16 



THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



sequent computations, were made at recent dates with the greatest 

 possible care and under quite favorable external conditions. 



The resistance that the arms alone experience for different velocities 

 must first be determined because this must be subtracted every time 

 from the total resistance of the disc and the arms. The following 

 table contains the measures made on this point. G is the weight [in 

 lothsj that is placed in each scale-pan, and t the number of seconds oc- 

 cupied by the index in passing over 1 inch. The velocity of the index 



is therefore equal to -- according to the adopted unit of measure. The 



v 



observations were made twice tor each load in the scale-pan, and in the 

 second column of the table the two values t r and t 2 thus found are given 

 separately, while the third column contains the mean value (t) adopted 

 in the succeeding computation. 



Earlier observations had shown that the resistances could be ex- 

 pressed by the simple formula 



G 



+ ? 8 



On attempting to introduce a third term containing as factor the first 

 power of the velocity the constant coefficient corresponding had a very 

 slight value and even sometimes a negative one. Therefore I now first 

 chose the preceding expression, and by the method of least squares 

 found 



z= - 0.531 



S = + 18.703 



By the introduction of these constants I obtained the values for G, 

 which are given in the column headed A. The next following column 

 shows the error or the differences {A—G) for each of the weights acta 

 ally used. We notice that these errors progress very regularly in that 

 both for the smallest and largest values of G they attain the largest 

 positive values while between these they become negative. From this 

 circumstance it may be inferred that the form of the formula has not 

 been appropriately chosen, and I therefore repeated the computation 

 using the expression 



G = z + 1 p + 1 s 

 1 t l 



