  It has long been known that scientific output proceeds on an exponential
increase, or more properly, a logistic growth curve. The interplay between
effort and discovery is clear, and the nature of the functional form has been
thought to be due to many changes in the scientific process over time. Here I
show a quantitative method for examining the ease of scientific progress,
another necessary component in understanding scientific discovery. Using
examples from three different scientific disciplines - mammalian species,
chemical elements, and minor planets - I find the ease of discovery to conform
to an exponential decay. In addition, I show how the pace of scientific
discovery can be best understood as the outcome of both scientific output and
ease of discovery. A quantitative study of the ease of scientific discovery in
the aggregate, such as done here, has the potential to provide a great deal of
insight into both the nature of future discoveries and the technical processes
behind discoveries in science.
