with water. Boil or cool, as the case may be. Run in the standard solution from a burette speedily, until the re-agent appears to have a slower action, and shake or stir all the time. Then run 1 c.c. or so at a time, still stirring, and finally add drops until the colour change is got.

(2) _When an outside-indicator is used._--Pour the standard solution from a burette into the a.s.say until 5 or 6 c.c. from the finishing-point; then run in 1 c.c. at a time (stirring and testing on the plate between each) until the indicator shows the change wanted, and deduct 0.5 c.c. for excess. When greater accuracy is sought for a duplicate a.s.say is made. In this case the standard solution is run in close up to the end, and the operation is finished off with a few drops at a time.

(3) _Where the finishing-point depends upon the absence of a precipitate and no outside-indicator is used._--As in the last case, run in the standard solution up to within a few c.c. of the end, then run in 1 c.c.

at a time until a precipitate is no longer formed, but here 1.5 c.c.

must be deducted for excess, since it is evident that the whole of the last "c.c." must have been, and a portion of the previous one may have been, in excess.

~Indirect t.i.tration.~--The action of permanganate of potash upon a ferrous solution is one of oxidation, hence it is evident that if any other oxidising agent is present it will count as permanganate. In such a case the t.i.tration can be used (indirectly) to estimate the quant.i.ty of such oxidising agent, by determining how much less of the permanganate is used. For example, suppose that 1 gram of iron dissolved in sulphuric acid requires 100 c.c. of standard permanganate to fully oxidise it, but that the same amount of iron only requires 35.6 c.c. of the same standard permanganate if it has been previously heated with 0.5 gram of black oxide of manganese. Here it is evident that 0.5 gram of black oxide does the work of 64.4 c.c.[4] of the permanganate solution, and that these quant.i.ties are equivalent; moreover, if 64.4 c.c.

correspond with 0.5 gram, then 100 c.c. correspond with 0.7764 which is the standard. On theoretical grounds, and by a method of calculation which will be explained further on (under the heading "Calculations from Formulae"), it can be found that if the standard for iron is 1 gram, that for the black oxide will be 0.7764 gram.

The principles of these indirect t.i.trations become clearer when expressed in a condensed form. Thus, in the example selected, and using the formulae Fe = Iron, KMnO_{4} = permanganate of potash, and MnO_{2} = oxide of manganese, we have:--

(1) 1 gram Fe = 100 c.c. KMnO_{4}

(2) 1 gram Fe = 35.6 c.c. KMnO_{4} + 0.5 gram MnO_{2} .". 100 c.c. KMnO_{4} = 35.6 c.c. KMnO_{4} + 0.5 gram MnO_{2} (100-35.6) c.c. KMnO_{4} = 0.5 gram MnO_{2} 64.4 c.c. KMnO_{4} = 0.5 gram MnO_{2}

The iron does not enter into the calculation if the same quant.i.ty is present in the two experiments.

An indirect t.i.tration thus requires three determinations, but if more than one a.s.say is to be carried on, two of these need not be repeated.

The standard is calculated in the usual way.

~Colorimetric a.s.says.~--These are a.s.says in which the colour imparted to a solution by some compound of the metal to be determined is taken advantage of; the depth of colour depending on the quant.i.ty of metal present. They are generally used for the determination of such small quant.i.ties as are too minute to be weighed. The method of working is as follows:--A measured portion of the a.s.say solution (generally 2/3, 1/2, 1/3, or 1/4 of the whole), coloured by the substance to be estimated, is placed in a white gla.s.s cylinder standing on a sheet of white paper or glazed porcelain. Into an exactly similar cylinder is placed the same amount of re-agents, &c., as the portion of the a.s.say solution contains, and then water is added until the solutions are of nearly equal bulk.

Next, a standard solution of the metal being estimated is run in from a burette, the mixture being stirred after each addition until the colour approaches that of the a.s.say. The bulk of the two solutions is equalised by adding water. Then more standard solution is added until the tints are very nearly alike. Next, the amount added is read off from the burette, still more is poured in until the colour is slightly darker than that of the a.s.say, and the burette read off again. The mean of the readings is taken, and gives the quant.i.ty of metal added. It equals the quant.i.ty of metal in the portion of the a.s.say. If this portion was one-half of the whole, multiply by two; if one-third, multiply by three, and so on. When the quant.i.ty of metal in very dilute solutions is to be determined, it is sometimes necessary to concentrate the solutions by boiling them down before applying the re-agent which produces the coloured compound. Such concentration does not affect the calculations.

~Gasometric a.s.says.~--Gasometric methods are not much used by a.s.sayers, and, therefore, those students who wish to study them more fully than the limits of this work will permit, are recommended to consult Winkler and Lunge"s text-book on the subject. The methods are without doubt capable of a more extended application. In measuring liquids, ordinary variations of temperature have but little effect, and variations of atmospheric pressure have none at all, whereas with gases it is different. Thus, 100 c.c. of an ordinary aqueous solution would, if heated from 10 C. to 20 C., expand to about 100.15 c.c. 100 c.c. of a gas similarly warmed would expand to about 103.5 c.c., and a fall of one inch in the barometer would have a very similar effect. And in measuring gases we have not only to take into account variations in volume due to changes in temperature and atmospheric pressure, but also that which is observed when a gas is measured wet and dry. Water gives off vapour at all temperatures, but the amount of vapour is larger as the temperature increases.

By ignoring these considerations, errors of 3 or 4 per cent. are easily made; but, fortunately, the corrections are simple, and it is easy to construct a piece of apparatus by means of which they may be reduced to a simple calculation by the rule of three.

The volume of a gas is, in practice, usually reduced to that which it would be at a temperature of 0 C., when the column of mercury in the barometer is 760 mm. high. But, although convenient, this practice is not always necessary. The only thing required is some way of checking the variations in volume, and of calculating what the corrected volume would be under certain fixed conditions.

Suppose that at the time a series of standardisings is being made, 100 c.c. of air were confined in a graduated tube over moist mercury. These 100 c.c. would vary in volume from day to day, but it would always be true of them that they would measure 100 c.c. under the same conditions as those under which the standardisings were made. If, then, in making an actual a.s.say, 35.4 c.c. of gas were obtained, and the air in the tube measured 105 c.c., we should be justified in saying, that if the conditions had been those of the standardising, the 105 c.c. would have measured 100 c.c., and the 35.4 c.c. would have been 33.7; for 105: 100:: 35.4: 33.7. The rule for using such a piece of apparatus for correcting volumes is:--_Multiply the c.c. of gas obtained by 100, and divide by the number of c.c. of air in the apparatus._

If it is desired to calculate the volumes under standard conditions (that is, the gas dry, at 0 C. and 760 mm. barometric pressure) the calculations are easily performed, but the temperature and pressure must be known.

_Correction for Moisture._--The "vapour tension" of water has been accurately determined for various temperatures, and it may be looked upon as counteracting the barometric pressure. For example, at 15 C.

the vapour tension equals 12.7 millimetres of mercury; if the barometer stood at 750 mm., the correction for moisture would be made by subtracting 12.7 from 750, and taking 737.3 mm. to be the true barometric pressure.

The vapour tensions for temperatures from 0 C. to 20 C. are as follows:--

-------+----------++-------+----------++-------+---------- Temp. | Tension. || Temp. | Tension. || Temp. | Tension.

-------+----------++-------+----------++-------+---------- 0 | 4.6 mm. || 7 | 7.5 mm. || 14 | 11.9 mm.

1 | 4.9 mm. || 8 | 8.0 mm. || 15 | 12.7 mm.

2 | 5.3 mm. || 9 | 8.6 mm. || 16 | 13.5 mm.

3 | 5.7 mm. || 10 | 9.2 mm. || 17 | 14.4 mm.

4 | 6.1 mm. || 11 | 9.8 mm. || 18 | 15.3 mm.

5 | 6.5 mm. || 12 | 10.5 mm. || 19 | 16.3 mm.

6 | 7.0 mm. || 13 | 11.2 mm. || 20 | 17.4 mm.

The _correction for pressure_ is:--Multiply the volume by the actual pressure and divide by 760.

The _correction for temperature_:--Multiply the volume by 273 and divide by the temperature (in degrees Centigrade) added to 273.

For all three corrections the following rules hold good. _To reduce to 0 C. and 760 mm. dry._

Volume 0.3592 (Pressure-tension) Corrected volume = -------------------------------------- Temperature + 273

To find the volume, which a given volume under standard conditions would a.s.sume, if those conditions are altered.

Volume 2.784 (Temperature + 273) Resulting volume = ------------------------------------ Pressure - tension

As an example, we will suppose that it is desired to enclose in the apparatus referred to on p. 45, a volume of air, which, when dry (at 0 C. and 760 mm.), shall measure 100 c.c., whilst the actual temperature is 15 C., and the pressure 750 mm.

The second formula is the one to be used, and we get 108.7 c.c.

100 c.c.2.784288 Required volume = ---------------------- 750-12.7

80179.2 = ------- 737.3

= 108.7 c.c.

FOOTNOTES:

[4] 100-35.6 = 64.4.

CHAPTER V.

WEIGHING AND MEASURING.

~Weighing.~--The system of weights and measures which we have adopted is the French or metric system; in this the gram (15.43 grains) is the unit of weight; the only other weight frequently referred to is the milligram, which is 0.001, or 1/1000 gram. The unit of volume is the cubic centimetre, which is approximately the volume of 1 gram of water, and which thus bears to the gram the same relation as grain-measures bear to grains. It is usual to write and even p.r.o.nounce cubic centimetre shortly as c.c., and the only other denomination of volume we shall have occasion to use is the "litre," which measures 1000 c.c., and is roughly 1-3/4 pints.

The weights used are kept in boxes in a definite order, so that the weights on the balance can be counted as well by noting those which are absent from the box as by counting those present on the scale-pan. The weights run 50, 20, 10, 10, 5, 2, 1, 1 and 1 grams, and are formed of bra.s.s. The fractions of the gram are generally made of platinum or of aluminium, and are arranged in the following order:--0.5, 0.2, 0.1, 0.1, and 0.05, 0.02, 0.01, 0.01. These may be marked in this way, or they may be marked 500, 200, 100, 100, 50, 20, 10, 10; the 500 meaning 500 milligrams.

Some makers send out weights in the series 50, 20, 20, 10, &c.

Weights of less than 0.01 gram are generally present in a box, but it is much more convenient to work with a rider. This is a piece of wire which in the pan weighs 0.01 gram; it is made in such a form that it will ride on the beam, and its effective weight decreases as it approaches the centre. If the arm of the beam is divided into tenths, then each tenth counting from the centre outward equals 0.001 gram or 1 milligram, and if these tenths be further subdivided the fractions of a milligram are obtained; and these give figures in the fourth place of decimals. A fairly good balance should be sensitive to 0.0001 gram. The weights must never be touched with the fingers, and the forceps for moving them is used for no other purpose. When not in actual use the box is kept closed. The weights must not be allowed to remain on the pan of the balance. The balance-case must not be open without some reason. It must be fixed level, and, once fixed, must not be needlessly moved. The bench on which it stands should be used for no other purpose, and no one should be allowed to lean upon it.

[Ill.u.s.tration: FIG. 25.]

When using a balance sit directly in front of it. Ordinarily the substance to be weighed is best put on the pan to the user"s left; the weights and the rider are then easily manipulated. Powders, &c., should not be weighed directly on the balance; a counterpoised watch-gla.s.s or metal scoop (fig. 25) should be used. In some cases it is advisable to use a weighing-bottle. This is a light, well-stoppered bottle (fig. 3) containing the powdered ore. It is first filled and weighed; then some of the substance is carefully poured from it into a beaker or other vessel, and it is weighed again; the difference in the two weighings gives the weight of substance taken. A substance must always be cold when weighed, and large gla.s.s vessels should be allowed to stand in the balance-box a little while before being weighed. Always have the balance at rest when putting on or taking off anything from the pans. Put the weights on systematically. In using the rider (except you have a reason to the contrary), put it on at the 5; if this is too much, then try it at the 3; if then the weights are too little, try at the 4, if still not enough, the correct weight must be between the 4 and 5; try half-way between.

It is best to work with the balance vibrating; equilibrium is established when the vibration to the left is the mean of the preceding and succeeding vibrations to the right. For example, if it vibrates 6 divisions to the right on one swing, and 5 divisions on the next, the intermediate vibration to the left should have been 5-1/2.

Note whether the substance increases in weight whilst on the balance. If it does it may be because it was put on warm, and is cooling, or it may be because it is taking up moisture from the air. Substances which take up moisture rapidly should be weighed in clipped watch-gla.s.ses or in light-weighing bottles or tubes.