( 460 ) 
The correction to be applied to the observed hour- 
angle to find the true is — Ô4. 
Hence by integration 
C — A 
— Jh — — tan À sin « cos nt. 
It is easy to verifv geometrically that if the great circle 
[IP be produced to meet the geographical equator in A’ 
the expression just found with its sign changed is AA’. 
Itis pretty clear that AA’ 1s the excess of the observed 
above the true hour-angle, and therefore the correction 
to pass from the observed to the true hour-angle 1s the 
opposite of AA/’. I have however thought it more satis- 
factory to give a more complete investigation. 
If we attribute to « its observed value of 0.15 and 
reduce it to time, 1t become 0*.01. Therefore the correc- 
tion to the observed sidereal hour-angle is 
— 05.01 tan À cos nt. 
In latitude 89°26’ the coefficient of the correction is 
4, and in latitude 84°20/ it is 05.1. It is clear that even 
in the higher of these latitudes the change of length in 
any given sidereal day is altogether insensible. 
The whole range of the amplitude of the oscillation of 
the astronomical about the geographical meridian is 
2 sin « sec À. Since sec 89°25/ is 100, sec 84015 is 10, 
sec 60° is 2, we find, with « still equal to 0’’.15, the 
range to be 50” in latitude 89°25/, 3/’ in latitude 
