186 Dr. E. J. Mills on Melting-point and 



in the same interval. Over this range, then, each infinite 

 olefine has, on the average, about ten isomeric modifications. 

 In general, there may be about nine melting-point curves 

 ending in one boiling-point. 



Applications. 



23. Among the practical applications of the theory, the 

 correction of experimental data by each other's aid is very 

 important. As an example of this may be taken the boiling- 

 points of the olefines distilled from Menhaden lime-soap and 

 Rangoon tar, and examined by Warren and Storer (Zeit. 

 Chem. 1868, p. 228). On grouping their formulae according 

 to even and odd coefficients of C, it was evident, after a few 

 approximations, that the even group contained the modulus 

 x 11, and the odd the modulus x 9. If we write the usual 



Q( x c) 



equation y= ^ , , — ---;- in such a form as to impose the con- 

 dition l + ^-c) 



& 



- =z?i modulus, 

 7 



and write h instead of the product of y and c, we shall have 



y + {y — n modulus)y# — (y — n modulus) A = 0, 

 an expression containing only two unknown constants. In 

 order to arrive at the values of these constants, I adopted the 

 method of least squares for <r = 6, 8, 10, and 9, 11, 13 respec- 

 tively, considering all the determinations to have the same 

 weight. The resulting equations were 



/rkJJX 47-357 0-4-5775) 



■ ( 0dd > V= 1 + -0*5484 0-4-5775/ 

 fj? ^ 40-709 Q- 4-2280) 



{ ^ ven ^- 1 + '060123 O-4-2280)' 



Subjoined are the numbers taken for the calculations (" M "), 

 the numbers given by Warren and Storer for the Menhaden 

 olefines (W S H)and Rangoon olefines (W S E), and the values 

 deduced from the equations : — 



cc. M. WSH. WSR. Calc. 



6 64-5 64-65 ... 65-19 



7 94-1 ... 95-04 



8 125-2 125-2 ... 125-17 



9 153-0 153-0 ... 151-97 



10 175-2 174-6 175-8 174-44 



11 195-7 195-4 195-9 196-35 



12 212-6? 219-5? 215'64 



13 232-75 ... 232-75 231-90 



