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with the value of the shunt, and the multiplying power of the latter, m, having been obtained from the afore
G + 8 mentioned formula
we have, as the formula for
Es m dl + d. calculating the required value of E,
d Lumsden's or Lacoine's method, so-called from the fact that both gentlemen named devised this system independently of one another at or about the same time, is represented diagrammatically in Fig. 53.
Es and E represent, as before, the standard and E.M.F. under test respectively, G the galvanometer, and R, RI adjustable and fixed resistances respectively. The two electromotive forces are connected in series as shown, and R is adjusted until a balance is obtained on the galvanometer. Then the respective electromotive forces Es and E will bear the same proportion to one another as
Es RI do the resistances R and Ri, or E =
R Before proceeding with a description of any further tests for the determination of electromotive force, I must digress for a moment to describe a modification of the sets of plug resistances as usually constructed in the Wheatstone bridge form of instrument. The modification alluded to consists of a species of extended slide wire ;
it is obviously impossible, with the ordinary stretched slide wire, to command a resistance of any magnitude between its extremities, without producing it to an enormous and therefore practically inconvenient length. The modification consists of a series of resistance coils, a, b, c, etc., Fig. 54, connected to metallic blocks as shown,
but, instead of being manipulated, as in the case of the Wheatstone bridge, by plugs, they are cut in or out of circuit by a sliding contact B, working along a 'bus bar A, so that any required resistance, within the limits of the apparatus, may be inserted between terminals 1 and 2 by moving the slider B along the bar without, at the same time, disturbing the value of the total resistance between terminals 2 and 3, a condition sometimes required in testing. This apparatus may conveniently be arranged in circular form, with a radial contact slider.
Having described this modification, which we shall require very shortly, we will now proceed to deal with Fahie's method of determining electromotive forces. This is essentially a combination method for measuring simultaneously the E.M.F. and internal resistance of a given battery, and is an adaptation of Poggendorff's and Mance's respective methods for these determinations, both of which have already been singly dealt with in the preceding paragraphs.
Fig. 55 represents a diagram of the connections for the test, in which a and b are the resistances on either side of the slider B in the apparatus depicted in the foregoing figure; c is an adjustable resistance, and G the galvanometer. E and Es are the battery under test and the standard respectively, whilst K is an ordinary circuit key employed to connect the two junctions, as shown.
The mode of procedure is as follows:-K being open, the resistance c is manipulated until a balance is obtained on the galvanometer G. When such a balance has been obtained, the key K is manipulated in conjunction with the slider B until the latter is brought to such a position on the slide resistance a b, that the manipulation of K has no effect upon the resultant galvanometer deflection, then the resistance R of the bat
and the required electromotive force Es (c + b).
What is known as the Potentiometer Direct Method of determining electromotive force also involves the use of a slide resistance such as that described above. The connections for this test, which is an extremely simple one, are represented in Fig. 56, where a b represent the two resistances on either side of the slider B as
before, El, a cell of constant electromotive force, Es the standard cell, and G the galvanometer.
Es is first connected up, as shown, and the slider B manipulated until no deflection results upon the galvanometer G. Note the resistance a, substitute E, the battery or E.M.F. under test, for Es, and repeat the
Es al operation, obtaining a second value al ; then E
The Measurement of High Potential Differences.There are several methods of ascertaining the E.M.F. or P.D. of a current when the latter is much above the normal, as in high tension work, for instance, of which the following is probably the most satisfactory.
Let it be required to know the E.M.F. between the points A and B, Fig. 57; a number of equal condensers, c, cl, c2, etc., are connected in series between the points A and B, and the electromotive force E between the terminals of one of them, c, is ascertained by any of the usual methods, and multiplied by the number of condensers in the series.
Departing from the subject of electromotive force determination, we come to the next important item on our list of electrical measurements, viz.—
(9) The Determination of Current Strength.
One of the most direct methods for the determination of current strength in ampères consists in passing the current to be measured through a Siemen's electro-dynamometer, the construction and principle of which useful instrument we will now proceed to discuss.
Referring to Fig. 58, if we have two rectangular circuits A B C D, a b c D, one lying in a plane at right angles to the other, and connected in series at D, shown, and, moreover, if one of the rectangles a b c D
be fixed, and the other suspended by a frictionless suspension as indicated in the figure, and a current be passed through the system by way of the terminals 1
and 2, it is obvious, from certain well-known laws governing the action of neighbouring currents upon another, that the movable rectangle A B C D will be attracted on one side and repelled on the other, and will, in consequence, tend to set itself in the same plane with the fixed rectangle a b c D, as represented in the figure. From the same laws it follows that this force, tending to produce motion of the movable rectangle A B C D, varies as the square of the current, and it is this principle, practically applied, which constitutes the Siemen’s electro-dynamometer.
The instrument, as commercially constructed, is represented in the accompanying illustration, and consists of a fixed composite coil, composed of a few turns of thick wire, and a number of turns of thin wire. These two coils are connected together at one end, and to a common terminal which is the centre one of the three indicated in the figure. The remaining ends of the thick and thin coils are brought respectively to the two outer terminals, the object of the two coils being to increase the