ALTAZIMUTH SOLAR OBSERVATIONS. 32I 
rotation however, also causes an aberration, which, on the con- 
trary, is dependent on locality, and cannot therefore be thus 
generally treated. The effect of this daily rotation is to displace 
a star towards the east, the displacement being called the diurnal 
aberration. Its ratio to the annual aberration is obviously that 
of the rotational velocity of a terrestrial point to the velocity of 
the earth’s centre. This rotational velocity varies as the product 
of the geocentric radius of the earth p’, and the cosine of the 
geocentric latitude ¢’, that is as p’ cos ¢’. As the compression is 
less than =}; and consequently the astronomical and geocentric 
latitudes differ never more than 11’ 44’, we may assume that the 
rotational velocity varies as the cosine of the astronomical latitude 
and this will never lead to sensible error, since the aberration 
itself is a very small quantity.! Assuming the orbit to be circular 
and its radius to be unity, the value of the earth’s equatorial 
radius will be sin 8-’848; and as there are 366-256 axial rotations 
for one revolution about the sun, and as moreover according to 
Struve? the coefficient of the annual aberration is 20°"4451, the 
value of the diurnal aberration o in seconds of arc is 
7 = 20-4451 sin 8-’848 cos 6=0°"3212 cos ¢...... (18)8 
which is tabulated hereunder. 
Taste IV.—Coéficient of Diurnal Aberration for Different 
Latitudes. 
Latitude 0° 20°56’ 38°53’ 51°29’ 62°10’ 71°52’ 90° 
Coeff. Diur. Aberr. 0:32” 0°30” 0:25” 0:20” 0-15” 0-10" 0” 
The constant of aberration gives at once the effect on the right 
ascension of a star on the celestial equator when crossing the 
LMS Wao nore tT RR RE 
1 The rotational velocity may also be expressed by the formula p cos 4, 
where p is the distance along the normal, from a point whose astronomical 
latitude is , to the rotation axis of the eatth. If the equatorial semi- 
axis be denoted by unity, p = 1+ s$e (1—cos 2g) very approximately, 
which clearly shews how small the error of the assumption is. 
? Astronomische Nachrichten, No. 484. 
3 The coéfficient 0°’311 given in Chauvenet’s Astronomy, Vol. 1., p. 640, 
and in Clarke’s Geodesy p. 190 depends upon Encke’s value for the 
Parallax, viz. 8-”57116. 
U—Dee. 2, 1996, 
