A METHOD

OF

COMPUTING THE COMMON LOGARITHM

OF A NUMBER WITHOUT MAKING USE OF ANY LOGARITHM BUT TH AT OF SOME POWER OF 10,

By Artemas MARTIN (W ashington).

The sériés usually given in text-books on Algebra for the computation of Logarithms contain, at least, the logarithm of one other number besides tlie one sought, and lherefore necessitate the use of a Table.

It is the object of ibis paper to deduce from the ordinary logarithmie sériés, converging sériés for the computation of the common logarithm of any given number independent of any other logarithm but the logai’ithm of i om, which is readily seen by inspection to be m.

I s h a 11 make use of the various known forms of logarithmie sériés without stopping to show how they were deduced.

I. In the well-known sériés

loge(a H- x) = logea -f

X

a

logc(a

x) = logea —

x

a

put a= iom; then will

(G

(U)

log10(ïom-T- x) = m-+- A1

log10(io"î— x) = m — M

where M = 0,43429448190325182765 Brigg’s logarithms.

the modulus of common or

---

Le texte affiché peut comporter un certain nombre d'erreurs. En effet, le mode texte de ce document a été généré de façon automatique par un programme de reconnaissance optique de caractères (OCR). Le taux de reconnaissance estimé pour cette page est de 84,87 %.

La langue de reconnaissance de l'OCR est le Français.

---