Such a mode of taking the specific gravity of different substances—viz., by the weight of equal bulks, whether cubic feet or inches, could not be employed in consequence of the difficulty of procuring exact cubic inches or feet of the various substances which by their peculiar properties of brittleness or hardness would present insuperable obstacles to any attempt to fashion or shape them into exact volumes. It is therefore necessary to adopt the method first devised by Archimedes, 600 b.c., when he discovered the admixture of another metal with the gold of King Hiero's crown.
This amusing story, ending in the discovery of a philosophical truth, may be thus described:—King Hiero gave out from the royal treasury a certain quantity of gold, which he required to be fashioned into a crown; when, however, the emblem of power was produced by the goldsmith, it was not found deficient in weight, but had that appearance which indicated to the monarch that a surreptitious addition of some other metal must have been made.
It may be assumed that King Hiero consulted his friend and philosopher Archimedes, and he might have said, "Tell me, Archimedes, without pulling my crown to pieces, if it has been adulterated with any other metal?" The philosopher asked time to solve the problem, and going to take his accustomed bath, discovered then specially what he had never particularly remarked before—that, as he entered the vessel of water, the liquid rose on each side of him—that he, in fact, displaced a certain quantity of liquid. Thus, supposing the bath to have been full of water, directly Archimedes stepped in, it would overflow. Let it be assumed that the water displaced was collected, and weighed 90 pounds, whilst the philosopher had weighed, say 200 pounds. Now, the train of reasoning in his mind might be of this kind:—"My body displaces 90 pounds of water; if I had an exact cast of it in lead, the same bulk and weight of liquid would overflow; but the weight of my body was, say 200 pounds, the cast in lead 1000 pounds; these two sums divided by 90 would give very different results, and they would be the specific gravities, because the rule is thus stated:—'Divide the gross weight by the loss of weight in water, the water displaced, and the quotient gives the specific gravity.'" The rule is soon tested with the help of an ordinary pair of scales, and the experiment made more interesting by taking a model crown of some metal, which may be nicely gilt and burnished by Messrs. Elkington, the celebrated electro-platers of Birmingham. For convenience, the pan of one scale is suspended by shorter chains than the other, and should have a hook inserted in the middle; upon this is placed the crown, supported by very thin copper wire. For the sake of argument, let it be supposed that the crown weighs 17½ ounces avoirdupois, which are duly placed in the other scale-pan, and without touching these weights, the crown is now placed in a vessel of water. It might be supposed that directly the crown enters the water, it would gain weight, in consequence of being wetted, but the contrary is the case, and by thrusting the crown into the water, it may be seen to rise with great buoyancy so long as the 17½ ounces are retained in the other scale-pan; and it will be found necessary to place at least two ounces in the scale-pan to which the crown is attached before the latter sinks in the water; and thus it is distinctly shown that the crown weighs only about 15½ ounces in the water, and has therefore lost instead of gaining weight whilst immersed in the liquid. The rule may now be worked out:
| Ounces. | |
| Weight of crown in air | 17½ |
| Ditto in water | 15½ |
| ——— | |
| Less in water | 2 |
| ——— | |
| 17½ / 2 = 8·75 |
The quotient 8¾ demonstrates that the crown is manufactured of copper, because it would have been about 19¼ if made of pure gold.
Fig. 68.
a. Ordinary pair of scales. b. Scale-pan, containing 17½ ounces, being the weight of the crown in air. c. Pan, with hook and crown attached, which is sunk in the water contained in the vessel d; this pan contains the two ounces, which must be placed there to make the crown sink and exactly balance b.
Table of the Specific Gravities of the Metals in common use.