565,462. Determining dimensions of materials ; resistance and power measurements. AUGHTIE, F. April 22, 1943, No. 9843/44. Divided out of 565,378. [Class 37] A number of electrical strain gauges are combined with a circuit in such a manner that a mathematical function of the effects of the several strains is evaluated and the result recorded or indicated on a single instrus ment. The difference between two strains can be obtained by connecting the gauges in adjacent arms of a Wheatstone bridge. Either or both of the gauges may be associated with fixed resistances so that the difference between fractions of the strains can be evaluated. Two strains can be added by connecting the gauges in opposite arms of a Wheatstone bridge or by connecting them either in series or in parallel in one arm of the bridge. Subtraction and addition may be combined. Two strains, or two algebraic sums of a number of strains, may be multiplied by connecting the two coils of a dynamometer wattmeter in place of the galvanometers of the respective bridge circuits, an amplifier being inserted between the bridge and the corresponding wattmeter coil. The bridge circuits are preferably operated by A.C. to facilitate amplification with valve amplifiers. By introducing a phase displacement between the supplies to the two bridges the wattmeter deflection, which is also proportional to the cosine of the phase angle, contains a third factor, so that the product of the strains may be obtained and multiplied by this third factor in one stage. Alternatively, a thermionic wattmeter may be employed comprising two valves operating so that the anode current or a component thereof is proportional to the square of the voltage applied to the control electrode. One valve of the pair is supplied with the sum of voltages proportional to the two quantities to be multiplied and the other pair with their difference. The difference between the two anode currents is then proportional to the product of the voltages. Other electronic devices incorporating rectifiers can also be used for the same purpose. The quotient of two strains may be obtained by connecting the outputs from the two bridges, operated by D.C., to the two coils of a ratiometer. A thermionic wattmeter may be employed for rapidly varying strains by the arrangement shown in Fig. 5 in which one input to the wattmeter 15 comes directly from one bridge circuit via leads 14 and the second input 16 is supplied by an amplifier 17 which in turn is supplied via leads 18 with the difference evaluated in an element 19 between the output from the wattmeter 15 via leads 20 and that from the second bridge circuit via leads 21. In this way the second input via leads 16 is that which, when multiplied by the output from the first bridge circuit is nearly equal to the output from the second bridge circuit, the difference being smaller as the gain of the amplifier is decreased. In an example, a number of strain gauges are put on the shaft of a brake drum and are oriented at 45 degrees to the axis of the shaft and mutually at right angles. The difference between the resistance changes of the two gauges then depends on the torque transmitted by the shaft. The effect of disturbing factors such as bending, axial load, or temperature changes may be eliminated by taking the algebraic sum of appropriate fractions of the changes in a number of suitably disposed gauges. The output so obtained, proportional to torque, may then be divided by that produced by the elastic strain of a part which transmits pressure to the brake shoes to obtain a quotient which is a measure of the coefficient of friction. A product proportional to horse power may be obtained by multiplying the output proportional to torque by a quantity proportional to speed. In another application any one load on a bar carrying an axial load, a torque, and two bending moments, can be directly indicated or recorded. The vectorial relations between strains may be determined by oscillograph records or by supplying one coil of a wattmeter with the sum and the other with a current of known strength and adjustable phase. The time differential of a voltage may be obtained by means of a condenser in series with a resistance, for example, the additional braking torque due to angular acceleration of a brake. drum may be obtained by differentiating a voltage proportional to the angular velocity. When two quantities are obtained as functions of time, differentiation of one quantity with respect to the other may be obtained as the quotient of the time differentials of the two quantities, and the integral of the first quantity with respect to the second may be obtained as the product of the first quantity and the time .differential of the second. Displacement of the time origin of one electrical quantity with respect to another can be effected by means of a time-delay circuit, or by converting the quantity into a mechanical movement, as by the use of piezo-electric or magnetostrictive material, propagating this movement as a wave through a solid or fluid medium, and reconverting it to an electrical quantity, delayed by the transmission time, either by a similar piezo or magnetostrictive element or by optical means such as a polarizer, analyser, and photo-cell. Electrical quantities derived from strain may be converted into a mechanical disturbance in an optical medium and the disturbance scanned with an optical device which in effect moves along the general direction of the propagation of the disturbance whereby the original quantity is reproduced as a second quantity on a different time scale. The scanning device may in effect move at such a speed that the time scale of the reproduced quantity is reversed.