THE PHYSICAL PROPERTIES OF METHYL-ALCOHOL. 529 



affording a sufficient approximation, as seen by the following comparison. 

 " Ay " means the uncertainty in the y as determined experimentally (see 

 p. 524). 



X. 



y calculated. 



y by exp. 



Ay. 



0-05008 



8-465 



8-46 



±0-060 



010019 



15-609 



15-65 



0-040 



0-20033 



27-582 



27-42 



0-025 



0-30025 



39-281 



39-49 



0-035 



0-40029 



54-104 



54-02 



0-050 



As a glance at the two columns u y " shows, the error of the formula 

 amounts to — 0'209 in the case of # = 0-3; the other errors, arithmetically, 

 range from 0-005 to 0162. 



Second Interval. 

 x = 0-3 to 0-7. 



By proceeding exactly as in the case of the first interval, we found 



a= +129-871; 



log a = 2-113 



512. 



b=- 26-5315; 



log 6 = 1-423 



762. 



c = +102-71; 



log e = 2-011 



629. 



Having found before that a general formula of the third degree for the whole 

 interval from a? = 03 to 10 gave fair, though not quite sufficient approxima- 

 tions, we made only two comparisons between y calculated and y found. 



as. y calculated. y found. A y. 



0-30 39-332 39-49 0-035 



0-70 113-021 113-09 0-060 



y calculated. 



y found. 



39-332 



39-49 



113-021 



113-09 



Third Interval 



x = 



= 0-6 to 1-0. 



Again, operating as before, we found 



a=+ 89-001; log a = 1-949 395. 

 b = + 109-012 ; log b = 2-037 476. 

 c= - 8-2891; log c = 0-918 51. 



We made only one comparison this time : 



Forz=l; ?/ = a+6 + c = 189-724. 

 By experiment, y = 189'69. 



After having made sure of perfect arithmetical correctness all round, we 

 next calculated by means of the formulae the values 4 S for all the experimental 



