As one which may be allowed to stand, _instar omnium_, we may mention the steam engine; that legitimate child of physical and chemical science--at once more powerful than the united force of the strongest and largest animals, and more manageable than the smallest and gentlest; raising from the bowels of the earth the massy treasures of its mines, drawing up rivers from their channels, and pouring them, in streams of life, into the bosom of cities; and, above all, propelling against the currents, the winds, and the waves of the ocean, those stupendous vessels, which combine speed with certainty, and establish upon the bosom of the deep the luxuries and accommodations of the land. The successful execution of this magnificent design was first witnessed upon the waters of the Hudson, but is now imitated in almost every civilized country; and it remains to be seen whether they will emulate us by transporting, by the same means, and against the same obstacles, the most formidable trains of artillery. The mechanical inventions of this country are numerous; many of them are ingenious, and some are highly important. In no way can a knowledge of them be so readily and extensively diffused as in a scientific journal. To this object, therefore, a part of our labours (should there be a call for it,) will be devoted, and every necessary aid will be given by plates and descriptions. Science and art mutually assist each other; the arts furnish facts and materials to science, and science illuminates the path of the arts. The science of mathematics, both pure and mixed, can never cease to be interesting and important to man, as long as the relations of quantity shall exist, as long as ships shall traverse the ocean, as long as man shall measure the surface or heights of the earth on which he lives, or calculate the distances and examine the relations of the planets and stars; and as long as the _iron reign of war_ shall demand the discharge of projectiles, or the construction of complicated defences. In a word, the whole circle of physical science is directly applicable to human wants, and constantly holds out a light to the practical arts; it thus polishes and benefits society, and every where demonstrates both supreme intelligence, and harmony and beneficence of design in THE CREATOR. ART. I. _Essay on Musical Temperament._[3] By Professor FISHER, of Yale College.