Were this an ordinary work we might regard it as due to the author to notice the many excellencies which characterise it, in spite of the defects which we notice. But as our author evidently realises, the eminent dignity of the topic challenges and its singular importance demands unsparing criticism. He who offers to instruct the world on the foundations of geometry draws his sword and throws away the scabbard, and like a doughty champion he will scorn to accept any favor, prizing only such success as he shall take at the point of an efficacy of treatment that conquers all competent and candid criticism. Stringent as are such terms of contest an author who is a worthy competitor in the field of geometric research can be well content with them in the perception that the very same conditions apply in full force to the comments of his critics. The author is undoubtedly an able man and a close thinker. He has concentrated his mind upon a work that is worth the energy of a lifetime. But we must confess our judgment to be that in spite of his capacity and evident devotion he has come short of the high result to which he has aspired. ρσλ. LES FÊTES DE MONTPELLIER. PROMENADE A TRAVERS LES CHOSES, LES HOMMES ET LES IDEES. By _J. Delbœuf_. Paris: Félix Alcan. We have here a charming narrative by the well-known Professor at the University of Liège of his visit to the fêtes of Montpellier, undertaken in great measure to make the personal acquaintance of M. Dauriac, the critic in the _Revue Philosophique_ of the author’s work “La matière brute et la matière vivante.” The description given of the fêtes, which marked the sixth centenary of the University of Montpellier, is very entertaining, as is the account of the journey through the South of France; but as M. Delbœuf says that he was more curious to become acquainted with men than with places, what he tells us about the former will be the more interesting.