Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. This process of finding the logarithms of large numbers supposes that they increase in the same ratio as their' numbers, which is not strictly true, though sufficiently near the truth for general practice. It may be remarked, however, that these ratios approach that of equality, the larger the num bers, and the less they differ from each other.