The following essay is adapted from one with the same title read to the British Society for the History of Science on 20 October 1958—the anniversary, by a striking coincidence, of the birth of W. H. Young (1863–1942). To his memory I dedicated the talk, and now rededicate its publication, not only because I am his daughter and of all that means, but because he invented a method, the method of monotone sequences, which shows the powerfulness of inequalities as a mathematical tool supremely.

The University of Leyden was founded in 1575 as the reward of the city's endurance of the Spanish siege in 1574. Its influence on botany in the seventeenth and eighteenth centuries is part of its far-reaching influence during this period on medicine, to which botany was then ancillary. In this it was the successor of Montpellier and Padua. The first university founded after the Reformation to practise and maintain religious tolerance towards its students, Leyden became the great international university of Europe, drawing students from Scandinavia, Germany, Switzerland and France, from all parts of the British Isles and the British American colonies (roughly 4,000 English-speaking students between 1600 and 1750) and even from Barbados, Jamaica and Constantinople. It offered facilities for higher education then denied, for example, to dissenters in England or else not available, as in Scandinavia. Owing to this religious tolerance in an age of intolerance and also to the personal eminence of a succession of professors, its influence spread widely. Directly and indirectly, Leyden made its greatest contribution to botany and medicine through the work and personality of Herman Boerhaave (1668–1738) and led to the founding or restoration of botanic gardens at Edinburgh, Göttingen, Uppsala and Vienna. Beginning with Clusius, its influence upon botany may be traced through Hermann and Boerhaave to Haller, Linnaeus, Lettsom and others. No other university has a more sustained and continuous record of service to botany and medicine during these two centuries than Leyden. This paper also touches upon the history of other universities.

Taking Isaac Newton at his own word, historians have long agreed that the decade of the 1660s, when Newton was a young man in his twenties, was the critical period in his scientific career. In the years 1665 and 1666, he has told us, he hit on the ideas of cosmic gravitation, the composition of white light, and the fluxional calculus. The elaboration of these basic ideas constituted his scientific achievement. Nevertheless, the decade of the 1660s has remained a virtual blank in our knowledge of Newton. It need not remain so always. His papers contain a wealth of manuscripts from his undergraduate years and the period immediately following. The first volume of his mathematical papers, which will soon be published, will demonstrate how extensive the information on his early mathematical development is. The development of his non-mathematical studies, especially of what I shall call his scientific studies to distinguish them from the mathematical, can be followed as well—in his reading notes, in his notebooks, above all in the passage in his philosophical notebook labelled Quaestiones quaedam Philosophicae. In this passage we see emerging into consciousness for the first time the questions on which Newton's philosophy of nature was built.

The years between 1660 and 1800 were important ones in the study of light. For most of the period the work, especially in this country, was largely dominated by the theories advanced by Newton; unfortunately the protagonists of these theories were much more rigid in their approach than was Newton himself. There was, in effect, almost a century of ‘rear-guard actions’ to maintain the corpuscular theory at all costs.

Fortunately, the advance of geometrical optics and the design of optical instruments was not retarded to a very great degree by this partisan approach. The workers in these fields were not, as a rule, too involved in speculation, and worked largely empirically.

Some of the modifications to the original corpuscular theory are interesting. Attempts were made to explain, with varying degrees of success, total internal reflection, dispersion, interference effects, diffraction and phosphorescence. Considerable speculation about the velocity of light occurred in connection with these topics. At the same time, wave theories never completely died out and, although they were not developed until the early part of the nineteenth century, their influence was felt even in this country.

George Greenough (1778–1856) was one of the influential group of early nineteenth-century English geologists who rejected both Hutton's and Werner's attempts to propound all-embracing geological theories, and followed a deliberately empirical approach. He travelled through Scotland in 1805, studying geological phenomena in the light of both the Plutonist and the Neptunist theories, and generally concluded that neither was entirely satisfactory as an explanation of the observable facts. He was also the first to suggest that the ‘Parallel Roads’ of Glen Roy were the successive beach-levels of a former lake: this theory was later attacked by Darwin but ultimately vindicated by Agassiz's glacial theory. The more important geological passages from Greenough's MS. journal of the tour are reproduced and discussed in this paper. They illustrate some of the scientific problems that were involved in accepting either Hutton's or Werner's theory entire.

The paper is an attempt to set the social and historical background against which the Royal Institution was founded, and to trace the events in its very early history. The founder of the Institution was Benjamin Thompson, Count Rumford, that soldier of fortune who took service with the Elector Palatine of Bavaria, and it was in the course of his duties in Munich that his interest in the practical problems of philanthropy was aroused.

In London, in the concluding years of the eighteenth century, he was drawn into the group of philanthropists and reformers among whom William Wilberforce was the leading figure, and Sir Thomas Bernard, Treasurer of the Foundling Hospital, one of the most active members. The focus of their activities was the Society for Bettering the Condition and Increasing the Comforts of the Poor, and to this Society Rumford submitted his proposals for a new scientific institution in London, designed to improve the lot of the poor and the working classes by the application of science to useful purposes.

It was decided to make an appeal for funds, Rumford's proposals were circulated, and the Count succeeded in interesting the President of the Royal Society, Sir Joseph Banks, who took the Chair at the early meetings and allowed them to be held at his house, 32 Soho Square. At a meeting held there on 7 March 1799, the new institution was formed by resolution of the subscribers of 50 guineas each, who became the first Proprietors of the Royal Institution of Great Britain, as it was afterwards named in its Royal Charter.