minute details of the phenomena of motion which are involved in this turbulence. Let one, for example, watch the movement of the water at a point in a brook. There is indeed a fairly steady average velocity of the water at the point and a certain mean rhythmic variation, but superposed upon this average motion there is an erratic variation of velocity which is infinitely manifold, the details of which are beyond the scope of any descriptive science. A descriptive science like mechanics is concerned with how things progress as a phenomenon develops itself; how the structural parts of a bridge stretch and shorten as a car passes across the bridge; how the pressure and temperature of steam vary during the successive stages of admission, expansion and exhaust of a steam engine; how electro-motive force, current strength, electro-magnetic force and all of the changing variables play in the operation of a dynamo. But who could recite the story of the most minute details of these phenomena? It can not be done, and if it could be done, it would be of no avail, for these details can never be twice alike and the very essence of a science lies in the discovery of types which in their important features recur so that a knowledge of these types may serve as a basis for anticipation and design.
Fire is the most familiar example of a turbulent phenomenon, and its most striking characteristic is that its progress is not dependent upon any external driving cause; when once started it goes forward of itself and with a rush. Tyndall in referring to this matter says that to account for the propagation of fire was one of the philosophical difficulties of the eighteenth century. A spark was found sufficient to initiate a conflagration, and the effect seemed beyond all proportion greater than the cause; herein lay the philosophical difficulty. Indeed the simple idea of cause and effect is not applicable to physical phenomena involving turbulence. Every physical phenomenon involving turbulence is to some extent self-sustaining, and every such phenomenon has a certain impetuous quality which may carry it beyond anything that is commensurate with the original initiating cause. These remarkable characteristics of turbulence are now definitely formulated as the second law of thermodynamics.
The most important practical thing in connection with the turbulent aspect of any physical phenomenon is its general result or consequence, just as the important thing about the burning of a house is the loss. How utterly useless and uninteresting it would be, for example, to study the minutest details of a conflagration (assuming such study to be possible), recording the height and breadth and the irregular and evanescent distribution of temperature throughout each flicker of consuming flame, the story of each crackling sound and the extent and character of every yield and sway of timber and wall! The fact is that we are immersed in an illimitable sea of phenomena, every single detail
