554 REPORT — 1881. 



7. On an Early Attempt at a Secondary Battery. 

 By Dr. C. W. Siemens, F.B.S. 



8. On an Electro- Ergometer. 

 By Professor Sir William Thomson, M.A., F.B.S. 



9. On a Problem in Stream Lines. By Professor A. W. Ruckee, M.A. 



li (f> = const, aud yfr = const, be the equations to the curves of equal velocity- 

 potential and to the stream-lines in the case of a liquid possessed of irrotational 

 motion in two dimensions, let us, in accordance with a well-known property 

 of these functions, assume 



Then, rationalising the denominator we get 



,|, = _V- 



i/~ 



X- + 



Now when x and y are very great compared with « \|/- = — Yy, and ^ vanishes 

 when y = 0, and also when 



.!■' + 



(y - y = «^ or A'2 + (y + y = «^ 



Hence, at an infinite distance from the origin, all the stream-lines are parallel to the 

 axis of X, and that axis, together with the two circles whose equations are given 

 above, constitutes a stream-line. 



The equations thus solve the problem of the flow of a liqiud past a cylindrical 

 obstacle, the generating lines of which are perpendicular to the undisturbed direc- 

 tion of the flow of the liquid, and the boundary of which is such that a section at 

 right angles to the generating lines is made up of the external portions of the 

 circumferences of two equal circles which pass through each other's centres, the 

 line of centres being perpendicular to the undisturbed lines of flow. 



The expression for <f) may conveniently be written in the form — 



where r and r' are the distances from the centres of the two circles. 



The above formulae may also be arrived at from elementary considerations, and 

 they have been tested, as applied to the electric current, in the Physical Laboratory 

 of the Yorkshire College. The apparatus used was similar to that described by 

 Prof G. C. Foster and Dr. Lodge in the 'Proc. Phys. Soc.,' part iii., 1875, except in 

 so far as brass bars were used as linear electrodes. 



When the apparatus was adjusted so that the eqmpotential lines were, as 

 nearly as possible, parallel to these bars, a portion of the tinfoil was i-emoved, 

 and the form of the disturbed lines determined. 



At first, to test the accuracy of the method, some experiments were made when 

 the part removed was circular. Afterwards the two equal circles were cut out. 



Some specimen results are given below. As it was difiicidt to make the equi- 

 potential lines exactly parallel to the bars in the first instance, points on the same 

 disturbed equipotential line were measured at approximately equal distances from 



I 



