PAPER BY WILLIAM FEKREL. 



;23 



in which 



P„. = 2il' iL„, 



K,. 



Q„ = 2:.,., K,,< -^'^a + ^V'^n) 



(20) 



With the values of P„ and Q,^. (19) gives w, and this in (6) gives /i, 

 the amplitude of the tide. 



Laplace computed the values of 2/<, that is, the range of the tides at 

 the equator, at the times of conjunction of the moon and sun, for the 

 several values of /i « qual 40, 10, and 5, to which, l>y(2), correspond the 

 several values of ?, the dei)th of the ocean, equal to s-gVo^ 72^21 and 

 3-gV.i of the earth's radius, or approximately 1.4, 5.5, and 11 miles 

 respectively. 



Taking as an example the case in which /::^=10, we get from (4) and 

 (5) by ]Hitting Ki = 0, the following values of K„ in terms of U in the 

 last column of the following table, and from (7) and (8) the correspond- 

 ing values of ^„ in the second column. 



Putting 7i' equal 20, 40, CO, we get the following corresponding values 

 from this table when complete for all the values of n from 2 to GO, 



^.,0=-. 00927 

 A,o= - .00322 

 ^60=- .00174 



1+^r A„= .17621 

 1+ 2f A^= .12536 

 l-\-^f ^„= .10254 



From the values of iin we likewise get 



K20 = - .0548 K,o I ^20 = 5. 9 L 

 K,, = -.0172 JL40 / ^40=5. 18 

 A'6o=-.0001 ireo/Ao=5.23 



P2o=- 1.7647 

 P,o = -2.0488 

 Pfi„:=-2.16S7 



We therefore get from (19) and (20) with the preceeding data, 



«<-1.7647-5.91x. 17621 or <-2.8061 

 ?K-2.04S8-5.18x. 12536 or <-2.7157 

 «<-2.1687-5.23x. 10254 or <— 2.6870 



