Excerpt from Logarithmic Tables of Numbers and Trigonometrical Functions

For tables to five figures the interval of one minute may be considered the proper one, because the differences will not be too large to admit of the proportional part for seconds being men tally calculated with readiness. In tables to seven figures this interval has always been recognized as highly inconvenient, on which account Gardiner directed his attention to the diminution of the interval. It is even necessary to diminish the interval to one second, if it be made a condition that the proportional part in this case too is to be mentally calculated. This very small interval, however, gives rise to several new inconveniences, which diminish the advantage of smaller diflerences to such a degree, that tables of this kind have never come much into use, at least with pro fessional computers. Their large form, the excessive number of columns on every page, and the circumstance that even then there is not nearly room enough for all the figures, (the initial figures of the logarithms having to be placed at the top of the columns and the difi'erences altogether omitted, so that they must be calculated by the computer,) make the advantage of the smaller interval very questionable.

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