382 Dr. Gerlach on the Mechanical Theory 



therefore 



AE + FB-AB 8t 4 



AB = 135 near1 ^ 



which, when t is small, approximates to 



4320 



Glasgow University, 

 September 28, 1867. 



Addendum, 



The error of the rule in this second Supplement, in fractions 

 of the length of the arc, when developed to two terms, is 



, fl 4 101 6 6 . 



+ l 4320 + 3483648' 



and the error of Ilule III., in the Appendix to the paper as pub- 

 lished in the Philosophical Magazine for October 1867, is 



J*_ 6 6 



1080 54432 ; 



therefore, to four -fifths of the length found by the rule with the 

 positive error, add one-fifth of the length found by the rule with 

 the negative error, and the sum will be an approximate length 

 whose error, in fractions of the length of the arc, will be ap- 

 proximately 



+ 



Glasgow University, 

 October 16, 1867. 



870912 



LI. Contribution to the Mechanical Theory of the Electrical Cur- 

 rent. By Dr. Gerlach*. 



THE principle of the mechanical theory of heat, that in the 

 transformation of heat into work or of work into heat 

 the unit of heat always corresponds to a definite amount of work, 

 has both theoretically and practically been confirmed in the pro- 

 cess of electrodynamic heating ; and in consequence thereof the 

 hypothesis that electricity is a phenomenon of motion has ac- 

 quired fresh support. Hence it may be anticipated that electro- 

 dynamic laws and those of the motion of solid substances will 

 * Translated from Poggendorff's Aunalen, July 1867. 



