first part of this lecture is without special interest for us here; but the second part is of the greatest possible significance as an exhibition of the tendency of physicists to postulate determinate last elements, absolute spatial limits, and invariable physical standards in the construction of material phenomena. For this reason, I shall take the liberty of reproducing, as literally as is possible in a translation, the most important passages of this part of the lecture.
"The principles of the Galileo-Newtonian theories," says Prof. Neumann (loc. cit., p. 11), "consist in two laws—the law of inertia proclaimed by Galileo, and the law of attraction added by Newton. . . . A material point, when once set in motion, free from the action of an extraneous force, and wholly left to itself, continues to move in a straight line so as to describe equal spaces in equal times. Such is Galileo's law of inertia. It is impossible that this proposition should stand in its present form as the corner-stone of a scientific edifice, as the starting-point of mathematical deductions. For it is perfectly unintelligible, inasmuch as we do not know what is meant by "motion in a straight line," or, rather, inasmuch as we do not know that the words "motion in a straight line" are susceptible of various interpretations. A motion, for instance, which is rectilinear as seen from the earth, would be curvilinear as seen from the sun, and would be represented by a different curve as often as we change our point of observation to Jupiter, to Saturn, or another celestial body. In short, every motion which is rectilinear with reference to one celestial body, will appear curvilinear with reference to another celestial body. . . . . .
"The words of Galileo, according to which a material point left to itself proceeds in a straight line, appear to us, therefore, as words without meaning—as expressing a proposition which, to become intelligible, is in need of a definite background. There must be given in the universe some special body as the basis of our comparison, as the object in reference to which all motions are to be estimated; and only when such a body is given, shall we be able to attach to those words a definite meaning. Now, what body is it which is to occupy this eminent position? Or, are there several such bodies? Are the motions near the earth to be referred to the terrestrial globe, perhaps, and those near the sun, to the solar sphere? . . . .
"Unfortunately, neither Galileo nor Newton gives us a definite answer to this question. But, if we carefully examine the theoretical structure which they erected, and which has since been continually enlarged, its foundations can no longer remain hidden. We readily see that all actual or imaginable motions in the universe must be referred to one and the same body. Where this body is, and what are
trittsvorlesung gehalten in der Aula der Universität, Leipzig, am 3. November, 1869. Von Dr. C. Neumann, ord. Professor der Mathematik an der Universität, Leipzig," etc. Leipzig, B. G. Teubner, 1870.