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 ;).