RECENT PROGRESS IN GEODESY. 
263 
derivation of empirical formulae embodying a fixed law of 
nature may, besides establishing the truths which were the 
original objects of the investigation, accidentally bring out 
an unsuspected fact. Some years ago it was discovered that 
terrestrial latitudes were subject to a change, and that the 
law of these changes could be formulated in a simple linear 
equation containing two unknown quantities. When the 
equations of condition were formed, which theoretically 
should entirely satisfy the observations, and when a solution 
was effected giving results which were supposed to leave 
outstanding only accidental errors, there appeared to be 
systematic discrepancies. Moreover, the differences showed 
a well-defined, uniform change, increasing at one season of 
the year and decreasing at another. This phenomenon was 
none other than the effect of the aberration of light. It is 
well known that the velocity of light is about 10,000 times 
as great as that of the earth, so that while the earth travels 
one mile in its orbit, the ray of light by means of which we 
take cognizance of any celestial object and make our meas¬ 
urements has traveled 10,000 miles. This amounts to saying 
that our telescope must be inclined at a slight angle in order 
to receive the ray of light, the angle depending, of course, 
on the direction of the earth’s motion with reference to the 
observed ray, and the so-called “ constant of aberration ” is 
nothing more than the maximum displacement of the appar¬ 
ent position of the star. This, of course, obtains when the 
motion of the earth is at right angles to that of the ray of 
light. With these facts before us, it is quite evident that the 
observations for the variation of latitude contained not only 
data sufficient to show how the latitude was changing, but 
also the effect of the aberration besides. They could there¬ 
fore be utilized to determine this last quantity, and after 
that to find the size of the earth’s orbit. This was suggested 
by Professor Newcomb, and has been done in the case of the 
observations made at Honolulu and San Francisco, and the 
results of the work have now been published in Appendix 
10, Report of the Coast and Geodetic Survey for 1896. In 
