The Author has vainly sought for the rules which govern the hind feet of a playfully disposed mule; but the inquiry has usually been unsatisfactory, and upon some occasions disastrous. Should these movements be controlled by any general law, it is of such a complex nature that all attempts to expound it have hitherto been fruitless. The figures in the series of circles (see appendix A) were selected from "ANIMAL LOCOMOTION" and arranged by the Author for his less ambitious work, "POPULAR ZOOPRAXOGRAPHY." (See Appendix C). They were traced by the well known artist, Erwin Faber, and are reproduced one-third the diameter of the circles arranged for the zoöpraxiscope. Many of the original phases of movement are omitted on account of the optical law which in the construction of a zoöpraxiscope requires that the number of illustrations must bear a certain relationship to the number of perforations through which they are viewed. The popular number of thirteen having been selected for the latter, the same number of figures illustrate actions without lateral progressive motion. When the number of illustrated phases is less than the number of perforations, the succession of phases is in the direction of the motion, and the disc is necessarily revolved in a reverse direction. When the number of phases is greater than the number of perforations, the phases succeed each other in a direction contrary to that of the motion, and the disc is revolved in the direction of the motion. An increased or diminished number of figures will respectively result in an increased or diminished apparent speed of the object. For further information on the subject, the reader is referred to the ZOOPRAXISCOPE. * * * * * _APPENDIX A._ SYLLABUS OF A COURSE OF TWO LECTURES ON ZOOPRAXOGRAPHY OR THE SCIENCE OF ANIMAL LOCOMOTION IN ITS RELATION TO DESIGN IN ART.