I have purposely reserved this subject to be distinct, on account of its great general importance in the arts, and have placed it last, in order that the various applications of the hammer might have been rendered comparatively familiar; for, although the plane surface may appear to be of more easy attainment than many of the complex forms which have been adverted to, such is by no means the case.

The methods employed are entirely different from that explained at page 153, in reference to flattening thick rigid plates, which are corrected by enlarging the concave side, with blows of the sharp rectangular edge of the hack-hammer, applied within the concavity. A method which bears some analogy to that employed by the joiner in straightening a board which is curved in its width, namely, the contraction of its convex side by exposure to heat. In thin metal plates neither of these modes is available, as the near proximity of the two sides causes both to be influenced in an almost equal degree by any mode of treatment.

Thin plates are flattened by means of solid and hollow blows, which have been recently explained, but they require to be given with considerable judgment; and a successful result is only to be obtained by a nice discrimination and considerable practice. All therefore that can be here attempted is an examination of the principle concerned, and of the general practice pursued; as the process being confessedly one of a most difficult nature, success is only to be expected or attained by a strict and persevering regard to principle.

As respects thin works, no figure is so easily distorted as the true plane, and this arises from the very minute difference which exists between the span or chord of a very flat arch, and its length measured around the curve. For example, imagining the span of an arch to be one inch, and the height of the same to be one-twentieth of an inch, the curve would be only about one 200th of an inch longer than the span: and therefore, if any spot of one inch diameter were stretched until, if unrestrained, it would become one inch and one 200th in diameter, such spot would raise up as a bulge one-twentieth of an inch high. This trivial change of magnitude would be accomplished with very few blows of the hammer, and much less than this would probably distort the whole plate.

In general, however, there would be not one error only, but several, the relationship of which would be more or less altered with nearly every blow of the hammer; thence arises the difficulty, as the plane surface cannot exist so long as any part of the plate is extended beyond its just and proportional size, and which it is a very critical point to arrive at.

There is another test of the unequal condition of flat works besides that of form, namely, their equal or unequal states of elasticity, and which is an important point of observation to the workman. For instance, if we suppose a plate of metal to be exactly uniform in its condition, it will bend with equal facility at every point, so that bending a long spring, or saw, will cause it to assume a true and easy curve; but supposing one part to be weaker than the remainder, the saw will bend more at the weak part, and the blade will become as it were two curves moving on a hinge. When such objects are held by the one extremity and vibrated, the perfect will feel as a uniformly elastic cane; the imperfect, as a cane having a slight flaw, which renders it weak at one spot; and in this manner we partly judge of the truth of a hand-saw, as in shaking it violently by the handle, it will, if irregularly elastic, lean towards the character of the injured cane, a distinction easily appreciated.

Fig. 272.

A thin plate of metal can only be perfectly elastic, when it is either a true plane or a true curve, so that every point is under the same circumstances as to strength. Thus a hemisphere, as at a, 272, possesses very great strength and rigidity owing to its convexity, but as the figure becomes less convex it decreases gradually in strength, and when it slides down to the plane surface, as at f, the metal assumes its weakest form.

A nearly plane surface will necessarily consist of a multitude of convexities or bulges varying in size and strength, connected by intermediate portions, which may be supposed to be plane surfaces; the whole may be considered as greatly exaggerated in the figure. The bulged parts are stronger than the plane flat parts, it follows that the bending will occur in preference at the plane or weak parts of the plate, precisely as in the injured cane.

When the bulges are large but shallow, they flap from side to side with a noise at every bending, as their very existence shows that they cannot rest upon the neutral or straight line; such parts are said to be buckled, their ready change of position renders them flaccid and yielding under the pressure of the fingers, and they are therefore called loose parts, but at the same time it is certain that they are too large.

On the contrary, those parts which are intermediate between the bulges, feel tight and tense under the fingers, because they are stretched in their positions and rendered comparatively straight, by the strong edges of the bulged or convex parts: the flat portions are the hinges upon which the bulged parts move, and such flat parts are sensibly too small for their respective localities, the others being too large.

Now, therefore, in prescribing the rule for the avoidance of these errors, it is simply to treat every part alike, so that none may be stretched beyond its proper size so as to become bulged, and thereby to distort the whole plate. When the mischief has occurred, the remedy is to extend all the too-small parts, or the hinges of the bulges to their true size, so as to put every part of the plate into equal tension, by allowing the bulged or too-large parts room to expand. Uniform blows should be therefore directed upon all the straight or too-small parts of the plate, the force and number of the blows being determined by the respective magnitudes of the errors, and the rigidity of the plate.