For instance, a hollow ball six inches diameter is made of two circular pieces of copper, each seven and a half inches diameter: now calling the original circumference of the disk twenty-two and a half inches, this line eventually becomes contracted to eighteen inches, or the circumference of the ball; although at the same time the original diameter of the disk, namely a line of seven and a half inches, has become stretched to that of nine inches or the girth of the hemisphere.

This double change of dimensions, accomplished by the malleability or gliding of the metal, occurs in a still more striking manner in the illustration of spinning the tea-pot, in which the disk, originally about one foot diameter, becomes contracted to two or three inches only at the mouth. The precise nature of the change is seen on inspecting figs. 207 and 209, p. 383, in connection with the radiated pieces, 208 and 210, required for the formation of such polygonal vases, when bent up and soldered at their edges.

The same vases wrought to the circular figure from round plates, either by spinning or by the hammer, would not require disks of metal so large as the boundary circles in figs. 208 and

210; as the pieces between the rays would be entirely in excess, they would cause the vessels to rise beyond their intended sizes, and would require to be pared off. But the original disks for making the vases should be of about the diameters of the inner circles, as then the pieces d, beyond the inner circles, would be nearly equal to the spaces e, within these circles, which would leave the vessel of uniform thickness throughout, and without deficiency or excess of metal supposing the conversion to be performed with mathematical truth.

The first and most important notion to be conveyed in refer-ence to raising works with the hammer, is the difference between those which may be called opposed, or solid blows, that have the effect of stretching or thinning the metal; and those which may be called unopposed, or hollow blows, that have less effect in thinning than in bending the metal; in fact, it often becomes thickened by hollow blows, as will be shown.

Figs. 262

263.

For example, the hammer in fig. 262 is directly opposed to the face of the anvil, or meets it face to face, and would be said to give a solid blow; one which would not jar the hand grasping the plate, weree the latter ever so thick or rigid: and this blow would thin the metal by its sudden compression between two hard surfaces, the face of the hammer being represented at f.

The hammer in fig. 263 is not directly opposed to the anvil, or rather to that point of it which sustains the work, consequently this would be called a hollow blow, one which would jar the hand were plate thick and rigid; and it would bend the plate partly to the form of the supporting edge, by a similar exhibition of the forces a, b, c, referred to in the diagrams, figs. 230 to 233, pages 388 and 389; not however by the quiet pressure therein employed, but by impact, or by driving blows. The hand situated at a, fig. 263, would be insufficient to withstand the blows of the hammer at c, but for the great distance of a b, compared with b c, and the thin flexible nature of the material.

From these reasons the coppersmith and others never require tongs for holding the metal, the same as the blacksmith, except at the fire, as in annealing and soldering; in hammering thin works, a constant change of position is required, and which can be in no way so readily accomplished as by the exquisite mechanism given us by nature, the unassisted hand. When however the works are too rigid or too small to be thus held, the anvil is made to supply the two points a, c, as in fig. 264, and the blow of the hammer is directed between them.

We will now trace the effects of solid and hollow blows given partially on a disk of metal a a, fig. 265, supposed to be twelve inches diameter; first within a central circle c c, of three inches diameter; and then around the margin a b, to the width of three inches, leaving the other portions untouched in each case; the thickness of the metal is greatly exaggerated to facilitate the explanation.

The solid blows within the circle cc, would thin and stretch that part of the metal, and make it of greater superficial extent; but the broad band of metal a c, would prevent it from expanding beyond its original diameter, and therefore the blows would make a central concavity, as in a cymbal, or like fig. 266. And the more blows that were given, either inside the bulge upon a flat anvil, or outside the bulge upon an anvil or head of a globular form, the more would the metal be raised, from its being thinned and extended; and thus it might be thrown into the shape of a lofty cone or sugar-loaf.

The hollow blows given within the same limited circle, would also stretch the metal and drive it into the hollow tools employed, such as fig. 264; thus producing the same effect as in 266, but by stretching the metal as we should the parchment of a drum, by the pressure of the hand in the center, or by a blow of the drumstick.

The solid blows around the three inch margin, would thin the metal and cause it to increase externally in diameter; but the plate would only continue flat, as in fig. 267, if every part of the ring were stretched proportionally to its increased distance from its first position. Were the inner edge towards b, thinned beyond its due amount, its expansion, if resisted by the strength of the outer ring a, would throw part of the work into a curve, and depress the metal, not as in the cymbal, but in the form of a gutter as in fig. 268; it would however more probably happen, that the inner edge alone of the marginal ring would be expanded, leaving the outer edge undisturbed, and producing the coned figure, 269.