Gravity DeterTninations in Australia. 91 



standard pressure of 26 -in. of mercury at 32 °F. His criticism is sound! 

 as regards the form, but in error as to the numerical coefficient. 

 The formula employed by previous workers was — 



) ^ I 



^•^2 I l+0-0023(F-32) " 2^ j vibration/day. 



where B denotes the uncorrected barometer reading and F that of the 

 Fahrenheit thermometers employed. But according to the data sup- 

 plied to us by General Walker.s the coefficient 0-32 should be replaced 

 by 0-34. The formula used by us was, however, 



B-26 

 ^ ■ ^^ l+0-0023(P-32) vibration/day. 



where B now denotes the corrected barometer reading; the computed 

 vibration numbers for the pendulums were accordingly too large^ 

 Now the expression, 1 + 0*0023 (F— 32) , is really an approximation to 

 [+ 0'0022(F-32)] [1-fO-OOOl (F-32)], the first factor being the 

 density-temperature reduction for air (containing moisture), the 

 second the barometer reduction. To correct the eror we must there- 

 fore add to the mean observed vibration number of each pendulum 

 at each station the appropriate numerical value of 



r 0-0001(F-32) 0-0023(F-32) j 



'-'' { ^^-''^-^^T000:(F=^32y - 26 ITD o02:UF-32) [ 



For these values I obtain 



Pendulum No. Melbourne. Sydney. 



4 -0-438 -0 703 



6 -0-438 —0-704 



11 -0-438 -0-708 



which give for the corrected vibration numbers and their differences, 

 in place of those in our previous papers (q.v.) 



Pendulum. Melbourne. Sydney. Difference. 



4 86098-83 86086-40 12-43 



6 85998-99 85986-42 12-57 



11 86050-62 86037-69 12-93 



Mean difference 12-64+0-15 



To obtain the difference, g (Melbourne) —gr (Sydney), we have, there- 

 fore, to a sufficient appro-ximation 



[g (Melbourne)—^ (Sydney)]/^ (Melbourne) = 2 -94 10-*; also 

 g (Melbourne) =980- O.cm sec-2 - - (q.p.) whence g (Melbourne) - 

 g (Sydney) = 0-288 + 0-003.cm sec-2. For reasons given in Appendix 1, 



this figure is increased by 0-002, giving 



g (Melbourne) -fir (Sydney) = 0-290.cm sec-2 

 so far as the Kater pendulumss are concerned. The Kater pendulum 



5. General "Walker's letters and " Instructions to Observers " are pre- 

 setted at the Melbourne Observatory. 



6. The differences obtained with half -seconds pendulums range from 

 0-299 to 0-313. cm sec-2. 



