The lognormal distribution

The context of this little mishap was that apparently (Kazil et al., 2007), aerosol in cirrus cloud was defined by a size distribution with a geometric mean of 62.5 nm (diameter) and a geometric standard deviation of 1.45 nm. So I figured that since the lognormal distribution is defined:

f(x) = 1 / ( x sigma sqrt[2 pi] ) * exp ( - [ ln x - mu ]^2 / [ 2 sigma^2 ] ) ,

that it was a simple case of using mu = 62.5 and sigma = 1.45 and I would have defined f(x). This was giving very weird results though, until I realised that mu is not the geometric mean and sigma is not the geometric standard deviation. Instead:

geometric mu = exp(mu)
geometric sigma = exp(sigma) .