PRIMARY CONCEPTS OF MODERN SCIENCE. 227 



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, ab- 

 solute spatial limits, and invariable physical standards in the construc- 

 tion 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 pro- 

 claimed 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 " mo- 

 tion in a straight line," or, rather, inasmuch as we do not know that 

 the words " motion in a straight line " are susceptible of various in- 

 terpretations. 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 celes- 

 tial 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 in- 

 telligible, 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 e*arth 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 re- 

 ferred to one and the same body. Where this body is, and what are 



trittsvorlesung gehalten in der Aula der Universitat, Leipzig, am 3. November, 1869. 

 Von Dr. C. Neumann, ord. Professor der Mathematik an der Universitat, Leipzig," etc. 

 Leipzig, B. G. Teubner, 18 70. 



