Dumbleton was one of the first to express functional relationships in graphical form. He gave a proof of the mean speed theorem stating that "the latitude of a uniformly difform movement corresponds to the degree of the midpoint" and used this method to study the quantitative decrease in intensity of illumination, stating that it was not linearly proportional to the distance, but was unable to expose the Inverse-square law, which was postponed nearly 250 years until its discovery by Johannes Kepler in 1604.