In Fig. 7 is shown a cross section of the sphere turning rest further illustrated in Fig. 4. In machining this the following suggestions should be followed. The piece M should be cast with a lug projecting from the face PQ to chuck it by and all the turning done at one chucking. It should be made a close fit to R and bolted tight against DG and ED´ with the bolts S_{3} and S_{4}, clearance being given along the line HF. To compensate for ware the face DG and ED´ can be releaved from time to time with a file. The base N, should be planed along AB, where it fastens to the cross slide of the carriage, then bolted to a face plate of the lathe and finished, care being used to leave the setting of the compound rest unchanged between machining the faces CD and C´D´ of the pieces M and N. The dove tail on R should be first planed and then this bolted to a face plate and the boss GHFE and the faces KG and EL turned at one setting. If these directions are followed almost no hand work will be needed. W is a brass worm wheel held by screws not shown and J is the sliding tool post clamped at X with the tool at K´. NOTES ON THE ZYGNEMALES.[A] EDGAR NELSON TRANSEAU. The following notes principally concerning North American Zygnemales are based on a study of the specimens accumulated in the course of eight years collecting in central Illinois; a collection made by Mr. Charles Bullard, of Cambridge, Mass., in Massachusetts and New Hampshire; the specimens distributed in the Phycotheca Boreali-Americana by Collins, Holden and Setchell; the specimens distributed in American Algae, by Miss Josephine E. Tilden; the specimens in the U. S. National Herbarium; and small collections sent me by Professor Farlow, Miss Tilden, Professor A. B. Klugh, Professor D. S. Johnson and Miss Grace Stone. They have been compared with the species distributed by Wittrock and Nordstedt in their “Algae Aquae dulcis exsiccatae,” and other valuable European and South American specimens sent me by Professors O. Borge and O. Nordstedt. In determining almost any species of the Zygnemales it is absolutely essential that the specimens show both the vegetative cells and the mature spores. With the exception of a few species of Mougeotia the spores are colored either yellow, brown, or blue when they are mature. The characteristic markings of the median spore wall do not develop usually until this color appears. Consequently it is useless to attach names to vegetative specimens based on dimensions and number of chromatophores. Keys based on such characters are not only useless, but misleading.