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



extend a memoir, necessarily somewhat long, by the addition 

 of a list of references. Except in a few cases, where a mean 

 has been taken, authentic numbers have been used throughout. 

 Special mention deserves to be made of the large number of 

 results due to Kraffts, in connexion with ketates, ketones, and 

 paraffins, and relating also to boiling-point*. Baeyer's re- 

 markable discovery that melting-point is affected by the cir- 

 cumstance that x is even or odd, will be found to be confirmed, 

 and will be subsequently extended to boiling-point f. 



7. Series Q x H 2ir _4 4 . — Of this series of acid bodies no 

 members are known in which x is odd. The only values 

 of x at present ascertained are 16, 18, and 22, corresponding 

 to the melting-points 67°, 86°, and 90°. 



Hence 



_ 473-28Q-15-49) 



y= 



1 + 5-1051O-15-49/ 



When x= oc,y = 92-707. 



8. Normal Paraffins, 0* H 22:+ 2. — The equation to the odd 

 series, calculated from all values, is 



_ 8-Q12Q-13-7) 



1 + -059711(^-13-7) 



x. y. y calc. 



9 -51 -52-35 



11 26-5 25-79 



13 6-2 5-85 



15 +10 + 9-67 



17 22-5 22-09 



19 32 32-26 



21 40-4 40-73 



23 47-7 47-91 



27 59-5 59-39 



31 68-1 68-18 



35 74-7 75-12 



oc 134-18 



Sum of the errors, +*16; probable error of a single compa- 

 rison, *38. 



The equation to the even series, similarly calculated, is 



7-518(^-13-4) 

 y 1 + -051987O-13-4)' 



* Berichte, xv. pp. 1687 and 1711. t Ibid. x. p. 1286. 





