Patent GB-306401-A (GB)
Title: Apparatus for the mechanical evaluation of integrals in gravity calculations
IPC: G01V7/06
Filed: 1929-02-16
Abstract: 306,401. Askania-Werke Akt.-Ges. vorm. Centralwcrkstatt Dessau und C. Bamberg-Friedenau. Feb. 18, 1928, [Convention date]. Calculating apparatus. - Relates to means in connection with the determination of gravity by torsion balance for calculating gravity gradients according to the formula uxz = Gs/(<1>/r2-<1>/G2+<1>/G1-<1>/r1)dy when r1<SP>2> = x1<SP>2> + y2 + z<2>, G1<SP>2> = x1<SP>2> + y<2>, &c. z being vertical and U the gravity potential, the apparatus effecting this by forming the two integrals /(<1>/r-<1>/G) dy and combining them. The apparatus shown in Fig. 3 is constructed on the principle according to the diagrams in Figs. 1 and 2. The point O, Fig. 1, on a chart is that for which the topographical correction, to be obtained by using the integrals calculated above, is required, and the form of terrain is given by the contour lines h, h<1>, h<11>. Around the origin O pivots a line L carrying a slider S with a perpendicular SA which can be set to the constant line difference. At A a double slider A works on the perpendicular and on a second straight line M through the origin. The slider S has a tracing point to be carried round each element of area bounded by a pair of contour lines and a roller R is mounted on the line L as axis and connected to the tracer point so that the distance OR is always equal to or a chosen fraction of OS. A roller R1 is similarly mounted on the line M and connected so that the distance OR1 is also equal to or the same fraction of OA. The rollers R, R1 are mechanically driven from a roller R2 which is arranged to be rotated proportionally to the amount of movement dy of the tracer point parallel to the y-axis. The distances OS (i.e. OP) and OA are G and r respectively. Discs E, E1, rotating round the origin O in planes parallel to the plane of the chart are driven by engagement with the rollers R, R1 respectively and carry scales on their edges to be read against pointers. The perpendicular SA need not be in the plane of the two lines L and M but can conveniently be perpendicular to their plane, and the planes E. E1 need not be concentric with O but their pivots O1, 02, Fig. 2, may be at a distance from O provided the distances R01, and R1, 02 are maintained by their control cords at the values kG and kr respectively when k is the chosen fraction. In the mechanical construction, a straight edge L, Fig. 3, has a slide S with a tracer point P and a vertical rod to take a slide A, which can be set to any height z corresponding to the vertical distance between a pair of contour levels, and rotates on a vertical axis at O, on the other side of which from the slide S it carries a housing. The, latter carries on pivots the parallel discs E, E1 with graduated edges to read the values of the second integral mentioned above against pointers I. The discs are driven by the rollers R, R1 feathered on shafts geared with a pinion T, on the drum hub F2 of which is wound a, cord carried around guides to a straight edge U kept in contact with the tracer P. The drum hub F2 is the equivalent of the diagrammatic roller R2 of Figs. 1 and 2. The rollers R, R1 are positioned by forks Q, Q1 threaded on screw shafts carrying drums F, F<1> on which are wound cords which pass round guides to the tracer P and the slide A respectively. The drums F, F, F1, F2, have springs to keep the cords in tension. The tracer point P is carried round an element on the chart bounded by a pair of contour lines the difference of level of which is set as the height for the slide A, and the movement of P and the straight edge U is such that its component dy parallel to the y-axis is continually communicated to the drum F2. The required number of elements having been thus traced the total rotation of one disc relative to the other gives the desired quantity uxz. For second gradient uyz the arrangement is made that the traced point and straight edge U give the drum F2 the displacement parallel to the x-axis.