=The ‘Institute’ at Yverdon and the Culmination of the Pestalozzian Methods.=--As a result of political changes, Pestalozzi was obliged in 1805 to transfer his school to Yverdon. The ‘institute’ here sprang into fame almost immediately, and increased in numbers and prosperity for several years. Children were sent from great distances, and teachers and visitors thronged there to learn and apply the new principles at home. The work of the institute formed a continuation and culmination of the observational methods started at Stanz and Burgdorf. The simplification introduced through the ‘syllabaries’ and ‘table of units’ was further elaborated. A ‘table of fractions’ was also devised for teaching that subject concretely. It consisted of a series of squares, which could be divided indefinitely and in different ways. Some of the squares were whole, while others were divided horizontally into two, three, or even ten equal parts. There was further developed a ‘table of fractions of fractions,’ or compound fractions, in which the squares were divided, not only horizontally, but vertically, so that the method of reducing two fractions to the same denominator might be self-evident. [Sidenote: drawing,] [Sidenote: writing,] [Sidenote: and constructive geometry;] Further, in order to draw and write, the pupil was first taught the simple elements of form. Objects, such as sticks or pencils, were placed in different directions, and lines representing them were drawn on the board or slate until all elementary forms, straight or curved, were mastered. The pupils combined these elements, instead of copying models, and were encouraged to design symmetrical and graceful figures. This also paved the way for writing. The children wrote on their slates, beginning with the easiest letters and gradually forming words from them, but soon learned to write on paper with a pen. Writing was, however, taught in connection with reading, although begun somewhat later than that study. Constructive geometry was also learned through drawing. The pupils were taught to distinguish, first vertical, horizontal, oblique, and parallel lines; then they learned right, acute, and obtuse angles, different kinds of triangles, quadrilaterals, and other figures; and finally discovered at how many points a certain number of straight lines may be made to cut one another, and how many angles, triangles, and quadrilaterals can be formed. To make the matter concrete, the figures were often cut out of cardboard or made into models. [Sidenote: nature study and geography;] [Sidenote: and music.]