Reply to the criticism on Demonstration of Parallels. 69 
in such cases is a single isolated cup or radiated disk, and the 
coral animal is a-solitary flower. ‘These simple polyp-flowers 
instead of being microscopic, are often of large size. While 
many are but one or two lines in diameter, others are one or two 
feet. The large Fungia with its stellate surface and sprinkling 
of emerald tentacles around its central mouth, is one of the 
most beautiful objects of the coral reef. 
The foregoing remarks are presented as.an introduction to a 
more particular account of the structure and habits of zoophytes. 
Ant. VII. ree ig to the criticism on Prof. Twining’s Demon- 
stration relating to Parallels.* 
To the objections to my proof of Euclid’s postulatum offered 
by the Editors of the Journal of Science, upon authority which 
is shown by the appended initials-to be highly worthy of cre- 
dence, I should have sooner replied but for excess of occupation. 
Even now I feel constrained to such brevity as may involve the 
hazard of a want of clearness, except for such readers as may 
care to refer back to the original proposrr1on.t 
The objector first observes “there must be some fallacy” in the 
ning, as cases might be pointed out “ where false conclu- 
sions would result from applying it with proper modifications, 
though without essential change.” In reply it is sufficient to 
remark, that, as the principle on which the proof depends, is 
competent, in my own view, to sustain the most rigid scrutiny, I 
ould not but be increduildus ae #8” th possibility of any such 
case—even were it shown that my particular application of the 
Principle to the proof in question involves a fallacy. It is the 
less necessary to protract discussion, at this point, inasmuch as 
the objector has preferred the method—the more masterly one 
if it can prevail—of specifying the eee respects or steps in 
which the reasoning fails. 
He intimates the existence of several—all however “ similar” 
to the one which alone he specifies as the type of all. A par- 
ticular conclusion on page 95 is pointed out as “ inadmissible,” 
on the ground that “it is founded plainly on the assumption, that 
tenets 
* See this Journal, yol. i, Second Series, p. 147. _t Ib. pp. 94-96. 
