286 SIXTH REPORT— 1836. 



pends partly upon the phfenomena as deducible from Bernoulli's 

 equilibrium' theory, and partly upon the law of the intervals be- 

 tween the moon's successive transits. I therefore directed Mr. 

 Jones and Mr. Russell to discuss the observations with reference 

 to the iifth transit preceding, or that two days before the high 

 M'ater under consideration. 



The results which we obtained, and the comparisons with 

 theory which I instituted, are printed in the Phil. Trans. The 

 observations of 19 years amount to 13,370 ; but notwithstanding 

 their multiplicity, wlien they come to be separated into numerous 

 categories, as for the purpose of ascertaining the diurnal inequa- 

 litjr, the irregularities which the results present show clearly that 

 even a greater number is required in order to arrive at averages 

 which can be sufficiently depended upon. Still the general con- 

 clusion to which my discussions lead is that the equilibrium 

 theory of Bernoulli satisfies the phsenomena nearly if not quite 

 within the limits of the errors of the observations, and that it 

 leaves very little, if anything, to be accounted for otherwise. 



This question is extremely interesting, and seems to me to 

 deserve the fullest investigation which the materials within our 

 reach can justify. If the discussion were extended by taking in 

 all the observations which have been made at the London Docks 

 (which would give us about 16 years more, or nearly double the 

 number), I have no doubt that the results would be much more free 

 from irregularity. It would also be worth while to brinj^ up the 

 interval and the height to what they ought to have been in 

 Tables* I. and X. if the moon's parallax had been exactly 57', and 

 in Table VI. to what they ought to have been if the moon's de- 

 clination had been exactly 15°. I have hitherto neglected the 

 minute quantities, which would thus have given a second ap- 

 proximation on account of the great additional labour which 

 they would have occasioned, but I have no doubt that sometliing 

 would be gained by supplying this cori'ection. 



Besides all the work which I have detailed, the grant of the 

 Association has enabled me to employ Mr. Jones to effect a dis- 

 cussion of the Liverpool observations for 19 years, also with 

 reference to a back transit in order to obtain the calendar month 

 and diurnal inequalities. It would be desirable to complete this 

 discussion, in order to obtain in the same manner the moon's 

 parallax corrections. It would also be desirable to extend the 



* Phil. Trans. 1836. The correction for the difference of the moon's de- 

 clination from 15° is, I apprehend, insensible, and that for the difference of the 

 moon's parallax will seldom, if ever, exceed one minute for the interval, and 

 one tenth of a foot in the height. 



