I have explained at some length, in my “Reply to Prof. Boltzmann,” the circumstances under which the present inquiry originated and has been pursued. Of these I need now only mention two:—first, the very limited time which I can spare for such work; second, the very meagre acquaintance I possessed of what had been already done with regard to the subject. My object has been to give an easily intelligible investigation of the Foundations of the Kinetic Theory; and I have, in consequence, abstained from reading the details of any investigation (be its author who he may) which seemed to me to be unnecessarily complex. Such a course has, inevitably, certain disadvantages, but its manifest advantages far outweigh them.