We have now eight series of experiments upon this ratio, representing thirty distinct estimations. Combining, we get a general mean as follows:

The ratio between silver and crystallized barium chloride has also been fixed by Marignac.* The usual method was employed, and two series of experiments were made; in the second of which the water of crystallization was determined previous to the estimation. Five grammes of chloride were taken in each determination. The following quantities of BaCl2.2H2O correspond to 100 parts of silver:

* Journ. f. Prakt. Chem., 74, 212. 1858.

The general mean from both series is 113.113, ± .0067.

The direct ratio between the chlorides of silver and barium was early established both by Berzelius* and Turner. Berzelius found that 100 parts of dry barium chloride gave of silver chloride:

138.06 138.08

Mean, 138.07, .007

Turner made five experiments, with the following results:

137.45

137.54

137.70

137.62

137.64

Of these, Turner regards the fourth and fifth as the most exact. These give a mean of 137.63, .007, while the other three are in mean 137.563, .049. Combining Berzelius' figures with those of Turner, we get as follows:

Incidentally to some of his other work Marignac‡ determined the percentage of water in crystallized barium chloride. Two sets of three experiments each were made, the first upon five grammes and the second upon ten grammes of salt. The following are the percentages obtained:

*Poggend. Annal., 8, 177.

Phil. Trans., 1829, 291.

Journ. f. Prakt. Chem., 74, 212. 1858.

The ratio between barium nitrate and barium sulphate has been determined only by Turner.* According to his experiments 100 parts of sulphate correspond to the following quantities of nitrate:

112.060

III.990

112.035

Mean, 112.028, ± .014

For the similar ratio between the sulphate and the chloride there are experiments by Turner, Berzelius, Struve, and Marignac. Turnert found that 100 parts of chloride ignited with sulphuric acid gave 112.19 parts of sulphate. By the common method of precipitation and filtration a lower figure was obtained, because of the slight solubility of the sulphate. This point bears directly upon many other atomic weight determinations.

Berzelius, treating barium chloride with sulphuric acid, obtained the following results in BaSO, for 100 parts of BaClg:

112.17 112.18

Mean, 112.175, ±.0034

Struve,|| in two experiments, found :

112.0912
112.0964

Mean, 112.0938, ± .0018

Phil. Trans., 1833, 538.

+ Phil. Trans., 1829, 291.
Poggend. Annal., 8, 177.

|| Ann. Chem. Pharm., 80, 204. 1851.

The data from which we are to calculate the atomic weight of barium may now be tabulated as follows:

(1.) Ag2: BaCl, :: 100: 96.3596, ± .0009

(2.) Ag2: BaCl2.2H2O :: 100: 113.113, ± .0067

(3.) BaCl,: 2AgCl :: 100: 137.841, ± .0047

(4.) Per cent. of H2O in BaCl2.2H2O, 14.799, ± .0014

(5.) BaSO, BaN,O:: 112.028, ± .014

(6.) BaCl, BaSO :: 100: 112.106, ± .0015

From these ratios, with the aid of the atomic weights already established, we can immediately calculate four independent values for the molecular weight of BaCl2 :

We have here an interesting example of the compensation of constant errors. Ratios (2) and (4) both represent work done by Marignac upon barium chloride containing water of crystallization. If now, as is not improbable, the salt contained a trifling excess of water, the molecular weight of barium chloride as calculated from (2) would come out too high, while on the other hand the result from ratio (4) would err in the opposite direction. In point of fact, the

*Journ. f. Prakt. Chem., 74, 212. 1858.

two results in the present calculation nearly compensate each other, and, on account of their relatively high probable errors, they exert but an unimportant influence upon the general mean.

In conclusion, we have three independent values for the atomic weight of barium:

If O

=

16, then Ba= 137.007. In other words, the ratio between oxygen and barium is almost an exact ratio between two whole numbers.

In the above discussion it will at once be noticed that the second and third values for Ba have very high probable errors, and that they therefore exert almost no influence upon the general mean. This fact by no means renders them worthless however, for, at the lowest estimate, they are useful in confirmation of the better determinations. It is also highly probable that the method of discussion, rigidly carried out, does not do them absolute justice.