Further, the solution which I have made is a first trial. I think I
can do better by fitting A to at more points with the smaller v
values of and fewer of the more remote points. In this way I hope
that it may prove possible to restrict the integral's effective portion
to the region from o to io°. That remains to be seen.
By this means I hope that it may be possible to determine N
at central points in U.S.A., Western Europe and Mediterranean,
U.S.S.R., India and neighbourhood and Australia. These can form
the basis of a network of astro-geodetic traverses.
8. Astro-Geodetic Traverses. For these it is necessary
to relate astronomical observations of the vertical to the Model
Earth System. I do not find it possible to include much detail in the
present lecture. Suffice it to say that the M.E. anomalies of the
vertical can be computed from the surface distribution AgEl2n,
taken to a moderate distance. The Actual Earth deflexion, relative
to the M.E. is due to the condensed topography (h H)(2 6y).
9. Conclusion. I hope I have sketched a fully logical and
consistent process, leading from the results of field observations to
the practical determination of Earth Shape. In the discussions,
which I look forward to having with you tomorrow, I hope any flaws
will come to lightfor then it may be possible to eradicate them.
For the moment I will conclude by thanking you for giving me
a hearing.
Earth Shape and Potential Formulae
Reference System:
Potential J coV sin2 0 - (1 8F (1)
r r2 r4
in which co, E, B, C are constants
and (1 2h cos 0 h2) ~i P„hn. (2)
Level surfaces of (1) are
r a (1 s cos2 0 p2 cos2 0 sin2 0) 8a (3)
in which a is variable and s, p2 are related to a by following:
,_(K—C«-« (K-t)(3Jf 2.|.))
3 5 (4)
where A 4 -=r- ill -£a~2 x Ca~4.
2 E Y 2 8 J
Modified Stokes relation for Model Earth Surface:
-±- (Rl AgE), f sin vv (Ng) P (5)
2 Rp*«
where Rp radius vector from the centre of gravity to P or
M.E surface
AgE M.E. surface anomaly g y -j- A H h) 0
H regional average h
A 0.112 mgal/meter
v anomaly of potential
201
0
