The evidence presented is believed to justify the following conclusions: (1) Chromosomal fibers (half-spindle fibers) are in reality pseudopodial-like processes. They are put forth by definite chromomeres, therefore normally are fixed in position. (2) Due to mutation, using this term in a broad sense, some other chromomere may assume this function with a resultant change in position of the spindle processes which does not involve either inversion or translocation of chromosomal segments. (3) At anaphase the processes, beginning with the heavier basal parts, are reincorporated into the sister chromatids as they move towards the poles. (4) The interzonal fibers behave as one would expect under the existing conditions; namely, flexible, viscous protoplasmic rods are separating in such a manner that the final contact is end to end. As these ends separate the viscous protoplasm belonging to each is drawn out between them in varying degree depending on such factors as the rapidity of the movement and the density of the chromatid. (5) Both chromosomal fibers and interzonal fibers are integral parts of the chromosomes and return to them during anaphase without loss of chromatin or linear derangement of their constituents. The work is based on six species belonging to the following four genera of Acrididæ; Trimerotropis, Circotettix, Derotmema and Brachystola. In addition, the paper contains a summary of what are believed to be well-established facts concerning the various components of the mitotic spindle.