In proportion as the various branches of the human tree of knowledge have developed during the century, and the methods of the different sciences have been perfected, the desire has grown to make them _exact_; that is, to make the study of phenomena as purely empirical as possible, and to formulate the laws that result as clearly as the circumstances permit--if possible, _mathematically_. The latter is, however, only feasible in a small province of human knowledge, especially in those sciences in which there is question of measurable quantities; in mathematics, in the first place, and to a greater or less extent in astronomy, mechanics, and a great part of physics and chemistry. Hence these studies are called "exact sciences" in the narrower sense. It is, however, productive only of error to call all the physical sciences _exact_, and oppose them to the historical, mental, and moral sciences. The greater part of physical science can no more be treated as an _exact_ science than history can; this is especially true of biology and of its subsidiary branch, psychology. As psychology is a part of physiology, it must, as a general rule, follow the chief methods of that science. It must establish the facts of psychic activity by empirical methods as much as possible, by observation and experiment, and it must then gather the laws of the mind by inductive and deductive inferences from its observations, and formulate them with the utmost distinctness. But, for obvious reasons, it is rarely possible to formulate them mathematically. Such a procedure is only profitable in one section of the physiology of the senses; it is not practicable in the greater part of cerebral physiology.