PHYSICAL ASTRONOMY. 125 
axis, or half the axis of rotation to 3261139.33 toises (20,853,681 English 
feet). Consequently the flattening of the earth’s spheroid amounts to 
almost 515. 
45. One important consequence of the centrifugal force is the local 
_ variation of gravity. It has actually been observed that there is a difference 
in the gravity or weight of the same body, when brought in succession to 
places of different geographical latitude. The methods by which these 
variations of gravity can be indicated, and their magnitude determined, are 
both statical and dynamical. The statical method consists in bringing the 
gravity of the weight in equilibrium with some natural force of entirely 
different character, upon which the local situation exerts no influence. 
Such a force is the elasticity of a spring. Let ABC (pl. 6, fig. 10) repre- 
sent a strong beam of brass, standing on a firmly connected foot, AED. In 
this latter a flat plate of agate is inserted, and the whole foot rendered 
capable of being placed in a perfectly horizontal position by a water-level. 
To C is fastened the spiral spring G, carrying at its lower extremity the 
polished weight F, the length and strength of the spring being so adjusted 
that, even in the highest geographical latitude, the weight attached shall not 
at any time touch the agate plate D. If now the apparatus in perfect order 
be carried to a place of Jess geographical latitude, and again erected, it will 
soon be perceived that the weight F, loaded with the same additional 
weights as before, will no longer have power to stretch the spring to the 
degree necessary for bringing about contact between the weight and agate 
plate. It will therefore be necessary to add more weight, and this addition 
will evidently measure the difference of gravity in the two places, in so far 
as it operates on the sum of the suspended matter, that is, upon the sum of 
the weight F’, and the half weight of the spiral spring G. 
The dynamical method, on the other hand, consists in determining the 
velocity which is communicated in a second to a freely-falling body, by that 
force which draws a given heavy body to the earth. This velocity can 
only be determined indirectly by observations, as the oscillation of a pendu- 
lum. It is shown by the laws of mechanics, that when the same pendulum 
oscillates in two different places, and consequently under the influence of 
different forces of gravitation, the intensities of gravitation will be to each 
other as the squares of the numbers of oscillations made in a given time, 
and hence their ratio is readily determinable. 
Compound Motion; Parallelogram of Forces. 
46. Two or more forces acting on the same body in different directions 
cause it to assume a compound motion. If, however, these forces act on 
each other in such a manner that no motion can result to the body, they 
are said to hold one another in equilibrium. If any two forces act upon the 
same body in directions forming a known angle with each other, and with 
known intensities, it is evident that in its course it can obey exclusively 
neither the one nor the other of these forces. We must therefore investi- 
125 
