Electric Residue in the Leyden Jar. 479 



from being correct. Again, if t' and t" be two of the times of 

 observation, and the corresponding Q^ and r^ be written with the 

 same accents, we deduce from equation II. 



lo£ 





log ^'— log/" 



■1, 



and 



b=- 



'^lognat^^Z!i); 



so that from two observations, properly chosen, approximate 

 values for these magnitudes may be immediately found. 



With these approximate values for the constants />, b and m, 

 those of the several r^ may be calculated, which even now will be 

 found to agree pretty weU with the observed values ; the cor- 

 rection of the constants may then be determined according to 

 the method of minimum squares. 



The values which we obtain in this manner from the Table a" 



jo = 0-4289; A = 0-0397 ; to= -0-5744. 

 If we examine the values of these constants for the Tables b" 

 and c", we soon notice that the constant m, and hence also the 

 function of the time which was introduced into the equation, 

 differs so little for the three observed cm'ves, which have 

 reference respectively to a common cylindrical jar with tinfoil 

 coatings, to a narrow-necked bottle filled with mercury, and to 

 a Franklin^s plate, that it is evidently a number common to each 

 of these pieces of apparatus. If, therefore, from the above value 

 of m we determine the two other constants which belong to the 

 observations in the Tables b" and c" , we obtain the three follow- 

 ing equations for the calculation of the residues, as they are 

 given in the three Tables a", b" and c" : — 



■]- 



0'02237 ,0-4256-1 



r.= 0-4289 



r,=0-5794LQ,-Qoe """' J' 



r,=0-2562 



Herein the values of Q^, corresijonding to tlie times t, are to be 

 taken from the tables. In the following Tables a'", b'" and c"'> 



