shall account for the nature of the properties of that studied in its relations with things already known and with those conditions or categories among which it exists. It is certain that it is only possible to carry out these investigations when we have taken as a basis some incontestable fact which is self-evident to our understanding; as, for instance, number, time, space, motion, or mass. The determination of such primary or fundamental conceptions, although not excluded from the possibility of investigation, frequently does not subject itself to our present mode of scientific generalisation. Hence it follows that in the investigation of anything, there always remains something which is accepted without investigation, or admitted as a known factor. The axioms of geometry may be taken as an example. Thus in the science of biology it is necessary to admit the faculty of organisms for multiplying themselves, as a conception whose meaning is as yet unknown. In the study of chemistry, too, the notion of elements must be accepted almost without any further analysis. However, by first investigating that which is visible and subject to direct observation by the organs of the senses, we may hope that in the first place hypotheses will be arrived at, and afterwards theories of that which has now to be placed at the basis of our investigations. The minds of the ancients strove to seize at once the very fundamental categories of investigation, whilst all the successes of recent knowledge are based on the above-cited method of investigation without the determination of 'the beginning of all beginnings.' By following this inductive method, the _exact sciences_ have already succeeded in becoming accurately acquainted with much of the invisible world, which directly is imperceptible to the organs of sense (for example, the molecular motion of all bodies, the composition of the heavenly luminaries, the paths of their motion, the necessity for the existence of substances which cannot be subjected to experiment, &c.), and have verified the knowledge thus obtained, and employed it for increasing the interests of humanity. It may therefore be safely said that _the inductive method of investigation_ is a more perfect mode of acquiring knowledge than the deductive method alone (starting from a little of the unknown accepted as incontestable to arrive at the much which is visible and observable) by which the ancients strove to embrace the universe. By investigating the universe by an inductive method (endeavouring from the much which is observable to arrive at a little which may be verified and is indubitable) the new science refuses to recognise dogma as truth, but through