large, mathematics, otherwise erect, meets with its fall, it has eaten of the apple of knowledge and there has been opened up to it the path of limitless progress as well as that of error. The virgin condition of absolute purity, the undisturbable certainty of all mathematics has vanished forever, a period of controversy has intervened, and we have now arrived at the state of affairs in which most people carry on the operations of multiplication and division not because they really understand what they are engaged in, but from mere belief because the operation has so far always given correct results. Astronomy and mechanics, physics and chemistry are in a still more confused state, and hypotheses crowd one another thick as a swarm of bees. It cannot be otherwise. In physics we investigate the movements of molecules, in chemistry the development of molecules from atoms, and if the theory of light waves should not be correct we have no absolute knowledge that we even see these interesting things. The lapse of time produces a very thin crop of final truths of last instance. In geology we are in a still more embarrassing situation for we are here involved in the study of preceding epochs in which, as a matter of fact, neither we ourselves nor any other human being ever existed. Here there is much labor spent in the harvesting of truths of last instance, and they are a scanty crop withal.
The second division of knowledge is occupied in the investigation of living organisms. In this field the changes and causalities are so complex that not only does the solution of each question bring about the rise of an unlimited number of new questions, but the solution of each of these separate new questions depends upon years, frequently centuries, of investigation, and can then be only partially completed. So that the need of sys-
