334 
NATURE 
[August 12, 1886 
each other, the theory of which has been so lucidly ex- 
plained by Dr. Fritz Miiller (see NATURE, vol. xxvi. p. 87, 
and vol. xxvii. p. 481). A genus of Longicornes has been 
named Lycédola, and its eight known species are all said 
to resemble species of Lycus. Besides these there are at 
“east a score of Longicornes which are evidently mimickers, 
though the exact species imitated does not happen to be 
represented on the plates. There are also many of the 
smaller species which evidently mimic ants or wingless 
Mutillida, Three such species are named by Mr. Belt, 
and two of these are figured, but they do not appear to 
resemble ants half so much as at least a score of other 
species ; showing how difficult it is to determine whether 
a species is protectively coloured by means of figures 
however carefully drawn and coloured. The extensive 
collections on which these volumes are founded would, I 
feel sure, afford a mass of interesting cases of mimicry if 
search were made for them, since, besides those already 
mentioned, there seems to be a considerable number of 
Longicornes which resemble som? of the Cleridz figured 
among the Malacodermata, and these also are probably 
cases of mimicry, although I am not aware that the 
Cleridze have been proved to be an uneatable group. 
Looking at the copious series of figures here given 
there does not seem to be any superiority of colouring 
over the corresponding Eastern groups. 
larger proportion of Cerambycide to Lamiidz in tropical 
America gives it an advantage over the Eastern tropics, 
because the former family comprises most of the elegant 
forms and gay colours of the tribe ; but notwithstanding 
their inferiority in this respect the Longicornes of Penang, 
of Java, and of New Guinea appear to be quite equal in 
their development of colour to those of Central America. 
The present work has been got up at so great an 
expense both of time, labour, and money to its origina- 
tors, Messrs. Godman and Salvin, that it must be con- 
sidered one of the noblest individual contributions to 
the study of natural history that has ever been made. 
Its great bulk and cost must, however, render it inacces- 
sible to many students who would wish to possess it, 
while its value to them would have been considerably 
increased if descriptions of all the recorded species had 
been given as well as of those which are new, rendering 
it a complete book of reference to the Insecta of Central 
America. 
I would therefore suggest to Messrs. Godman and 
Salvin that they would confer a still greater boon on 
entomological students if they could make arrangements 
for the preparation of a series of compact octavo volumes 
giving the letterpress only of the present work, together 
with either the original descriptions or sufficient diagnoses 
of all the species enumerated which are not here described. 
These volumes could be issued after the completion of 
the great work, all brought up to one uniform date ; and 
if published at a moderate price they would be sure to 
command a very large sale. Complete faunal hand-books 
of the kind suggested are among the most generally useful 
works that can be published, because they obviate the 
enormous waste of time and labour involved in consulting 
scores of expensive volumes in order to determine the 
name and history of perhaps half the insects which a 
student may possess. 
It is quite unsafe to venture on any detailed criticism 
The much | 
| 
of the work of one so thoroughly acquainted with Longi- 
corn Coleoptera as Mr. Bates, but my attention was 
attracted to Table II. by the figures of two alleged female 
Prionide, which are represented of a rich green colour, 
while the respective males are bronzy olive. If this is the 
fact, it is a curious case of reversed sexual coloration, 
though by no means unprecedented. In one of these 
species, WWadllaspi beltz, however, two varieties are figured, 
one green, the other olive brown, both said to be females ; 
but the green specimen (as figured) differs greatly from 
the brown specimen, in having the femora of the second 
pair of legs much longer and more slender, in the some- 
what different dentation of the thorax, and especially in 
the very different form of the scutellum, important differ- 
ences which seem inconsistent with identity of species. 
Should any error have crept into the plates, the author 
will no doubt be glad to have his attention called to it. 
ALFRED R. WALLACE 
GEOMETRICAL OPTICS 
An Elementary Treatise on Geometrical Optics. By W. 
Steadman Aldis, M.A. (London: Deighton, Bell, and 
Co., 1886.) 
HIS is a second edition of a work which appeared 
first in 1872, and which was designed to meet the 
requirements of students reading for the first three days 
of the Mathematical Tripos. The new edition does not 
differ greatly from the old, except in form. The type 
is larger and clearer, and in this respect the book is con- 
siderably improved. 
The laws of reflection and refraction, and the reflec- 
tion and refraction of direct pencils at plane and spherical 
surfaces, are treated in a clear and comprehensive 
manner. In Article 36 reference is made to a useful 
method of illustrating from co-ordinate geometry the 
relations between a point and its image. If , d’ be the 
principal focal lengths of an optical system, « and z’ the 
distances of an object and its image from the principal 
points, we have PEED, =1. Thus taking rectangular 
Ce 
axes, and measuring along them distances ¢ and ¢’, we 
see that # and x’ are the intercepts on the axes made by 
a straight line passing through the point d, ¢’. This has 
been worked out in an interesting paper in the Pfz/o- 
sophical Magazine for December 1884, by Prof. J. Loudon, 
of Toronto. 
The next chapter deals with the oblique reflection and 
refraction of small pencils. The general explanation is 
extremely lucid, but it surely is a mistake not to have 
introduced the notation of the differential calculus. Of 
course this is excluded from the first three days of the 
Tripos, but so too are oblique reflection and refraction, 
and the work is rendered unnecessarily cumbersome by 
the omission.. A similar remark may apply to some of 
the sections of the next chapter on refraction through 
prisms and plates. 
Chapter VI. treats of lenses, which are dealt with in 
the ordinary manner. This part of the book would have 
been improved by the introduction of some of the geo- 
metrical results in which the main consequences of 
Gauss’s work have been expressed by various writers. It 
is really a misfortune that the theory of principal and 
nodal points is so little known to English authors. It is 
