252 J. A. GRAY AND M. D. FRANCIS 



sion, as deviations from linearity would he expected if either inhibi- 

 tion or enhancement were involved. The anion could have been 

 expected to change the rate because of its effect on dissociation of 

 lactic acid or because of its weak calcium complex ( Bjerrum, 1957 ) . 

 Mathematicallv, the rate of incipient carious lesion formation (i.e., 

 the enamel dissolution during incipient carious lesion formation) 

 can be expressed as follows, using the usual first order rate expression 

 ( Laidler, 1950 ) , assuming that the buffer anion is inert and all other 

 conditions (e.g., calcium and phosphate concentrations) are con- 

 stant: 



^ = A-o[//+] + UHB] (1) 



where 



dEn/dt = rate of enamel dissolution during incipient carious lesion 



formation (mg enamel/cm-/ 96 hrs.) 

 [i/+] = hydrogen ion concentration (moles/liter) 

 \HB^ = undissociated acid concentration (moles/liter) 

 A'o, fci = constants 



For combinations of several different l)uffers, the expression would 

 take the following general summation form : 



^ = k,[m] + Z lUHB]^ (2) 



Then, for any buffer system and in terms of total buffer concentra- 

 tion (for ease of calculation), the following expressions (3 and 4) 

 for the total buffer concentration [TB] and the dissociation constant 

 K of the buffer are substituted in equation 2: 



[TB] = [HB] + [B-] (3) 



^ [m]\B-] 



[HB] ^^ 



where 



[■B~] = dissociated acid buffer anion concentration (moles/ liter) 

 The result of the substitution is the following equation: 



dt ~^"^^ J + ^^'"K„, + [//+] ^^^ 



