Balance Hydrostatic, is a balance furnished with apparatus adapted to ascertain the specific gravity of bodies, by weighing them in liquids, as well as in air. A common balance, of a good construction, and furnished with a small hook beneath one of the pans, is, with the usual appendages, quite sufficient for a hydrostatic balance. An accurate and delicate balance, that may be adapted to this purpose, and is easily constructed, is thus described in Brewster's Philosophical Journal. Let a slender beam of wood be procured, about eighteen, or twenty-four inches long, and tapering a little from the middle to each end. Let a fulcrum of tempered steel, resembling the blade of a penknife, be made to pass through the middle of the beam a little above the centre of gravity. Similar steel blades are also made to pass through the ends of the beam for suspending the scales. The fulcrum rests on two small portions of thermometer tubes, fixed horizontally on the upright support e f. The support ha3 a slit along the middle, to allow the needle at e f to play freely between the sides. A small scale, made of card, and divided into any number of parts, is placed at f for the purpose of ascertaining the point at which the needle remains stationary.

This balance possesses extreme delicacy.

It may even be made more sensible than that belonging to the Royal Society of London. l have said nothing of the perfect equality of the two ends, as this condition is not at all necessary to the accuracy of the balance, according to the method of double weighing. To ascertain the weight of any body, place it in one of the scales, and bring the needle to any point by means of small shot placed in the other scale; observe the point opposite to which the needle rests, or the middle, between its extreme points of oscillation; remove the body, and put into the same scale as many known weights as will bring the needle to the same division as before. These weights will, evidently, be equal to the weight of the body, whether the arms of the balance be equal or not. This method of weighing is due to Borda. The steelyard is sometimes employed to ascertain specific gravities, as in the balances of Lukin and Coates.

Lutein's Hydrostatic Balance is extremely simple, and is considered to be a very accurate instrument. The appearance is given in the accompanying figure. When unloaded, the arms are equipollent. C the body, whose specific gravity is to be found, is suspended to the shorter arm of the instrument. On the longer arm, the movable weight D indicates the weight of the substance in air or water. If great accuracy is required, a second weight, which is a sub-multiple of the first, may be added on the longer arm. Then the division marked by the larger weight may be units, and that of the smaller, tenths, or hundredths, as may be thought proper.

Coates's Hydrostatic Balance is upon the same principle as Lukin's, but differs in the mode of graduation. This being adapted for finding the specific gravity of minerals, instead of pointing out the actual and relative weights, it shows at once their specific gravity. The instrument is accurately balanced when unloaded, by making the shorter arm much larger than the longer one; and the latter is graduated, and marked with numbers, which every where show the quotient of the entire length of the longer arm, divided by the distance of the given mark from the end. Thus, at half the length, is marked the number 2; at one-third, the number 3; and so on. These numbers extend on the scale to rather more than 20, in order to render the instrument applicable to the heavier metals. In using this instrument, a weight is suspended by a hook at A, and the body under examination is to be hung by a horse hair on the shorter arm, and slid along as on the steelyard, till an equipoise is obtained, say at D.

Then without altering its situation on the beam, the body is to be immersed in water, and balanced a second time, by sliding the weight C along the graduated arm, till the two are again in equilibrio.

The hook of the weight will then at once indicate, by its situation on the scale, the actual specific gravity of the body, water being considered as unity. The instrument being supposed in equilibrio, and the distance B D and the weight of the counterpoise being constant, the weight of the body varies as the distance of the counterpoise from B. Thus, if the counterpoise have to be removed i nearer to the centre B, to balance the body when weighed in water, the specific gravity, as seen on the scale, will be 4, or four times greater than that of water. If it have to be removed 1/12 nearer, the specific gravity is 12, and so on. The truth of the principle will appear, if we consider that the specific gravity of any body, as compared with water, is found by dividing its weight in air by its loss of weight in water. Now its loss of weight in water is proportional to the approximation of the weight C towards the centre. If, therefore, the whole arm, which always represents the weight in air, be divided by the quantity by which the weight approximates to the centre, it is clear that the quotient which is marked on the scale will be the true specific gravity required.

The annexed figure represents a balance beam, invented by Mr. J. H. Patten, Rhode Island, United States, for the purpose of taking the specific gravities of different bodies, and for the accurate weighing of minute quantities. The manner of using the instrument, it will be seen, is similar to that of Lukin' balance, just described. The beam a b c is made of steel sufficiently strong, but light. The dish is suspended at a; the beam itself upon an axis at b; at c is the milled head of a. long screw, which is fitted with a shoulder and axis, and goes through the slide e that traverses upon b c, and carries the weight d. Now, suppose it required to obtain ten grains, place that weight in the dish f, and screw back the weight d until it exactly counterbalances it. If the weight be now removed, and a quantity of the substance to be weighed be substituted, until the index points to where it did at first, there will then be very nearly the exact weight, differing only by the amount of the friction of the instrument This beam may be used as a steelyard, by screwing the weight d to any number marked upon the scale; and should a greater quantity be required than that marked in the first line, another weight, double that of d, may be substituted.