March 6, 1885.] 



SCIENCE, 



201 



He does not state whether there is any difference 

 in elevation or in character of soil at the corners of 

 this triangle; but, if there is none, then this observed 

 difference of motion is highly interesting and impor- 

 tant, and should be tested and verified in every possi- 

 ble way by interchange of instruments, resetting of 

 supports, etc., in order to be sure in every way that 

 there is no local peculiarity of instrument or method 

 of attachment to the soil. Doubtless this will have 

 been fully attended to in Professor Milne's continu- 

 ation of these interesting experiments. 



H. M. Paul. 



A RECENT DISCUSSION OF THE AXIOMS 

 OF MECHANICS. 



The logic of the physical sciences will al- 

 wa} T s remain a fascinating field for the philo- 

 sophic inquirer, and doubtless also for the 

 special student of those sciences. The recent 

 efforts towards a ' reform in logic ' in Germany 

 have not left this field untouched ; and one of 

 the first in importance, among the books that 

 bear on the general topic, is the work whose 

 title is given below. The author has quali- 

 fied himself for the task by a lengthy study of 

 the historj- of the development of his science, 

 and he has the power to suggest much more 

 than he directly says. In short, we have here 

 a man who combines definiteness with depth 

 of thought ; and his book, whether useful or 

 not to the specialists in mechanics, is surely 

 very suggestive to the student of logic. 



The author represents in his wa} r the new 

 empiricism of Germany, — a doctrine that has 

 grown up out of a study of Kant and the Eng- 

 lish philosophy combined, and that as certainty 

 points back again into the realm of specialty 

 philosophic discussion as it appears anxious to 

 be forever bej'ond that realm. This new em- 

 piricism is much more suggestive than the 

 older empiricism of J. S. Mill. He had 

 founded all inductive interpretation of nature 

 on the causal principle, and the causal princi- 

 ple itself again on an inductive interpretation 

 of nature. The new empiricism escapes from 

 this circle hy assuming a relatively a priori 

 principle in all induction, but seeks to remain 

 empiricism still b}^ making this principle no 

 abstract axiom, but a sort of ultimate form or 

 tendency of intelligence, viz., the tendency to 

 conceive of the facts of experience in the most 

 economical way. This interest in economy of 

 thought shall, in the new empiricism, take the 

 place of the old axiom of causality, and, in 

 fact, of all the mysterious axioms of past 

 logicians. This tendenc} 7 to economy is to be 



Die mechanik in ihrer entwickelung historisch-kritisch 

 dargentellt. Von E. Mach, professor an der Universitat zu 

 Prag. Leipzig, Brockhaun, 1883. 10+483 p., illustr. 8°. 



the true a priori that Kant sought. It is to 

 give us no knowledge transcending experience, 

 but onty a necessary presupposition concerning 

 experience. What for bare experience would 

 seem a confused mass, becomes for the scien- 

 tific thinker, by virtue of this tendency to 

 economy, a world of law. All the laws are 

 indeed statements of empirical fact ; but the 

 statements never could assume this form save 

 by virtue of the effort to economize thought. 



Such is the general statement of the new 

 empiricism. Our author, for the most part, 

 confines his use of it to his special task, and 

 lets general philosophy as much as possible 

 alone. Yet he cannot but constantly suggest 

 to the reader the philosophic problems peculiar 

 to his method. For the rest, he lays claim in 

 ' the preface to considerable relative originality 

 in the development of his own doctrine. Be- 

 fore Kirchhoff and Helmholtz applied to me- 

 chanical science the general theories of the 

 new empiricism, Mach had outlined his views 

 in a published essay. He is thus entitled to 

 individual credit, and open to separate criticism. 



Applied to mechanical science, the new em- 

 piricism, as our author and Kirchhoff have 

 expressed it, takes the form of declaring the 

 purpose of mechanics to be, "the simplest 

 possible description of the motions that are in 

 the world." Thus at a stroke the science is 

 to be freed from all mysterious elements. 

 Those old ideas of force, of inertia, and the 

 rest, are to be defined afresh in such a way as 

 to conform to this logical theory. The science 

 is to have its two perfectly plain bases ; viz., 

 experience of motion, of velocity, of direction, 

 etc., and the effort to think this experience 

 with the least effort and the greatest unit}'. 



The historical form that Mach gives to his 

 doctrine makes it especially attractive and en- 

 lightening ; and we hope for much good effect 

 from this element in the book. Mechanical 

 science, as Mach frequently repeats, had its 

 origin very plainly in the need of men whose 

 handiwork, owing to its technical complexitj', 

 was difficult to describe to those new in the 

 craft. The learner must be enabled to see the 

 permanent elements of the experience of his 

 craft beneath, and in all their endlessty various 

 applications ; he must be brought to an ' iiber- 

 sichtliche erfassung der thatsachen : ' hence 

 the need of quite general and simple descrip- 

 tions, applying to fundamentally important 

 facts. Economy of description thus from the 

 first becomes the artistic principle, as it were, 

 of this technical instruction. 



If this is the origin and general method of 

 the science in its embiyonic stage, the origin 



