To begin at the beginning, Euclid built up a system of geometrical theory two thousand two hundred years ago. What perfect clearness there is in his logical procedure! The logic is not only sound, but evident. No wonder that Spinoza wanted to write a geometry of ethics ; the reason was that he wanted a perfect logical sequence.

The following paper was read at the meeting of the London Branch, which took place on the 8th of March last at the London Day Training College. It contains in outline the substance of the first few chapters of A School Course in Geometry, to be published shortly by Messrs. Longmans, Green & Co. Many details, necessarily omitted in a short preliminary paper, will be found fully treated in the forthcoming volume.

It occasionally happens that logarithms and anti-logarithms are required to many figures, and in default of tables must be calculated. If a series of such logarithms are required, they are probably most easily obtained by interpolation between nntnbers, the logarithms of which have been calculated to many figures by Briggs, Gardiner, Sharp and others.

If only a few values aro required, this method is practically inapplicable, since it is tedious and requires somewhat large tables. Many ingenious methods have been suggested to meet such cases, but in general they necessitate special artifices and tables, which require considerable practice to use with safety.