Peter Mark Roget

“ Since the scale of the instrument presents to view the proportion of logarithms to each other, while the slider represents the ratios of their respective numbers, it becomes a means of illustrating many points relative to the general theory of logarithms, whether to exhibit a series of logarithms formed according to any particular modulus, or by an inverted position of the slider to find the moduli of all different systems, and accordingly in that, for instance, in which the modulus is equal to the basis. ”

“ For in the same manner as numbers are considered as powers of 10, so their indices, whether integral or decimal, being, in fact, numbers, may again be regarded as powers of 10; and their secondary indices, or logarithmic logarithms, may be laid down as logometric intervals, to which other logometric intervals may be added or subtracted mechanically, so as to present to view any multiples or aliquot part of a logarithm, and consequently any powers whatever of the number to which that logarithm is index ”

“ To all cases of geometrical progression the application is obvious for finding the common ratio, the number of terms, or any particular term in the series. An approximate solution is thus given to all questions of compound interest, to regularly progressive increase of population, and to many calculations of chances. ”