394 OBSEBVATIONS AND EXPERIMENTS 



w AJ + w A + AA 1 

 If we add 6 to A on both sides, we get 



E 



\ 



If we put for n its value from the above equation, the left side of 

 the inequality is found to be the greater. 



The proof may also be got at by differentiating with respect to 

 A the expressions 



_ H 

 a ~ a b ~~ 



and thus obtaining the quotients 



% and . 



*a h 



Without regard to the sign, the latter is the greater ; and by both 

 methods one finds that the difference in favour of the conductor A 

 is so much the greater as the actual resistance w is greater. 



This is an illustration of what occurs in comparing the sources of 

 electricity of our laboratories with the shocks of electrical fish. In 

 those we avoid short circuiting as carefully as possible ; in the 

 electrical fish, even when removed from the water, there is 

 always derivation through the body (see above, p. 380). As 

 I emphatically remarked in my first work, its shock is always 

 obtained by derivation 1 . The actual resistance of the organ is very 

 considerable. Consequently an induction shock with a com- 

 paratively inconsiderable diminution of strength, can bear much 

 greater resistance than that of an electrical fish of equal or even of 

 much greater strength. Thence may be derived the important rule 

 in experimenting with electrical fish, not to be deceived by the 

 great actual resistance, but always to diminish the resistance of the 

 experimental-circuit as far as possible. This is also the reason of 

 the usefulness of an apparatus, which, like the leading-off covers, 

 diminishes derivation in the experimental circuit as far as possible. 



3. Passage of Sparks. 



In order to observe sparks, the experimental circuit must be 

 opened suddenly at the instant of the shock and as nearly as possible 



1 Vorliiufiger Abriss, etc. Poggendorff's Annalen, etc., 1843, vol. Iviii. p. 30. 76. 



