloride in the an increase of either acid or sodium chloride increases the error; a rapid rate of precipitation decreases it, but so far as our experiments have been carried, there is not in this factory corrections. Constants may be used in making all case sufficient uniformity in the results to allow of satisthese corrections if the conditions set down are carefully followed, but otherwise they must be determined by methods given in the body of this paper. These corrections have been fully worked out by studying the precipitation of pure data on the sulphides appear the more certain since they sodium sulphate under various conditions. The analytical have been controlled by complete analyses of material which gave both positive and negative evidence of nearly theoretical purity.

nitude of the errors caused by ammonia which has been kept in glass involved in the grinding, should not be over o2 per cent The sum of the errors in this method, apart from that

does not appear to have been generally recognised.

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