ceit hatched under my own time-tonsured pate, but genuine wisdom which I have simply borrowed from an old, clear-headed fellow, who lived and died a long while ago—Leonhard Euler. If you will read his seventy-fourth letter to a German princess, written on the 11th day of November, 1760, you will find it all set forth at great length. In reading it you must bear in mind, though, that in Euler's time the imponderables, as they were then called, were not so distinctly known or believed to be modes of motion as they are now. And you must also remember that he was writing to a princess who probably knew more about madrigals and operatic airs than about scientific terms, in consequence whereof his exposition became a little diffuse. If, however, you should reject old Euler's reasoning as "belonging to a past age of thought," which, I see, is one of your favorite ways of getting rid of irrefutable truths, I may refer you to a gentleman who is yet among the living—Hermann Helmholtz. You will find what he has to say on the "matter in hand," on the third and fourth pages of his first essay, "Ueber die Erhaltung der Kraft" (not included in the collection of his essays).
Now, hombre querido (I am still preaching), if after this you will carefully read again the first twelve chapters of my book, you will probably find that they are somewhat less absurd than you fancied they were. But you will say, no doubt—in fact, you do say, though not in so many words—that all this is mere speculative trash, in which the man of science has no concern. One of my reviewers in the New York "Critic"—whom I at one time suspected, perhaps unjustly, from certain peculiarities of his phraseology, and from the fact that, like yourself, he sneers at me for having "wasted" two long chapters on transcendental geometry, of having had oral confabulations with you, in which the mouth of the speaker was not and could not be applied to the ear of the listener—disposes of my discussion of the relation of the mechanical theory to the laws of thought by the following oracular dictum (a travesty of a saying of Carlyle): "A sound digestion has little self-consciousness of the operations of the stomach; the sound thinker gives himself little uneasiness respecting the laws of thought." I can not stop, at this moment, to show you how and why a little knowledge of the laws of thought is useful to the physicist and mathematician. I shall come to that by-and-by, when I have considered what you say about the kinetic theory of gases and space of an indefinite number of dimensions. For the present I only want to tell you how I ventured upon the audacity of intruding the theory of cognition into the science of physics.
In Europe, as well as in this country, there are certain idle fellows who, during the first half of the present century, for want of more useful occupation, took to tracing the ramifications of forms of speech, and finally got to digging for their roots. These absurd persons abound chiefly in Germany, where, as you know, the people are always