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LIFE, WRITING S, and

the number xo. Then the last logarithm 1024 and the fuccefilve quo-tients divided (ten times) by the number 2, will give these (ten) loga-rithms 5x2, 256, 128, 64, 32, 16, 8, 4, 2, i, &c. to which the respec-tive correspondent numbers may be found, by extracting the squareroot, the square root of the square root, the square root of the squareroot of the square root, &c. of the number (found as above directed)corresponding to the logarithm 102-4. By addition these (twenty) lo-garithms, and by multiplication their respective natural numbers servefor finding a great many other logarithms and their numbers*

The second method is this: The logarithms (o and 10000000000 forexample,) of any two numbers j and 10 being given, the logarithmof any intermediate number (2 for example) may be found by takingcontinually geometrical means, first between one of these numbers (10)and this mean, then between the same number (1 o) and the last mean,and so on till there be found the number (2) wanted ; of winch the lo-garithm will be the corresponding arithmetical mean (30x0209957) be-tween the two given logarithms (o and 10000000000).

The third method is as follows: Suppose the common logarithm ofa number not an integral power of 10 (2 for instance) find the num-ber of figures in the 10th, :00th, 1 oooth, &c. power of that number;The successive numbers of figures (4, 31, 302, 3011, Lee.) in these pow-ers (2 10 , 2 100 , 2 ICO °, 2 10000 , &c.) will always exceed by less than unity,but continually approach to the logarithm [30x02999566, &c.] re-quired.

Tks