OF THE TIDES IN THE PORT OF LONDON. 39 



The semimenstrual inequality of the heights is given by equation (3.). 

 Expanding, we have 



omitting ulterior terms, since the coefficients diminish according to powers 

 h 



h' 



of 



1 + 



Hence the variable part of this expression is of the form 



K cos (2 (p — 2 a) — L cos (4 <p — 4 a). 



The expression of the semimenstrual inequality of heights, found from observation, 

 was (in feet) 



S' = 17 cos (2 (p - 51°) — -23 cos (4 (p — 30°), 



which agrees with the theoretical expression, except as to the values of the arcs which 

 take the place of 2 a and 4 a. 



4. To find the effect of lunar parallax on the heights, substitute as before for 5 h', 

 in equation (3.), and let p' be this effect ; then 



, _ h> + hCOSQ(<p-u) y P - P 



^ 3/ * P • 



Here y is the mean height. 



Therefore p is of the form (p — P) (a-\- h cos 2 (^ —- a)). 



The form as given by observation is (p — P) (a + ^ cos 2 (p), where, however, the 

 existence and constancy of h are doubtful. 



5. To find the effect of lunar declination on the heights, substitute for S^, as before, 

 — k' cos 2 /sin'^. We thus find from equation (3.), q' being the effect, 



, H ■\- h. cos 2 ((» — a) , , ^ 7 • a V 



o' = y cos 2 / sm^ I ; 



and referring the correction to the mean declination A, it becomes of the form 

 (( = (sin* A — sin*^) (c'\-d cos 2 (<p ~ a)Y 

 The form given by observation was 



</' = (sin* A - sin*^) (c + rfcos 2 ((p + 45°)), 



where, however, d was not determined as to quantity, the observations being too 

 anomalous. 



It appears, therefore, that the results of observation and theory for the variations of 

 height agree as to form, with the exception of the epochs a, j8, y. 



