78 Proceedings of Royal Society of Edinburgh. [sess. 
that these differences are quite independent of the absolute 
positions of the spectra in the field of view ; any relative dis- 
placement of the one spectrum with regard to the other, which 
might be due to instrumental deficiencies, is indeed eliminated by 
the purely differential method employed in the observations. The 
instrument permits the throwing of the opposite solar points of any 
desired heliographic latitude upon the slit, and thus enables us to 
investigate the solar rotation from the equator to the immediate 
vicinity of the poles. It is also noticed that any shift of the solar 
lines which is due to the motion of the observer to or from the 
sun, since it affects both limbs in the same direction, disappears 
completely from the differences. 
While this constitutes the method by which the effect of solar 
rotation is investigated, another interesting field of investigation 
is opened by a different treatment of the observations. Suppose, 
instead of taking the differences [a&] R - \ab] x and [c<i] R - [cd] A , we 
form their arithmetical means, J([a&] R + [a&] A ) and i([ c ^]it + [ccf] A ). 
Obviously we then eliminate the effect of rotation, and each of 
these bracket terms represents the distance \ah\ or [cd] as it would 
appear if we made our measurements in the centre of the solar 
disc. But now these distances are affected to the full extent by 
any displacement of the solar lines which is due to the motion of 
the observer in the direction of the radius vector earth-sun. And 
here we have therefore an exquisite test for the accuracy of the 
measurements, most simply obtained by investigating how far and 
with what amount of precision these motions of the observer are 
portrayed in our observations. I think the following results of my 
computations cannot but reflect very favourably on the achieve- 
ments of our instrument, and convey a feeling of confidence in 
the reliability of the results obtained with regard to the main 
object of my investigation, the measurement of solar rotation. 
Altogether there are three motions of the observer in the line of 
sight by which the positions of the solar lines can be affected. 
First, the diurnal rotation of the earth, in consequence of which 
the lines must be shifted towards the violet in the morning, and 
towards the red in the evening. Secondly, there is a motion of 
the earth in the direction of its radius vector, changing with 
the position of the earth in its orbit, and therefore having an 
