Electrical measurementsA laboratory manual . quilibrium through an angle 0, the work done on it inmoving its poles a distance Aa (Fig. 99) against thecontrolling force BSin on each pole is 2S8m. Aa. But Aa = I (1 — cos 6^. Hence the work done onboth poles in producing a deflection 6 is 2BSml (1 - cos (9) = BSdlb (1 - cos 6). Therefore J^w^... g^^97S (1 - cos 6*). But from equation (1) Hence imaqy^ ^^^ _ ^^^ ^ ^^^ ^_ e_ ^ K 2 Solving, 0= — \/ sm- = — \ .2sin-. (2) The time of a single vibration of the magnet is givenby the equation &S3m _/3JbG\ K -^\ from which ^ ^~^Jl &88m Substituting in (2),
Electrical measurementsA laboratory manual . quilibrium through an angle 0, the work done on it inmoving its poles a distance Aa (Fig. 99) against thecontrolling force BSin on each pole is 2S8m. Aa. But Aa = I (1 — cos 6^. Hence the work done onboth poles in producing a deflection 6 is 2BSml (1 - cos (9) = BSdlb (1 - cos 6). Therefore J^w^... g^^97S (1 - cos 6*). But from equation (1) Hence imaqy^ ^^^ _ ^^^ ^ ^^^ ^_ e_ ^ K 2 Solving, 0= — \/ sm- = — \ .2sin-. (2) The time of a single vibration of the magnet is givenby the equation &S3m _/3JbG\ K -^\ from which ^ ^~^Jl &88m Substituting in (2), « = f .?...„?. ... (a) This is the full equation for quantity Avithout anydamping coefficient. If 6 is small, sin 6 may be taken equal to - 6^ and2 2 or the quantity is proportional to the first angular throw. 210 ELECTRICAL MEASUREMENTS. If T is the observed time of a single oscillation foran amplitude a, then the time for an infinitely small arcis given by the equation Table III. in the Appendix contains the Fig. 100. If d is the deflection in scale parts and a the distancebetween the mirror and scale, then ^« = ^C-i?) For accuracy the value of To should be used in theabove formulas for Q. A ballistic galvanometer complete is shown in Fig. 100. QUANTITY ANB CAPACITY. 211 The astatic system, consisting of four bell magnets, isat the right of the cut. W is the soft iron ring nutwhich is employed as a magnetic shunt to adjust the sen-sibility of the whole astatic system. When it is turnedup toward the poles ns the magnetic moment of thislowest magnet is diminished 98. Correction for Damping. — A correction to thedeflection 6 may be necessary on account of the damp-ing action on the needle due to setting the air in motion,and to the induced currents produced in the coil by themovement of the needle. If the deflection is small, so that we may write theangle for the sine of the angle, and if the damping alsois small, we may write where 6 is the first defl
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Keywords: ., bookcentury1800, bookdecade1890, bookpublisherbosto, bookyear1895
