140 Messrs. Robson and Smith on the 



electrode, and the ordinates the excess of potential over that 

 of the negative electrode. 



A spark will pass when the curve representing the potential 

 before discharge cuts the curve AB. When the field is 

 uniform the potential curve before discharge is a straight line 

 passing through the origin, and if OF represent the distance 

 between the electrodes OB will be the position of the potential 

 curve before discharge when it first intersects AB; in this case 

 FB is the potential necessary for discharge, and the relation 

 between it and the sparking-distance is represented by 

 equation (2). When, however, the electrodes are small the 

 electric field is very far from uniform ; there are great changes 

 in the value of the potential near the electrodes, but at some 

 distance from them the potential changes very slowly. The 

 potential curve before discharge in this case will be somewhat 

 of the form OCDE, and we see from the figure that this may 

 intersect the line A B (when a spark will pass) when the 

 difference of potential between the electrodes FE is less than 

 FB, the difference when the field is uniform. We see in 

 this way that the sparking-distance will be greater for small 

 electrodes than for large ones, and will increase more rapidly 

 with the difference of potential. We notice, too, that in 

 this case the maximum electromotive intensity is greater than 

 in a uniform field. 



XIII. On the Diurnal Variation of the Magnet at Keiv. By 

 W. G. Robson and S. W. J. Smith, of the Normal School 

 of Science and Royal School of Mines *. 



rpHE multiplication of magnetic observatories makes it 

 JL extremely desirable that the methods of reducing the 

 observations should be as similar as possible. It is, however, 

 practically impossible that all observatories should determine 

 the diurnal variations of the elements by the elaborate 

 method in use at Greenwich, which, in the case of any one 

 element, necessitates the measurement of the hourly ordinates 

 of the curves at 24 points on all but a very few days of the 

 year under discussion. 



Dr. Wild (Rep. Brit. Assoc. 1885, p. 78) advocates the 

 determination of the mean diurnal range from measurements 

 on the comparatively small number of days of very small 

 disturbance, and points out that the inclusion of disturbed 



* Communicated by the Physical Society : read June 6, 1890. 



