Observations zvitJi Rater's Pendulums. 9 



In order to render these results compai-able with those taken 

 at other places they must be reduced to vacuum and sea-level. 

 The reduction to vacuum is 



0-34 ^^ =26xO-34-^l-069 = 8-2693. 



1 + -0023 X 30 



The height of the pendulum-bob above the sea-level is given 



by Mr. Russell as UO feet. 



140 

 The reduction to sea-level is therefore —-- = "STGl. 



243 



The sum of the two corrections is 8-8454 or to a sufficient 



degree of approximation 8 "85. 



Hence we obtain as the finally reduced vibration numbers 



Pendulum No. 4 ... ... 86095-95 



6 ... ... 85995-97 



11 ... ... 86047-25 



The values given by Mr. Baracchi for Melbourne are 



Discussion of the Results, and Comparison with Theory. 



The first conclusion deducible from these results is that the 

 diff"erence between the vibration numbers for Melbourne and 

 Sydney cannot be deduced from a comparison of the investiga- 

 tions of the U.S. Coast Survey officers with those of Mr. 

 Baracchi, for the difference between the value thus obtained, 

 viz.:— 8-58 + 0-32, and the value 12-15 + 0-19 given above, 

 is more than eleven times the probable eiTor of the first, and 

 nineteen times the probable error of the second. It cannot, 

 therefore, be attributable to unavoidable errors of observation. 



Furthermore, the difference cannot be attributed to personal 

 equation as between Mr. Baracchi and myself ; for if I use my 



