10 Proceedings of the Royal Society of Victoria. 



own (Melbourne) observations* instead of Mr. Baracchi's, I get 

 nearly the same mean result, though with a larger probable error, 

 J/- 6* coming out 12-20 + 0"47 ; the difference 0*05 between the 

 two values (which is less than the probable error of the determi- 

 nation made by either of us, and therefore within the limit of 

 experimental error), is only one-seventieth part of the difference 

 between the results of the two investigations at Sydney. 



On the other hand the difference between the values for Af—S 

 obtained by Lieutenant Elblein and myself is not extravagant, 

 seeing that our apparatus and mode of experimenting are quite 

 different ; moreover, Lieutenant Elblein told me that he looked 

 upon 1 in 1 00,000 as about his limit of accuracy for any one 

 place; hence his limit of accuracy for the difference between two 

 places would be about L7 vibrations per day. My own probable 

 error for a similar difference is about 0*2 vibrations per day; 

 hence the diffei^ence of 1-33 between Lieutenant Elblein and 

 myself is well within the limit of experimental error. 



We may therefore feel tolerably certain that, if we adopt 12*2 

 as the value of the difference between the vibration numbers at 

 Melbourne and Sydney, we shall not be far from the truth. 



If we compute by Clairaut's formulaf the differences between 

 the vibration numbers at Greenwich, Melbourne, and Sydney, 

 and compare the figures thus obtained with the experimental 

 values, we obtain some interesting results, which strongly bear 

 out the deductions of the previous section. 



The calculation is effected thus : — 



Clairaut's theorem may he put into the form 



F- = r„- I 1 + ('\n - d-^sin- A j. - - - - (1). 



where V denotes the vibration number in latitude A, V„ the 

 equatorial vibration number, m the ratio of the centrifugal 

 force at the equator to the force of gravity there, e the ellipticity 

 of a meridian. 



* Refen'ed to suprn p I. Tliere is, indeed, uo reason to suppose tliat personal equation bas 

 any effect on the results of pendulum observations ; the results for each station are them- 

 selves deduced from the differences between pairs of epochs, and as each epoch of a pair will 

 be affected by the observer's personal equation to the same extent, this source of error is 

 in all cases eliminated. 



tit should be mentioned that— in order to avoid any risk of bias in favour of either 

 Lieutenant Elblein's result or that of the U.S. Coast Survey— the calculations here given 

 were intentionally not effected until the observations at Sydney liad been completed and 

 reduced. 



