The natural logarithm (log base e) used to be called the *hyperbolic logarithm* (see here).
Other than the understandably old fasioned notation, Gompertz article is wonderfully written, so much so that I can follow all his math, even with the strange notation (although obviously I had to look hyperbolic logs up).
He makes a number of brief excursions to set up the problem, including a reference to "the great age of the patriarchs of scripture".
He even takes a break to clarify his exponent notation. I love this guy.

All the non-symbolic math was starting to confuse me, so I went back and Googled a bit more, turning up this paper which claims to help fit the Gompertz distribution, and even (gasp) uses the same Gompertz distribution that Gompertz does :p. It even talks about probability density functions. I dunno if I'm ready for another relationship yet though, I've been hurt so many times before ;).