S On Machines in General, 



consonances, and of Mr, Maxtvell on the system of perfect 

 consonancijy arc in danger of falling into utter contempt. 



1 beg here to mention, respecting the new notation for 

 musical intei»als, which I have explained vol. xxviii. p. 140, 

 that the Octave, happening to contkin just 12 of the lesser 

 fractions f, and one of these to fall near each note of the 

 equal temperament ; in almost all calculations respecting 

 DoJizeaves, the temperaments or results, are free of f, and 

 two only of the three independent or prime terms, of which 

 every accurate notation must consist, are in general found 

 at last ; while the smallness of the most minute, m, it being 

 less than the ttj^^ P^i^t of the Schisma, 2, which is itself 

 but a very trifle more than -y^th part of a Comma, c, 

 (6r 7?T 2 + -rV I") render it allowable in most practical 

 cases to neglect m, and to consider the S s as elevenths of a 

 comma, in the results ; although I would advise the pre- 

 vious calculations to be always carried on strictly, in 2, 

 f and m, especially, as the number of f s will generally point 

 out, to what finger-key or number of half notes, any step 

 in the process answers. 



I am, sir, your obedient servant, 



John Fa ret. 



12, Upper Crown-Street, Westminster, 

 l?€bruary I, 1808. 



II. Essay upon Machines in General. By M, Carnot, 



Member (f the French Institute, &c, &c.* 



Preface, ■ 



AuTHOUGH tlie theory to be discussed be applicable to 

 every subject which concerns the communication of motion, 

 I have given to this work the title of Essay upon Machines 

 in General ; — in the first place, because it is principally 

 machines I purpose to treat of, as being the most important 



♦ For a 'f ranslat Jon of Carnot's " Reflections on the Theory of the Infini- 

 fpsimal Calculus," see Phil. Mag. vol. vjii. p. 222, and 335 j and vol. ix. p. 89. 



' branch 



