THE PHYSICAL PROPERTIES OF METHYL-ALCOHOL. 



527 



II. From p = 0Q to p = 030. Again adopting the function a + bt + ct 2 , and 

 calculating by the method of the least squares (which in this case, it is true, is 

 almost out of court), we found — 



a =- 6-388; loga = 0'805 37 

 b =+207'53 ; log & =2-317 08 

 c =-127-88 ; logc =2106 82 



which gives the following values 



p. 



«0- 



By Formula. 



a . 

 By Direct Det 



0-6 



72-09 



72-17 



0-5 



65-41 



65-26 



0-4 



56-16 



56-20 



0-3 



44-36 



44-39 



III. For alcohols of less than 30 per cent, we adopted the function 



S -S t = at + bP, 



and accordingly had to establish the relations between a and p and between b 

 and p. No doubt the best mode of procedure would have been to bring the 

 equation into some form like 



S - S ( = (a + xp + yf)t + (J3 + zp + wp*)& , 



and to calculate the constants directly from all the experimental data by means 

 of the method of the least squares ; but we shrank from the very troublesome 

 calculations which this would have involved, and satisfied ourselves with estab- 

 lishing the relations a=/(p) and b = <f>(p) by separate graphic interpolations. 

 The results were as follows : — 



V 



Const, a. 



Const, b. 





Curve. 



Exp. 



Curve. 



Exp. 





 0-05 



o-io 



0-20 

 0-30 



- 6-0 



- 2-2 

 + 3-3 

 + 20-0 

 +44-0 



- 5-65* 



- 4-05 

 + 3-06 

 + 21-30 

 +43-59 



+ 0-705 

 + 0-648 

 + 0-581 

 + 0-398 

 + 0-060 



+ 0-685* 

 + 0-672 

 + 0-535 

 + 0-408 

 + 0055 



The values a and b for ^> = 001, 0-02 up to 0-30 were read from their 



curves and tabulated (see the alcohometric table below). 



The agreement between experiment and calculation is not as perfect as we 



* Eosetti's Table. 



