It is scarcely necessary to state, that, all these suppositions being false, none of the consequences deduced from them can be true. Nevertheless, as it is the business of art to bring machines as near to this state of ideal perfection as possible, the conclusions which are thus obtained, though false in a strict sense, yet deviate from the truth in but a small degree. Like the first outline of a picture, they resemble in their general features that truth to which, after many subsequent corrections, they must finally approximate. After a first approximation has been made on the several false suppositions which have been mentioned, various effects, which have been previously neglected, are successively taken into account. Roughness, rigidity, imperfect flexibility, the resistance of air and other fluids, the effects of the weight and inertia of the machine, are severally examined, and their laws and properties detected. The modifications and corrections, thus suggested as necessary to be introduced into our former conclusions, are applied, and a second approximation, but still _only_ an approximation, to truth is made. For, in investigating the laws which regulate the several effects just mentioned, we are compelled to proceed upon a new group of false suppositions. To determine the laws which regulate the friction of surfaces, it is necessary to assume that every part of the surfaces of contact are uniformly rough; that the solid parts which are imperfectly rigid, and the cords which are imperfectly flexible, are constituted throughout their entire dimensions of a uniform material; so that the imperfection does not prevail more in one part than another. Thus, all irregularity is left out of account, and a general average of the effects taken. It is obvious, therefore, that by these means we have still failed in obtaining a result exactly conformable to the real state of things; but it is equally obvious, that we have obtained one much more conformable to that state than had been previously accomplished, and sufficiently near it for most practical purposes. This apparent imperfection in our instruments and powers of investigation is not peculiar to mechanics: it pervades all departments of natural science. In astronomy, the motions of the celestial bodies, and their various changes and appearances as developed by theory, assisted by observation and experience, are only approximations to the real motions and appearances which take place in nature. It is true that these approximations are susceptible of almost unlimited accuracy; but still they are, and ever will continue to be, only approximations. Optics and all other branches of natural science are liable to the same observations. CHAP. XIII. OF THE LEVER. (233.) An inflexible, straight bar, turning on an axis, is commonly called a _lever_. The _arms_ of the lever are those parts of the bar which extend on each side of the axis. The axis is called the _fulcrum_ or _prop_.