511 
ASTRONOMICAL PROBLEMS. 
BY 
LIEUTENANT-COLONEL H. H. CROOKENDEN, R.A. 
HAVING received a presentation copy of Thirty Thousand Years of 
the Earth’s Past History from the Author, Major-General A. W. 
Drayson, F.R.A.S., late R.A., and further having seen models designed 
by him practically and ocularly demonstrating the possibility of a 
second rotation of the Earth, I attempted to solve a few of the problems 
set by him to enable even a moderate mathematician to determine the 
obliquity of the ecliptic at any past, present or future date, and to 
calculate the Declination and Right Ascension of certain fixed stars. 
The results were in the majority of cases obtained without my knowing 
how much or how little they differed from the records, as I had no 
catalogues of stars to refer to to verify my calculations. 
Once the theory of the Second Rotation of the Earth is accepted 
the calculations will be readily understood by anyone acquainted with 
the solution of spherical triangles, and if the assumptions such as the 
distance of the Pole of the Kcliptic from the centre of the second 
rotation, or the distance of the Pole of the Heavens from the same 
point, are not absolutely correct, they are close approximations to them ; 
Major-General Drayson does not claim that they are mathematically 
accurate, but the results they give are so near the truth that the 
calculations of the positions of stars for any dates are much more 
reliable than the accepted methods can give them by observation and 
an annual empirical rate + or — of Decl. and R. A. 
The calculations which follow have been made from data extracted 
from the Nautical Almanack for 1887; at that date the refraction 
tables were the same as those at present in use*; with these data the 
future positions of certain stars were calculated for 1895, their past 
* The refraction tables in 1820 were the same as those used by Bradley and differ by 
some seconds of angle in small altitudes of stars. 
IRV OT XX TEre 69 
