386 
altogether to have coincided with that of the author, we 
have done so feeling that to pass over these points of dif- 
ference would be to pay Mr. Pearson but a poor compli- 
ment. For we fully recognise the great value of the 
work in all essential matters, and we cannot but admire 
the energy with which a task of no ordinary difficulty 
has been carried to completion. Mr. Pearson has laid 
British botanists under great obligations, and has 
succeeded in producing a book that ought to serve to 
rescue from comparative though altogether unmerited 
oblivion a family, by no means the least interesting, of 
the vegetable kingdom. J. B. FARMER. 
STRUCTURALLY ACTIVE MEDIA. 
De la Double Refraction elliptique et de la Tétraré- 
Sringence du Quartz dans le Votsinage del’Axe. Par 
G. Quesneville. Pp. xiv + 361; avec 4 planches. 
(Paris: Gauthier-Villars et Fils, 1898.) 
HE peculiar phenomena exhibited by quartz in direc- 
tions slightly inclined to the optic axis were explained 
by Airy in 1831 on the hypothesis that in any such 
direction two streams of permanent type can be propa- 
gated, these streams being oppositely and elliptically 
polarised with their planes of maximum polarisation re- 
spectively parallel and perpendicular to the principal 
section. With the aid of these assumptions, he calcu- 
lated the forms of the interference patterns displayed in 
plane and circularly polarised light by plates of quartz 
perpendicular to the optic axis, and also discussed the 
remarkable phenomena that are observed when two such 
plates of equal thickness but of opposite rotations are 
superposed and traversed by a convergent stream of 
polarised light that is subsequently analysed. The close 
agreement between these calculated results and the ex- 
perimental forms of the curves led to a general accept- 
ance of Airy’s views, and the conviction of their correctness 
has since been strengthened by experimental investiga- 
tions of a more direct character. 
This theory M, Quesneville, without disguising the 
magnitude of the task, has undertaken to refute, replacing 
it by a new one devised by himself. He maintains that 
the interference exhibited by plates of quartz in polarised 
light is in at least one important particular at variance 
with the results calculated by Airy, and claims that 
Jamin’s investigations (the only experiments that he dis- 
cusses), so far from confirming the accepted theory, 
actually lend support to that which he himself enunciates. 
Further, he alleges a theoretical objection to Airy’s 
hypotheses. According to these there is, of course, a 
continuous change in the polarisation of the waves of 
permanent type as the position of their normal changes 
from a direction inclined to the optic axis to that of the 
axis itself, while it is the circular polarisation, and not the 
rotary phenomenon, that is ‘the fundamental property of 
an active crystal in this latter direction. M. Quesneville, 
however, contends that Airy’s formulz involve a discon- 
tinuity in the phenomenon, inasmuch as a rotation of 
the primitive plane of polarisation nowhere occurs therein, 
for “s'il existe suivant l’axe, il est inadmissible que tout 
pres l’axe, alors que les ellipses sont presque des cercles, 
elle ait disparu.” 
NO, 1712, VOL. 66] 
NATURE 
[AuGusT 21, 1902 
This idea is the key-note of his own theory, according 
to which the streams in an active crystal, propagated in 
a direction slightly inclined to the optic axis, only become 
of permanent type after a certain zone has been traversed 
within which a rotation of the plane of polarisation is “le 
phénoméne primordial.” On entry into the crystal, a 
beam of plane polarised light is supposed to be resolved 
into two elliptically polarised streams of opposite sign 
with their planes of maximum polarisation respectively 
parallel and perpendicular to the primitive plane of 
polarisation ; after a small distance has been traversed, 
these are regarded as having for their resultant a stream 
that is plane polarised in a new azimuth, while this is, 
again, equivalent to two fresh elliptically polarised 
streams ; this process is supposed to continue during 
passage through the first zone, within which the 
elliptic vibrations change both in form and in orientation. 
It is not clear what circumstances determine the limita- 
tion of the zone, but it is assumed that after a certain 
length of path, that diminishes as its inclination to the 
axis increases, the two elliptically polarised streams cease 
to occasion a rotation of the last plane of polarisation, 
and that they then enter the second zone, where each 
gives rise to two streams of the permanent type assumed 
by Airy. In this manner the four-fold refraction of 
quartz in the vicinity of the axis is arrived at ; there is, 
however, no assumption of more than two wave-velocities 
corresponding toa given direction, neither is there any 
recognition of a separation of the streams by refraction, 
so that the four elliptically polarised waves may be 
grouped together in pairs, the constituents of each group 
travelling with the same speed in the same direction, and 
there consequently is no question of a four-fold refraction, 
even if the author’s contention be correct. 
The limitation of this review precludes a discussion of 
the physical and mechanical difficulties involved in these 
ideas ; they are, however, sufficiently obvious. It is 
claimed that the theory is not merely kinematical, but 
that it represents the actual state of things that occurs 
during the passage of light through a plate of quartz, 
though its author confesses his inability to formulate any 
hypothesis respecting the distribution of the ether round 
the axis of an active crystal from which it could be 
deduced. 
The book in which this theory is expounded is divided 
into three sections, preceded by an introduction giving a 
sketch of the plan and scope of the work. In the first 
section the author discusses some investigations prior to 
his own. MacCullagh, in 1836, showed that the addition 
of certain terms to the differential equations of motion 
for inactive uniaxal crystals would lead to the elliptic 
polarisation assumed by Airy. Starting from a mistaken 
conception of the significance of these equations, M. 
Quesneville professes to show that “‘Convenablement in- 
terpretées,” they prove that 
“Tl existe dans le quartz une premiére zone pendant 
laquelle les rayons dés entrée donnent lieu & la rotation 
du plan primitif de polarisation, non seulement suivant 
Yaxe, mais obliquement a l’axe jusqu’a la périphérie.” 
He then proceeds to a discussion of Jamin’s experiments, 
deducing therefrom the result that in calculating the 
difference of phase between the two oppositely polarised 
