548 
GEOPHYSICS: W. BOWIE 
Proc. N. a. S. 
reference. The one which has been almost universally adopted is mean 
sea level. It may be defined as the surface which would coincide with 
the surface of the oceans and their tide water branches if the tide producing 
forces should cease to act and there were no movements of the air and the 
barometric pressure were uniform. This surface can be determined at 
any point on the exposed coast by continuous tidal observations for ap- 
proximately three years. The mean of the hourly readings of the tide 
record for such a period is practically free from error. If observations 
were made for a long period of years, it would be found that the average 
position of the surface of the ocean, for one three-year period, would agree 
very closely with the position of the surface for any other three-year 
period. The difference, if any, would be very minute. 
It has been assumed by geodesists that, insofar as engineering work is 
concerned, mean sea level at each place along an open coast is in the same 
equipotential surface. This, of course, cannot be absolutely true because 
of different densities in the waters of the oceans, different barometric 
pressures, trade winds, and possibly other causes, but the deviation of 
mean sea level at one station from the equipotential surface containing 
mean sea level as determined at another station is so small as to be negligi- 
ble in surveying, mapping, and other engineering work, and for practic- 
ally all scientific purposes. 
After the mean sea level surface has been determined, lines of very 
accurate spirit leveling are extended inland from the fundamental tidal 
stations. Each country of the world has done more or less of this work 
and in the United States we have tens of thousands of miles of this grade 
of leveling. 
When a network of triangulation has been extended over a large area 
and astronomical latitudes, longitudes and azimuths have been observed 
at many of the stations, differences between the astronomic and geodetic 
positions of the stations are found. These differences are due to the de- 
flection of the vertical, as was explained in the case of Porto Rico, and to 
the fact that the spheroid of reference used in computing the geographic 
positions of the triangulation stations differs from the actual figure of 
the earth. The former differences, namely, those due to deflections of 
the vertical, tend to be more or less accidental in character, while those 
due to an erroneous spheroid of reference are systematic. 
After the triangulation and astronomic work have been done over an 
extensive area, the shape and size of the mean figure of the earth may 
be computed with a higher degree of accuracy, possibly, than the spheroid 
of reference on which the triangulation was originally based. For one 
hundred years or more we have made closer and closer approximations 
to the true figure of the earth, as the triangulations of the various nations 
have been extended. In the earlier of these determinations there was 
considerable uncertainty, owing to the deflection of the vertical caused by 
