The boys from this school are almost uniformly successful in obtaining admission to the École Centrale des Arts et Manufactures, and a fair proportion of them pass the unusually difficult entrance examination of the École Polytechnique.

This young man has a strange name - his name is Badoureau, a vaudeville name - but remember that name, and you will hear it repeated later ...

Two players play a mathematical game together; their probabilities of winning depend on their respective abilities. We will assume that these probabilities can, for each of the players, also take all the values from 0 to 1, because nothing is known about these probabilities when the two players have never played together.

Suppose now that the two players have agreed in advance that the first to win N games will take both stakes; let us suppose that they have won respectively m and n games, m and n being less than N: they stop the game, and we ask how they should share the stake. It is clear that the success of the games played gives some information on the relative strength of the players, and it is by comparing this information with the number of games that each player still has to win, to have definitely won, that we will solve the problem posed.

The purpose of this Memoir, presented to the Academy of Sciences on 25 November 1878, is to make known the result of geometrical research to which I was led by the study of the work of Bravais on symmetry and crystallography, and to Élie de Beaumont on the pentagonal grid. Some of the results which are exposed here had been previously obtained, without my knowledge, in 1808, by Lidonne; in 1819, by an anonymous contributor to the Annales de Gergonne, and finally, in 1862, by M Catalan, in a Memoir presented to the Academy of Sciences and inserted in the Journal de l'École Polytechnique. Lidonne had only enumerated, under the name of Archimedean solids, some of the polyhedra studied later by Gergonne and by M Catalan.

Uniform polyhedra have regular faces meeting in the same manner at every vertex. Besides the five Platonic solids, the thirteen Archimedean solids, the four regular star-polyhedra of Kepler (1619) and Poinsot (1810), and the infinite families of prisms and antiprisms, there are at least fifty-three others, forty-one of which were discovered by Badoureau (1881) and Pitsch (1881).

Thirty-seven of them are due to Badoureau (1881) who systematically considered each of the Platonic and Archimedean solids in turn with a view to finding regular polygons or regular stars on their facial planes or cutting through the interior of these solids.

This is a different approach from that of stellation. If such a polygon is found, it is evident that its vertices coincide with some of the vertices of the related convex polyhedron. The planes of these polygons may intersect.

If portions of the solid are removed symmetrically, another uniform polyhedron may result. This process is called faceting, a sort of reverse of stellating. Stellating implies the addition of cells to a basic polyhedron which serves as a core. Faceting implies the removal of cells, so that the basic polyhedron may still be imagined as a case or enclosing web for the new one.

If there is an undisputed fact today, it is the absolute necessity for all industrialists to know the experimental sciences on which their work is based.

The 'La Bibliothèque des sciences et de l'industrie' was therefore to begin with an overview of the present state of experimental sciences. It is this account that we set out to write. Its publication will have the advantage of freeing the other volumes of the 'La Bibliothèque des sciences et de l'industrie' from some technical developments, which might have seemed a little difficult to some readers.

This work will first include an account of the properties of matter in the different states in which it occurs, an overview of experimental sciences and their most recent progress, and, finally, a very rapid review of the various industries and the very varied aid that they receive from science and return to it in their turn.

Such a synthesis of science and industry would require, to be successful, forces much superior to ours, and in the performance of this work we have often been nearly stopped by discouragement. If, in spite of our efforts, we do not succeed well, we will ask for the reader's indulgence, even because of the goodwill we show in tackling such a vast subject.

Moreover, we have already dealt briefly with the same questions in a speech which we delivered at the Académie d'Amiens on 11 March 1887, on the various objects of human intellectual activity (sciences, letters, arts, religion), and in a glimpse at the sciences that we gave in a conference given on 25 April 1888, to the Société industrielle d'Amiens.

We will endeavour to traverse the vast field of science, as a volunteer whose mission it is to point out the positions conquered and the points on which researchers must concentrate their efforts.

No experiment will be cited, nor any complicated mathematical demonstration, and we will confine ourselves to stating certain facts or probable hypotheses, accompanying this exposition with a few mathematical formulas, which the readers will be able to pass without much inconvenience, if they deem it appropriate.

We will even find in our book the sign of summation $\sum$, the sign of differentiation $d$ and the sign of integration $\int$, and we apologise in advance for the obligation in which we find ourselves to introduce in a popularisation book like this one, symbols which do not yet have the right of citizenship in everyday language. We urge the readers to whom these signs would be frightening to be good enough not to reject far from them the volume which we put in their hands, but on the contrary to read it until the end while passing over the calculations, and while believing us then on the words. The word "infinitely small" is sometimes used in a mathematically inaccurate sense, to designate a quantity which is negligible alongside another quantity.

The novel that we have just presented to the public rests, like all our previous works, on the most serious foundations, despite its ultra-fantastic appearances. After having designed the broad outlines, we asked our friend, M Badoureau, Mining Engineer, author of the learned exposition of 'Experimental Sciences', which has just appeared in the Quantin bookstore, the exact measurement of the various phenomena described in this novel. ...

Were it not for the price of a climb, I would happily do it again every now and then, with or even without a conductor.

... transforming power of beautiful nature! Scandinavia has changed how our learned colleague appears changed to us, it has filled his soul with poetry. - Now we are not used to seeing M Badoureau as a lyric. - You should have heard him speak to us with a new accent of the magnificent countries he visited.

We apologise first for this title which is a little too pretentious: these informal talks are only modest chatter, and, as a philosopher, we are only an old apprentice.

Philosophy sums up and crowns all human knowledge. Before we try to do it, we need to introduce ourselves to the reader. During our long career, we have published in particular: four Notes in the Proceedings of the Academy of Sciences; in 1878 on isosceles figures; in 1884 on the upper light clouds of the atmosphere; in 1890 on sedimentation; in 1893 on the proofs and causes of the Scandinavian uplift; an article in the 'Revue Scientifique' in 1890 on geometric space and algebraic spaces; a speech at the Amiens Academy the same year under a Greek title; and an article in the 'Revue Scientifique' in 1891 on electricity and matter ... In 1889, 1892, 1898, we published three editions of a volume on experimental science. In 1889, 1892, and even 1898, we were young and a little too inclined to take our assumptions for granted. In 1900, we had the pleasure of seeing some of them confirmed by the Congress of Physics. In 1905, we published two articles in the 'Revue Scientifique' under the title: "What is Mechanics?". In 1911, we published a booklet on the atmosphere, terrestrial and air traffic, where we exposed the history of the conquest of the air ...

Gambling is a major cause of loss of activity and time; it absolutely distorts ideas on the value of money and on the fair remuneration of labour and capital; it almost inevitably leads to extravagance and disorder. How many husbands seek hidden income in the game that allows them to meet hidden expenses! ... Gambling is very often the road to debauchery, dishonour and suicide; it is a social disease capable of destroying the habits of order, work and economy which make up France's fortune.

In summary, baccarat is the most dangerous of all games, and the expansion it has had over the past few years, particularly in the casinos of thermal or maritime resorts, must be regarded as a public misfortune; the gambling halls of these establishments are real gambling dens open to all comers and the government would be doing essential moral work by closing them absolutely.