846,956. Variable resistors, electric analogue calculating. KATZ, D. Oct. 10, 1957, No. 31751/57. Class 37. A variable resistance comprises an insulating sheet bearing closely adjacent, non-crossing, thin, conductive lines, a fixed contact extending across the sheet making permanent connection to the lines, a second contact movable across the sheet and shaped to contact a selected group of lines at any one of its positions, the length of the lines being delimited by the spacing between the two contacts. The conductive lines are imprinted by printed circuit techniques such as printing with aluminium, copper or carbon ink on plastic or paper; printing with silver ink on ceramic then firing; etching copper clad laminate; spraying metal into depressions in a plastic plate and bonding stamped conductors to a plastic plate. In Fig. 1 the sheet 11 is attached to a cardboard, wood, plastic or metal base 10. The upper end of each line 111 is delimited by a copper, silver, aluminium or carbon contact 12, the lower edge 121 of which is shaped according to the law required. Alternatively, the contact 12 may be printed over the conducting lines. A second contact 16 is arranged to slide along the lower edge of the base. Each line has extensions, zl, z2 which make contact with the moving and fixed contacts respectively. As the contact 16 is moved from right to left, the resistance between terminals 123, 163 becomes reduced as more conductors 111 become connected in parallel. Instead of the strip type contact 16, another type, Fig. 4, having a spur 151 which contacts a group of a few lines in any of its positions may be used. The spur may be replaced by a roller 155 pivoted at 156, Fig. 8. The imprinted lines 111 may take the form of circular arcs, sinusoidal patterns or any other shape provided the exact length between the sliding contact and the fixed contact can be readily determined. Fig. 6 shows a dual device using conductive lines at an angle # to the base. The upper (non-linear) section has a strip type contact 16 whilst the lower section uses a spur type 15. The ends of the contacts are cut to the same angle as the lines 111. Fig. 11 shows an embodiment in which the lower part 112 of the sheet 11 is folded over the lower edge of the base. A conducting ribbon 14 anchored at 141 and tensioned by a spring attached to a roller 183 acts as a swash plate for the strip type contact 16. The ribbon 14 may be of metal or woven ribbon composed partly or wholly of metallic threads. The printed sheet may be attached to a cylindrical base with the lines disposed either at right angles or parallel to the axis. As shown in Fig. 8 the moving contact 15 having a roller 155 is pivoted at 102. A scale, 116 is provided. Micrometer screw feeds may be provided. Electric analogue, calculating systems. Resistors may be made according to the invention to follow any form of variation of resistance value R with slider position X, Fig. 1, which does not involve negative values of R. In embodiments using the spur type of moving contact such as Fig. 6 (lower part) or the roller type such as Fig. 8, the law of the curve 121 has the same form as the required resistance variation. Zero values may be obtained by arranging the moving contact 15 to engage the fixed contact at.. the appropriate positions. Infinite values are obtained by cutting windows in the sheet. The fixed contact 12 may be shaped to provide a discontinuous law. Embodiments using a strip type of contact 16, Fig. 1 are restricted to functions in which R decreases in the direction of slide motion. The effect of a window in the printed sheet in these embodiments is to provide a constant value over a range of slide positions. Expressions are deduced for the conductance between terminals 123, 163 using a strip type contact 16 moving from either direction. Table 1, not reproduced, gives expressions for the curve 121 in terms of x=X/L (Fig. 1) corresponding to the laws:- for roller or spur type contacts and corresponding to:- for strip type contacts, where c, a, h are constants. The cylindrical embodiment of Fig. 8 may be used for such functions as:- R=a# R=a#2 R=a## R=a log (1+#) a being a constant. Figs. 9, 10 show forms using radial conducting lines 111 and spur or roller type contacts 15 pivoted at the centre. In Fig. 9 the law is governed by the form of the outside contact 12, the spur 151 of the contact 15 engaging the inner ends of the lines 111. In Fig. 10, the spur contact 15 engages the outer end of the line, the law being determined by the shape of the inner contact 12. This form is suitable for laws such as R=a-b cos<SP>2</SP>#. 2