68 Intelligence and Miscellaneous Articles. 
choucs which I have examined have all led to the same result; it 
would certainly be the same with that which Wertheim used, and 
this physicist found, by measuring directly the diminution of cross 
section,o=3. Since then MM. Naccari and Bellati have shown, by 
Regnault’s method, that for the same substance the value of o may 
amount to 0°41; but this number satisfies the ratio (4) no better than 
that of Wertheim; assuming o’=3 it would give ae = 0:36, 
—240 
a value quite out of proportion to that which should be found. 
As it is difficult to assume that Wertheim, and then MM. 
Naccari and Bellati, have made experimental errors as great as 
appears from the preceding,—as, on the other hand, there is no 
reason why caoutchouc supposed to be homogeneous, and submitted 
to small deformations, should not conform to general laws, it may 
be asked how far the formule assumed are really the expression of 
these laws. It is not, then, superfluous to submit these formule 
to the test of experiment, following in this the advice given by 
Regnault ; it is with this object that I have had made the differ- 
ential apparatus mentioned above ; these researches are in course 
of execution.—Comptes Rendus, July 21, 1884. 
ELEMENTARY PHYLLOTAXY. BY PLINY EARLE CHASE, 11,7 
I have shown? that the “numerics” of the chemical elements 
can be better represented by various phyllotactic divisors than by 
Prout’s law. Phyllotactic submultiples of the organic elements 
C, H, O, N give a mean residual ratio of -05654, while Prout’s 
law gives ‘12007, the probable ratio of merely accidental residual 
being -18394. This indicates comparative aggregate probabilities 
which are represented by the reciprocals of :05654, -12007°, and 
18394", or by 1999 x 10°°, 1098 x 10°, and 1. 
In the Philosophical Magazine for November 1884, Dr. Edmund 
J. Mills gives additional evidences of phyllotactic influence. He 
represents all the elementary numerics, except that of hydrogen, 
by the equation 
y= p15—15(-9375). 
This introduces the first five numbers of the phyllotactic series 
1, 2, 3, 5, 8, being of the form 
5x 3, p—(8x38+2~x 8)*]. 
The sum of the infinite series which is represented by 15x 
(5x 3+2 x 8)* is the product of the first five phyllotactic numbers, 
1x2x3x5x8. The series itself is of the form (n+n-+1 1)*, thus 
representing cumulative harmonic rupturing tendencies, of the 
same kind as are shown in the inter-stellar influence upon plane- 
tary positions (Phil. Mag. September 1884, p. 197). 
* Communicated by the Author. 
+ Proc. Amer, Phil. Soc. xix. pp. 591-601; xx. p. 431, &e. 
