# [tz] Potted history of timekeeping from the BBC

Zefram zefram at fysh.org
Tue Apr 4 15:29:11 UTC 2017

```Randal L. Schwartz wrote:
>And you should also note that the location where they charge you to take
>that photograph is about 20 meters to the west of where it should be.

It's more complicated than that.  The line on the ground (and laser
beam at night) is genuinely lined up with the historical transit circle
instrument which defines the meridian which in 1884 was selected as the
international prime meridian.  There is a discrepancy between that and
350 ms of rotational time, and about 100 m on the ground at Greenwich).
This discrepancy mainly arises from differing definitions of longitude,
interacting with non-uniform mass concentration in the Earth.

One would normally expect that if one erected a plumb line, and
extended the vertical of that line to the north and south, then the
resulting meridian plane would pass through the centre (and entire
rotational axis) of the Earth.  In fact it's not quite so.  In the case
of Greenwich, there is a relative mass concentration to the west, which
gravitationally attracts any plumb bob, making a plumb line lean slightly,
by some 5.3 arcseconds.  A meridian plane based on this local vertical
misses the centre of the Earth, passing about 100 m to the west of it.
When a transit circle is installed, it is aligned very precisely to
match the local vertical.  In the case of the Greenwich instrument,
installed in 1851, this process involved a dish of mercury to provide
a horizontal plane.

The result of the mass concentration is that, where we think of the
transit circle being directed precisely upwards, this does not mean that
it's looking precisely away from the Earth's axis.  The direction in which
the Greenwich instrument looks is 5.3 arcseconds to the east of that.
All of its observations, which defined GMT and our prime meridian,
are based on this local vertical direction.  It is the direction of
that meridian plane, not the location of the observatory relative to
the Earth's axis, that defined the prime meridian.

GPS takes a different view of longitude.  It doesn't measure local
vertical, but instead works in a strictly geometrical manner, producing
coordinates in 3D space.  When those coordinates are geometrically
reduced to latitude and longitude, one's implied local meridian is
strictly the plane passing through one's location and the Earth's axis.
One's longitude, then, is the angle between this geometrically-defined
meridian and the prime meridian, the latter necessarily still being
based on the observations made using the local gravitational vertical
at Greenwich.  Thus it is that the GPS-based (geometric) longitude at
the location of the Greenwich instrument is 5.3 arcseconds west.

So neither the line on the ground nor GPS is wrong; they're just the
zeroes of different ways of reckoning longitude.  There is also presumably
some discrepancy between the astronomical longitude of the transit circle
and the modern prime meridian due to inaccuracy in historical switches
between ways of realising the prime meridian, but this is probably two
orders of magnitude smaller than the difference between astronomical
and geometric longitude.

-zefram
```