Page:Scientific Memoirs, Vol. 2 (1841).djvu/430

 418 $$Z$$, because the ordinate $$Z W$$ is equal to that of $$A F$$. If the circuit were touched at the place where the two parts $$A B$$ and $$B C$$ join, but so that the contact was made within the part $$B C$$, we should have to imagine $$A D$$ advanced to $$N O$$; the electrical force at the point $$S$$ would in this case be increased to the force indicated by $$T Y''$$. But if the contact took place, still at the same point, viz. where the parts $$A B$$ and $$B C$$ touch each other, but within the part $$A B$$, the line $$A D$$ would be moved to $$P Q$$, and the force belonging to the point $$S$$ would sink to the negative force expressed by $$U Y''$$. If, lastly, the pile had been touched abductively at the point $$D$$, we should have prescribed for the line $$A D$$ the position $$R L$$, and the electrical force at the point $$S$$ would have assumed the negative force indicated by $$V Y''$$. The law of these changes is obvious, and may be expressed generally thus: each place of a galvanic circuit undergoes mediately, in regard to its outwardly acting electrical force, the same change which is produced immediately at any other place of the circuit by external influences.

Since each place of a galvanic circuit undergoes, of itself, the same change to which a single place was compelled, the change in the quantity of electricity, extending over the whole circuit, is proportional, on the one hand, to the sum of all the places, i. e. to the space over which the electricity is diffused in the circuit, and moreover, to the change in the electric force produced at one of these places. From this simple law result the following distinct phænomena. If we call $$r$$ the space over which the electricity is diffused in the galvanic circuit, and imagine this circuit touched at any one place by a non-conducting body, and designate by $$u$$ the electric force at this place before contact, by $$u$$ that after contact, the change produced in the force at this place is $$u_1 - u$$; consequently the change of the whole quantity of electricity in the circuit is $$(u_1 - u) r$$. If, now, we suppose that the electricity in the touched body is diffused over the space $$R$$, and is at all places of equal strength, and, at the same time, that at the place of contact itself the circuit and the body possess the same electric force, viz. $$u$$, it is evident $$u R$$ will be the quantity of electricity imparted to the body, and whence we obtain