804 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
Hence if (225) are identical with. (71) and (29) of “ Precession,” we must have 
i , , a'b — ab' 
‘ a(a + b) 
J _ a'b—ab' 
~i~~‘ b(a + b) 
But i/j = b/a ; therefore the condition for the identity of (225) with (71) and (29) of 
“ Precession ” is that 
(ad-b)(gh+ad)d-a / b—ah' = 0 .(226) 
Or if the viscosity be not small, a similar equation with G and D for g and d. 
We cannot prove that this condition is satisfied until a' and b' have been evaluated, 
but it will be proved later in § 16. 
This discussion shows that the obliquity of the earth’s equator (Lf) to the invariable 
plane of the moon-earth system, when the solar influence is infinitesimal, degrades into 
the amplitude of the nineteen-yearly nutation, when the influence of oblateness is 
infinitesimal. The one quantity is strictly continuous with the other. 
This completes the verification of the differential equations (224) in the two extreme 
cases. 
§ 16. Evaluation of o', a' &c., in the case of the earth’s viscosity. 
The preceding section does not involve any hypothesis as to the constitution of the 
earth, but it will now be supposed to be viscous, and the various functions, which 
occur in (224), will be evaluated. 
By (184-5) we have 
\ r ~7.=-f~ sin 4fj.(227) 
Jc dt * g 
. . < 228 > 
The last equation is approximate, for by writing it in this form we are neglecting 
r' 2 (sin 4f—sin 4f 1 )/r 2 sin compared with unity. 
This is legitimate, because when (sin 4f—sin 4f 1 )/sin 4f x is not very small, t^/t 2 is 
very small, and vice-versa; see however § 22. 
Hence (228) may be written 
