By William Frederick Durand

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer booklet records mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

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**Additional info for Aerodynamic Theory: A General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics**

**Example text**

2) The relative values of any set of the variables, such as ~. a 2, a, will therefore depend only on the differences in the known quantities on the right hand side of the equation. (3) If the known terms on the right hand side of such a set of equations be multiplied by any factor, at will, the value of all the unknowns will be multiplied by the same factor. 6) are made - ~ b, - n 2 b, - n 3 b, the values of the unknowns will be increased in the ratio bfb1 . 7), with the knowns made up of two parts, the values of the unknowns will be the sum of the two values which would result from two sets of equations, one with the terms in a for the knowns and the other with the terms in b.

I I " We next multiply each value of y = f (0) by the value of cos 0. 828 and 0 = 54°. 074 and similarly for the others. 6611. We then repeat for 2 0. 5649. 0778. ons cos 3 e A computation and summation of these several terms will then give the values of y as represented by this equation. These values are shown in Fig. 8 by the dotted line. The approximation is seen to be very good except at the ends. This is due to the fact at x = 10, for instance, there is control, so to speak, only on one side.

A V. ALGEBRA: TWO-DIMENSIONAL VECTORS Law of commutation. In an algebraic sense, we know that: A+B=B+A or again the sum of A + B + C + . . . is the same regardless of which one of the various different sequences we may take in associating these letters in a sum. With algebraic quantities, associated in a sum, therefore, the order or sequence is indifferent. To examine the case for vector quantities we first ask whether, in AB BC = BC AB the vector sense The meaning of this is: Starting from an initial point A and executing first a vector with the specifications of AB and then in sequence a vector with the specifications of BC, thus arriving at 0, will the result be the same if instead we should take the c vectors in the inverse order 1 In Fig.