638 ALEXANDER MACFARLANE ON THE 
attached are marked with a cross thus, x. The 6th column gives the same 
quantity expressed in absolute measure, the 7th gives the value calculated from 
the equation at the top of the table, and the 8th gives the differences between 
the most probable observed value (column 6th) and the calculated value. The 
letter ¢ denotes that the spark was observed to pass from the edge of the dise 
in a bent path, and not from the centre in a straight path. The series of — 
readings was continued until the distance was reached at which the spark 
began to pass from the edge, but not further, as the spark then passes under 
new conditions. This distance was found to be 1 centimetre. In fig. 1 and in 
all the following figures the intersection of the cross marks the mean observed 
value, and the curve is drawn by means of the equation at the top of the table. 
The reading when the spark passed from the edge was invariably less than 
when central and straight. 
The five equations agree well with one another. In the case of the first 
four the differences are negative at the beginning, but in the case of the fifth 
positive. The equation for the curve, Table VI., squared, is 
V’?=3°7142s*— 494-685" + 4348°5s’ + 889°52s, 
where V denotes the difference of potential of the discs, and s the length of 
the spark. 
Here the terms involving s* and s’ are small compared with the terms involy- 
ing s’ and s, so long as s is not greater than 1 centimetre, the distance at which 
the spark begins to pass from the edge. Their existence is therefore probably 
due to the want of infiniteness in the diameter of the discs compared with the 
greater lengths of spark. By neglecting these higher terms we get the following 
results :— 

| Table. Genchiorsaear 2 b. 

II. | 66°687 /{s?+-20393s} | -10196 | 6-8000 
IV. | 66510 /{s?-+-20305s} | 10152 | 6:7523 
V. | 67:337 /{24+ 20351s} | 10175 | 6-8520 
VI. | 65-945 /{s%4 -20455s} | 10227 | 6-7445 
VIL | 68-:167,/{+ 21015s} | -10507 | 71627 



Mean, | 66:940 ,/{s?+°20503s} | ‘10251 | 6°8623 



Here a and } are the semi-axes of the hyperbola represented by the equation; 
a@ meaning the number of centimetres which must be supposed added to the 
length of spark to make the difference of potential proportional to the length 
of the spark, and } the amount of difference of potential due to such a distance. 
The values for a, being independent of the absolute value of the entries, afford 

