380 PROCEEDINGS OF THE AMERICAN ACADEMY. 



the conclusion that this action was a fortunate one for me, as the 

 investigation would certainly have been tedious and expensive and 

 would probably have been inconclusive. 



But the easterly deviation also was, incidentally, measured in my 

 experiments at the Jefferson Laboratory, and the general mean value 

 found for it was 0.149 cm., whereas the value given by the theoretical 

 formula, 



y = 1 gu COS A X t S , 



where u is the angular velocity of the earth's rotation, A is the latitude, 

 and t is the time of fall in seconds, is 0.177 2 cm. for the case in 

 hand. The probable error of the observed general mean is perhaps 

 greater than that for the southerly deviation, but is not great enough 

 to account for the difference between the observed and the theoretical 

 easterly value. I did not give in any of my previous papers on this 

 subject the formula of Gauss or that of Laplace for the easterly devia- 

 tion of a body falling in air, though I had given considerable attention 

 to their treatment of the effect of air resistance, but closed my discus- 

 sion of the matter thus : " The mean easterly deviation actually found 

 in these experiments, 0.149 cm., differs 0.03 cm. from this theoretical 

 value, — a quantity too large to be accounted for by the resistance of 

 the air. I attach but little significance to this discrepancy, as the con- 

 ditions for determining the easterly deviation in my work were plainly 

 not so good as those for determining the southerly deviation." 



Thus the matter stood till last April, when I received from Professor 

 Hagen of the Vaticana Specola Astronomica the suggestion that I should 

 make some experiments to find out how much the resistance of the air 

 really amounted to, in order to see whether it might not after all go 

 some distance toward explaining the discrepancy between the observed 

 and the calculated easterly deviation. Father Hagen puts the state- 

 ment of Gauss concerning the effect of air resistance so clearly, that I 

 shall copy his words, changing, however, the nomenclature slightly. 

 He writes : 



" Gauss puts the height of the fall, determined by linear measure, 

 = f, and \gf- =/ '+ 8, determined from the observed time of the fall. 

 The difference S is owing to the resistance of the air. Then 



Deviation y = |cos \ut (/— £8)." 



It was easy to carry out the suggestion thus given, and accordingly 

 in October I reestablished the releasing part of my apparatus at the top 



2 I have given this previously as 0.179, but 0.177 is more nearly correct. 



