History of chemistry
An important breakthrough in making sense of the list of known chemical elements (as well as in understanding the internal structure of atoms) was Dmitri Mendeleev's development of the first modern periodic table, or the periodic classification of the elements. Mendeleev, a Russian chemist, felt that there was some type of order to the elements and he spent more than thirteen years of his life collecting data and assembling the concept, initially with the idea of resolving some of the disorder in the field for his students. Mendeleev found that, when all the known chemical elements were arranged in order of increasing atomic weight, the resulting table displayed a recurring pattern, or periodicity, of properties within groups of elements. Mendeleev's law allowed him to build up a systematic periodic table of all the 66 elements then known based on atomic mass, which he published in "Principles of Chemistry" in 1869. His first Periodic Table was compiled on the basis of arranging the elements in ascending order of atomic weight and grouping them by similarity of properties.
Annuity (European)
"Commutation tables", aptly so named in 1840 by Augustus De Morgan (see his paper "On the Calculation of Single Life Contingencies," "Assurance Magazine", xii. 328), show the proportion in which a benefit due at one age ought to be changed, so as to retain the same value and be due at another age. The earliest known specimen of a commutation table is contained in William Dale's "Introduction to the Study of the Doctrine of Annuities", published in 1772. A full account of this work is given by F. Hendriks in the second number of the "Assurance Magazine", pp. 15–17. William Morgan's "Treatise on Assurances", 1779, also contains a commutation table. Morgan gives the table as furnishing a convenient means of checking the correctness of the values of annuities found by the ordinary process. It may be assumed that he was aware that the table might be used for the direct calculation of annuities; but he appears to have been ignorant of its other uses.