SECTION I.

ON THE METHODS OF PERFORMING ANALYTICAL PROCESSES.

CHAPTER I.

OPERATIONS.

§ 1.

THE operations performed in quantitative research are generally the same as in qualitative analysis-of these I have treated in my former work. I shall here describe such modifications as those may require which are common to both, and shall enter more minutely into such as belong exclusively to quantitative inquiries.

§ 2.

The amount of solids, and generally also that of fluids, is determined by weight; the amount of gases and sometimes fluids by measure: upon the care and accuracy with which these operations are performed, depends the value of all our results; I shall therefore dwell minutely upon them.

$3.

WEIGHING.

Our success in determining the weight of substances we are studying, depends, 1st, upon our possessing a good BALANCE, and 2d, WEIGHTS perfectly accurate.

1st. As to the balance,-there are several points which every chemist must understand, respecting the construction and properties of the balance. The usefulness of this indispensable instrument of quantitative chemistry depends upon two points: 1st, its accuracy, and 2d, its sensibility.

§ 4.

The ACCURACY of a balance depends upon the following circum

stances:

a. The fulcrum must be placed above the centre of gravity of

the beam.

This is a condition essential to every balance. If the fulcrum were placed in the centre of gravity of the beam, it would not vibrate, but remain in any position in which it is placed, assuming the scales to be equally loaded. If the fulcrum be placed below the centre of gravity of the beam, the balance will be overset by the slightest impulse.

When the fulcrum is above the centre of gravity of the beam the balance represents a pendulum, the length of which is equal to that of the line uniting the fulcrum with the centre of gravity, and this line forms right angles with the beam in whatever position the latter may be placed. Now if we impart an impetus to a ball suspended by a thread, the ball, after having terminated its vibrations, will invariably fall back into its original perpendicular position under the suspension point. It is the same with a properly adjusted balance-impart an impetus to it, and it will vibrate for some time, but it will invariably return to its original position; in other words, its centre of gravity will finally fall back into its perpendicular position under the fulcrum, and the beam must consequently reassume the horizontal position.

B. The point of suspension of the scales must be on an exact level with the fulcrum, since if the fulcrum be placed below the line joining the points of suspension, the loading of the scales being gradually increased, will continually tend to raise the centre of gravity of the whole system, so as to bring it nearer and nearer the fulcrum; the weight which presses upon the scales, combining in the relatively high-placed points of suspension; at last, when the scales have been loaded to a certain degree, the centre of gravity will take its position in the fulcrum, and the balance will consequently cease to vibrate-any further addition of weight will finally cause the beam to overset by placing the centre of gravity above the fulcrum. If, on the other hand, the fulcrum be above the line joining the points of suspension, the centre of gravity will become more and more depressed in proportion as the loading of the scales is increased; the line of the pendulum will consequently be lengthened, and a greater force will be required to produce an equal turn; in other words, the balance will grow the less sensible the greater the load. But when the three edges are placed on a level with each other, increased loading of the scales will, indeed, continually tend to raise the centre of gravity towards the fulcrum, but the former can in this case never entirely reach the latter, and consequently the balance will never altogether cease to vibrate upon the further addition of weight, nor will its sensibility be lessened; on the contrary, a greater degree of sensibility is imparted to it This increase of sensibility is, however, compensated for by other circumstances.

y The beam must be so strong and inflexible, that the greatest weight which the construction of the balance admits of, must not cause the slightest perceptible bend in it, since the bending of the beam would of course depress the points of suspension so as to place them below the line of the fulcrum, and this would, as we have just seen, tend to diminish the sensibility of the balance in proportion to the increase of the load. It is therefore necessary to avoid this fault by a proper construction of the beam. The

form best adapted for beams, is that of a rhomb, or of an equilateral obtuse-angled triangle.

8. The arms of the balance must be of equal length, i. c., the points of suspension must be equi-distant from the fulcrum or point of support, for if the arms be unequal, the weights in equipoise will be unequal in the same proportion; i. e., the weights in one scale acting upon the longer arm of the lever, will preponderate over the exact equivalent in the other scale, and this in direct proportion to the greater or less excess of length of one arm over the other.

§ 5.

The SENSIBILITY of a balance depends principally upon the following circumstances:

a. The friction of the edges upon their supports must be as slight as possible.

The greater or less friction of the edges upon their supports depends upon both the form and material of those parts of the balance. The edges must be made of good steel, the supporters may be made of the same material; it is better, however, that the centre edge should rest upon perfectly even stone (agate) supporters. To form a clear conception of how necessary it is that even the lateral edges should have as little friction as possible, we need simply imagine what would happen were we to fix the scales in immoveable points, by means of inflexible rods. Such a contrivance would at once altogether annihilate the sensibility of the balance, for if a weight were placed upon one side, this certainly would cause the loaded scale to sink, but at the same time being compelled to form constantly a right angle with the beam, it would incline inwards, whilst the other scale would turn outwards, and thus the weight would be made to act upon the shorter arm of the lever. The more considerable the friction becomes at the end edges of a balance, the more the latter approaches the state just now described, and consequently the more is its sensibility impaired.

crum.

B. The centre of gravity must be as near as possible to the fulThe nearer the centre of gravity approaches the fulcrum, the shorter becomes the pendulum. If we take two balls, the one suspended from a short and the other from a long thread, and impart the same impetus to both, the former will naturally in the extent of its vibrations swing at a far greater angle from its perpendicular position than the latter. The same must of course happen with a balance; the same weight will cause the scale upon which it is placed to turn the more rapidly and completely, the shorter the distance between the centre of gravity and the fulcrum. We have seen above, that in a balance where the three edges are on a level with each other, increased loading of the scales will continually tend to raise the centre of gravity towards the fulcrum. A good balance will therefore become more delicate in proportion to the increase of weights placed upon its scales, but on the other hand, its sensibility will be diminished in about the same proportion by the increased friction attendant upon the increase of load; in other words, the sensibility of a good balance will remain the same whatever may be the load placed upon it, ranging from the minimum to the maximum that its construction will enable it to bear.

y. The beam must be as light as possible.-The remarks which we have just now made will likewise show how far the weight of the beam may influence the sensibility of a balance. We have seen that it is necessary that a balance should increase in sensibility in proportion to the increase of load, since the increased friction tends to diminish its sensibility in the same proportion; and further, we have seen that this increase in sensibility is owing to the increased weight continually tending to raise the centre of gravity towards the fulcrum. Now it is evident, that the more considerable the weight of the beam is, the less will an equal load placed upon both scales alter the centre of gravity of the whole system, the more slowly will the centre of gravity approach the fulcrum, the less will the increased friction be neutralized, and consequently the less sensibility will the balance possess.