164 Scientifie Intelligence. [Fes. 
Nothing new remains to be demonstrated but the other theorem, 
namely, that mo power exists beyond the square, which can be 
divided into two other powers of the same degree. 
A demonstration of this theorem for the fourth power was given 
by Fermat himself, in one of his marginal notes on Diophantus.’ 
Euler afterwards demonstrated in a similar manner the theorem as 
applied to the third power; but we still want a demonstration for 
the higher powers, or for those whose exponent is a prime number, 
for from them all the others may be immediately deduced. 
In this state of things the Class, wishing to pay respect to the 
memory of one of the philosophers who have done the most honour 
to France, and desiring at the same time to give mathematicians an 
opportunity of completing this part of the science, proposes for 
the prize of mathematics to be given in January 1818, the general 
demonstration of the problem stated above. 
The prize will be a gold medal of the value of 3000 franes 
{1251.) : 
' Disturbances of the Planeis.—The Class of Sciences had pro- 
posed as the subject of a double prize, which might be kept in 
reserve, if necessary, till the first of January, 1816, the theory of 
the planets whose excentricity and inclination are too considerable to 
putit in our power to calculate their disturbances exactly by methods 
already known. The Class did not require any numerical applica- 
tion, it required only analytical formulas, lut dispased in such a 
manner, that an intelligent calculator might be able to apply them 
with certainty either to the planet Pallas, or to any other hitherto 
discovered, or which should be afterwards discovered. The period 
of five years, which it had assigned, has just expired. Two me: 
moirs only have been received, the authors of which have not con=" 
formed sufficiently to the intentions expressed in the annunciation 
of the prize. Both (especially one) have left too many analytical 
developements to be executed by the mathematicians who should 
wish to put themselves in a situation to understand and judge of 
the solution of the problem which they have given. They have 
neglected too much to come down to the level ofthe’ calculator, 
who should Wish to form tables of Pallas, or of any other planet. 
The supplements sent at different times are very far from removing 
all the difficulties. 
The Class peceiving by these supplements, and by the notes 
transmittéd by the anonymous authors, that they had not time to 
enter into all the developements necessary; and considering fur- 
ther, that the same cause might prevent cther mathematicians, 
possessed of the requisite knowledge and abilities to treat so difficult 
a subject, from coming forward as candidates, has thought proper 
to prolong the time for deciding the prize for another year. The 
prize will be voted in the meeting of January 1817, to the paper 
which shall fully satisfy the conditions above stated. The prize 
shall be double, that is tosay, a gold medal of the value of 6000 
franes (250/.). The Essay sent to the Institute must be written in 
