( 277 ) 



The neulral ester is stipuiiitiod In iiidlivl jilcoliol and llieii yields 

 an aeid one like all sul{)lioiüe estei's. With ainmojiia i( yields an 

 ainuiüiiium salt of the sidplioiiic eslci- ('iiiiction, which is also an 

 estei' of the eai'boxA'lie arid. 



The aeid ester, namely the earl>o.\y lie ester of the snl|)li(ini(' acid, was 

 also obtained from the sodinni salt of snlpiio-isohiilyric acid l>y means 

 of hydrogen chloride and methyl alcohol and is hygroscopic, its isomer, 

 the carl)o.\ylic acid of the sulphonic estei-, which was prepared from the 

 acid silver salt with methyl iodide, is not hygroseopie, it crystallises 

 from benzene and melts at *J()^ Dr. Moi.i, \ an ('n ak antk's (\\|)erienees 

 with the esters of snlpho-isobulyi-ic acid agi-ee faii'ly well w illi those 

 of Wegscheidek with melasnlphobeir/oic acid. 



The melting points of the compounds obtained behave as nnght 

 be expected; those of the sulphonic acid chlorides arc more elevated 

 than those of the snlphonic esters; those of the carboxylic chlorides 

 are lower than those of the carboxylic esters. The melting |)oints of 

 the esters as Avell as those of the chlorides of the carboxylic acids 

 are lower than those of the carboxvlic acids themselves. 



Mathematics. — ''TJie relation hetu^cen. the nulius of carvature, of 

 <i tiristed curve in a point P of the curve aiul the r(f(lius of 

 curvature in P of the .section of its developable uuth its oseulatiu;/ 

 plane in point P." By W, A. Veusllys. (Connnnnicated by 

 Prof. P. H. Schoute). 



(Communicated in the meeting oi" September tJi-, l'.K)l.) 



§ 1. Theore.m. For each tivisted cubic C' the ratio is constant 

 of the radius of curvature in anij point P to the radius of curvature 

 of the section of the osculatiuij plane in tlw point P with, the developable 

 0^ belonyiwj to C'. 



Proof. If we take /"* to be origin of coordinates and the tangent, 

 principal normal and binomial of the curxe C in the point P to 

 be the axes of coordinates, then 6"' is the cuspidal cur\e (»f the 

 surface (>., enveloped by the plane 



A f — 3 B t' -^ 3 C t — I) — 0, 

 where 



I)= z, 

 C = c, .V, 



7i =: l>, .r. + A, ,/ + h, C, 



A — a, .c -f a., // + «3 ^ + a,. 



