374 Prof. H. C. Plummer on the 



3. The ethers form a double series, O s H 2s +i — — C r H 2r +i, 

 for which a considerable number of boiling-points have been 

 determined, and it seems desirable to connect them if 

 possible by a single formula. Since the composition of 

 these substances is symmetrical the absolute boiling-points 

 T rs =T« r are symmetrical functions of r and s. Hence a 

 function of the form 



T rs =a + b(r + s)+c(r + S y + d{r- S y 



is suggested, and a simple calculation gives 



T rs =189 o -75 + 32 o -42(r + 5)-0 o -557(r + 5 ) 2 4-0°-138(r-^) 2 , 



the last term allowing for some variation among isomeric 

 compounds. The numbers resulting from this formula are 

 given in Table V*(a), and the result of subtracting these 



Table V. (a). 





Ethers 



: atL 



ls+1 — O- 



— L> T li 2 r+l» 



Lyg caic 



. 



r. 



*=1. 



2. 



3. 



4. 



7. 



8. 



1. 



2524 



282-1 



o 

 311-1 



339-2 ... 



418°5 



443-2 



2. 



282-1 



310-5 



338-1 



364-8 ... 



439-9 



463*2 



3. 



311-1 



338-1 



364-2 



3895 ... 



460-5 



482-4 



f- 



39-2 



364-8 



389-5 



413-5 ... 



480-2 



500-8 



7. 



418-5 



439-9 



460-5 



480-2 ... 



534-5 



550-9 



8. 



443-2 



463-2 



482-4 



500-8 .... 



550-9 



565-9 









Table V. (6). 













Ethers :, 



o-c. 







r. 



s=l. 



2. 



3. 



4. 



7. 



8. 



1. 



o 

 -3-0 



o 

 + i-7 



+0^8 



o 

 +4-1 ... 



o 



+4-3 



o 



+2-8 



2 # 



+1-7 



-2-9 



-1-5 



-0-4 ... 



-0-3 



-1-0 



3. 



4-0-8 



-1-5 



-0-5 



+0-6 ... 



+01 



-2-4 



4. 



+4-1 



-0-4 



+06 



+04 ... 



-1-5 



-2-1 



7. 



+4-3 



-0-3 



+0-1 



-1-5 ... 



+0-4 



+0-9 



8. 



+2-8 



-10 



-2-4 



-2-1 ... 



+0-9 



-1-2 



from the observed boiling-points, which it is unnecessary to 

 reproduce, is shown in Table Y. (b) . The comparison may 

 be considered satisfactory on the whole, though when 

 r (or s) = l the discrepancies are not altogether negligible. 



