176 Ernst Lecher on the Measurement of 



really be equal. Since the discrepancy follows no sort of 

 rule either here or in later cases, and since the values are 

 sometimes too great and sometimes too small, both for the 

 ventral segment a and the ventral segment c, the latter of 

 which corresponds to a vibration twice as rapid as the former, 

 and finally seeing that there appears to be no definite relation 

 between the discrepancies and the distance apart of the con- 

 denser-plates, we must attribute them to errors in the measure- 

 ments, and most of all to the difficulty of moving the plates 

 parallel to each other. The above agreement of the results 

 with each other would, however, be fairly satisfactory; but it 

 obviously becomes worse when we pass to the actual calcula- 

 tion of the dielectric constant ; the deviation then becomes 

 greater as the dielectric constant itself increases. In this and 

 all other cases I take the mean of these differences and make 

 use of it in determining the dielectric constant. 



The mean of the three measurements given above is 0*479 

 centim. The value so calculated is subtracted from the 

 thickness of the dielectric (0'716) ; this thickness, divided by 

 the difference (0 - 237), gives the dielectric constant*. For 

 ebonite, I thus obtain 3*01 as the value of the dielectric con- 

 stant for such short times of charge as are measured by 

 hundred millionths of a second. 



The half wave-length of the shorter oscillation c was about 

 1000 centim. 



* Note by Translator : — Perhaps the following will make the process of 

 calculation more clear: — 



Let C be the capacit} r of the condenser in each case, A the area of each 

 of its plates. For the condenser with air alone let t x be the thickness of 

 air (i. e. the distance between the plates). Finally, for the ebonite con- 

 denser of total thickness t 2J let there be a thickness t 2 — e of air, and a 

 thickness e of ebonite whose specific inductive capacity is k. 



A A 



C = 



«(1) ^+t 2 -e) 



for the ebonite condenser; and also 

 A 



for the air condenser. 

 Hence 



C ^nt l 



K 



which gives 



