In one respect indeed a very great improvement appeared with the commencement of the 19th century; the number of phytotomists working contemporaneously, checking and criticising one another, became all at once much larger. Hitherto ten or twenty years had intervened between every two works on phytotomy; but in the course of the twelve years after 1800 nearly as many publications followed one another, and scientific discussion enlivened enquiry. Now we meet with a Frenchman for the first time in the field of phytotomy, Brisseau Mirbel, who brought out his ‘Traité d’Anatomie et de Physiologie Végétale’ in 1802, and raised a series of questions in the discussion of which several German botanists, Kurt Sprengel (1802), Bernhardi (1805), Treviranus (1806), Link and Rudolphi (1807), at once took part. It was a step in advance and one affecting all botanical studies, that with the exception of Rudolphi all these men, like Hedwig before them, were botanists by profession; it was at last felt that the examination of the internal structure of plants, as well as the describing them according to Linnaean patterns, was a part of botanical enquiry; it is at the same time true that the botanical knowledge of these observers was often of service to them in their phytotomical investigations, and directed their work decidedly and from the first towards that which was worth knowing, and towards the objects which claimed the first attention. This remark applies to the younger Moldenhawer even more than to the botanists above-named; his ‘Beiträge,’ published in 1812, may be taken as closing the first section of this century, during which time he improved the methods of observation, compared his own observations and those of others with great acuteness of judgment, and did all that could be expected with the microscopes of the time. The period of sixteen years after Moldenhawer, from 1812 to 1828, has nothing of material importance to show in phytotomy. On the other hand, it produced a series of the most important improvements that the compound microscope has undergone since its invention. As early as 1784 Aepinus had produced objectives of flint and crown glass, and in 1807 Van Deyl[72] made similar ones with two achromatic lenses, and still the phytotomists complained of the condition of their instruments. Their figures show that they could not see clearly with them, though the magnifying powers were not high; Link says expressly in the preface to his prize-essay of 1807, that he usually observed with a lens that magnified a hundred and eighty times. Moldenhawer in 1812 gives the preference over all the microscopes he had used to one by Wright, which was serviceable with a magnifying power of four hundred times, while the German instruments, especially those by Weickert, could not be used with higher powers than from one hundred and seventy to three hundred.