82 Proceedings of Royal Society of Edinburgh. [sess. 
maximum shift towards the red in spring, and the maximum 
displacement towards the blue in autumn. We also conclude 
from the curves that the amplitude of this annual displacement 
amounts to about 0*010 t.m., agreeing well with the shift 
required by theory, viz. 0*0105 t.m. A more minute numerical 
investigation will, however, be given later on. 
In looking at these curves, a most peculiar and, in my opinion, 
quite enigmatic feature will at once attract attention. One 
would naturally expect that the annual waves should proceed 
along a horizontal line. There is certainly no other motion in the 
line of sight which may account for the remarkable tendency of 
these curves to assume higher levels as we proceed from 1901 
onwards. Nor is there much possibility of systematic errors in 
the measurements which might produce this progressive shift. 
No alteration, either in the instrument or in the method of 
observation, took place during the time from 1901 to 1903, 
when the shift was most pronounced. If it were due to any 
such cause, one would expect the change to be abrupt ; but 
in reality it has taken place gradually. I think this fact 
becomes much more obvious if we study the curve shown in 
fig. 3, which exhibits the curve of the distances of Table I., after 
the annual displacement has been eliminated. Instead of the 
expected grouping of the values along a horizontal straight line, 
we see a curve which steadily rises from its minimum value in 
1901 to an almost stationary position between 1904 and 1905, 
indicating in its last branch, towards the end of 1905, a tendency 
to further elevation. I have satisfied myself that this enigmatic 
change affects chiefty the distances between the solar and telluric 
lines. If we investigate the distance between the two solar lines 
during the same interval of time, we find only feeble indications 
of a successive shortening and widening, the observed values 
ranging between 0*998 t.m. in 1902 and 0*995 t.m. in 1905. I 
think that even this much smaller difference is greater than its 
probable error, but no doubt it is insignificant if compared with 
the above fluctuation. 
I shall not venture upon hypothetical explanations of this 
singular phenomenon. What I should like to state here is simply 
the outcome of my observations. But if the shift is confirmed 
