RECENT PROGRESS IN GEODESY. 
9 
refraction at a zenith distance of 60 degrees is about four 
times that at 20 degrees; hence the two refraction pairs will 
furnish an effective method of determining any peculiarities 
of refraction which are sufficiently great to produce any ap¬ 
preciable effect upon the latitude pairs, provided such effect 
is one which increases with the zenith distance. 
Any refraction effect which is analogous to a displacement 
of the apparent zenith, by a persistent barometric gradient, 
for example, will not be put in evidence by this test. To 
eliminate such an error, dependence is placed upon the fact 
that the final result is based upon observations at several 
stations varying greatly in longitude and in the surround¬ 
ing climatic and local conditions. 
It may seem at first sight that an annual variation in re¬ 
fraction would produce an apparent annual motion of the 
pole. This would be true if the motion of the pole were de¬ 
rived from observations at one station only. It will be seen, 
however, on further reflection that annual variations in re¬ 
fraction would tend to make all the latitudes along one par¬ 
allel apparently increase and decrease together, and that 
therefore the computed motion of the pole would not be ap¬ 
preciably affected if these annual variations were of about 
the same magnitude at the different stations distributed 
around the pole. 
To sum up, the discovery of the periodic motions of the 
pole was first made by a purely inductive method. The 
laws governing those motions have been slowly and pain¬ 
fully deduced by a continual application of the same method 
to old series of observations and to many new series made 
for the special purpose. Now a new campaign of observa¬ 
tions, promising results more accurate than any hitherto ob¬ 
tained, has been commenced. The mean position of the pole 
for each fortnight of the next five years will probably be 
known within a radius of five feet. There is little prospect 
for improvement of the observational side of this question 
for many years. The new observations will furnish mate¬ 
rial for new triumphs of the inductive method in furnishing 
2—Bull. Phil. Soc., Wash., Vol. 14. 
