the passage of an electric current. In Carey Foster's method these extra gaps are utilised as represented in the figure. The resistance to be measured, x, in this case bridges gap 3, whilst 1 and 2 are occupied by resistances whose ratio to one another does not differ from unity more than does the ratio of the resistance x to the total resistance of the slide wire A B. The testing battery E and the galvanometer G are connected as shown, gap 4 being bridged by its link of negligible resistance. The slider S is adjusted until a balance is obtained on the galvanometer G. The scale reading a is then noted, and x is disconnected from gap 3 and connected instead across gap 4, 3 being in this case bridged by its conducting link. A fresh balance is then obtained, and the second scale reading dl is noted, then a d. It is, of course, essential to this test that the value of the scale reading in ohms or fractions of an ohm resistance of that section of the slide wire bounded by such scale reading be known. If such knowledge be not immediately available it may readily be attained by inserting a resistance of known value, such as .lw, in the place of X, and similarly obtaining readings d and dl as before, then since a = dl – d, la dl d, and consequently the difference between dl and d will give the number of scale divisions corresponding to lw, or that difference multiplied by ten will give the number n corresponding to one ohm, so that our formula, to read directly in ohms, becomes dl . d = dl = X n It is essential for the accurate conduct of this test that the conducting link and its concomitant connections should be massive, and of absolutely negligible resistance. Thomson's bridge method of determining low resistances is a modification of the first described fall of poten. tial method, and is represented diagrammatically in Fig. 45, where A B is a circuit, the resistance of a section x of which, lying between the points a and b is required, whilst B C is a standard slide wire of known resistance per unit of length, joined in series with it, and a battery E and key K. The contact resistance at B is not of any import in this test. ef, el fi, are subsidiary resistances making contact with A B and B C at the points a b and cd, through knife edges if possible, with a view to clear definition. G is a high resistance galvanometer, controlled by means of the key ki, The principle of the test consists in selecting two points c and d on the standard slide wire B C, such that a balance is obtained on the galvanometer when K and Kl are closed, then е у e:f:: 2 : y, or X f The Post Office form of Wheatstone bridge may be adapted to Thomson's method of low resistance measurement, as indicated by Fig. 46, the lettering being the same as in Fig. 45. The INF plug is removed for this test, and a subsidiary resistance f of known value is introduced as shown, together with the extraneous key K. The remainder of the figure needs no explanation. Müller's and Wallau's Method of Comparing very Low Resistances is indicated in Fig. 47, where A and B are the two low resistances to be compared, connected in series, and with the source of constant current E (a battery of accumulators answers the purpose). The termini of the resistances A and B as regards their precise value are represented by the points a, b, c, and d. G is a galvanometer, one side of which is permanently connected, as shown, to the junction of the standard resistances r and rl, which are made up in resistance box E 2 form with accompanying plugs, to the value of 10,000 ohms apiece. All plugs are omitted in one and inserted in the other, thus leaving a total of 10,000 ohms con a a nected, which total must always be maintained in the the test, which is conducted as follows:- The galvanometer G has its free terminal connected in turn to the points a, b, c, and d, and is balanced to zero in each case by withdrawiny plugs from the box r, say, and inserting them in rl such that r + rl still equals 10,000 ohms. Let the values withdrawn in this manner from r be respectively a, b, c, and d, corresponding to the balancing required when G is connected to each of these Adpoints in turn, then B= 6 For the practical measurement of resistances over range extending from zero to five megohms, Evershed's Ohm-meter is especially applicable, and has withstood the test of time. It is shown in general view in the accompanying illustration, and consists of two essential parts, viz., the ohm-meter proper and the generator. The former consists of an astatic system of magnetic needles delicately suspended at the centre or point of intersection of two coils placed at an angle of 45 degs. with one another. One coil (outer) is connected in series, and the other (inner) in shunt with the circuit containing the resistance to be measured. In the latter pattern of instrument the astatic needles are magnetised by the actual current from the generator, so that, by obtaining a mean of two readings consequent on turning the generator handle first in one direction and then in the other, the instrument may be employed with a fair degree of accuracy in the immediate neighbourhood of strong magnetic fields due to dynamos, etc., in addition to being, through its astaticism, independent of the earth's magnetic field. The generator, which is contained in a separate case, consists of a special magneto machine capable of producing a range of voltages varying from 10 to 500 at a moderate speed imparted to it by means of a convenient handle, in either direction. The instrument is direct reading, and only requires connecting up according to the directions supplied with it, and a subsequent rotation of the generator handle at a moderate speed. To check the accuracy of an ohm-meter, it is best to first measure a resistance of convenient current-carrying capacity by the ordinary bridge method, and then measure its resistance by ohm-meter, rather than compare with the bridge coils direct, in order to eliminate possible temperature errors due to heating of the coils. |