Page:The Construction of the Wonderful Canon of Logarithms.djvu/119

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Notes, 95


Logarithms computed by Napier's
Method.
Logarithms computed by
Present Method.
1.000000050000005000000500 1,000000050000003
100.000005000000500000050000 100.000005000000333
100.000500003333525000225002 100.000500003333358
5000.025000166676250011250094 5000.02500016667917
5001.250416822987527739839231 5001.250416822979193
100025.008336459750554796784618 100025.008336459583854
100503.358535014579332632226320 100503.358535014411835
6834228.380380991394618991389791 6834228.380380980004813
6934253.388717451145173788174409 6934253.388717439588668
6931471.805599464646041962236367 6931471.805599453094225
23025850.929940495214660989152136 23025850.929940456840180

this, the Magnus Canon may safely be used to correct the figures in the text and in the Canon of 1614, as the latter is to one place less.

I find no reference by Ursinus to the discrepancies between the logarithms of the two Canons. The mistake in the Second table may possibly not have been observed by him, as the preparatory tables for the Canons were different.

The mistake was observed by Mr Edward Sang in 1865, when recomputing in full the preparatory tables of Napier’s Canon to 15 places.

It had been previously pointed out by M. Biot, in his articles on Napier in the ‘Journal de Savants’ for 1835, p. 255. The following

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