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L, we have at hand the values of the coefficient for the latter case, the same coefficient may be employed for the case in hand. , to all quantities representing the values of functions of non-dimensional or II I groups of variables as developed in 3. jA and utility arises from the fact that being Fig. 9. non-dimensional, the value is independent of the particular system of units employed-metric or English. The value of :n;, the relation between ten feet and two feet, twelve meters and four meters, six per cent-these and other like values are independent of any system of units of measurement, so long as a single consistent system is used in each case.
3}, affected with suitable exponents as the individual term may require. It will be noted that the general form of the physical equation of zero dimension will contain unity as one of its terms, resulting from dividing through the general equation, not of zero dimension, by some one of its terms. This term unity, however, is, of course, of zero dimension and admits of representation by a term of the form (lit II~) simply by making A. and p. both zero. Furthermore, it is clear that in any such mathematical expression as f (Il1 Il2) = 0, we may always assume some form of solution for Il1 28 A IV.
In any such case involving a relation between physical quantities, there will be a certain minimum number which will be necessary and sufficient for the definition of all the others. These must, of course, be independent. The selection of the particular group (composed of this minimum number) to be taken for this purpose, is usually a matter of choice. In mechanics, in the broad sense, the number is three. For the present assume such number and suppose, for example, the total number five. Let these be denoted by Ql, Q2, x, y, z the three latter representing the fundamentals.