The multiple-pendulum apparatus then provided a method of determining the flexure of the stand from the action of one pendulum upon a second pendulum hung on the same stand. This method of determining the correction for flexure was a development from a "Wippverfahren" invented at the Geodetic Institute in Potsdam. A dynamometer was used to impart periodic impulses to the stand, and the effect was observed upon a pendulum initially at rest. Refinements of this method led to the development of a method used by Lorenzoni in 1885-1886 to determine the flexure of the stand by action of an auxiliary pendulum upon the principal pendulum. Dr. Schumann, in 1899, gave a mathematical theory of such determinations,[88] and in his paper cited the mathematical methods of Peirce and Cellérier for the theory of Faye's proposal at Stuttgart in 1877 to swing two similar pendulums on the same support with equal amplitudes and in opposite phases. [Illustration: Figure 29.--THE GULF PENDULUM is about 10.7 inches long, and has a period of .89 second. It is made of fused quartz which is resistant to the influence of temperature change and to the earth's magnetism. Quartz pendulums are subject to the influence of electrostatic charge, and provision is made to counteract this through the presence of a radium salt in the case. The bearings are made of Pyrex glass.] In 1902, Dr. P. Furtwängler[89] presented the mathematical theory of coupled pendulums in a paper in which he referred to Faye's proposal of 1877 and reported that the difficulties predicted upon its application had been found not to occur. Finally, during the gravity survey of Holland in the years 1913-1921, in view of instability of supports caused by the mobility of the soil, F. A. Vening Meinesz adopted Faye's proposed method of swinging two pendulums on the same support.[90] The observations were made with the ordinary Stückrath apparatus, in which four Von Sterneck pendulums swung two by two in planes perpendicular to each other. This successful application of the method--which had been proposed by Faye and had been demonstrated theoretically to be sound by Peirce, who also published a design for its application--was rapidly followed for pendulum apparatus for relative determinations by Potsdam,[91] Cambridge (England),[92] Gulf Oil and Development Company,[93] and the Dominion Observatory at Ottawa.[94] Heiskanen and Vening Meinesz state: The best way to eliminate the effect of flexure is to use two synchronized pendulums of the same length swinging on the same apparatus in the same plane and with the same amplitudes but in opposite phases; it is clear then the flexure is zero.[95]