28 
function of 4, the form of which is the same for all 
values of s. The quantities #, are the roots, different 
from each other, and from zero, of a cyclical equation of 
degree (7-1). The exponents 7, 7,-- +7 :-9 are the 
least positive residues of 1, g, g*,.-..g" * to the modulus 
2; ¢ being a primitive root of 7. The 7 values of é, 
obtained from this formula by giving to the radicals 
r, their different values, are the roots of one and the 
same rational equation. 
““ Moreover every quantity & of this form is the root of 
an equation of the zth degree rational in the corpus k, 
whose elements are the coefficients of the equation 
satisfied by 4, 2, .-- 4n-». This equation in §€ is irre- 
ducible, except in the special case when one of its roots 
is rational.” (With regard to the last clause, see the 
Corrigenda at the end of vol. II.) If the corpus K is 
real, the quantities # are either all real or all imaginary 
(see p. 551); in the first case one root € is real and the 
rest imaginary, in the second case all the roots € are real. 
The last five pages of this volume contain the explicit 
determination of all metacyclic quintic equations. 
An account of vol. II., and a general review of the 
whole work, is reserved for another article. 
G. B. M. 
OUR BOOK SHELF. 
Hours with Nature. By Rambramha Sanyal, C.M.Z.S. 
Pp. 168, (Calcutta: Lahiri, 1896.) 
As a first attempt on the part of a native Indian naturalist 
to familiarise his countrymen with some of the lead- 
ing facts in nature, and to cultivate in them the faculty 
of observation, this little volume is clearly entitled to a 
welcome at our hands. To criticise the English would 
obviously be unfair, seeing that the author is writing in 
a foreign tongue ; and, indeed, if this be borne in mind, 
his work is worthy of all praise, so far as this point is 
concerned. 
Babu Sanyal, as stated on the title-page, is Super- 
intendent of the Calcutta Zoological Gardens, where he 
has many opportunities of observing the habits of animals 
but little known in Europe. One communication from 
his pen—on the habits of Bennett’s Mungoose (Cynoga/e 
bennett?) —has already appeared in the London Zoological 
Society’s Proceedings ; and it is a matter for regret that 
other observations on the habits of animals under his 
charge have not found a place in this volume. As the 
book is essentially a medley, to give an account of its 
contents is somewhat difficult. It commences with the 
description of an excursion in Bengal, in the course of 
which we are introduced to the Gangetic dolphin, king- 
fisher, and various other birds, squirrels, and the famous 
Botanical Garden at Calcutta. Chapter i. gives us a 
history of the former superintendents of that institution, 
mainly compiled from the official handbook. In the 
third chapter the author takes the misapplication of the 
term ‘“ mole” to the Indian musk-shrew as the text for a 
NATURE 
sermon on moles and shrews ; while in the next section | 
We pass to such a widely different subject as an aquarium 
and its denizens. Of the other chapters, we can only 
mention that the sixth describes the tour of a party of 
Bengalis round the Indian Museum, Calcutta, while the 
ninth relates to Indian snakes; perhaps the best 
in the book, the author emphasising the “ rib-walking ” 
character of these animals. If the book reaches a second 
edition, we would, however, advise him to study Mr. 
Boulenger’s works, when he would probably amend his 
NO. I4II, VOL. 55] 
[ NoveMBER 12, 1896 
classification of reptiles, and point out some means of 
distinguishing between snakes and limbless lizards. 
It may be hoped that this little work may succeed in 
its object of awakening a love of nature, and exciting 
observation among our Bengali fellow-subjects. 
15 Ie 
Elements of Astronomy. By Sir Robert Ball, LL.D., 
F.R.S. New edition, thoroughly revised. Pp. 469. 
(London: Longmans, Green, and Co., 1896.) 
THIS edition has been subjected by the author to a 
thorough revision, special attention having been paid to 
the last chapter, which deals exclusively with astro- 
nomical constants. These latter will be found most 
interesting and valuable to all classes of astronomical 
students, for besides being presented with the facts in 
each case, references as to the source of information are 
always added. Little need be said about the other 
chapters, as the revision seems to have been very 
thorough, although occasional omissions have been 
found. We may, however, mention that the illustra- 
tion on page 44 seems to be rather out of date, and 
might have been changed for one more modern. In 
paragraphs relating to stellar classification, perhaps it 
would have been better to refer to a more recent classifi- 
cation, in which we have every reason to believe that 
stars do not simply decrease in temperature, but both 
increase and decrease. Putting aside these two minor 
details, the book will prove an excellent text-book for 
those wishing to acquire a knowledge of the more im- 
portant problems relating to astronomy. The admirable 
index attached will be found most complete. 
Practical Work in Physics. By W. G. Woollcombe, 
M.A., B.Sc. Part iii. Light and Sound. Pp. x + 
94. (Oxford : Clarendon Press, 1896.) 
THIS is the third part of a course of practical physics, 
the two previous ones dealing with heat and general 
physics. A fourth part, on electricity and magnetism, 
will complete the work. The optical experiments in the 
present volume illustrate photometry, reflection at plane 
and at spherical surfaces, refraction at plane surfaces, 
and through lenses. The experiments in sound demon- 
strate the laws of transverse vibrations of wires, velocity 
of sound through gases and through solids, and inter- 
ference of sound-waves. Only inexpensive apparatus is 
needed in order to carry out the experiments described, 
and the instructions, both as to construction of apparatus 
and performance with it, are clear and _ practicable. 
Experiments in sound depend upon the physiological 
perception of tone, and some students are unable to 
accurately perform them. The number of students with 
no “ear for music” (musicians will, perhaps, pardon the 
designation of the twanging of a monochord as music) 
is, however, very small. Mr. Woollcombe says that only 
five per cent. of his students have so little musical sense 
that the experiments in sound he describes cannot be 
satisfactorily carried out by them ; and his experience is 
about the same as that of most teachers and demonstrators 
of physics. 
Peasblossom. The Story of a Pet Plant. By Caroline 
Pridham. Pp. 180. (London: John Heywood.) 
TAKEN altogether, this book is very attractively written. 
The descriptions are couched in the simplest words, 
and no botanical terms are used without full explanation. 
Observation is the basis of the text, and the development 
of a plant is traced from germination upwards, all the 
parts and all the stages being considered. The book 
will interest young readers, and will encourage them to 
study the life-history of common plants ; the knowledge 
they will thus gain from text and nature will be worth 
having. 
