8 NATURE 


gauges were established, at Newlyn, Felixstowe, and 
Dunbar respectively. In the selection of these places 
the late Sir George Darwin was consulted. 
The levelling shows that the equipotential surface 
through the mean level of the sea at Newlyn passes well 
below mean sea level at Dunbar and slightly above that 
at Felixstowe. There is thus a question as to what 
should be adopted as the datum for the levelling. 
Either the mean of the different sea levels might have 
been used or the equipotential through mean sea level 
at one point might be the datum for all. The latter 
was decided on and the decision was unquestionably 
right. 
An interesting chapter is devoted to the effect of 
meteorological conditions on the level of the sea. This 
shows that part of the discrepancy of 0-81 ft. between 
mean sea level at Newlyn and Dunbar can safely be 
attributed tothe fact that, for the six years during 
which the observations continued, the average baro- 
metric pressure was higher at Newlyn than at Dunbar 
by o-108 in. ; this would depress the level of the sea at 
Newlyn by about o-12 ft. The greater portion of the 
difference still remains to be accounted for, however, 
and it seems that the cause may best be sought in the 
effect of wind. 
The relation between the daily mean level of the sea 
at Newlyn and the atmospheric pressure-gradient has 
been studied and a formula deduced that gives results 
in wonderfully good accordance with observation. 
That the levelling was carried out with conspicuous 
care and success is. demonstrated by the smallness of 
the probable error of the long line from Newlyn to 
Dunbar ; and the heights of the bench-marks are now 
known with such accuracy that if in the future these 
are found to have changed it will undoubtedly indicate 
that the marks have moved. The old levelling of 1850 
was unfortunately not precise enough to permit of the 
differences found, considerable though they were, being 
attributed to real movement. 
Particular attention has been paid to the design and 
to the selection of the situations of the bench-marks, 
on the stability of which the value of the work depends. 
The sites have been chosen with special regard to the 
geological conditions, “ avoiding as far as possible the 
softer rocks and those hable to surface changes.” 
In the design of the primary bench-marks an interest- 
ing detail is that two reference marks, situated side by 
side, are provided in each; one is a piece of gun- 
metal and the other a polished flint. The number of 
primary bench-marks is large, the interval between them 
being on the average about thirty-five miles, and it is 
scarcely possible that any upheaval or subsidence of 
a geodetic kind can take place without affecting the 
heights of some of them. 
NO. 2775, VOL. 111] 

[JANUARY 6, 1923 
The discussion in Chapter IV. of the dynamic and 
orthometric connexions is clear and good, but it should 
perhaps have been stated, with reference to the formula 
for the value of gravity, that though in all probability 
the results obtained by the use of Helmert’s constants 
are sufficiently accurate, yet the correct quantity to 
employ is not the computed value of gravity but the 
actual value obtained by observation. We may feel 
tolerably sure, from experience gained in other countries, 
that the difference between these two values will not 
be great, but as no gravity survey of this country has 
ever been made we cannot say that we know that that 
is the case. 
The errors to which levelling is liable are fully dis- 
cussed in Chapter VIII. The origin of the systematic 
errors, which are undoubtedly met with, is obscure. It 
is here stated that ‘“‘ the systematic error must be 
systematic with respect to something and there is 
always the possibility of finding out what the deter- 
mining condition or thing is. It is a matter of almost 
universal experience that the direction of levelling is 
one such condition.” Until, however, some satisfac- 
tory explanation has been given of the way in which 
the direction affects the errors it cannot be said that 
the connexion has been definitely established. 
The French levellers, under the direction of M. Ch. 
Lallemand, have probably paid more attention to this 
question than any one else, and it is worth noticing that 
the early procedure was to do the levelling in both 
directions on the same day, whereas now the rule is to 
do the second levelling on a different day. If the 
systematic error were principally due to the direction 
the best procedure would clearly be to do the two 
levellings on the same day, under as similar conditions 
as possible, when the effects of direction on the two 
results could be expected to be equal but opposite. It 
seems that this was the original expectation ; experi- 
ence, however, showed that the expectation was not 
fulfilled, and so the preference was given to separate 
dates, ‘‘ qui assure” (to quote M. Lallemand) “ une 
plus grande variété dans les conditions atmosphériques 
d’exécution des deux nivellements et, par suite, en cas 
de concordance de ceux-ci, autorise davantage 4 penser 
qu’ils sont exempts d’erreurs systématiques.” 
This evidence, however, is not very conclusive. 
Concordance may merely indicate that the errors were 
equal and of the same sign in both cases, so that 
whatever error there was will appear undiminished in 
the mean. Discordance means that most probably the 
errors were of opposite sign, but, the conditions under 
which the two levellings were done having been different, 
it would be unjustifiable to assume that the errors were 
equal. In neither case, therefore, have we any certainty 
that the mean of the two results will be free from error. 
