498 REPORT— 1880. 



corresponding to zinc, and D',, D'n, D'3, &c. be those correspoudincr to copper, tlien 

 the difference of the two readings of zinc and copper -would be the diiference 

 between the mean of any consecutive readings of one pole and the reading of the 

 other taken between those two consecutive readings, such, for example, as 



— L— — a - D'jjor — !-i - Dj, &c. Thus we get many values very nearly the 



same, if not exactly the same, of the true difference in question ; if, therefore, we 

 take the mean of all these, the error due not only to a small loss of charge, but also 

 to a little inaccuracy in the readings, will be avoided. This is the method I used 

 in measuring the E. M. F. of 30 Daniell cells, and the result I obtained is the mean 

 defined as above = 13'283 divisions of the micrometer screw-head. As regards the 

 mathematical calculation we have 



V = 2 (D - D') . / 



where V - V is the E. M. F. of the battery, D-D' the difference of the 

 distances corresponding to the readings of the two poles, F the attracting force of 

 the continuous plate on the disc, Rj the radius of the disc, and R., that of the 

 aperture. Since, now, one division of the micrometer screw-head corresponds to a 



distance of -^^ cm. we get, V - V = -904187 (C. G. S.) 



The E. M. F. of Thomson's gravity Daniell was measiu'ed by comparing it 

 before and after the above experiment directly with that of the above battery 

 by means of Sir Wm. Thomsons Quadrant Electrometer. The E. M. F. e of the 

 cell was 



« = \ ~A'' = 0-034:381 (0. G. S.) electrostatic imits. 

 26-299 



(B). Absolute electro-magnetic measurement of the E. M. F. 



This measurement was made by determining the strength of the current given 

 by the E. M. F. by means of a tangent galvanometer, and then measuring the 

 resistance of the circuit in the way to be described presently. 



The tangent galvanometer employed consists of a circular coil of mean radius 

 18-2 cm., containing 400 turns in 19 layers of insulated copper wire, the breadth 

 and the depth of the coil being 2 and 1-3 cm. respectively. The needle of the 

 galvanometer consists of a magnet only about ^ cm. long, made of bard tempered 

 steel wire, and suspended in the centre of the coil by a single sillr fibre. To the 

 needle is attached a very fine straight glass fibre, of such a length that its ends 

 travel round a graduated dial of radius a little less than that of the coil, thus 

 serving for taking readings. 



The mathematical theory show^ that in a tangent galvanometer, 



27r«. 8q-?y X d"-{q" -I) ^ '' 



where c is the current strength, H the horizon comp. of earth magnetism, a the 

 angle of deflection, n the number of turns of wire in the coil, ?•(, the mean radius of 

 the coil, b half the breadth of the coil in tlie plane at right angles to the plane of 

 the coil, d half the depth of the coil in its plane, q the number of layers in the coil. 

 If E be the E. M. F. producing the current c in a circuit of resistance R, then by 

 Ohm's law and fi-om the preceding equation we get 



J, _ 'RH V^V^'^rsnana 3 g"' r^^ ,^. 



2 n- M ■ 3 ?" ?-o- + d:" if - 1) * ■ ■ ■ ^'^'' 



The formula (2) shows that in order to measure an E. M. F. in absolute 

 electro-magnetic units we have to determine, (a) the deflection a, {b) the resistance 

 R, and (c) the horizontal component of earth-magnetism H. 



(ff) To determine a. The formula (2) also shows that whatever be the value 

 of R the product R tan a is a constant quantity as long as E is kept constant, 

 "W^hicb furnishes this important suggestion that by varying the resistance R we 



