JANUARY II, 1917] 
fundamental matters: the nature of light, the 
production of colour, colour mixture, colour 
terminology, the analysis of colour, colour and 
vision, the effect of environment on colour, 
theories of colour-vision, and colour photometry. 
In connection with colour mixture we have the 
subtractive and additive methods dealt with, and 
also the “juxtaposition method” as if it were a 
third method, though it is this only from a prac- 
tical point of view, being really a form of the addi- 
tive method. The mixture of both the subtractive 
and additive methods which exists in three-colour 
typographic half-tones is not referred to, but in 
omitting this the author only follows in the foot- 
steps of those who have preceded him. It seems 
to be generally taken for granted, perhaps because 
“subtractive ”’ colours are used, that this is simply 
a modification of that method, but the most cur- 
sory examination of a print will show that the 
dots of colour, while often more or less super- 
posed, are also often juxtaposed. 
A few pages that should be of much interest 
to those who need to make critical observations 
of minute detail, as in some microscopical work, 
deal with acuteness (or “acuity ”) of vision. For 
the same brightness in all cases vision is more 
acute with monochromatic than with white light, 
and for this purpose yellowish-green is superior 
to any other colour. The reviewer would observe 
that microscopists generally prefer this colour, 
which is also that for which the eye is most sensi- 
tive and for which objectives are generally best 
corrected. But the superior resolving power of 
light of shorter wave-length has led to the occa- 
sional use of bluish-green light, in spite of its 
obvious disadvantages. It seems from the figures 
given that the microscopist may lose more by the 
reduction of his acuteness of vision, even assum- 
ing, equal brightness, than he can possibly gain 
by the increase in resolution, unless he can com- 
mand a higher magnification without introducing 
other troubles. 
With regard to the applications, colour photo- 
graphy is briefly dealt with in eleven pages, 
but the next group of chapters, “Coiour in Light- 
ing,” “Colour Effects for the Stage and Dis- 
plays,” and “Colour Phenomena in Painting ” 
(which deals chiefly with questions of illumina- 
tion), occupies more than a quarter of the whole 
volume. This is evidently the subject that most 
interests the author, as, indeed, one would expect 
from the position that he occupies. Colour- 
matching as a special art, an account of various 
attempts to make “colour-music,” borrowing more 
or less the notation of sound-music, and a few 
notes on coloured media, complete the volume. 
CHI: 
QUARTIC SURFACES. 
Quartic Surfaces with Singular Points. By Prof. 
C. M. Jessop. Pp. xxxv+198. (Cambridge: 
At the University Press, 1916.) Price 12s. net. 
WE have in analytical geometry a great con- 
trast between the general and the par- 
ticular. For algebraical curves and surfaces of 
NO. 2463, VoL. 98] 
NATURE 367 
the nth order or class we have a comparatively 
large number of results, such as those given by 
Cayley, Cremona, and others half a century ago; 
but when we take a particular value of n and try 
to investigate, say, the distinct types of surfaces 
of that order, the task is a very formidable one if 
n exceeds 3. The present work deals with the 
case when n=4, and that only so far as relates 
to surfaces that have nodes or nodal curves, or 
both. 
Chap. i. shows us very simply the forms of 
equation corresponding to quartics which have 
from four to sixteen (ordinary) nodes; this gives 
twenty-four types of surface, some types having 
further varieties. As we might expect, the 
sixteen-nodal surface is the easiest one to discuss 
in detail; practically we have Kummer’s surface 
and particular cases of it, and by introducing 
theta-functions we can obtain many elegant 
properties with ease (this is shown in chap. jii.). 
Among the six-nodal quartics we have Weddle’s 
surface (discussed pp. 173-188); here double - 
theta-functions are useful auxiliaries.  - 
Chap. iii. gives an account of quartics with~ 
a nodal conic; when this conic is the imaginary 
circle at infinity, the surface becomes a cyclide. 
Prof. Jessop might have remarked that since any 
two conics in space are projectively equivalent, 
the theory of cyclides includes that of all quartics 
with a nodal conic. Hence we may, if we like, 
read chap. v. (on cyclides) and translate all its 
theorems into properties of every quartic with a 
nodal conic, and thus deduce the theorems of 
chaps. iii. and iv. However, the author’s sequence 
has the advantage of introducing us at an early 
stage to Segre’s wonderful projection of quartics 
from four-dimensional space (p. 55), and to 
Geiser’s one-one relation between points on a 
plane and those on a general cubic surface (p. 46). 
The value of Segre’s method becomes still more 
obvious in chap. iv., which ends with his table 
of types of quartics with a double conic, arranged 
according to indices of elementary factors; this is 
one of the most valuable tables in the book. 
Chap. vi. deals with surfaces with a double line, 
among which Pliicker’s surface appears; chap. vil. 
with quartics that contain an infinite number of 
conics (here Steiner’s surface comes in); chap. viii. 
with rational quartics in general; and chap. ix. 
with determinant surfaces (Weddle’s surface being 
the symmetric case). All are well worth reading ; 
and, in fact, the treatise has the great merit of 
introducing us to the main methods which have, in 
this inquiry, replaced tiresome algebra by a com- 
bination of abridged notation, pure geometry, and 
function-theory suited to the particular problem 
in hand. Without making any invidiots distinc- 
tions, we may fairly assert that, in this particular 
domain, Segre and Humbert have, each in his 
own way, immensely simplified the discussion of 
the theory. 
Prof. Jessop’s book has, of course, the defects 
of its qualities. Among these we may note that 
he never points out that in writing a treatise on 
algebraic loci with certain singularities he is at 
, the same time writing on algebraic envelopes 
