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If we take a series of ophiuroids ranging from forms with indirect, larval development to those with direct, non-larval development, and place their eggs in order of increasing volume, a remarkable fact at once becomes obvious (see Table II). It is found that the eggs of small volume fall into a group the common character of which is the possession of a long period of indirect development involving a pelagic Ophiopluteus stage and metamorphosis. The largest eggs form another group whose common character is the absence of indirect development, the loss of the larval stage, and no metamorphosis. Eggs of intermediate size form a third category exhibiting intermediate stages in the suppression of the larval development. This we can express as a simple and fundamental principle—“The degree of larval development of an embryo varies indirectly as the volume of the egg from which the embryo is derived.” Grave (1916) anticipated this “law,” but as no cases of completely direct development were known at that time, and the development of only two ophiuroids had been worked out, he was unable to express the fact in a full or convincing manner. His work will be further considered below.

The same relationship between egg-size and development appears to hold good in the other four classes of living echinoderms, but in no case is there as yet so complete a series as is now known from the Ophiuroidea.

In my previous paper on the development of Kirk's ophiuroid (1941) it was suggested that the immediate ontogenetic factor causing the direct development and unexpected method of development of the organs might be the presence of yolk material in the tissues of the developing embryo. The yolk material, it was suggested, might act as a retarding agent, being inert and lifeless. This interpretation of the effect of yolk material accords well with the facts revealed by the sequence of egg types shown in Table II, for in all the cases it is the larger eggs—and consequently those with the greater amount of nutritive material—which have direct development.

In the literature it has been customary to speak of eggs as being “yolky” or “very yolky” or “not yolky”—a method of description which is necessarily inexact. It seemed to the writer that a more precise definition of these arbitrary terms would be of use in determining more accurately the influence exerted by the yolk. Accordingly the following method of quantitative estimation of yolk content in minute eggs was devised, and proved susceptible to mathematical treatment. Sections of known thickness were cut through the egg of an ophiuroid whose yolk content it was desired to estimate. Haematoxylin was used to stain the yolk granules deep black. Then, by using a squared eyepiece the average number of granules in an area of known size was f oxind. Knowing the thickness of the section, it was then possible to calculate the number of granules in a given volume of egg. Next the average diameter of the yolk granules was estimated, and, combining this result with the former, it was possible to estimate approximately the actual volume of yolk material in a given volume of egg. In practice the yolk was estimated as a percentage of 100 cubic microns of egg material. Knowing the average diameter of the egg, it was then possible to determine the absolute volume of yolk material present in the entire egg.

A calculation made in this way shows that in Kirk's ophiuroid there exists in the egg approximately 5.3 × 10⁶ cubic microns of yolk material.

A similar estimation for Amphipholis squamata, a form with only “moderately yolky” eggs, yields a figure of circ. 8.8 × 10⁴ cub. μ. Thus we have a much more clear-cut picture of the relative “yolkiness” of these two types of egg, and can now proceed to compare the yolk value with the other variables.

Tabulating the yolk value against the diameter of the egg, as in Table III, it is seen that in these examples yolk content increases with size of egg. This, of course, was merely what has usually been assumed hitherto, though without actual demonstration.

Having noted that the yolk increases with increasing diameter of the egg, we can now consider the case in regard to the cytoplasm. In this matter the literature provides no information. The tendency, however, has been to suppose that in large, yolky eggs the cytoplasm becomes proportionately reduced, remaining more or less constant in amount while the yolk increases. This attitude is maintained by Grave (1916) who also states that it is impossible to measure the ratio of yolk to cytoplasm. In his latter statement he is, of course,

incorrect, since it is possible to make such, measurements by the method described above. In the calculation illustrated, at the stage when the yolk-volume per 100 cubic microns was estimated, the resultant is also automatically an expression of the percentage content of yolk of the whole egg. By a simple subtraction, therefore, we obtain an expression of the percentage content of cytoplasm—ignoring the nucleus in both measurements. Taking now the cytoplasm value as a percentage of egg-volume, it is clear from Table III that comparatively little change in the ratio of cytoplasm to yolk has taken place in the transition from smaller egg-size to larger. This means that as the amount of yolk has increased, so also has the amount of cytoplasm, keeping pace each with the other. The older vague methods of describing “yolky” and “less yolky” eggs failed to bring out this fact, and hence the mistaken notion that the yolk increased and not the cytoplasm. It is therefore necessary to modify the conclusion expressed in my earlier paper on Kirk's ophiurpid (1941) in regard to the influence of increasing yolk-mass, by adding that the effect is associated with a parallel increase in the cytoplasm.

FIG. 1.—Graph showing interrelationship between size of egg, amount of yolk, and type of development in the Ophiuroidea. A, Ophiothrix fragilis and Ophiocomina, nigra; B, Amphipholis squamata.; C, Ophiura, brevispina; D, Ophiopus arcticus; E, Kirk's Ophiuroid; P, Ophiomyxa brevirima.