“Mr. John T. Graves on the Logarithms of Unity. 281 
pulsive,) since the only direction in which the mass ‘could ad- 
mit of any tension being impressed upon it would be, as just 
stated, that parallel to the first system. It seems to be me- 
chanically impossible that any second system of parallel fissures 
could be thus formed except in the direction here stated. 
[To be continued.] 
LVII. On the lately proposed Logarithms of Unity, in Reply 
to Professor De Morgan. By Joun T. Graves, of the Inner 
Temple, Esq., M.A. 
To the Editors of the Philosophical Magazine and Journal. 
GENTLEMEN, 
| the Philosophical Transactions for 1829, and in the abs- 
tract of a memoir printed in the Fourth Report of the 
British Association, it is proposed to modify the ordinary 
formule for the logarithms of unity and of numbers in general 
by certain rather startling extensions. These innovations 
Prof. De Morgan is not disposed to admit, as appears from sec- 
tions (158.) and (245.) of his able and useful Treatise on the 
Calculus of Functions, recently published in the Encyclopedia 
Metropolitana. His principal difficulty seems to be founded 
Qin 
on his dissent from the proposition that e 247-vW—-1 = i, 
and accordingly be challenges the supporters of the new 
theory to the proof of that equation. Now in one sense I do 
Qin 
not either assert or admit its accuracy; for e2t™—W—1 has 
many values, while 1 has only one. I am bound, however, 
Qin 
to show that 1 is among the values of e2in— V¥—=1, To 
show this would be to prove, that, according to my under- 
standing of the term, tho is a Neperian* logarithm 
of 1. Icall} an e-log. of —1/e as wellas of +c. If 
I am told that logarithm ought to be so defined that x ought 
to be called an a-log. or a logarithm to base a only of the® 
* I have been accustomed to write “ Neperian” instead of “ Napierian,” 
because the inventor of logarithms, in the title of his original work on the 
subject, signs his name in Latin, “ Neperus”’ ; because the Scottish mode 
of spelling the name was unfixed in his time, and because foreigners have 
generally adopted the Latin orthography. 
Third Series. Vol. 8. No. 47. April 1836. 2G 
