For many years past great efforts have been made to devise methods of obviating the necessity for making navigational calculations by logarithms, on the grounds that the logarithmic process is too slow for modern navigational purposes. For some such purposes it undoubtedly is; but all these short methods suffer from some disadvantage or other, and when the preliminaries (which generally involve calculating the hour angle) common to both are completed, the difference in time between completing the sight by inspection and interpolation, and by logarithms, is not so great. For this reason it seems possible that logarithms would still be considered preferable for a wider range of purposes than at present, were it not that most of the volumes of logarithms still commonly used for navigation are designed for more accurate calculations than are necessary or justifiable for the practice of navigation, and hence are unnecessarily cumbrous and slow in use.