THE PHYSICAL PROPERTIES OF METHYL-ALCOHOL. 525 



With these data before us we began by formulating the relation for the 

 several kinds of aqueous alcohol operated upon, between specific gravity on 

 the one hand, and temperature between 0° and 20° as limit values on the other. 

 With the stronger alcohols the simple formula S — S t = at afforded quite a 

 satisfactory degree of approximation ; the actual function, it is true, proved 

 obviously non-linear, but, when the formula S — S t = at + b? was substituted, 

 b assumed, in general, so very small a value that, with its own a, the simpler 

 function was practically as correct as the more complex one. Thus we found 

 for absolute alcohol : — 



At 0° 



9°-7 



19°-7 



& = 81018 



80120 



79202 



S -St= 



898 



1816 



S — St 



t 



92-58 



92-17 



S — St 



t 



= 92-98 -- 0-041$; 





whence 



or, if we adopt the linear function 



?<LZ^ = 92-37 dz 0-20, 



which latter function gives, for 20°, S — S. 20 = 1847*4 ± 4*0, i.e., an uncertainty 

 of ±0*00004 only. 



Our general formula for S t =/(t), however, gives calculated values for 0°, 

 10°, and 20°, which when used as a basis for the calculation of the a, of the 

 linear function, assigns to it the value 91 75 ± 0'43. We found subsequently 

 that this value falls in better with the general relation between a and per- 

 centage than the value 92-37. 



For the aqueous alcohols we found the following values for the constant of 

 the linear function : — 



Percentage of CH 4 0. 



Value of a. 



100 



91-75 ± 0-43 



95 



89-40 ± 0-48 



90 



86-81 zfc 0-41 



80 



82-86 ± 012 



70 



76-35 ± 0-79 



60 



72-17 =h 0-09 



50 



65-26 ± 0-11 



40 



56-20 ± 0-53 



30 

 20 



44-39 dz 0-27 



27-30 ± 2-04 



10 



8-25 for 9°-7 and 13-60 for 19 c 7 



VOL. XXXIII. PART II. 



4h 



