850 

wire, but it was found by Eétvés that a quartz fibre | 
which is sufficiently strong to carry the loaded beam 
is more rigid than the platinum iridium wire and in 
consequence a smaller deflexion of the beam results. 
It was partly owing to this fact and partly owing to 
the exceptional fragility of the quartz fibre that it 
was not adopted by Eétvds in his field instrument. 
' The action of the balance and the nature of the 
quantities measured may be appreciated from the 
following consideration. Let a system of rectangular 
co-ordinates Ox, Oy, Oz, Fig. 2, have its origin O at 

Fic, 2.—Diagram of beam system, 
the centre of gravity of the balance beam, the axis Oz 
directed downwards in the line of resultant gravity at 
O, and the axes Ox, Oy towards the geographical north 
and east respectively. It is assumed that a potential 
function U exists for the gravitational field about O 
and that, for points not outside the range of swing of 
the balance beam, we can put 
U=Up + 802 + BU yx” + SU gy? + $U 353" 
+ Uzaxy + Ujgx2 + Ung yz, 
where Up is the value of U at O. 
He 20-2 3) oe tbe resultant force ara, 
and U,,, Uj, etc. depend only on O, not on x, y, and 
z. Such an assumption is justified whenever gravity 
is normal, or even if there are irregularities in the field, 
provided the disturbing masses are fairly distant from 
the balance. 
If the balance beam lis in any position in the plane 
Oxy, making an angle a with the axis Ow, its main mass 
is concentrated at two points of which the co-ordinates 
are (l' cos (a+7), l’ sin (a+7),O) for the upper weight 
and (J cos a,/ sina, h) for the lower. The potential of 
the whole system will therefore depend on a, and will 
only bea minimum or maximum for a limited number 
of values of a. For all other azimuths the beam will 
tend to rotate so as to set itself in a position of mini- 
mum potential, and will actually rotate until this 
tendency is balanced by the torsion.of the suspension 
wire. The latter, measured by means of the telescope 
and scale, affords a means of determining the twisting 
moment due to the gravitational field at any value a, 
and thus enables us to evaluate the quantities which 
specify the field and the torque due to it. It is shown 
NO. 2799, VOL. 111] 
NATURE 

[June 23, 1923, : 
in the mathematical theory that these quantities are 
none other than the magnitudes 
(Ugg — Uy), Ugo, Ung, and Ugg, 
which are thus determined for every station O. 
- 
APPLICATION OF THE BALANCE. 
The magnitudes (Ug. — 
mined by the balance are not sufficient to enable 
us to reproduce the complete gravitational field about 
O—in other words, to describe its equipotential sur- 
faces—since we require to know both Uj, and Uss 
separately, and also Ugg and gy. Edétvoés, however, 
has shown that, by means of the four magniiudes 
determined by his balance, and one or two pendulum 
measurements, the magnitude of g, the force of gravity, 
can be determined throughout a region where the 
earth’s surface deviates only slightly from the equi- 
potential surface through the base point. The balance 
is thus of great service to geodesy. 
In recent years, however, the balance has been 
extensively employed for work having a wider appeal 
than the: problems of geodesy. By its capacity to 
explore the regions below the earth’s surface, not by 
penetrating it but by remaining always on the surface, 
it has proved itself a valuable ally to the geologist, and 
its use is superseding much of the costly boring and 
drilling hitherto necessary in locating mineral de- 
posits. Wherever such deposits differ sufficiently in 
density from their surroundings, and are sufficiently 
extensive to cause appreciable irregularities in the 
gravitational field at the surface above them, the 
balance not only registers their existence, but also 
helps to determine their density, shape, extent, and 
depth below the surface, so that, in favourable cir- 
cumstances, a single boring may suffice to settle any 
remaining doubts regarding the nature and size of the 
deposit. In this work of exploring subterranean dis- 
turbing masses, the same four quantities (Us,—Uj,), 
Uj, Us3, and U,3 are employed, but the influence of all 
known disturbing masses, and the normal field due to 
the size and shape of the earth, must be calculated and 
eliminated before accurate conclusions regarding the 
unknown masses can be drawn. This may be a very 
laborious and complicated process, and may even be 
impossible in unfavourable regions, e.g., where there 
are mountain ranges of an irregular character in the 
vicinity. 
In such regions, however, the variations of strata as 
regards character and shape are frequently sufficiently 
apparent from surface indications to render the use of 
the instrument unnecessary, so that the balance is of 
most use where it is most accurate, namely, in regions 
presenting a regular and comparatively unbroken 
surface, but having important irregularities below the 
surface. 
In this work, certain simple combinations of 
(Usa — U3), Uig, Us, Uys, are more useful than the 
magnitudes themselves. Those mainly used are S, R, 
A, », Where ; 
SwhD A Ups {Un Uj) sec 2A, 
Usg 2U js 
tan p= Us? tan 2A= — Use 
Uj), Uyg, Usg, Uys deter- 
