273 
filament is indefinitely and progressively lengthened, as compared 
with the rate of increase of the surface of a disk of similar volume 
indefinitely and progressively flattened. Everything is therefore in 
favor physiologically of the discoidal form of a mass of plasma as a 
hemoglobin bearer over and above that of a filament or any other 
shape whatever. The advantages which accrue to the discoidal 
form of the blood-corpuscle over a hypothetical filamentous form 
are thus seen to be conditioned by the geometrical laws which hold 
in respect to the progressive and equal change of the ratios of two 
of the dimensions of a solid or fluid body as compared with an un- 
equal change in its third dimension, provided there is no change 
of volume. 
This form of the blood-corpuscle by means of which its area is 
increased is also one which involves the conception that the 
average path traversed by all of its constituent particles is less than 
that by means of which it would be transformed into a filamentous 
body. A further conclusion derivable from this fact is that in the 
transformation of the globular embryonic blood-cell there is less 
expenditure of energy involved in transforming it into a disk than 
if it were transformed into a filament. There is therefore an actual 
saving of energy consequent upon transforming the primitively 
globular blood-cells into disks instead of into filaments. Viewed, 
therefore, as a kinetic problem alone, it can be proved that the 
discoidal shape of the blood-corpuscles of vertebrates requires the ex- 
penditure of a relatively small amount of energy as compared with 
that of any other form that might be assumed. 
Notwithstanding this fact, however, there has been an extension 
of the disks of many forms in one of their dimensions, so that in 
the greater proportion of vertebrates, including birds, reptiles, 
batrachia and fishes, the red corpuscles are elliptical, while in a 
mollusc Arca they are flattened and pyriform in outline. Nowhere, 
however, does the eccentricity of the elliptical form of the corpuscles 
develop great proportions ; in fact, I know of no instances in which 
the great diameter of an elliptical corpuscle is as great as twice its 
least diameter. The law enunciated in the preceding paragraphs 
therefore still holds essentially even in those cases where the cor- 
puscle becomes quite markedly elliptical, since nowhere does this 
ellipticity reach such an extreme as to become the expression of an 
extension of the substance of the corpuscle into the form of a fila- 
mentous body. 
PROC. AMER. PHILOS. SOC. XXXII. 143. 21. PRINTED FEB. 7, 1894, 
