It is because of this hesitancy to bring mental phenomena under the same mechanistic principle as all the other phenomena that the philosophical systems had to search for some other means to connect the mental world with the mechanical, and the efforts of the philosophers to bring about this end have been most varied. Of the various doctrines that have come down to us, that of the _pre-established harmony_ proposed by Leibnitz is in the ascendant in our day, and is now called the theory of the _psycho-physical parallelism_. According to this theory it is assumed that the mental world exists alongside, and quite independent of, the mechanical, but that the things have been so prearranged that mental processes take place simultaneously with certain mechanical processes (according to some, with all mechanical processes) in such a way that, although the two series do not influence each other in the least, they always correspond to each other precisely. How such a relation has come about and how it is maintained remains unsaid, or is left to future explanation. We need only think of the content of this hypothesis with an unbiased mind to lose all relish for it at once. In fact, it has no other _raison d'être_ than the presumption that the mental and the mechanical world are opposed to each other. As soon as we abandon the thesis that the non-mental world is exclusively mechanical, we acquire the possibility again of finding for the theory of mental phenomena a constant and regular connection with the theories of all other phenomena, especially with the phenomena of life. Therefore it will be found most expedient in every respect, instead of rendering scientific research one-sided and almost blind to nonconforming facts by preconceived hypotheses, such as the mechanistic hypothesis, to seek, as hitherto, from step to step, the new elements of manifoldness which must be taken account of in the progressive upbuilding of science and to limit ourselves faithfully to them in the formation of general ideas. =48. Complementary Branches of Mechanics.= The field of pure or classical mechanics is limited to the above two kinds of energy, work and kinetic energy, though these do not exhaust the manifoldness of the mechanical energies. Accordingly, other branches of mechanics dealing with the corresponding phenomena are added to the classical mechanics described above. If by mechanical energies we understand all energies in which _changes of space are connected with changes of energy_, there are as many different forms as there are spacial concepts that seem applicable. _Form_, _Volume_, and _Surface_ of bodies in space are especially recognizable as the field of action for energy, which shows different properties or manifoldnesses according to each of these relations.