CHAP. VII., 6.] 



ELECTRICITY. OHM DANIELL. 



185 



Munich. He died on the 7th July 1854. His 

 theory of electrical conduction was not highly appre- 

 ciated in Germany until it had received, in 1841, an 

 eminent mark of approval from the Royal Society of 

 London, by the award of their Copley medal. His 

 principal work on the Galvanic Circuit (Die galvan- 

 ische Kette mathematisch bearbeitet ; Berlin, 1827) 

 has had a somewhat peculiar fate. Accepted by only 

 a few persons as a great discovery, it met with com- 

 paratively little attention, at least until recently ; yet 

 notwithstanding the long anticipation by Ohm of his 

 results, it has been his misfortune to have their ori- 

 ginality contested. 



It seems not difficult to account for the diversity 

 o f estimation in which this work has been held. The 

 primary fault is the author's own. He deduces the 

 strength of a voltaic current in any given circuit, and 

 the electroscopic excitement of each part of the cir- 

 cuit, by means of reasoning seemingly a priori, from 

 certain assumed axioms submitted to mathematical 

 reasoning. The axioms are very simple ; the theory 

 founded on them is intended to correspond to Fourier's 

 theory of heat, of which, indeed, in point of form, it is 

 a mere and literal copy ; but as every circumstance 

 which introduces real complication is soon left on 

 one side, the leading propositions are almost self- 

 evident results of the axioms. In short, the pa- 

 rade of mathematics is uncalled for, and the whole 

 structure of the theory seems so slight and ques- 

 tionable that one is surprised that it should ever 

 have been regarded as more than a clever expres- 

 sion of some approximately true experimental laws. 

 It appears, indeed, that this is the simple fact ; 

 that the axioms were obtained from the results 

 which they seem to predict, and that Ohm was an 

 experimentalist before he became an author. In 

 this guise we understand how to treat the so-called 

 " Laws of Ohm." They are truly important empi- 

 rical laws, calculated to guide the practical man in 

 applying and measuring galvanic forces, to enable 

 the theorist to form clearer notions of the different 

 (often confusing) effects of these forces, and to reduce 

 their varying energy to calculation ; but we must be 

 allowed to doubt whether Ohm has thrown any new 

 light on the real first axioms of electrical excitement 

 or transmission. 



The most important of these laws refer to the 

 numer i ca i measure of the voltaic stream circulating 

 i n the conductor of a closed circuit. Such a closed 

 circuit may be imagined to consist of (1.) an exciter 

 or battery ; (2.) a conductor homogeneous or other- 

 wise, but necessarily continuous, uniting the ends of 

 the battery. The exciting force is derived (we will 

 assume) from the chemical or thermo-electric action 

 present in the battery. The electric equilibrium 

 being disturbed, is restored more or less speedily 

 through the medium of the conductor which connects 

 the poles. If the conductor be good, the electricity 

 passes rapidly through it, and does not accumulate in 



the battery ; if the reverse, it accumulates until it ac- 

 quires power to overcome the resistance, and then it 

 passes through in a stream less abundant, but of a 

 higher intensity. If the construction of the battery 

 does not permit that degree of intensity to be reach- 

 ed, the electricity stagnates in the battery, the con- 

 ductor cannot perform its office, no effect results. The Iltustra- 

 whole maybe compared to a spout of water discharged tion ' 

 into a trough, from the bottom of which extends a 

 long narrow horizontal pipe. The water is the elec- 

 tricity, the trough is the battery, the pipe is the con- 

 ductor. If the pipe be very long and narrow, no 

 water at all will pass through it until the water in 

 the trough has attained a certain height, or has a 

 head of pressure sufficient to overcome the resistance 

 in the pipe. If the trough be filled to the brim 

 without the resistance being overcome, the trough is 

 as good as plugged, no motion takes place, the stream 

 regurgitates. The longer the pipe the feebler the 

 stream that passes; shorten the pipe indefinitely, 

 and the efflux depends only on the construction of 

 the trough. Indeed, the illustration might be pushed 

 considerably farther. The depth of the cistern re- 

 presents the electro-motive force of the voltaic com- 

 bination ; its area the size of the plates. By in- 

 creasing the latter, we do not give the means of 

 overcoming more resistance; but when the resist- 

 ance is small, we afford a larger supply without 

 lowering the level i. e,, the intensity. 



Ohm regards the current as proportional to the elec- (843.) 

 tro-motive force directly, and to the resistances in- Resist - 

 versely ; and the latter are divided into (a) the re- g^Jmated. 

 sistance of the battery itself to the passage of the cur- 

 rent ; (6) the resistance of the conductor. Now the 

 latter varies as the length of the wire completing the 

 circuit. We may therefore double its amount by 

 doubling the length of wire joining the poles ; and 

 if we observe the strength of the current passing 

 before and after this has been done, we have a mea- 

 sure of a + 6 in the first experiment, and of a + 2 b 

 in the second ; and b being assumed to be known, a, 

 or the comparative resistance within the battery, 

 becomes known also. 



The resistance of a standard copper wire a foot (844.) 

 long may be taken as the unit of resistance. Mr Standard 

 Wheatstone finds it convenient to assume a copper r * sl 

 wire a foot of which weighs 100 grains. M. Jacobi 

 prefers a metre of copper wire one millimetre in dia- 

 meter. The resistance is as the length, and inversely 

 as the sectional area. 



To measure the current two methods have chiefly (345.) 

 been used, and the results agree closely. One is Force of 

 the tangent compass. A voltaic current is allowed the current 

 to pass through a thick wire arranged in a vertical ~ 

 circle. At the centre of the circle is placed a very 

 short magnetic needle. When a current passes the 

 needle is deflected ; and it is easy to show that the 

 deflecting forces are as the tangent of the angle of 

 deflection. A double or treble force in the circuit 



