816 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
Now consider tlie filial condition. 
Since the integrations of the two periods have extended from 1 to '88, and again 
from +=1 to '76, 
r=r 0 (-88 X •76)- fi , fi = /2 0 (-88 X ‘76)~ 3 , Jc=Jc 0 (' 88 X '76)~\ 
also the value of n which gives the day of 9 hrs. 55 m. is given by log ?2 = 3'74451, and 
log 5+10 = 1-21217, when the year is the unit of time. 
We now have i— 17° 4 \j—6° 21b 
Using these values in (115) and (112), I find 
a= ’10872, /3=-00627, a='00563, b=*00510. 
ab is still small compared with (a — j3), but not negligeable. 
Then by (117) 
2ab 
■k 2 = — \/(a — /3) 3 + 4ab = — (a — /3)-—, also ^ + * 2 = — (a+/3) 
Now 2ab/(a—/3) = ‘00056. 
Hence we have 
k: 1 + k' 2 = — -11499"1 whence k y = — '10900 
k x — k 3 = — -10301 f Ko= —-00599 
Burckhardt from the combined observations of Bradley and Maskelyne to be 8” (Grant’s 1 Hist. Pbys. 
Astr.,’ 1852, p. 65). 
For the amplitude of the 19-yearly nutation, Airy gives (‘ Matb. Tracts,’ 1858, article “ On Precession 
and Nutation,” p. 214) 
6tt"B T t • O- 
mia , -cos I sm h 
T ^iv(n-\- 1) 4w 
B is the precess. const. = my e; his T'= my 2w//2; his n— my v; his w— my w; his 1= my i; his i— my j ; 
and his t is the period of revolution of the nodes, and therefore = my 2+(«—/3). 
Then since my t= 3/2 2 /2(1 + v), the above in my notation is 
1 t£ 1 . . q . 
*-cos i sm 2; 
2 n a.—p J 
Now by (115) and (112) b= — cos i cos 2 i, when £=1. 
n 
Therefore his result in my notation is 
j b sin 2 j 
2 Oi— ft cos 2 i 
This is the result used above (in 260) for computing the nutations of the earth. 
If my formula is to be used for the heterogeneous earth, c must be replaced by the precessional constant, 
and therefore the result in the text must he multiplied by 232 x '003272 or '759. Hence for the hetero¬ 
geneous earth the 11"*86 must be reduced to 9" - 01. Airy computes it as 10”'33, but says the observed 
amount is 9"'6, hut he takes the precessional constant as '00317, and the moon’s mass as l-70th of that 
of the earth. I believe that '00327 and l-82nd are more in accordance with the now accepted views of 
astronomers. 
