Natural science and natural philosophy are not two provinces mutually exclusive of each other. They belong together. They are like two roads leading to the same goal. This goal is the domination of nature by man, which the various natural sciences reach by collecting all the individual actual relations between the natural phenomena, placing them in juxtaposition, and seeking to discover their interdependence, upon the basis of which one phenomenon may be foretold from another with more or less certainty. Natural philosophy accompanies these specialized labors and generalizations with similar labors and generalizations, only of a more universal nature. For instance, while the science of electricity, as a branch of physics, deals with the relation of electrical phenomena to one another and to phenomena in other branches of physics, natural philosophy is not only concerned with the question of the mutual connection of all physical relations, but also endeavors to include in the sphere of its study chemical, biological, astronomical, in short, all the known phenomena. In other words, natural philosophy is the most general branch of natural science.

Here two questions are usually asked. First, how can we define the boundary line between natural philosophy and the special sciences, since, obviously, sharp lines of demarcation are out of the question? Secondly, how can we investigate and teach natural philosophy, when it is impossible for any one person to master all the sciences completely, and so obtain a bird's-eye view of the general relations between all the branches of knowledge? To the beginner especially, who must first learn the various sciences, it seems quite hopeless to devote himself to a study that presupposes a command of them.

Since a discussion of the two questions will afford an excellent preliminary survey of the work in hand, it will be well to consider them in detail. In the first place, the lack of complete and precise boundary lines is a general characteristic of all natural things, and science is a natural thing. If, for instance, we try to differentiate sharply between physics and chemistry, we are met with the same difficulty. So also in biology if we try to settle beyond the shadow of a doubt the line of separation between the animal and the vegetable kingdoms.

If, despite this well-known impossibility, we consider the division of natural things into classes and orders as by no means useless and do not discard it, but regard it as an important scientific work, this is practical proof that such classification preserves its essential usefulness, even if it does not attain ideal definiteness. For, this imperfection notwithstanding, classification reaches its end, which is a comprehensive view, and thus a mastery, of the manifoldness of phenomena. For example, with the overwhelming majority of organic beings there is no doubt whether they are animals or plants. Similarly, most phenomena of inorganic nature can readily be designated as physical or chemical. For all such cases, therefore, the existing classification is good and useful. The few cases presenting difficulty may very well be considered by themselves wherever they occur, and we need merely take cognizance of them here. It follows from this, to be sure, that classification will be all the better fitted to its purpose the less frequently such doubtful cases arise, and that we have an interest in repeatedly testing existing classifications with a view to finding out if they cannot be supplanted by more suitable ones.

In these matters it is much the same as when we look upon the waves on the surface of a large body of water. Our first glance tells us that a number of waves are rolling there; and from a point giving us a sufficiently wide outlook, we can count them and gauge their width. But where is the line of division between one wave and the next? We undoubtedly see one wave following another, yet it is impossible for us to indicate precisely the end of one and the beginning of the next. Are we then to deduce that it is superfluous or unfeasible to designate the waves as different? By no means. On the contrary, in strictly scientific work we will endeavor to find some suitable definition of the boundary line between two consecutive waves. It may then be called an arbitrary line, and in a degree arbitrary it will certainly be. But to the investigator this does not matter. What concerns him is, if, with the help of this definition, wave lengths can be unequivocally determined, and if this is possible, he will use the definition as suitable to the purposes of science, without dismissing from his mind the idea that possibly some other definition may provide an even easier or sharper determination. Such an one he would instantly prefer to the old one.

Thus we see that these questions of classification are not questions of the so-called "essence" of the thing, but pertain merely to purely practical arrangements for an easier and more successful mastery of scientific problems. This is an extremely important point of view, much more far-reaching than is apparent here at its first application.

As to the second objection, I will admit its validity. But here, too, we have a phenomenon appearing in all branches and forms of science. Therefore we must familiarize ourselves with it in advance. Science was created by man for man's purposes, and, consequently, like all human achievements, possesses the indestructible quality of imperfection. But the mere fact that a successful working science exists, with the help of which human life has been fundamentally modified, signifies that the quality of incompleteness in human learning is no hindrance to its efficiency. For what science has once worked out always contains a portion of truth, hence a portion of efficiency. The old corpuscular theory of light, which now seems so childishly incomplete to us, was adequate, none the less, for satisfactorily explaining the phenomena of reflection and refraction, and the finest telescopes have been built with its help. This is due to the true elements in it, which taught us correctly to calculate the direction of rays of light in reflection and refraction. The rest was merely an arbitrary accessory which had to fall when new, contradictory facts were discovered. These facts could not have been taken into consideration when the theory was propounded, because they were not yet known. But when the corpuscular theory of light was replaced by the theory of waves of an elastic ether, geometric optics at first remained quite unchanged, because the theory of straight lines of rays could be deduced from the new views also, though not so easily and smoothly. And geometric optics was then concerned with nothing but these straight lines, in no wise with the question of their propagation. It did not become clear until recently that this conception of straight lines of rays is incomplete, though, it is true, it made a first approach toward the presentation of actual phenomena. It fails when it comes to characterize the behavior of a pencil of rays of large aperture. The old idea of a straight line of rays was to be replaced by a more complex concept with more varied characteristics, namely, the wave-surface. The greater variety of this concept renders possible the presentation of the greater variety of the optical phenomena just mentioned. And from it proceed the very considerable advances that have been made, since the new theory was propounded, in optical instruments, especially the microscope and the photographic objective, for the purposes of which pencils of rays of large aperture are required. The astronomic objective with its small angle of aperture has not undergone particularly important improvements.

Experience in every province of science is the same as in this. Science is not like a chain which snaps when only a single link proves to be weak. It is like a tree, or, better still, like a forest, in which all sorts of changes or ravages go on without causing the whole to pass out of existence or cease to be active. The relations between the various phenomena, once they become known, continue to exist as indestructible components of all future science. It may come to pass, in fact, does come to pass very frequently, that the form in which those relations were first expressed prove to be imperfect, and that the relations cannot be maintained quite generally. It turns out that they are subjected to other influences which change them because they had been unknown, and which could not have been taken into consideration at the discovery and first formulation of these relations. But no matter what changes science may undergo, a certain residue of that first knowledge will remain and never be lost. In this sense, a truth that science has once gained has life eternal, that is, it will exist as long as human science exists.

Applying this general notion to our case, we have the following. How far and how generally at any given time the relations of the various phenomena are summed up in fixed forms, that is, in natural laws, will depend upon the stage attained by each of the special sciences. But since science has been in existence it has yielded a certain number of such general laws, and these, though they have been filed down a good deal in form and expression, and have undergone many corrections as to the limits of their application, nevertheless have preserved their essence, since they began their existence in the brains of human investigators. The net of the relations of phenomena grows ever wider and more diversified, but its chief features persist.

The same is true of an individual. No matter how limited the circle of his knowledge, it is a part of the great net, and therefore possesses the quality by virtue of which the other parts readily join it as soon as they reach the consciousness and knowledge of the individual. The man who thus enters the realm of science acquires advantages which may be compared to those of a telephone in his residence. If he wishes to, he may be connected with everybody else, though he will make extremely limited use of his privilege, since he will try to reach only those with whom he has personal relations. But once such relations have been established, the possibility of telephone communication is simultaneously and automatically established. Similarly, every bit of knowledge that the individual appropriates will prove to be a regular part of the central organization, the entire extent of which he can never cover, though each individual part has been made accessible to him, provided he wants to take cognizance of it.

The mere beginner in learning, therefore, when receiving the most elementary instruction in school, or from his parents, or even from his personal experiences in his surroundings, is grasping one or more threads of the mighty net, and can grope his way farther along it in order to draw an increasing area of it into his life and the field of his activity. And this net has the valuable, even precious quality of being the same that joins the greatest and most comprehensive intellects in mankind to one another. The truths a man has once grasped he need never learn afresh so far as their actual content is concerned, though not infrequently—especially in newer sciences—he may have to see the form of their presentation and generalization change. For this reason it is of such especial importance for each individual from the first to perceive these unalterable facts and realize that they are unalterable and learn to distinguish them from the alterable forms of their presentation. It is in this very regard that the incompleteness of human knowledge is most clearly revealed. Time and again in the history of science form has been taken for content, and necessary changes of form—a merely practical question—have been confused with revolutionary modifications of the content.

Thus, each presentation of a science has its natural philosophic portion. In text-books, whether elementary or advanced, the chapter on natural philosophy is found usually at the beginning of the book, sometimes at the end, in the form of a "general introduction," or "general summary." In the special works in which the latest advances of science are made known by the investigators, the natural philosophic portions are usually to be found in the form of theses, of principles, which are not discussed, often not even explicitly stated, but upon the acceptance of which depend all the special conclusions that are drawn, in the case in hand, from the new facts or thoughts imparted. Whether at the beginning or at the end of the book, these most general principles do not quite occupy the place that befits them. If at the introduction of the text-book, they are practically devoid of content, since the facts they are meant to summarize are yet to be unfolded in the course of the presentation. If at the end, they come too late, since they have already been applied in numerous instances, though without reference to their general nature. The best method is—and a good teacher always employs this method, whether in the spoken or the written word—to let the generalizations come whenever the individual facts imparted require and justify them.

Thus, all instruction in natural sciences is necessarily interspersed with natural philosophy, good or bad, according to the clearheadedness of the teacher. If we wish to obtain a perfect survey of a complex structure, as, for instance, the confusion of streets in a large city, we had better not try to know each street, but study a general plan, from which we learn the comparative situation of the streets. So it is well for us in studying a special science to look at our general plan, if for no other reason than to keep from losing our way when it may chance to lead through a quarter hitherto unknown. This is the purpose of the present work.