through Space occupied by Ether. 



187 



undisturbed ether. The formula of col. 2 makes r=l when 

 r = 1, that is to say the total quantity of the disturbed ether 

 within the radius of the atom is the same as that of undis- 

 turbed ether in a sphere of the same radius. Hence the sum 

 of the quantities of ether calculated from col. 5 for con- 

 secutive values of r, with infinitely small differences from 

 r = to r=l, must be zero. Without calculating for smaller 

 differences of r than those shown in either of the tables, we 

 find a close verification of this result by drawing, as in fig. 2, 



Fig. 2. 







































































































































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5 





4 





5 





6 





7 





3 





9 



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a curve to represent (p — l)r 2 through the points for which 

 its value is given in one or other of the tables, and measuring 

 the areas on the positive and negative sides of the line of 

 abscissas. By drawing on paper (four times the scale of the 

 annexed diagram), showing engraved squares of '5 inch and 

 *1 inch, and counting the smallest squares and parts of 

 squares in the two areas, I have verified that they are equal 

 within less than 1 per cent, of either sum, which is as close 

 as can be expected from the numerical approximations shown 

 in the tables, and from the accuracy attained in the drawing. 

 § 7. In Table I. (argument r') all the quantities are shown 

 for chosen values of r 1 , and in Table II. for chosen values 

 of r. The calculations for Table I. are purely algebraic, 

 involving merely cube roots beyond elementary arithmetic. 

 To calculate in terms of given values of r the results shown 

 in Table II. involves the solution of a cubic equation. They 



