D'ALEMBERT. 443 



giving his own solution more generally and more rigor- 

 ously, but assailed Clairaut's hypothesis. However, this 

 controversy was carried on with much less heat than the 

 former. Geometricians appear to be agreed that in the 

 one case, that of the lunar tables, Clairaut had the 

 decided advantage over his adversary, whose mind did 

 not easily lend itself to such details ; but that the balance 

 inclined in his favour upon the question of the earth's 

 figure, D'Alembert's solution being certainly more 

 general and less dependent upon assumption. His 

 treatise on this subject is universally admired by geome- 

 tricians, and it contains both the differential equations, 

 then first given, of the equilibrium of fluids, and the new 

 and most important theorem upon the relation between 

 the polar oblateness and increase of gravitation on all 

 possible suppositions of the earth's internal structure. 

 Finally, as regards this controversy, so painful to every 

 reflecting geometrician, all men must be satisfied that in 

 point of courtesy and candour there is no comparison 

 between the two combatants. D'Alembert's blunt habits, 

 which were excused in society as marks of simplicity, 

 gave an unpleasant tinge of bitterness to his controversial 

 writings, wholly unworthy of a philosopher, and little to 

 be expected and less to be excused on questions of pure 

 mathematics. 



Let us, for relief from the pain which this portion of 

 D'Alembert's history gives, do, as he did in the actual 

 circumstances, retreat to geometry for comfort and for 

 calm. In the midst of the virulent attacks which his 

 ' Melanges' called forth, and which were at the bottom of 

 his soreness towards Clairaut on very different topics, see 

 how he himself describes the trulv philosophical course 



