352 Maj. Barnard on the Dynamic Theory of the Tides, | 
Calling p the total fluid pressure at any point, arising from the 
action of all the forces, p’ the pressure due to the earth’s attrac: 
tion, were its surface undisturbed, p” the pressure due to the 
attractions of the disturbing body, p’” the pressure due to the 
orces of inertia in the fluid, we shall have 
p = p'+p"! +p". 
If we desire to have the value of p at the undisturbed surface of 
the earth, put p'=0 and we have p=p’+p"". 
If we call w the height of the fluid column due to the p 
p, and q the height due to p”, we shall have (considering the 
» density as unity) p=gw, p”=gq, an 
1) gu=gq tp”; 
in which w is the total tidal elevation due to the disturbing attrac 
tions, and to the inertia of the fluid, and ¢ is the elevation due 
to the disturbing attractions alone; in other words, it is t 
height due to the equilibrium theory. : 
Confining the investigation, for simplicity, to the attractions of 
the sun alone, we shall find from the equilibrium theory (vile 
Airy’s “ Tides and Waves” par. 44,) 
3 
(2) 7=5(5-) [(ee0s 2¢ —1) (1—3 sin? 4) 3sin 24sin 200s (I-8)+ 
" 3 cos 24. cos 20 cos 2 (J—s). ce 
Tn which S and ¢ are the celestial right ascension and cen 
of the sun; 2 and / the terrestrial latitude and longitude Pthe 
place, (the latter referred to a meridian fixed in space); & 
actual and P,, the mean parallax of the sun and S’a coefficient 
2 3 
which (vide par. 41 and 42) = (F ) (the density of oa 
earth’s polar radius,* and g the force of terrestrial gravy 
é. : 
call s the longitude of the point, referred to a meri ‘able 
earth’s surface, and n the velocity of rotation, then the 
longitude of the point of observation, at the end od by nit 
a to a meridian fixed in space, will be represen y . 
the angle /—s, by nt+a—s. ; the 
If instead of the latitude Awe use the polar distance 6 of 
point of observation we shall have 
cos4=sin 4, and sin 24=sin 26. a 
_* The epheroidal form is disregarded, as the tidal displacements are YX : 
the sateen the atk araeted oe si. 88 or spheroid. 
