1905 - 6 .] Dr J. Halm on the Spectro-heliometer. 
79 
annual period. It is due to the ellipticity of the earth’s orbit, 
and in consequence of it the earth moves most rapidly from the 
sun in the beginning of April, and most rapidly towards the sun 
in the beginning of October. Thirdly, a very small motion is 
caused by the revolution of the earth round the centre of gravity 
of the system earth-moon. 
The mathematical expressions for these motions (in km. per 
second) are easily derived. For the diurnal motion we have 
+ 86400 ° 0S * aosBsmt > 
where a represents the equatorial radius of the earth in km., <£' 
the geocentric latitude of Edinburgh, and S, t the declination and 
hour-angle of the sun, the positive sign denoting an increase in 
the distance of the observer from the sun. 
The annual term is expressed by 
2ttA e 
T J 1 — e 2 
sin 
(0 -tt) = 
2-7T. a e 
sin p.T Jl _ e 2 
sin (0 — 7r), 
A being the mean distance of the earth from the sun, T the 
number of mean time seconds in the year, e the eccentricity of the 
earth’s orbit, O the true longitude of the sun and tt the longitude 
of the perihelion, and p the solar parallax (8 ,r, 80). 
The small “ lunar ” term may be sufficiently expressed by 
+ 0*014 sin(0 - <[ ) km. per sec., 
0 and <[ being the longitudes of sun and moon. 
Turning to the measurements, I may first state that my computa- 
tions refer to the arithmetical means of the two distances, viz. — 
i[0+ + [«6 ]a + Hu + Hj. 
In other words, I have formed the means of the micrometer 
readings, J(a R + a A + c R + c A ) for the two telluric lines, and 
+ d A ) for the solar lines, and taken the difference 
between the two. 
The screw value, expressed in wave-lengths, had to be determined 
on each day. It is based throughout strictly on the distance 
between the two telluric lines \bd\. Possibly the assumed 
distance between these two lines, 0*760 t.m., is still slightly 
