20 



Mr. G. J. Burch. 



[Nov. 21, 



vary for different points along its length. It is required to determine 

 the amount of this variation. 



Two normal excursions are photographed. In one, the zero is 

 below the field of view, and the movement is directed upwards. In 

 the other, the zero is raised above the field of view, by a suitable 

 alteration of the pressure bulbs, and the connections with the 

 potentiometer are reversed, so that the movement of the meniscus is 

 downwards. The exact limits and relative position of the two 

 excursions are immaterial so long as the capillary itself has not been 

 shifted. The object is to obtain two curves in opposite directions, 

 running right across the plate. 



Let p be a point on the capillary, the position of which is deter- 

 mined by its distance from the reference-circle, or upper limit of the 

 photograph, in each case. 



Using Y p to represent the acting P.D., indicated by the velocity 

 of the meniscus at the point p, we may write 



— V p — —x for the upward excursion, 



and similarly 



+Vp = for the downward excursion. 



Let —a — the P.D. necessary to bring the meniscus from p to a 

 point q, above p. Then by the known law of the capillary electro- 

 meter + a is the P.D. necessary to bring the meniscus from q to p. 

 And the acting P.D. at q is 



— Y q = — x + a for the upward excursion, 



and 



+ Y r q = + x' + a for the downward excursion. 

 Subtracting, we have 



Y q +Y' q = x + x' = Yp+Y'p. 



That is to say, in any pair of oppositely directed excursions which 

 overlap, the algebraic difference between the acting P.D. of the 

 upward movement and the acting P.D. of the downward movement 

 at the same level is constant for all points common to both curves. 



But the velocity of the meniscus at any point is measured by the 

 polar subnormal to the curve, whence it follows that " The algebraic 

 difference between the polar subnormals to corresponding points upon two 

 oppositely directed excursions is constant if the time-relations of the 

 instrument agree with the formula r = ae -c0 -" That is to say, repre- 

 senting the subnormals to the two excursions by the letters N" and 

 N' respectively, 



k(J$j>+W$ = x + x r = k(N q + W q ). 



