JUNE 14, 1901.] 
planation. Such a result might be expected 
when we consider the difficulties of the question. 
The student should understand that he must 
face the difficulties, and that he can not over- 
come them without serious study. A good 
analytical exposition will be found in the ‘ Me- 
eanique’ of Poisson. But the most satisfac- 
tory investigation of such motions is given by 
Poinsot, by means of the theory of couples. 
An interesting example is that of the pre- 
cession and nutation of the equinoxes. If we 
form the couples around the earth’s axis of 
rotation, around the line of equinoxes, and 
around the line in the earth’s equator, directed 
toward the solstice; we find that the couple 
around the axis of rotation is zero; the couple 
around the line of equinoxes gives the preces- 
sion ; and the couple around the other axis pro- 
duces the nutation. By substituting the force 
arising from the action of the sun, expanding 
by the binomial theorem, and retaining only 
the first terms, the solar precession comes out 
15’’.6 ina year. The calculation for the moon 
is not so easy because the moon does not move 
in the ecliptic; but, since we can compound 
couples like forces, there is no difficulty except 
the length of the work. The precession pro- 
duced by the moon is 34/’.8 : hence the sum, or 
the luni-solar precession is 50/7.4. Observa- 
tion gives 50/’.35; this simple method therefore 
gives a good approximation to the true value. 
The mass of the earth disappears when we 
compound the couples, and the precession would 
be the same if the earth were a shell of the same 
figure. The precession has a secular character, 
since when we integrate we find a constant 
factor multiplied by the time. Again, since 
the precession is negative, the dynamical result 
shows that the earth is flattened at the poles, 
and not elongated as Cassini thought. 
The nutation can be found in the same way 
from the couple around the third axis, but it 
has a periodical character, and changes sign 
with the longitude of the moon. The computed 
value agrees well with observation. 
Poinsot’s work is a remarkable example of 
what can be done by the careful study and ex- 
amination of the geometrical conditions of a 
question. A. HALL. 
CAMBRIDGE, May 31, 1901. 
SCIENCE. 
949 
MODULUS OF CONSTANT CROSS SECTION. 
To THE EDITOR OF SCIENCE: In the last 
number of SCIENCE there appears a short article 
with the above heading, in which the author 
says he can find no mention anywhere of a modu- 
lus of constant cross section. The modulus 
here referred to will be found in a number of 
treatises on elasticity, among others the article 
‘Elasticity,’ in ‘ Encyclopedia Brittanica,’ Vol. 
VII., p. 807, and Rankine’s ‘Applied Me- 
chanics,’ p. 279, where a numerical value is 
quoted for brass. If k be the volume modulus 
and n the rigidity modulus the modulus for 
constant cross section is k + 4 n. 
The author may profit by the study of the 
thermodynamics of elasticity as given in the 
‘ Britannica’ article. 
THOMAS GRAY. 
ROsE POLYTECHNIC INSTITUTE, 
May 27, 1901. 
NOTE ON THE GENUS HOLLANDIA OF KARSCH. 
In reading over the sixth volume of the Cam- 
bridge Natural History (Insects) by Dr. David 
Sharp, p. 396, the writer notes the following 
statement: ‘‘The tropical African Arbelidz 
are considered by Karsch to be a distinct family, 
Hollandiide.”’ 
Upon looking up the matter I discover that 
Dr. F. Karsch, in the twenty-second volume of 
the ‘Entomologische Nachrichten’ (1896), p. 137, 
erected a genus in honor of Dr. W. J. Holland, 
of Pittsburgh, calling it Hollandia, and select- 
ing as the type of the genus the species named 
and described by him as Hollandia togoica. He 
further made this genus the type of a new 
family, the Hollandiidx, to which he referred 
the genera Hollandia Karsch, Arbelodes Karsch, 
Lebedodes Holland, and Metarbela Holland. 
Dr. Karsch unfortunately overlooked the 
fact that in the Annals and Magazine of Natural 
History for October, 1892 (p. 295), Dr. Arthur 
G. Butler had already described a genus of 
African moths, naming it Hollandia, in honor 
of the same gentleman, whom Dr. Karsch states 
it to be his wish to recognize. Dr. Karsch’s 
name, therefore, falls into the list of synonyms 
together with the family name, which he has 
proposed. 
The writer suggests for the genus described 
