Gravity Determinations in Australia. 95 



The anomalies for Hobart and Brisbane are reduced, those for Perth 

 increased, by employing the new formula; the large negative values 

 ior Perth are very curious. For the reason given in §1, these ano- 

 malies must not be trusted too far; so far as they go, they favour 

 Helmert's new formula. 



Appendix 1. 



In order to ascertain the proper weight to assign to the Kater 

 pendulum determination of g for Melbourne we must investigate — 



(a) The differential character of the pendulums; 



(b) The relative precision of the sets of observations. 



The difference between the vibration numbers of any pair of the 

 pendulums, being small compared with the vibration numbers them- 

 selves, will be nearly the same in all four sets if differentiality is pre- 

 served. Arranging them in order of time we have — 





Sydney 



Kew Melbourne Sydney 



Pendulums. 



1882 (S). 



1889 (K). 1893 (B). 1894 (L). 



(4)-(6) 



100-61 



99-47 - 99-84 - 99-98 



<ll)-(6) 



51-76 



50-24 - 51-63 - 51-27 

 Mean: (4)-(6)=99-98i-24 

 Mean: (ll)-(6)=51-22i-34 



It is clear that the pendulums maintained their differentiality over 

 the whole eleven years. 



For the sets we obtain the following difference table: — 



Pendulum. 



K— S 



K— B 



K— L 



B— S 



B— L 



S— L 



4 



66-02 - 



- 58-12 ■ 



- 70-55 



- 7-90 - 



12-43 ■ 



- 4-53 



« 



67-18 - 



- 58-49 ■ 



- 71-06 ■ 



- 8-67 - 



12-57 - 



- 3-90 



11 



65-64 - 



- 57-10 



- 70-03 



- 8-54 - 



12-93 ■ 



- 4-39 



Mean 



66-28 



- 57-90 



- 70-55 



- 8-37 - 



- 12-64 ■ 



- 4-27 



Mean error - 



1-46 



- i-42 



- t - 30 



- i-24 - 



- t-15 



- i-19 



From these figures we conclude: — 



1. That there is no material difference between the precision of 

 sets S, B and L; the weakest set is K. 



2. That the pendulum support was distinctly less rigid in 1893-4 

 than in 1882 or 1889; but slightly more rigid during my observations 

 than during Baracchi's, by an amount apparently corresponding to 

 an incease in the difference, g (Melbourne) -g (Sydney), of about 

 0-002.cm sec-2 above that computed from the vibration numbers; 

 hence this addition in §2. The uncertainty, however, is not entirely 

 removed; so I have increased my estimate of the mean error from 

 +0-014 to the outside value +0-020. 



Appendix 2. 



Alessio found, by experiments made to test the point, that his 

 own coincidence clock was liable to accelerations of rale (sometimes 

 positive, sometimes negative) for a few days after starting. Hecker's 

 clock was of the same make; risky as it is to argue from the be- 



