26 IIIE MECHANICS OF THE EARTH'S ATMOSPHERE. 



selves the twenty-one observations made with circular and square disks, 

 in order to convince uij^self as to what assumed value of j> presented the 

 greatest agreement. 



If I assumed for j; the circumference of the disk, there resulted 



« = 2.210 

 ft = 0.0132 

 and the sum of the squares of the outstanding errors was 



[xx] = 0.01425 

 By introducing the square root of the surface I obtained 



a = 2.200 

 (5 = 0.0526 

 \xx\ = 0.0097G 

 I then pnt^, equal to three different transverse lines drawn through 

 the center of the disk. First, the smallest transversals, for which of 

 course the sides of the square and the diameters of the circles were 

 directly introduced. This gave 



Lx = 2.204 

 /? = 0.0487 

 [xx] = 0.01282 

 For the greatest transversals, namely, the diagonals of the squares 

 and diameters of the circles, I obtained 



a = 2.230 

 ft = 0.0354 

 [,r,r| = 0.02221 

 Finally, for the average transversals which I drew [centrally] across 

 the disks at distances apart of every 3 degrees, and took the arithmeti- 

 cal mean of all, I found 



a = 2.200 

 ft = 0.04675 

 [xx] = 0.00066 

 It is evident that this latter method must lead to very nearly the 

 same result as the introduction of the square root of the surface since 

 ft diminishes in the same ratio as the coefficient of ft increases. 



Judging by the sums of the squares of the errors it would, according 

 to this, be advisable to introduce the square roots of the surfaces as 

 factors, but this is impossible, even although the results of the observa- 

 tions made with the long disk should be included under this same law. 

 There only remains to introduce the circumference as a factor, even 

 although in this case notable departures still remain. These are in no- 

 wise however errors of observation, but result principally from the 

 inevitable variations in friction. An error of 1 per cent, in the time 

 could scarcely have been made, but still such discrepancies and even 

 larger ones show themselves very frequently since the friction induced 

 now faster and now slower motion. Nevertheless, from the following 

 collection of all the observations it results that these have led to a 

 quite trustworthy result. 



