1815.) Charles Bossut. 403 
which he afterwards converted into a complete course of mathe- 
matics. He shared with a son and pupil of Daniel Bernoulli 
a prize proposed by the Academy of Lyons on the Best Form of 
Ores ; with the son of Euler, and probably with Euler himself, a 
rize on Stowing Goods in Ships, proposed by the Academy of 
Rsices. “ Complete success would have been less brilliant,’ 
wrote to him Clairaut, one of the judges, “ because in that case it 
would have been unknown over whom you had triumphed.” 
He obtained alone the prize of the Academy of Sciences on the 
question, whether the planets move through a medium, the resistance 
of which produces any sensible effect on their motions. Albert Euler 
had undertaken an examination of the same subject. The two 
authors agreed perfectly in every thing regarding the principal 
planets. But Albert acknowledges that he had not ventured to 
enter upon the part which regards the moon. He congratulates 
Bossut upon having overcome difficulties which appeared to him so 
great as to induce him to abandon the task. It appeared to result 
from the memoir of Bossut that the acceleration observed in the 
motion of the moon might be explained by the resistance of the 
ethereal matter. But one of the great mathematicians of whom 
France has to boast found afterwards a more natural cause, which 
explains this acceleration, and the ethereal resistance has become a 
very problematic cause, the effects of which, if they are not abso- 
lutely null, are at least very little sensible. 
The same year, 1762, Bossut, in conjunction with Viallet, ob- 
tained the quadruple prize proposed by the Academy of Toulouse 
for the most advantageous construction of dykes. Three years after 
he divided a double prize proposed by the Academy of Sciences on 
the Methods of Stowing Ships; and he obtained alone at Toulouse 
two successive prizes for his researches respecting the laws of motion 
which fluids follow in conduits of all kinds. 
He owed to the friendship of Camus the place of Mezieres, 
which had enabled him to turn his undivided attention to mathe- 
matics. ‘The way in which he had filled bis situation and employed 
his intervals of leisure determined in his favour all the votes when a 
successor was to be appointed to his protector and friend. Vhe 
Government named him Examiner of Engineers, and the Academy 
gave him the place which Camus had left vacant. It was at that 
time that he gave his method of summing series, the terms of which 
are similar powers of the sines and cosines of arcs, which form an 
arithmetical progression. 
Euler in his introduction to the Analysis of Infinites had already 
given the sum of those series, which he referred to recurrent series. 
Bossut, in order to arrive at the same result, employs only the most 
elementary formulas of trigonometry, and some rules equally simple 
of the theory of progressions. This method has the advantage of 
being more clear, and therefore intelligible to a much greater 
number of readers. If the glory of a discovery belongs incon- 
testibly to him who first made it known, we cannot refuse a great 
2c2 
