In following the course of invention and rediscovery during the middle ages, and in subsequent times, we see two main causes of the superiority of our own useful arts to those of the ancients--the extended application of mechanical and chemical science. The discovery of the various problems in mechanics, which paved the way for the multiplication of human force, and the introduction of new motor powers, occupied chiefly the latter half of the sixteenth and the seventeenth century. The treatises of Stevinus and Galileo, with the first dawnings of the discovery of the steam-engine, appear to mark a new era, and prepare the way for those wonderful applications of moving power which have changed the face of the manufacturing world. The subsequent train of discovery is far too comprehensive for our limits, and ends at length in that crowning development of machinery--the Calculating Machine of Mr. Babbage. We need only mention that, by this extraordinary instrument, some processes of numeric and algebraic calculation may be effected, to an extent hitherto unattainable by mathematicians. A short view of the progress of the art of clockmaking, will well illustrate a gradual advance made in the application of mechanics to the uses of daily life. Striking clocks were known in Italy probably as early as the end of the thirteenth century--one other strong proof that we must date the revival of arts much earlier than that period. Their existence becomes certain about the middle of the fourteenth; probably at that period they were general. These clocks were all moved by the action of weights; and, though furnished with balance regulators, were still very inaccurate. Next followed the introduction of a spring as the moving power, marking a new era in the art. Then came the age of mechanical discovery, producing Galileo’s observation of the vibration of the pendulum in nearly equal times, whether the spaces traveled through were large or small. So valuable a discovery could not long remain dormant; and we find, accordingly, that it was applied by the discoverer, or, in a better form, by Huyghens, to the regulation of time-pieces by means of the pendulum. The advance of chemical science soon showed a source of error in the unequal size of the pendulum, caused by alternate expansion and contraction of the metal due to change of temperature. This was remedied by the use of the jar filled with mercury as a pendulum; and subsequently by the employment of a pendulum formed of different metals, so arranged that their different expansions should mutually balance each other. The mutual connection between the art of making clocks and the science of astronomy, in which each has alternately borrowed and lent so much, is an excellent illustration of the many points in which the useful arts are brought into contact with higher provinces. The remaining improvements would fill volumes, and we cannot pretend to enter more fully into them.