B ALANCE. The beginning and end of every exact chemical process consists in weighing. With imperfect instruments this operation will be tedious and inaccurate; but with a good balance, the result will be satisfactory; and much time, which is so precious in experimental researches, will be saved. The balance is a lever, the axis of motion of which is formed with an edge like that of a knife; and the two dishes at its extremities are hung upon edges of the same kind. These edges are first made sharp, and then rounded with a fine hone, or a piece of buff leather. The excellence of the instrument depends, in a great measure, on the regular form of this rounded part. When the lever is considered as a mere line, the two outer edges are called points of suspension, and the inner the fulcrum. The points of suspension are supposed to be at equal distances from the fulcrum, and to be pressed with equal weights when loaded. 1. If the fulcrum be placed in the centre of gravity of the beam, and the three edges lie all in the same right line, the balance will have no tendency to one position more than another, but will rest in any position it may be placed in, whether the scales be on or off, empty or loaded. 2. If the centre of gravity of the beam, when level, be immediately above the fulcrum, it will overset by the smallest action; that is, the end which is lowest will descend: and it will do this with more swiftness, the higher the centre of gravity, and the less the points of suspension are loaded. 3. But if the centre of gravity of the beam be immediately below the fulcrum, the beam will not rest in any position but when level: and, if disturbed from this position, and then left at liberty, it will vibrate, and at last come to rest on the level. Its vibrations will be quicker, and its horizontal tendency stronger, the lower the centre of gravity, and the less the weights upon the points of suspension. 4. If the fulcrum be below the line joining the points of suspension, and these be loaded, the beam will overset, unless prevented by the weight of the beam tending to produce a horizontal position, as in § 3. In this last case, small weights will equilibrate, as in § 3.; a certain exact weight will rest in any position of the beam, as in §1.; and all greater weights will cause the beam to overset, as in § 2. Many scales are often made this way, and will overset with any considerable load. 5. If the fulcrum be above the line joining the points of suspension, the beam will come to the horizontal position, unless prevented by its own weight, as in § 2. If the centre of gravity of the beam be nearly in B the fulcrum, all the vibrations of the loaded beam will be made in times nearly equal, unless the weights be very small, when they will be slower. The vibrations of balances are quicker, and the horizontal tendency stronger, the higher the fulcrum. 6. If the arms of a balance be unequal, the weights in equipoise will be unequal in the same proportion. It is a severe check upon a workman to keep the arms equal, while he is making the other adjustments in a strong and inflexible beam. 7. The equality of the arms of a balance is of use, in scientific pursuits, chiefly in making weights by bisection. A balance with unequal arms will weigh as accurately as another of the same workmanship with equal arms, provided the standard weight itself be first counterpoised, then taken out of the scale, and the thing to be weighed be put into the scale, and adjusted against the counterpoise; or when proportional quantities only are considered, as in chemical and in other philosophical experiments, the bodies and products under examination may be weighed against the weights, taking care always to put the weights into the same scale. For then, though the bodies may not be really equal to the weights, yet their proportions among each other may be the same as if they had been accurately so. 8. But though the equality of the arms may be well dispensed with, yet it is indispensably necessary, that their relative lengths, whatever they may be, should continue invariable. For this purpose, it is necessary, either that the three edges be all truly parallel, or that the points of suspension and support should be always in the same part of the edge. This last requisite is the most easily obtained. The balances made in London are usual. ly constructed in such a manner, that the bearing parts form notches in the other parts of the edges; so that the scales being set to vibrate, all the parts naturally fall into the same bearing. The balances made in the country have the fulcrum edge straight, and confined to one constant bearing by two side plates. But the points of suspension are referred to notches in the edges, like the London balances. The balances here mentioned, which come from the country, are enclosed in a small iron japanned box; and are to be met with at the Birmingha and Sheffield warehouses, though less frequently than some years ago; because weighing guineas and half-guineas has got possession of the market. They are, in general, well made and adjusted, turn with the twentieth of a grain when empty, and will sensibly show the tenth of a grain, with an ounce in each scale. Their price is from a pocket contrivance for wei 22 five shillings to half a guinea; but those which are under seven shillings have not their edges hardened, and consequently are not durable. This may be ascertained by the purchaser, by passing the point of a penknife across the small piece which goes through one of the end boxes: if it makes any mark or impression, the part is soft. 9. If a beam be adjusted so as to have no tendency to any one position, as in § 1. and the scales be equally loaded; then, if a small weight be added in one of the scales, that balance will turn, and the points of suspension will move with an accelerated motion, similar to that of falling bodies, but as much slower, in proportion, very nearly, as the added weight is less than the whole weight borne by the fulcrum. 10. The stronger the tendency to a horizontal position in any balance, or the quicker its vibrations, §§ 3. 5. the greater additional weight will be required to cause it to turn, or incline to any given angle. No balance, therefore, can turn so quick as the motion deduced in § 9. Such a balance as is there described, if it were to turn with the ten-thousandth part of the weight, would move at quickest ten thousand times slower than falling bodies; that is, the dish contain ing the weight, instead of falling through sixteen feet in a second of time, would fall through only two hundred parts of an inch, and it would require four seconds to move through one-third part of an inch; consequently all accurate weighing must be slow. If the indexes of two balances be of equal lengths, that index which is connected with the shorter balance will move proportionally quicker than the other. Long beams are the most in request, because they are thought to have less friction; this is doubt ful; but the quicker angular motion, greater strength, and less weight of a short balance, are certainly advantages. 11. Very delicate balances are not only useful in nice experiments, but are likewise much more expeditious than others in common weighing. If a pair of scales with a certain load be barely sensible to one-tenth of a grain, it will require a considerable time to ascertain the weight to that degree of accuracy, because the turn must be observed several times over, and is very small. But if no greater accuracy were required, and scales were used, which would turn with the hundredth of a grain, a tenth of a grain, more or less, would make so great a difference in the turn, that it would be seen immediately. 12. If a balance be found to turn with a certain addition, and is not moved by any smaller weight, a greater sensibility may be given to that balance, by producing a tremulous motion in its parts. Thus, if the edge of a blunt saw, a file, or other similar instrument, be drawn along any part of the case or support of a balance, it will produce a jarring, which will diminish the friction on the moving parts so much, that the turn will be evident with one-third or one-fourth of the addition that would else have been required. In this way, a beam which would barely turn by the addition of one-tenth of a grain, will turn with onethirtieth or fortieth of a grain. 13. A balance, the horizontal tendency of which depends only on its own weight, as in § 3. will turn with the same addition, whatever may be the load; except so far as a greater load will produce a greater friction. 14. But a balance, the horizontal tendency of which depends only on the elevation of the fulcrum, as in § 5. will be less sensible the greater the load; and the addition requisite to produce an equal turn will be in proportion to the load itself. 15. In order to regulate the horizontal tendency in some beams, the fulcrum is placed below the points of suspension, as in § 4. and a sliding weight is put upon the cock or index, by means of which the centre of gravity may be raised or depressed. This is a useful contrivance. 16. Weights are made by a subdivision of a standard weight. If the weight be continually halved, it will produce the common pile, which is the smallest number for weighing between its extremes, without placing any weight in the scale with the body under examination. Granulated lead is a very convenient substance to be used in this operation of halving, which, however, is very tedious. The readiest way to subdivide small weights, consists in weighing a certain quantity of small wire, and afterward cutting it into such parts, by measure, as are desired; or the wire may be wrapped close round two pins, and then cut asunder with a knife. By this means it will be divided into a great number of equal lengths, or small rings. The wire ought to be so thin, as that one of these rings may barely produce a sensible effect on the beam. If any quantity (as, for example, a grain) of these rings be weighed, and the number then reckoned, the grain may be subdivided in any proportion, by dividing that number, and making the weights equal to as many of the rings as the quotient of the division denotes. Then, if 750 of the rings amounted to a grain, and it were required to divide the grain decimally, downwards, 9-10ths would be equal to 675 rings, 8-10ths would be equal to 600 rings, 7-10ths to 525 rings, &c. Small weights may be made of thin leaf brass. Jewellers' foil is a good material for weights below 1-10th of a grain, as low as to 1-100th of a grain; and all lower quantities may be either esti 17. In philosophical experiments, it will be found very convenient to admit no more than one dimension of weight. The grain is of that magnitude as to deserve the preference. With regard to the number of weights the chemists ought to be provided with, writers have differed according to their habits and views. Mathematicians have computed the least possible number, with which all weights within certain limits might be ascertained; but their determination is of little use. Because, with so small a number, it must often happen, that the scales will be heavily loaded with weights on each side, put in with a view only to determine the difference between them. It is not the least possible number of weights which it is necessary an operator should buy to effect his purpose, that we ought to inquire after, but the most convenient number for ascertaining his inquiries with accuracy and expedition. The error of adjustment is the least possible, when only one weight is in the scale; that is, a single weight of five grains is twice as likely to be true, as two weights, one of three, and the other of two grains, put into the dish to supply the place of the single five; because each of these last has its own probability of error in adjustment. But since it is as inconsistent with convenience to provide a single weight, as it would be to have a single character for every num ber; and as we have nine characters, which we use in rotation, to express higher values very serviceable to make the set of weights according to their position, it will be found correspond with our numerical system. This directs us to the set of weights as follows: 1000 grains, 900 g. 800 g. 700 g. 600 g. 500 g. 400 g. 300 g. 200 g. 100 g. 90 g. 80 g. 70 g. 60 g. 50 g. 40 g. 30 g. 20 g. 10 g. 9g.8g.7g.6g.5g.4g. 3 3 2 7 TO 1 10 6 9 100 4 g. 2 T이 8.1 8. To이 g. With these the philosopher will always have the same number of weights in his scales, as there are figures in the number expressing the weights in grains. Thus 742.5 grains will be weighed by the weights 700, 40, 2, and 5-10ths. I shall conclude this chapter with an account of some balances I have seen or heard of, and annex a table of the correspondence of weights of different countries. Muschenbroek, in his Cours de Physique, (French translation, Paris, 1769), tom. ii. p. 247. says, he used an ocular balance of 4 great accuracy, which turned (trebuchoit) with of a grain. The substances he weighed were between 200 and 300 grains. His balance therefore weighed to the T식아이이 part of the whole; and would ascertain such weights truly to four places of figures. In the Philosophical Transactions, vol. lxvi. p. 509. mention is made of two accurate balances of Mr. Bolton; and it is said that one would weigh a pound, and turn with To of a grain. This, if the pound be avoirdupois, is ᄀ이아이이 of the weight; and shews that the balance could be well depended on to four places of figures, and probably to five. The other weighed half an ounce, and turned with Too of a grain. This is 비식아이이 of the weight. 1 24000 1 In the same volume, p. 511. a balance of Mr. Read's is mentioned, which readily turned with less than one pennyweight, when loaded with 55 pounds, before the Royal Society; but very distinctly turned with four grains, when tried more patiently. This is about 이이이이이 part of the weight; and therefore this balance may be depended on to five places of figures. Also, page 576. a balance of Mr. Whitehurst's weighs one pennyweight, and is sensibly affected with 이이이이 of a grain. This is 쉬여아이이 part of the weight. 4 2000 therefore about this weight may be known to five places of figures. The proportional delicacy is less in greater weights. The beam will weigh near a pound troy; and when the scales are empty, it is affected by T이아이 of grain. On the whole, it may usefully applied to determine all weights between 100 grains and 4000 grains to four places of figures. 1 a be A balance belonging to Mr. Alchorne of the Mint in London, is mentioned, vol. lxxvii. p. 205. of the Philosophical Transactions. It is true to 3 grains, with 15 lb. an end. If these were avoirdupois pounds, the weight is known to 에이아이이 part, or to four places of figures, or barely five. A balance, (made by Ramsden, and turning on points instead of edges) in the possession of Dr. George Fordyce, is mentioned in the seventy-fifth volume of the Philosophical Transactions. With a load of four or five ounces, a difference of one division in the index was made by 이이 of a grain. This is 여여니이이이 part of the weight, and consequently this beam will ascertain such weights to five places of figures, beside an estimate figure. TO I have seen a strong balance in the possession of my friend Mr. Magellan, of the kind mentioned in § 15. which would bear several pounds, and showed To of a grain, with one pound an end. This is 700이어 of the weight, and answers to five figures. But I think it would have done more by a more patient trial than I had time to make. The Royal Society's balance, which was lately made by Ramsden, turns on steel edges, upon planes of polished crystal. I was assured, that it ascertained a weight to the seven-millionth part. I was not present at this trial, which must have required great care and patience, as the point of suspension could not have moved over much more than the Too of an inch in the first half minute; but, from some trials which I saw, I think it probable that it may be used in general practice to determine weights to five places and better. From this account of balances, the student may form a proper estimate of the value of those tables of specific gravities, which are carried to five, six, and even seven places of figures, and likewise of the theoretical deductions in chemistry, that depend on a supposed accuracy in weighing, which practice does not authorise. In general, where weights are given to five places of figures, the last figure is an estimate, or guess figure; and where they are carried farther, it may be taken for granted, that the author deceives either intentionally, or from want of skill in reducing his weights to fractional expressions, or otherwise. The most exact standard weights were procured, by means of the ambassadors of France, resident in various places; and these were compared by Mons. Tillet with the standard mark in the pile preserved in the Courde Monnoies de Paris. His experiments were made with an exact balance made to weigh one marc, and sensible to one quarter of a grain. Now, as the marc contains 18432 quarter grains, it follows that this balance was a good one, and would exhibit proportions to four places, and a guess figure. The results are contained in the following table, extracted from Mons. Tillet's excellent paper in the Memoirs of the Royal Academy of Sciences for the year 1767. I have added the two last columns, which show the number of French and English grains contained in the compound quantities against which they stand. The English grains are computed to one-tenth of a grain, although the accuracy of weighing came no nearer than about two-tenths. The weights of the kilogramme, gramme, decigramme, and centigramme, which are now frequently occurring in the French chemical writers, are added at the bottom of this table, according to their respective values. See TABLES of WEIGHTS and Measures in the Appendix. * The commissioners, appointed by the British government for considering the subject of weights and measures, gave in their first report on the 24th June 1819. The following is the substance of it: "1. With respect to the actual magnitude of the standards of length, the commissioners are of opinion, that there is no sufficient reason for altering those generally employed, as there is no practical advantage in having a quantity commensurable to any original quantity existing, or which may be imagined to exist, in nature, except as affording some little encouragement to its common adoption by neighbouring nations. "2. The subdivisions of weights and measures at present employed in this country, appear to be far more convenient for practical purposes than the decimal scale. The power of expressing a third, a fourth, and a sixth of a foot in inches, without a fraction, is a peculiar advantage in the duodecimal scale; and for the operation of weighing and of measuring capacities, the continual division by two, renders it practicable to make up any given quantity with the smallest possible number of weights and measures, and is far preferable in this respect to any decimal scale. The commissioners therefore recommend, that all the multiples and subdivisions of the standard to be adopted, should retain the same re. lative proportions to each other as are at present in general use. "3. That the standard yard should be that employed by Gen. Roy in the measurement of a base on Hounslow Heath, as a foundation of the great trigonometrical survey. "4. That in case this standard should be lost or impaired, it shall be declared, that the length of a pendulum, vibrating seconds of mean solar time in London, on the level of the sea, and in a vacuum, is 39.1372 inches of the standard scale, and that the length of the French metre, as the 10 millionth part of the quadrantal arc of the meridian, has been found equal to 39.3694 inches. |