INTRODUCTION The Farlow Herbarium of Cryptogamic Botany at Harvard University houses substantial collections of diatom exsiccatae from the nineteenth and early twentieth centuries - c. 30,000 "samples." Many of these collections are unique, such as, the collections of the professional American diatomists Jacob W. Bailey (1811-1857) and William A. Terry (1828-1917), the Boston Society of Natural History (1854-1885), and serious amateur collectors. However, a large number of sets at the Farlow are not unique - they are published. Published exsiccatae were issued as replicates, and specimens in [a published] exsiccata can be cited as precisely as a passage in a book, and 'copies' will be found in several or many herbaria" [Sayre, Geneva. Cryptogamiae Exsiccatae -- An Annotated Bibliography of Published Exsiccatae of Algae, Lichenes, Hepaticae, and Musci. Mem. N. Y. bot. Gard., 19 (1969)]. More than fifty sets of published cryptogamic exsiccatae cited in the Sayre bibliography, which purportedly contained diatoms and/or algae, were examined, and thirty-four of these were found at the Farlow and contained diatom determinations (see pp. 4-8 for a listing). Sixteen algal exsiccatae also at the Farlow contained no diatom determinations; these are listed on pp. 8-9. Two major diatom exsiccatae cited by Sayre but not possessed by the Farlow have been omitted from this work; these are described on p. 9. Based primarily upon a detailed, sheet-by-sheet and slide-by-slide, examination of specimen labels and published indexes, over 13,000 records of associations between diatom taxa and geographical localities were tabulated from these published exsiccatae. I have shaped that information into the taxa and locality indexes that form the bulk of this work. Although much of this information has probably been available in various forms at leading diatom herbaria, I have endeavored in this work to collate this information and to disseminate it more broadly with the intent of promoting the use of these exsiccatae in diatom studies at the Farlow and other herbaria. The function of these indexes is simply to facilitate access to exsiccatae so that they might be examined - specimens, labels and all. The indexes are not intended to replace a first-hand examination of the exsiccatae. Bearing that in mind, the user should understand that the records in these indexes consequently display no necessarily literal fidelity to the labels. I have judged it desirable that an index should bring together specimens from the same locality, on the one hand, and specimens of the same taxon, on the other. Such a cohesion is unlikely if descriptions are treated literally. Orthographic variants and errors, a multilingual set of diatomists, and changes in the names of places over a century militate against a natural cohesion of the same elements. Consequently, I have molded what I have found in these sets of exsiccatae to accomplish this end. In straying from the path of literalness I have left in all cases a heavily annotated trail, so that the changes I have made and the exsiccatae which were affected are both clear. In addition, I have annotated the indexes to display connections among taxa and among localities, but I have limited the notes to connections that were explicitly expressed in the exsiccatae themselves. I have not examined microscopically any of the specimens cited in these indexes in the preparation of this work. The truth of the claim made by the slide label that H.L. Smith exsiccata slide 245 bears specimens of Navicula amphibiaena Bory is unknown to me. The truth of the claim based on the slide label that Cleve & Mölier slide 274 contains specimens from Bemis Lake in New Hampshire (United States) is unknown to me. Belief in the truth or falsity of claims rests upon arguments, and this work contains absolutely no arguments. Also, the names of taxa and geographical localities under which I have chosen to assemble the specimens in these indexes must be judged as arbitrary, although their choice has not been capricious. These names should not be viewed as effectively published, valid, recommended or society-certified; each such claim, if made, would again require an argument. I have indexed claims or reports and little more. Find herein means, not ends.