# Aerodynamic Theory: A General Review of Progress Under a by William Frederick Durand

By William Frederick Durand

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer publication 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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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. That is, if the range of n had extended on to x = 12, the approximation at 10 would doubtless have been much better. Continued terms in the equation will, of course, give a continuously closer approximation.

As an operator it implies a rotation through + 90°. Any letter used as a scalar, that is, simply as a measure of length, is understood to be laid off in the direction of the scalar axis which we here take as the axis of X. A vector expressed as x + i y is therefore to be understood as directing that a length x be laid off along the direction of X followed by a length y laid off at + 90° to the same axis. It should be noted that here, y does not, in itself, imply a length laid off in the direction of y, but simply a length, while the i operator tells us that this length is to be laid off at + 90° to the axis of scalars, or here in the direction of + Y.

Fl Fig. 6. 3) u where n is given successive values as may be required by the nature of the approximation desired. Suppose again a discontinuous form of the function as represented by 0 E G F, the branch G F being symmetrical about X with ED. Then with reference to the relation on the two sides of the y axis, we shall have f (0) = - f (- 0). In such case, in the formula for an A coefficient, the elements in the integration will form pairs equal in value and with opposite signs and hence the A coefficients will vanish.