Many of the phenomena of physical science are simple enough and well enough understood that they are amenable to complete mathematical analysis without recourse to auxiliary experimentation. There are other phenomena, however, which, though being made up of well-understood simple systems, are so complicated as a whole as to render complete mathematical analysis difficult or impossible. The distribution of stress in a complicated machine part, or the flow of water in an irregularly shaped vessel, would constitute examples of the latter kind.

When something must be known about one of these more complicated problems it is usual, whenever possible, to obtain the desired information empirically by direct experimentation. Often, however, the thing studied is too large to be experimented with. Or, as in the case of large engineering structures, the information on a bridge, dam, or building is needed in advance of designing the structure.

Under these conditions, where . . .

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