-3 2 Carnot on the Theory af 



For this rmrpofe, it will be fufficient to remark, that the 



i\jy MZ 



errors, included in the two equations TP =y ■ ■ , ar,d — ^ r 



v 

 = - — , may he rendered as fmall as we pleafe; and the 

 a — x 



fame thing would take place if there were any error in the 



refiilting equation TP — ~ — , and if that error depended 



on the arbitrary diftance of the lines MP and RS. But no 

 fuch error can exift in this laft equation; becaufe the point 

 Jlf, through which the tangent mult pais, is given, and not 

 one of the quantities, TP, a, x, oxy, is arbitrary. 



Hence it follows, that the compenfation of errors, which 



takes place in the equations TP = y -^, and — - = 



RZ RZ 



y 

 -w- — , is indicated in the refult by the abfence of the quan- 

 a — .%■ 



titics MZ and RZ, which caufed thofe errors. Confequent- 

 ]y, after having introduced thefe lalt quantities into the cal- 

 culation, to facilitate the expreffion of the conditions of the 

 problem, and having treated them, in the equations expreffmg 

 thofe conditions, as nothing in comparifon of the propofed 

 quantities, we have only to eliminate thofe quantities out of 

 the equations, in order to free them from error, and to ob- 

 tain an accurate refult. 



it. The inventor of this method might therefore have been 

 conducted to his difeovery by a very fnnple train of reafon- 

 ing. " If, inftead of a propofed quantity," might he have 

 faid, " I fubftilute in my calculation a quantity which is not 

 equal to it, fome error will certainly refult. But if the dif- 

 ference of the quantities in queftion be arbitrary, and I have it 

 in mv power to render that difference as fmall as I pleafe, the 

 error cannot be dangerous. I may even commit feveral fimilar 

 errors at once, without incurring any inconvenience ; becaufe 

 I have always in my own power the degree of precision, which 

 I choofe to give to mv refults. Befules, it may happen that 

 thofe errors will mutually compenfate each other, and, if fo, 

 mv refults will become perfectly accurate." But how is fuch 

 a cotnpenfation to be effected in all cafes ? A little reflection 



will 



