( 11 ) 



llie |n'(.'sciico of iinoi'üii p.ii-liclos, wliicli ivmhKm- (liis invert sno-ar 

 iiclive. Tlie vekK'ily ol" s>ji(liesis will llicii hc itropoi-lioiiate firsl lo 

 the product of Ihe concentration of «glucose and lacvuloye and fiirllier 

 to the extent of tlie active raiUal ion spliere siirroinKhni»- eacli enzyme 

 partiele. Tlie latter is inversely proportionate lo the join! concen- 

 tration of the invert sngar and the other dissolxed mailers evenluallv 

 present, each with their own al)sor[)lion coefllcienl. 



Tlie synthetical action of invei-tin in a solution containing [ii A 



grams of in^'ert sugar and .t' grams of canesngar in 100 cc. is 

 therefore : 



'a — X 



d.v = mp dt. 



The complete formula for the inversion velocity of canesngai', in 

 ease the original products of inversion suffered no change, would 

 then be ^) : 



( .c 1 (a—.vY ) 



— d.v = m — — y /) dt. 



{x-\- n {a — iv,) 4 .v -]- n {a — ./;) ) 



The point of e(juilil>rium would then be determined by the equation : 



1 



X p la — .rV = 0. 



4 



Or returning to relative fractions by substitutijig — '- z=z y. 



a 



1 



1 — y pa r/^ -=- 0. 



If now we have introduced into the solution such a quantity of 

 enzyme that this equilibrium point is attained before Ihe birotatory 

 glucose has been converted to any great extent into ordinary glucose, 

 the inversion will not actually come to a standstill, but the line, 

 indicating its progressive course, will exhibit a chai'actei'isiic [)ecu- 

 liarity in that place. Then, starting from that point, the formation 

 of fresh «-glucose by inversion will be dominated by the velocity 

 of the inversion of Ihe total «-glucose ju'eseni into ^-glucose. This 

 velocity is i»roportiouate to the concentration of the «-glucose. If 

 this is continually replenished by fresh foi*mation of «-glucose from 

 canesngar, both the said velocity and the inversion velocity will be 



ij The small increase in weight when Cjo FLo 0^ changes into 2 C^ Hi^ Og is here 

 noglec'led; we might also suppose tliaf it is taken into account in Ihecoellicient^j. 

 By substituting the variable y this lacloi- in p would in any case disappear again. 



