And in how many parts of water at 100° C. is one part of potassium nitrate soluble?

246.82 100 :: 1 : y,

.. y = 40516 part of water.

Liquids may be quite insoluble in one another, and when shaken together separate into two distinct layers e.g. water and mercury; or they may mix together in all proportions e.g. water and alcohol; or they may separate into two layers, the lower one consisting chiefly of one liquid mixed with a definite proportion of the other, and the upper one consisting chiefly of the second liquid mixed with a definite proportion of the first liquid e. g. water and ether.

No general numerical rules concerning the solubility of liquids have yet been obtained.

*(30) THE SOLUBILITY OF GASES IN LIQUIDS.

Gases are absorbed by water, when they do not act chemically upon it, in quantities depending upon three conditions:

1st. The nature of the gas. The volume of each normal gas absorbed by one volume of water at 0°C. is called the absorption coefficient of that gas.

2nd. The pressure on the gas. The quantity of a gas absorbed varies directly as the pressure upon it: or, equal volumes of the same gas are absorbed at all pressures.

3rd. The temperature. With few exceptions the volume of gas absorbed decreases as the temperature in

creases.

The volume of a gas absorbed at any temperature t° C. can be expressed by the empirical formula

V = a - bt+ct3.

Thus one volume of water between 0°C. and 20° C.

absorbs of

Hydrogen

Nitrogen

Oxygen

Carbon dioxide

Oxygen and

V = 0.0193.

V=0·020346-0·00053887t+0.000011156ť.

V 0.04114-0·00109t + 0·0000226ť2.

V=1.7967 - 0·07761t + 0·0016424ť.

nitrogen from V = 0·02471 – 0·0006525t + 0·00001345ť. air

If two or more gases are mixed together, the absorption of each constituent is proportional to the pressure to which it is separately subjected.

Thus suppose a large excess of air be shaken up with water at 0°C. in what proportions per cent. are the oxygen and nitrogen absorbed ?

100 volumes of air contain nearly 21 volumes of oxygen, and 79 volumes of nitrogen.

100%

Hence the pressure on the oxygen is pressure, and the pressure on the nitrogen is pressure.

The volume of oxygen absorbed by 1 volume of water

Hence 2-471274 volumes of gas are absorbed by 100 volumes of water, of which 0:86394 volume is oxygen and 1-60733 volumes are nitrogen.

And the percentage composition of the gas absorbed by water is

Oxygen 34.9 per cent. by volume.

(31) TO FIND THE LOGARITHM OF A NUMBER FROM TABLES.

The common logarithm of a number is the power to which 10 must be raised to be equal to the number.

If 10" = N. is the logarithm of N.

A logarithm may be either a whole number, a decimal or a mixed number. The part of a logarithm which is a whole number is called the characteristic, and the part which is decimal is called the mantissa.

Hence the characteristic

for a number greater than unity is one less than the number of figures in the integral part of the number.

When a characteristic is negative the minus sign is written over and not before the characteristic, to shew that

it affects only the characteristic and not the mantissa,

which always remains positive.

The characteristic of a decimal is negative and is one more than the number of ciphers following the decimal point. Or the characteristic of a decimal is represented by the same figure as the place of the first significant figure reckoned from the decimal point.

The characteristic is not given in the tables and must be determined by the above rules.

The mantissa, or decimal part of the logarithm, is found in the tables, and is always the same for the same figures wherever the decimal point may come.

Logarithm tables of different sizes may be obtained giving the mantisse to 7, 6, or 5 decimal places. Generally speaking the results obtained are correct to one figure less than the number of figures in the mantissæ of the logarithms used, the succeeding figure being only approximate.

For chemical purposes tables giving the mantissæ to four figures are usually sufficient, such tables give results correct to the third figure and nearly so to the fourth figure*.

To find in such a table the logarithm of a number consisting of three figures, look for the first two figures in the vertical column of numbers, and for the third figure look at the top of the page. Cf. Table XII.

The required mantissa will be found where the row and column meet. Prefix the characteristic.

Thus

log 64 = 1.8062, log 647 = 2.8109.

If the number consist of four figures, find the mantissa corresponding to the first three figures as given above, look along the same row into the subsidiary table on the right hand side of the page until the column under the fourth figure is reached, and add in the small logarithm found there.

Thus

log 6473

3.8109+2=3.8111,

log 65993-8189 + 6 = 3.8195.

The reason for adding in these small logarithms to represent the fourth figure is as follows:

The logarithm of 6470 is 3.8109,

and the logarithm of 6480 is 3.8116.

Hence a difference of 10 in the last two figures of the number produces a difference of 7 in the last figure of the logarithm, or a difference of 1 in the fourth figure of the number produces a difference of 7 in the fourth figure of the logarithm.

* Logarithm cards to 4 figures price 6d. may be obtained from Mr J. C. Wilbee, bookseller, Harrow.