458 
NATURE 
| March 15, 1883 
new species. The species which he considers my /zszus 
curtus is very different from the F. Sabzuz of Gray, or 
the F. fogatus and F. Pfaffi of Moérch (all enumerated by 
Friele as synonyms); and I regard the last-named three 
species as the F. edwr of Morch and not as my /. Sarsz. 
However, notwithstanding any trifling errors, if they be 
errors, the work of Herr Friele is not only admirable and 
valuable, but is imbued with that scientific merit and 
modesty which are peculiar to our fellow-workers in 
Scandinavia; and we shall look forward with great 
interest to the continuation of his papers on the Mollusca 
of the Norwegian North-Sea Expedition. 
J. GWYN JEFFREYS 
Tables for the Use of Students and Beginners in Vegetable 
Histology. By D. P. Penhallow, B.S., late Professor 
of Chemistry and Botany in the Imperial College of 
Agriculture, Japan. (Boston, 1882.) 
THIS little work by no means meets the expectations 
which its title arouses. The author states, indeed, in his 
preface that the scope of the work is purposely limited, 
but the limits are so narrow that the work will not be of 
much use to the student who has a competent teacher, 
and it will not be of any use to the beginner who is 
attempting the study of vegetable histology by himself. 
The book deals simply with the micro-chemistry of 
plants; the reagents are enumerated, as are also the 
various substances to be met with in the cells, but no 
attempt is made to give an account of the mode of appli- 
cation of the reagents for the detection of the substances, 
and in certain important cases (the chloriodide of zinc, 
for example) the mode of preparation of the reagent is 
not given. Nota word is said about imbedding, nor is 
any mention made of staining. The general mode of 
treatment of the subject is thoroughly unpractical. For 
example, silica is said to appear in plants “as a trans- 
parent deposit”; but every histologist knows that the 
silica in a cell-wall can only be made evident by incine- 
rating with nitric acid. 
The priority which the author claims can hardly be 
granted in view of the fact that Poulsen’s valuable 
**Microchemie” has been in the hands of European 
histologists for several years. The selection of litera- 
ture given atthe end also betrays the author’s want 
of acquaintance with his subject, inasmuch as no men- 
tion is made of such important works as Dippel’s 
““Mikroskop”” and De Bary’s “ Vergleichende Ana- 
tomie.” 
LETTERS TO THE EDITOR 
[The Editor does not hold himself responsible for opinions expressed 
by his correspondents. Neither can he undertake to return, 
or to correspond with the writers of, rejected manuscripts. 
No notice is taken of anonymous communications. 
[The Editor urgently requests correspondents to keep their letters 
as short as possible. The pressure on his space is so great 
that it ts impossible otherwise to insure the appearance even 
of communications containing interesting and novel facts. | 
The Matter of Space 
In his paper on ‘*The Matter of Space,” in NATURE, 
vol. xxvil. p. 349, Mr. Charles Morris has given us an excellent 
exposition, and, as I believe, in general a perfectly correct one, 
of the fundamental laws and properties of matter and motion, 
But as I have for some time been investigating the views which 
he describes with exactly the results and con-equences at which 
he has arrived (excepting only in one material difference to which 
I will presently return), a little outline of the mathematical 
form which I found that the discussion of the subject could 
receive, and to which it was accordingly submitted in my examina- 
tions of its scope and contours, will aid readers of Mr. Morris’s 
paper, perhaps, in attaching clear ideas to some of the ex- 
pressions which he uses, and in thereby discussing and estimating 
very easily and fairly the positive truth, in general, or ina few 
points, of the paper’s considerations, the just degree of reliability 
at all events, which the marvellous maze of internetted motions 
possesses, which he has most tersely and graphically, and at least 
in the main, as it appears to me, correctly and truthfully 
described. 
Angular momentum, or (for a particle of unit mass) the rate 
of description of sectorial areas, is, like actual energy, a quantity 
of two dimensions in space ; it is in fact the vector-product of 
(or the quadrilateral area between) the two radii of the particle’s 
orbit and hodograph. Tractivemomentum, or the product of the 
unit-particle’s radius-vector and the resolved part of the particle’s 
velocity a/ong (instead of across) the radius-vector, is equally a 
quadratic product (but differently estimated) of the two foregoing 
orbit and hodograph radii. It isnot the rate of description of 
an area, like angular momentum, but the time-rate of the square 
on the orbit-radius. The time-rates of each of these momenta 
are similar to them in space-relation, and are respectively angular 
moment or twirl (of a force-couple) and tractive moment or 
wrest (of a motor-couple). But if a small step of angle is the 
ratio of a circular-are step (or of a small step along its tangent) 
to the circle’s radius, this being numerical, a twirl’s work through 
this small step of angle is similar in space-relation to the twirl 
itself and to its time-effect, or angular momentum. 
The same similitude in space-relation will exist between a 
wrest, or motor-couple, and its time-effect (or tractive momentum), 
and its small step of work, if, in imitation of the practice for a 
twirl’s or force-couple’s action, a wrest’s space-step is defined to 
be the ratio of the particle’s step along the radius to the orbit- 
radius. This counterpart of angle-step may be called a traction- 
step; and it is the small percentage of elongation which the 
radius undergoes. If this construction is assumed, there ensues 
from it a close, and evidently significant, analogy between the 
time-rate of ordit-radius square (which denotes at once, in space- 
relation, a #zolfor-couple and its time- and space-effects) and the 
hodograph-radius square (which expresses simultaneously in space- 
relation a force-couple and its time- and space-effects). Although 
the square of the hodograph-radius signifies the square of the 
material point’s velocity, or its directed actual energy, I conceive 
that the square of the orbit-radius represents a square of un- 
directed velocity, or an undirected energy of ‘* higgledy piggledy ” 
motion of the material point ; and its time-rate is @ horse-power 
of the point’s quaquaversal, or undirected actual “ energy. 
Viewed in this light, twirls or force-couples and their time- and 
space-effects are all graphically synonymous with actual directed 
energy ; but wrests or motor-couples and /Hezr time- and space- 
effects are all graphically synonymous with orse-power of un- 
directed actual energy. For these latter quantities Mr. Morris 
uses indifferently the various words, ‘‘momentum,” ‘‘heat mo- 
mentum,” ‘‘heat velocity,” ‘‘heat,” ‘‘motor energy,” ‘heat 
energy,” ‘‘heat vibration,” ‘‘centrifugal energy,” and ‘centrifugal 
or motor vigour,” of a moving point ; but while they are all, as he 
rightly opines, convertible quantities in their relation to graphic 
space, yet the theory of force-couples with which (mzfato nomine) 
they are equally convertible in the same space, teaches us that 
a twirl-group falls mechanically, according to its association with 
time and angle, into three distinct divisions, of an action (the 
couple) and its time- and space-effects (angular momentum and 
accumulated work). It is so also with the motor-couple’s graphic- 
space measure, ‘‘vigour.”” In proper combinations with time 
and traction-ratio! it becomes either an action or a kind of 
momentum or a form of work. But in discussing these new 
quantities’ properties two maxims of construction and interpreta- 
tion must be kept constantly in view. 
In the first place, we must not expect a motor-couple (although 
it tends to alter @) which endows a point with undirected horse- 
power, to tend tv lengthen or shorten the point’s radius-vector i 
the same way that a force would do. If by their actions motor- 
couples can 2” any way oppose the action of a force or force-couple, 
it must be, not by exerting force themselves, but by giving rise 
to force where they act. Now motor-couples can no more act 
intelligibly upon a single pcint (to range a radius’s extremities to- 
wards or from each other) than a force-couple can (to turn a 
radius’s two ends round each other). Hence motor-couples must 
produce force in a material point in virtue of the point’s being an 
aggregation of material points, or in other words the appearance 
of force is a sign of the compositeness of the material point upon 
which it acts. Per contra, forces can produce force-couples, or 
* The integral of traction-ratio, [dp = oe = log 2 = 9,1 identify 
with Rankine’s “thermodynamic function’’ (for which he uses the same 
symbol, g) usually termed “‘ entropy ”’ in works on thermodynamics. 
