192 Mr. A. Schuster on the Disruptive Discharge 



(1) For two similar systems of two equal spheres in which 

 only the linear dimensions vary, the breaking-stress is greater 

 the greater the curvature of the spheres. 



(2) If the distance between the spheres is increased, the 

 breaking-stress at first diminishes. 



(3) There is a certain distance for which the breaking- 

 stress is a minimum. 



Let us consider how far all or some of these results may be 

 due to disturbing influences. 



I do not think there can be a doubt as to the reality of the 

 influence of curvature, as that influence shows itself persist- 

 ently at all distances and under all circumstances. Sparks 

 taken between two concentric cylinders show the same effect, 

 as appears from the experiments of Gaugain and Bailie. The 

 former*, in a valuable paper, came to the conclusion that when 

 the spark passes, the surface-density is independent of the 

 radius of the outer cylinder. This was to be expected, and 

 shows that Gaugain' s method of measuring potential, which 

 does not quite come up to our present standard, was sufficiently 

 accurate for the purpose in view ; that is to say, that the indi- 

 cations of his electrometer were really proportional to the 

 potential to be measured. The density a on the inner 

 cylinder increased, however, with its curvature, and Gaugain 

 found that the relation could be approximately represented by 

 the equation 



cr = a + /3/v / r, 

 where, with the units employed by him, 



a = 2-58 and /3=25-62. 

 Bailie has compared Gaugain's equation with his own experi- 

 ments, but the values for the surface-density calculated by 

 Bailie do not all agree with the numbers deduced by Gaugain 

 himself from the same formula. The cause of the discrepancy 

 is found in the fact that Bailie, by an oversight, took r in the 

 above equation to be the radius measured in centimetres, 

 while in the original memoir it stands for the diameter 

 measured in millimetres. I have recalculated Bailie's num- 

 bers, and the result is given in Table V. 



Column V. in that Table shows a decided though not very 

 regular increase of R. for diminishing radii of the interior 

 cylinder. This increase comes out more clearly in Gaugain's 

 observations, as he worked with cylinders of much smaller 

 radius. We may use the last column of this Table to reduce, 

 at any rate approximately, Gaugain's numbers to absolute 

 measure. Taking 1*25 as the ratio by means of which Gau- 

 gain's numbers are to be divided in order to reduce them to 



* Annates de Chimie et de Physique, viii. p. 75 (1866). 



