everyday needs, while the suggested method of constructing the table will enable anyone to lengthen the table easily and quickly to meet particular needs.

As is well known, the expansion of (a+x)" may be written: (a+x)" =a"+c1a1x+€ 2α22x2+ where c. means the number of different combinations of n things taken r at a time. The table gives values of c, for all values of n up to 20.

In order to simplify the construction of such a table, and finally to provide a check upon the work, two simple formulas are needed:

which means that if the values of c. are laid out in rows by r's (as in the table), the sum of any two adjacent values gives the value just below the second. A glance at the table will render this fact clear and show that it may be applied to construct as large a table as is desired solely by continued or cumulative addition.

Since cr+1C,+1 = 1

by (1)+c+rCr( =s+1Cr+1) = x+2x+1

Again, by (1)

x+2Cx+x+2Cr+1( = ‚Cr+s+1Cr) = x+zC2+1 Continuing in this way, we have finally

(2)

‚ Cr + x + 1 Cr + x + 2 Cr+ which means that the sum of the values, except the last one, in any column gives the last value in the next column to the right. Thus (2) can be used as a check upon the preceding work.

To those familiar with the finite calculus the following deriva

tions of formulas (1) and (2) should prove interesting and seem more direct:

as c. may be written nr! where n = n(n-1)(n−2) ・ ・ ・

When r exceeds 9, the table should be entered with r=n—r, remembering that cr= Car

RESEARCH IN CHEMISTRY.

Conducted by B. S. Hopkins.

University of Illinois, Urbana.

It will be the object of this department to present each month the very latest results of investigations in the pedagogy of chemistry, to bring to the teacher those new and progressive ideas which will enable him to keep abreast of the times. Suggestions and contributions should be sent to Dr. B. S. Hopkins, University of Illinois, Urbana, Ill.

TUNGSTEN, TANTALUM, COLUMBIUM.
By GEORGE W. SEARS,

Assistant Professor of Chemistry, University of Nevada. The chief characteristics in the history of many of the rarer metals may be summed up in the three phrases, a chemical curiosity, investigation from a purely scientific standpoint, the discovery of useful and valuable properties followed by a rapid development. Tungsten, tantalum, and columbium give us a picture, as it were, of this history. Less than twenty years ago tungsten was practically unknown, but a careful study of its properties soon led to its employment in the steel industry and later in the manufacture of filaments for incandescent electric lamps, so that now it is almost a household word. Tantalum is just coming into prominence as a useful metal, and tantalum dental and surgical instruments are eagerly sought by those who have learned their value. Columbium is yet but little more than a chemical curiosity with practically no commercial application.

Situated as they are in the fifth and sixth groups of the periodic table, these three elements show a relation in their physical properties and chemical activity which might well lead one to expect that both tantalum and columbium will attain the wide. range of usefulness which already has been reached by the more fully developed tungsten. In appearance, specific gravity, and melting point they are not widely different. Pure tungsten and tantalum are characterized by their ductility, toughness, and malleability, while in the less pure condition both are extremely hard and brittle. In columbium these properties are somewhat less marked. In the cold all three are very inert but rapidly oxidize on heating to redness. With the exception of hydrofluoric acid tantalum and columbium are unattacked by all acids or mixtures of acids. Tungsten is slowly dissolved in hot concentrated sulphuric or hydrochloric acid. All are stable toward solutions of caustic alkali but are attacked by molten alkali nitrates, sulphur, and fused caustic alkali.

The chief ores of tungsten are wolframite, scheelite, hubnerite, and ferberite. Although ores containing tungsten have been known for a long time it was not until 1781 that Scheele discovered in scheelite a peculiar acid which he named tungstic acid. A little later the same acid was shown to exist in wolframite. While tungsten ores occur in a number of localities in both Europe and America, the United States is by far the largest producer. In 1916 the output in the United States amounted to 3,200 tons valued at $9,400,000. Large deposits of ferberite and scheelite are found in Boulder County, Colorado, from which a large part of the United States production has been taken. Considerable amounts of hubnerite, wolframite, and scheelite are being mined in Nevada and California.

Owing to the high specific gravity of tungsten ores, their concentration by various mechanical settling processes is relatively simple. However, certain European ores contain large amounts of cassiterite from which it is very difficult to separate the tungsten by these processes. It has been found advantageous in these cases to make use of magnetic separators. The tungsten ore usually contains enough iron to give it magnetic properties. The further treatment of the concentrate varies somewhat with the nature of the ore. A method which has been used quite extensively with wolframite consists in fusing the concentrated ore in a reverberatory furnace with a mixture of Na,CO, and NaNO,. This produces a soluble sodium tungstate which is lixiviated with water, filtered from insoluble matter and the tungstic acid precipitated with hydrochloric acid. The method has not been wholly satisfactory owing to the large quantities of reagents necessary and the consequent loss due to the slight solubility of the precipitates. Scheelite may be decomposed with concentrated hydrochloric or nitric acids with the formation of a soluble calcium salt and insoluble tungstic acid.

For the production of pure tungsten, ammonium tungstate is precipitated from a solution of alkali tungstate with a current of ammonia gas. This is purified by further recrystallization and finally precipitated as WO, with nitric acid. The oxide. obtained in this manner is dried, ignited, and reduced in a current of hydrogen at a temperature of 1000° to 1200°. A pure tungsten cannot be obtained by reduction with carbon, owing to the formation of tungsten carbide (W2C).

By far the largest part of tungsten produced is used in the

manufacture of steel. This finds a ready market for high speed tools, armor plate, projectiles, and firearms. Perhaps the most important property which it imparts to steel is extreme hardness and toughness. It is added in proportions varying from 2 to 12 per cent of the steel. Either alone or as an alloy with molybdenum it is finding increasing use as a substitute for platinum in the manufacture of contact points for electric welding, spark coils, signal relays, sending keys, etc. Owing to its greater conductivity and higher melting point it remains much cooler during operation and lasts longer than the platinum. Alloyed with thorium it is used as a refractory material.

Compounds of tungsten also find considerable use. Sodium tungstate is used in fireproofing curtains and draperies. Calcium tungstate on account of its fluorescence is used as a screen to make X-rays visible. Other compounds are used in glass and porcelain coloring, in making certain bronze powders, and in weighting silks. The amount of tungsten used for these purposes, however, is still relatively very small. The total consumption of tungsten in 1915 for purposes other than steel was about five tons, or less than 1 per cent of the tungsten produced.

Tantalum and eolumbium occur in a large number of ores and almost invariably occur together. Only a very few of these ores, however, are as yet of commercial importance. Tantalite containing from 40 to 70 per cent Ta2O, is the chief source of tantalum. In most specimens of tantalite1 some of the iron is replaced by manganese and some of the tantalum by columbium. Columbite is similar to tantalite in composition except that it contains a larger proportion of columbium. Although small amounts of tantalite are mined in Connecticut and in the Black Hills, the large majority of the tantalum so far used is obtained from Western Australia, where a high grade tantalite is found. As a rule the Australian tantalite contains 50 to 70 per cent Ta2O, while that found in America seldom has more than 40 per cent.

Owing to the great similarity in the chemical nature of tantalum and columbium and the insolubility of their salts in the common acids, their separation and reduction are comparatively difficult and tedious operations. The metallurgy consists of two distinct procedures, first the preparation of a pure salt, and second its reduction to the metal. According to the method of Marignac (1866), the finely powdered ore is fused 'The general formula of tantalite is given in the table at the end.