Mr. Lubbock on Bernoulli's Theory of the Tides. 459 



The constant portion of the moon's parallax correction, 

 which for Liverpool is + 7 m, 9 for par. 54/, which I formerly 

 noticed as inconsistent with Bernoulli's table, is thus pro- 

 bably accounted for; and we see why this quantity should be 

 rather greater for London, when the argument of the moon's 

 parallax correction in the time of high water is the moon's 

 transit immediately preceding the tide, as in those tables which 

 I have given. When this last consideration is attended to, 

 I have ascertained that the theory of Bernoulli is not less con- 

 firmed by the moon's parallax correction as deduced from the 

 discussions of the Liverpool and the London observations 

 than by the semimenstrual inequality. Similar reasoning 

 might be applied to the correction arising from changes in 

 the declination of the luminaries ; but as results immediately 

 deduced from the Nautical Almanac would be more conclusive 

 and satisfactory than indirect inferences, I purpose to recur to 

 this view of the question and carefully to compare the results 

 with the expressions which are derived from Bernoulli's well- 

 known hypothesis. 



The irregularities which even results deduced from the 

 mean of an immense number of observations present, render 

 minute differences obscure. In order, therefore, to obtain the 

 concurrence of as many observations as possible to determine 

 the law of the inequality, I have adopted the following plan, 

 which seems to me the least objectionable. 



Let 8 P be the difference of parallax, or 

 The parallax — 57'- 



I suppose the correction to be proportional to 8P; hence 

 the correction for parallax 54-' = three times the correction 

 for parallax 56 1 , and the total of the absolute corrections for 



parallaxes 54', 55' 9 56 ! , 58', 59', 60', 61' = — , the correction 



o 



for parallax 54?'. Whatever the law of the correction may 

 be, it certainly may be considered as proceeding according to 

 powers of 8 P, and the preceding hypothesis amounts to neg- 

 lecting all the powers except the first. 



I now employ only the total of the corrections deduced 



3 

 from the discussions, and I multiply it by — , or the equi- 

 valent multiplier, in order to have the correction for 54?'. 

 The following table exhibits the results, together with the in- 



3N2 



