It was a curious invention--an invention the like of which one cannot easily specify; for the thing invented was not a material mechanism, or a theory, or anything exactly like anything else. It is difficult to classify a logarithm except as a logarithm:--yet Napier did create something; he did make something exist that had not existed before; he did conceive an idea and embody that idea in a concrete machine. That machine, in the hands of a man who understood it, could supply extraordinary assistance in making mathematical calculations, especially calculations involving many operations and many figures, as in astronomy. It has been in continual use since Napier invented it, and is used still. In order to indicate the simplicity and the value of Napier's invention, it may assist those who have forgotten what a logarithm is, or who have been so fortunate as never to have been compelled to study about them, to state that logarithms are numbers so adapted to numbers to be multiplied, divided, or raised to any power, that one simply adds their logarithm, subtracts one logarithm from the other or multiplies or divides a logarithm by the number representing the power, and then notes in a table the number resulting, instead of going through the long process of multiplying, dividing, squaring, etc. Of course, in the case of small numbers, the use of logarithms is not only unnecessary but undesirable; but in the case of the long numbers used in astronomy, and even in navigation, logarithms are inexpressibly helpful and time-saving. The mental feat of Napier consisted in conceiving the idea of accomplishing what he subsequently did accomplish, and then constructing and producing the "logarithmic tables" that made it possible. Another indication of the new intellectual movement in Europe was the experiments, deductions and inventions of William Gilbert, an English physician, who lived from 1540 till 1603. According to the use of the word invention followed in this book, only two actual inventions can be credited to Gilbert, that of the electroscope and that of magnetization. Gilbert's work was valuable in the highest degree, more valuable than that of most inventors; and yet it was more inductive and deductive than inventional. It is not the purpose of this book to suggest that invention has been the only kind of work that men have done which has had an influence on history; and the work of Gilbert gives the author an opportunity to emphasize the value of certain work which is not inventional. At the same time, the author cannot resist the temptation of pointing out that Gilbert's work was original and constructive, that it hovered around the borders of invention, and that it did more to assist the inventors of the electric and electro-magnetic appliances that were soon to follow, than the work of almost any other one man.