146 Royal Academy of Sciences of Brussels. 
thered before it is quite ripe. In this state it is of a geeenish eo- 
lour, and in form like an almond or elongated pear; the pulp, 
which is soft, agreeable to the taste, and of easy digestion, in- 
closes a stone like that of a plum, but smaller and harder. - The 
wood of the Persea is dense, and of a fine black colour, and is 
used for making tables and statues.” 
Prize Questions proposed by the Academy for 1820: 
To form by the theory of universal gravitation alene, and with- 
out taking from observstions any thing but arbitrary elements, 
tables of the movement of the moon as exact as the best tables 
in existence. 
- The following theorem of Fermat :—‘ Beyond the second de- 
gree there exists no power which may be divided into two other 
powers of the same degree.” 
The prize for each question is a gold medal of 3000 frances 
value, and the Ist of January 1820 is the latest time allowed 
for the reception of memoirs. 
ROYAL ACADEMY OF SCIENCES AND BELLES LETTRES OF 
BRUSSELS. 
The following questions have been proposed by this Society 
for competition in the Class of Sciences during the year 1819: 
l. If to each of the angles of a plane perfectly square, from 
the centre of which a certain weight P {say of 100 lb.) is sus- 
pended, a cord be attached, which passes vertically on a pulley ; 
and if each of these cords be charged with such a weight, as that 
Jirst, the sum of the four shall be equal to 100 lb.; and second, 
that the weights attached to each of the two angles diagonally op- 
posite, shall be equal to each other; as for example, two of them 
49 lb., and the two others one pound each, and so through an 
infinite series of numbers—it is known by the ordinary rules of 
statics, that this plane will remain horizontally in equilibrio. 
On the other hand, if these four cords, instead of being thus load- 
ed with weights, and passing ora pulley, are fixed to an immove- 
able board, it is obvious, but only on the metaphysical principle, 
that wherever there is a perfect equality of efficient causes, the 
effects are also necessarily equal; that the portions of the weight 
P, borne by each of these four points, will also be exactly equal 
to each other. 
The point then is, to assign a principle truly physical—that 
is to say, founded on the properties of matter alone, from which 
there may result, among the infinite series mentioned above, re- 
lations among the four weights all equally proper to establish the 
equilibrium in the first hypothesis, and the preference which the 
relation of equality bears in the second—that is to say, when 
the distribution of the force to sustain depends actively and 2 
tirely 
