r——_ —  -* — = -« 
June 23, 1923] 
NATURE 
851 

The magnitude S represents the “ maximum gradient 
of gravity in the horizontal surface,” 7.e., the maxi- 
mum amount by which the vertical force of gravity is 
increased as we proceed from the origin through unit 
distance in any direction in the horizontal surface, and 
is obviously the resultant of U,g and Ugg, the gradients 
in the direction Ox, Oy respectively. Also the direc- 
- tion of this maximum gradient is given by p, the angle 
which it makes with Ox. 
The magnitude R is equal to the difference between 
the reciprocals of the principal radii of curvature of 
the level surface at O, and is always positive. Thus, 
if p, is the least radius of curvature at O, and p, the 
greatest, ely 
while A is the angle which the plane of greatest 
_ radius of curvature, or least curvature, makes with the 
plane Oxs. : 
The work of survey consists in finding these values 
S, R, A, » at as many stations as possible, correcting 
them for normal gravity effects and known irregu- 
larities, and plotting the final values, representing 
the maximum gradient S by an arrow drawn through 
the station in the direction », and proportional in 
length to the magnitude of S, and indicating R by 
another arrow in the direction A. The positions, 
directions, and lengths of these arrows are then com- 
pared with the corresponding arrows given by certain 
simple mass distributions of which the effects can be 
calculated, and the probable distribution corresponding 
to the observed results is deduced. 
To illustrate the gravitational effect of a subterranean | 
mass and the variation of the magnitudes measured 
by the balance from point to point on the earth’s 
~ surface above such a deposit, we may consider the 
simple case represented in Fig. 3. Here a horizontal 
layer of matter, having a density greater by unity 
than its surroundings, is bounded on the top and 
bottom by horizontal surfaces at depths 200 and 300 
metres below the earth’s surface. The layer extends 
to infinity in the north, east, and west directions, but 
terminates at the south end in a vertical plane through 
surface on the line where this vertical boundary meets 
the latter, x'Ox the meridian through O, and Oz the 
downwards vertical meeting the faces of the deposit 
in A and B. Consider the force of gravity due to the 
deposit alone—which is thus to be regarded as having 
a density unity—at any point X on x’Ox. The force 
at X will be wholly in the plane xOz, and the corre- 
sponding potential surface through X will be a cylinder 
having its axis perpendicular to this plane. In these 
circumstances the magnitudes U,,, Ujp, etc., specifying 

Fic. 3-—Results for a simple case. 
the disturbing field due to the deposit, can easily be 
calculated. Moreover we have 
Ue = Ung = Ugg =O, 
and therefore 
A=p=0 or7z, 
R=Uy, 
S=Uj,. 
In Fig. 3 the values of U,, are plotted as ordinates 
-corresponding to the abscisse OX in the curve RRR, 
and the values of U,3 in the curve SSS. It will be 
noticed that the point O, vertically above the edge of 
the deposit, is strongly marked in each curve by a 
maximum on one and a zero value on the other. The 
maximum value of S has a magnitude 53 x 10 ® C.G.S. 
units, and the maximum of R is 26x 10~* units. Since 
values of R and S as low as 1x 107° unit affect the 
balance, it is apparent that the instrument would 
readily show the effects due to such a subterranean 
the east-west line. Let O be a point on the earth’s fe and indicate its extremity. 
He 
7 
7 
Science and Industry in Sweden. 
5 sae exhibition recently opened at Gothenburg 
to celebrate the tercentenary of the founding 
of that city by Gustavus Adolphus, with its display 
of Swedish manufactures, is an eloquent reminder of 
the part taken by Sweden in the development of 
certain industries and also of the debt of the world 
to Swedish men of science. Though she cannot lay 
claim to mathematicians of the rank of Leibnitz, 
Newton, or Euler, or to astronomers equal to Galileo 
or Herschel, in chemistry and mineralogy Sweden 
has often led the way, and few countries can boast 
of names more widely known than those of Bergmann, 
Scheele, Gadolin, Berzelius, Nilson, Cleve, and 
Arrhenius. 
The rise of science in Sweden is generally traced 
to Linnzus, but it really had its foundation in the | 
middle of the seventeenth century. Like all the 
western nations Sweden felt the influence of the dis- 
NO. 2799, VOL. 111] 

_ very limited population. 
-coveries of Copernicus, Kepler, and Galileo, and one of 
the objects the young and eccentric Queen Christina had 
in view when she invited Descartes to her capital, 
was to place him at the head of the academy she 
proposed to establish. The plans of Christina, however, 
came to nothing, for Descartes died in 1650 and four 
years later she herself abdicated. 
Sweden has a comparatively large territory but a 
Until recent times there were 
but two seats of learning, Uppsala and Lund. Both 
are still small cities, the former having about 20,000 
inhabitants, the latter some 4ooo less. Uppsala is 
about 4o miles north of Stockholm, while Lund is 
‘not far from Malmo in the extreme south. Lund 
University was founded in 1666, Uppsala in 1476. 
It was in Uppsala that Swedish science had its birth, 
and there it has found its principal home. Johann 
Gestrin and Magnus Celsius (1621-1679) were among 
