ASTRONOMY. 
223 
(*) 1. Whilst this law prevails between each particle 
of matter, the united attraction of a sphere, composed of 
that matter, observes the same law. This property of the 
law is necessary, to render it applicable to a system com¬ 
posed of spheres, but it is a property which belongs to no 
other law of attraction that is admissible. The law of va¬ 
riation of the united attraction is in no other case the same 
as the law of attraction of each particle, one case except¬ 
ed, and that is of the attraction varying directly as the dis¬ 
tance;* the inconveniency of which law, in other respects, 
we have already noticed. 
We may follow this regulation somewhat farther, and still 
more strikingly perceive that it proceeded from a designing 
mind. A law both admissible and convenient was requisite. 
In what way is the law of the attracting globes obtained? 
Astronomical observations and terrestrial experiments 
show, that the attraction of the globes of the system is made 
up of the attraction of their parts; the attraction of each 
globe being compounded of the attractions of its parts. Now, 
the admissible and convenient law which exists, could not 
be obtained in a system of bodies gravitating by the united 
gravitation of their parts, unless each particle of matter 
were attracted by a force varying by one particular law, 
viz. varying inversely as the square of the distance; for, if 
the action of the particles be according to any other law 
whatever, the admissible and convenient law which is adopt¬ 
ed could not be obtained. Here then are clearly shown reg¬ 
ulation and design. A law both admissible and convenient 
was to be obtained: the mode chosen for obtaining that law 
was by making each particle of matter act. After this choice 
was made, then farther attention was to be given to each 
particle of matter, and one, and one only particular law of 
action to be assigned to it. No other law would have an¬ 
swered the purpose intended. 
(*) 2. All systems must be liable to perturbations. And 
therefore, to guard against these perturbations, or rather to 
guard against their running to destructive lengths, is per¬ 
haps the strongest evidence of care and foresight that can 
be given. Now we are able to demonstrate of our law of 
* Let A, Fig. 5, Plate XXXIX, represent a sphere composed of par¬ 
ticles, which mutually attract each other with a force, which varies re¬ 
ciprocally as the squares of the distances ; their united attraction, on a 
similar particle P without the sphere, will be according to the same law 
that is, the particle will be attracted towards the sphere with a force, 
which will also vary reciprocally as the square of C P, its distance from 
the centre of the sphere.— Paxton. 
