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construction of

TRACT 21.

give 100'000005, for tlie logarithm of 9999000'0()019.50, thelast of the said 100 proportions.

Then, by the 2d theorem, it easily appears, that '0004950is the difference between the logarithms of 9999900'0004D50and 9999900, the last term of the first table, and the 2d termof the second table; this then being added to the last loga-rithm, gives 100'0005000 for the logarithm of the said 2dterm, as also the common difference of the logarithms of allthe proportions in the second table; and therefore, by conti-nually adding it, there will be generated the logarithms of allthese proportionals in the second table ; the last of which is5000'025, answering to 999500T222927, the last term of thattable.

Again, by the 2d theorem, the difference between the loga-rithms of this last proportional of the second table, and the2d term in the first column of the third table, is found to beI•223538'?; which being added to the last logarithm, gives5001'24S53S7 for the logarithm of 9995000, the said 2d termof the third table, as also the common difference of the loga-rithms of all the proportionals in the first column of thattable; and that this, therefore, being continually added, givesall the logarithms of that first column, the last of which is100024'97077, the logarithm of 9900473'5780, the last termof the said column.

Finally, by the 2d theorem again, the difference betweenthe logarithms of this last number and 9900000, the 1st termin the second column, is 478'3502; which being added to thelast logarithm, gives 100503'3210 for the logarithm of thesaid 1st term in the second column, as well as the commondifference of the logarithms of all the numbers on the sameline in every line of the table, namely, of all the 1st terms,of all the 2d, of all the 3d, of all the 4th, &c, terms, in all thecolumns; and which, therefore, being continually added tothe logarithms in the first column, will give the correspondinglogarithms in all the other columns.

And thus is completed what the author calls the radicaltable, in which he retains only one decimal place in the loga-