so that according to him, a curved surface shows finite soaring speeds when the angle of inclination is 0° or even slightly negative. [25] The following formulæ proposed by Mr. Chas. M. Manly show how the center of pressure may be moved any desired distance either forward or backward without in any way affecting the center of gravity, and by merely moving the front and rear wings the same amounts but in opposite directions, the total movement of each wing being in either case five times the amount that is desired to move the mean ‹CP›_1, and the direction of movement of the front wing determining the direction of movement of ‹CP›_1. In Figure 7, ‹CP›_{fw} and ‹CP›_{rw} are the centers of pressure of the front and rear wings respectively; the weights of the wings, which are assumed to be equal and concentrated at their centers of figure, are represented by ‹w›, ‹w›, and ‹a› is the distance of the center of pressure in either wing from its center of figure. The original mean center of pressure of the aerodrome is ‹CP›_1, ‹W› is the weight of the aerodrome, supposed to be concentrated at ‹CG›_1, while ‹m› is the distance from ‹CP›_{rw} to ‹CG›_1. Now, if we have assumed that the rear wing, being of the same size as the front one, has a lifting effect of only 0.66, and on this assumption is calculated the proper relative positions of the front and rear wings to cause the ‹CP›_1 to come directly over the ‹CG›_1, and upon testing the aerodrome find that it is too heavy in front and, therefore, wish to move the center of pressure forward an amount, say ‹b›, without affecting the center of gravity, we can calculate the proper relative positions of the front and rear wings in the following manner. While the aerodrome as a whole is balanced at the point ‹CG›_1, the weight of the wings is not balanced around this point, for the rear wing, owing to its decreased lifting effect, is proportionately farther from ‹CP›_1 than the front wing. In order, therefore, to avoid moving the center of gravity of the machine as a whole, any movement of the wings must be made in such a way as to cause the difference between the weight of the rear wing multiplied by its distance from ‹CG›_1 and the weight of the front multiplied by its distance from ‹CG›_1 to equal a constant: that is, ‹w›(‹m› + ‹a›)−‹w›(0.66‹m›−‹a›) = constant, and 0.33‹w›‹m› + 2‹w›‹a› = constant. [Illustration: FIG. 7.] [Illustration: FIG. 8.] [Illustration: FIG. 9. FIGS. 7–9. Diagrams Illustrating formulæ for moving C. P. without disturbing C. G.] If now the wings be moved so that ‹CP›_1 is moved forward a distance ‹b›, we may indicate the distance from ‹CG›_1 to the new ‹CP›_{rw} by ‹z›, and equating the difference between the weight of the rear wing multiplied by its new distance from ‹CG›_1 and the weight of the front wing multiplied by its new distance from ‹CG›_1 and making this difference equal to the constant difference, we can calculate ‹z› in terms of ‹m› and ‹b›, as follows: