644 ALEXANDER MACFARLANE ON THE 

ber is the ratio of the thicknesses of the insulators when they are equally 
strong, not the ratio of the strengths of the insulators when they are equally 
thick. The one ratio is not equal to the other, unless the function connecting 
the difference of potential with the length of spark is that of the straight line ; 
which was not the case under the conditions of his measurements. 
Measurement of the Difference of Potential required to pass a Spark between two 
Spherical Balls at Different Distances. 
Tables XXIV. to XXVII., and figs. 14 and 15.—The balls used 
as electrodes were each 1 inch in diameter, and when in use were 
screwed on to the rods. Observations were taken through a much 
greater range of distances than when the electrodes were discs, because no 
discontinuity was observed such as took place with the discs. I have not 
expressed the results in absolute measure in the tables, because the observa- 
tions necessary for the immediate comparison were not taken, and also because 
there is need of another series of observations taken with the improvements in 
the apparatus introduced after these observations were made to decide 
definitely between various hypotheses which they suggest. In the case of 
Table XXIV., fig. 15, the equation was chosen to satisfy the observations 
between ‘5 and 8, which it does very well; but it does not satisfy the rest of 
the observations. There certainly is a discontinuity in the observations, which 
was due to the commencement of an escape from the insulated wire. The 
four series of observations agree in giving the same kind of function for V. 
By making some assumptions the equations have been reduced to absolute 
measure, so that the relative magnitudes at least are correct. 



: Value of s for 
: 
Table. Pressure. Function for V. RS 
XXIV. 85 10:442s? —-36907s* 9:65 
xX Xa 40 6:847'7s? —-26015s? 8-77 
XORINET: 20 4-5069s? —-10043s! 14-96 
XKVEL 30 _-5'7920s* —-17822s! 10°83 





The values of s for a maximum coincide pretty closely with the values of s, 
at which the escape begins. This is seen well in fig. 15, where all the observed 
values up to the maximum lie well on the curve given by the function ; one 
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