K. E. Guthe — Measxwement of Self -Inductance. 141 



Art. XXI. — Measurement of Self Inductance by Alternating 

 Current and Electrodynamometer / by K. E. Guthe. 



In a recent article in this Journal (December, 1897), 

 Professor H. A. Rowland publishes a number of methods for 

 the measurement of inductances and obtains results of far 

 greater accuracy than is possible with the methods commonly 

 used. The principle on which he bases his experiments may 

 here be stated in a more general form : 



If alternating currents of the same period but of different 

 phase, traverse the coils of an electrodynamometer, the deflec- 

 tion is proportional to the product of the .maximum intensities 

 of the currents, multiplied by the cosine of their difference of 

 phase, or 



d = all' cos 

 It is apparent that we have no deflection, if the difference of 

 phase is 90°, and it is this special case which we employ in 

 practice. The above rule has first been formulated by A. Over- 

 beck,* and was also applied by him to measurements of capacities 

 and inductances which he arranged in various ways, especially in 

 the form of a Wheatstone's bridge. Since the number of resist- 

 ance boxes to be used in that arrangement decrease the accu- 

 racy of the method appreciably on account of their self-induct- 

 ance and capacity, I was led last summer to try the three 

 simplest arrangements possible, two of which have been given 

 in Rowland's list (3 and 6). Before describing the third 

 method, which I consider the simplest of all, I will give some 

 of the practical details of my work with the first two. 



As the source of the alternating current we use a small labor- 

 atory-alternator, which makes about 1850 revolutions per 

 minute. 



The electrodynamometer is of the Edelmann type and its 

 movable system is replaced by a few turns of fine copper-wire 

 wound on a light wooden frame, having a resistance of 156 

 ohms. Currents of '00001 ampere can easily be detected but 

 the self-inductance of the coils is quite appreciable, for the 

 stationary coil "116 henry and for the movable a little less than 

 •1 henry. Therefore the correction for self-induction in series 

 with the condenser must be applied. It may be mentioned 

 that the correction as given in Rowland's paper for method 3, 

 in which the self-inductance is put in parallel with the capacity, 

 is wronof ; the correct formula is 



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* Wied. Ann., xvii, p. 816, 1882. 



