author's preface. ix 



times been treated by several persons in a vivid and 

 interesting manner, so that it seemed unnecessary to 

 publish the corresponding part of the cycle of lectures 

 which I delivered on this subject ; the more so as some of 

 the more important subjects to be discussed will, perhaps 

 in the immediate future, be capable of more definite 

 treatment than is at present possible. 



On the other hand, I have invariably found that the 

 fundamental ideas of this subject always appear difficult 

 of comprehension not only to those who have not passed 

 through the school of mathematical mechanics ; but even 

 to those who attack the subject with diligence and in- 

 telligence, and who possess a tolerable acquaintance with 

 natural science. It is not to be denied that these ideas 

 are abstractions of a quite peculiar kind. Even such a 

 mind as that of Kant found difficulty in comprehend- 

 ing them ; as is shown by his controversy with Leibnitz. 

 Hence 1 thought it worth while to furnish in a popular form 

 an explanation of these ideas, by referring them to many 

 of the better known mechanical and physical examples ; 

 and therefore I have only for the present given the first 

 Lecture of that series which is devoted to this object. 



The last Lecture was the opening address for the 

 ' Naturforscher-Versammlung,' in Innsbriick. It was 

 not delivered from a complete manuscript, but from 

 brief notes, and was not written out until a year after. 

 The present form has, therefore, no claim to be con- 

 sidered an accurate reproduction of that address. I have 

 added it to the present collection, for in it I have treated 

 briefly what is more fully discussed in the other articles. 

 Its title to the place which it occupies lies in the fact 

 that it attempts to bring the views enunciated in the 



