Aucust 10, 1899] 
NATURE 349 
§ci trict +26c3 —10c* +e -1 
2c8(e+ 13(c— 1)* 
_ch—10c8+2c2—2c+1 , 
e#(c+1)3(c— 1)? 
Pj= 
B,=Qu+Qr 
where : 
oaer3le=4c— 0) poe. 47 fs 
“~~ ack(e+1)(e-1) 
(C= 4¢-1) (5c? +2c+1) 
chaz 52 ano 
2ck(¢ +1) (¢-1)? 
Stig +7e+1 , — 238 +227+1oct+2 
Cr») 
B,=72=9 = 
ra e(e + 1)*(e— 1) 
The same functions a, 8, y, 5, and their special alge- 
braical forms are suitable for Kirchoff’s case of the 
motion of a solid in infinite liquid, but now V is a quartic 
function of z, requiring resolution into factors. 
In the more general case invented by Clebsch, and 
developed in Halphen’s ‘“ Fonctions elliptiques,” t. II., 
the component rotation about OZ is no longer con- 
stant, and the solution is more complicated, introducing 
multiplicative elliptic functions to a parameter corre- | 
sponding to the infinite value of z. 
If the motion of the axis of the top is alone required, 
we take A =oo, and investigate the function A = a/y; 
this is a multiplicative elliptic function, with an effective 
parameter a—4é, which can be made algebraical when 
a— is made an aliquot part of o’, irrespective of the 
separate terms @ and #. - By a further restriction, the 
exponential function of the time can be made to dis- 
appear, by making 7 +/'=0, and then H is at L in 
Fig. 1; it was inthis way that the analysis was prepared 
of the algebraical cases, represented stereoscopically by 
Mr. T. I. Dewar, referred to on p. 199. 
The authors say they have refrained from utilising 
these stereoscopic diagrams, because they would not 
like to assume in the reader the possession of a stereo- 
scope. But our eyes should be drilled into control to 
pick up the solid appearance without any apparatus ; a 
little quiet practice will suffice. Treatises on Solid 
Geometry of the future should be profusely illustrated 
with stereoscopic figures, which the student should see | 
solid at will; and wall diagrams or lantern projections 
should also be drawn stereoscopically, and the solid 
effect obtained in the audience by crossing the two lines 
of sight. 
Mr. T. I. Dewar’s untimely death, at San Remo last 
May, has deprived us of any further diagrams from his 
skill, but the example he set will we trust be followed 
out completely in mathematical diagrammatic instruction. 
The unsymmetrical top, discussed in V. § 9, leads into 
such great analytical complication, that only a few 
special degenerate cases have so far received any ade- 
quate attention ; the next century will have its work cut 
out for the mathematical treatment of this problem and 
also of the dynamics of the bicycle. The symmetrical 
top of the boy, with the point free to wander over a 
smooth or rough horizontal plane, leads to similar 
analytical difficulties, and should be discussed in the 
same place. 
On the other hand, the many attempts at a popular 
explanation of the motion of the top, restricted princi- | 
pally to the case of regular precession, are described in 
V. § 3. Prof. Perry’s interesting little book on “Spin- 
ning Tops” comes in for praise, and the authors cite 
with pleasure the comparison of the top to a wilful beast 
(eigensinniger thier), always ready to move in some other 
direction to that in which it is pushed ; insomuch that the 
Irishman can persuade his pig to accompany him on the 
road only by pretending that his way lies in the opposite 
direction ; and so Bessemer’s invention to steady the 
NO. 1554, VOL. 69] 
motion of a cabin mounted on gimbals, by means of the 
controlling influence of gyrostats, was a failure. 
If the authors are in search of other practical elemen- 
tary illustrations, they should take the modern centrifugal 
machine, and examine the practical devices, as in the 
Weston machine, for controlling the nutations ; these 
devices discovered experimentally without any assistance 
from theory will serve to elucidate the abstract formulas 
with advantage. 
A third part of this book is still to appear, and we 
await it with great interest ; the work when complete 
will form an indispensable book of reference for all who 
wish to make themselves thoroughly acquainted ‘with 
this: complicated problem in Dynamics. 
A. G. GREENHILL. 
NOTES. 
Av Osborne, on Wednesday, August 2, the Queen conferred 
the honour of knighthood upon Sir William Henry Preece and 
Sir Michael Foster, Knight Commanders of the Order of the 
Bath, and invested them with the riband and badge of the 
| Civil Division of the Second Class of the Order, and affixed 
the star to their left breasts. 
Tue Hanbury Gold Medal of the Pharmaceutical Society of 
Great Britain has been awarded to Prof. Albert Ladenburg, of 
Breslau, for his work on alkaloids and their derivatives. 
Mr. J. S. BupceErt, of Trinity College, Cambridge, who 
accompanied Mr. Graham Kerr on his expedition in search 
of Lepidosiren, has been successful in obtaining eggs and 
larvee of the Crossopterygian Ganoid Polypterus. From a short 
account of his investigations, illustrated by sketches, which 
Mr. Budgett has sent to this country, it appears that the 
larva is very minute, and possesses a ‘‘cement organ” on 
the dorsal surface of the head. Mr. Budgett is now on the 
journey home, and the full account of his work will be looked 
forward to with much interest. 
ON a preceding page we have referred to some of the work 
performed by the Royal Gardens, Kew. Coincidently we have 
received the number for July 21 of our American contemporary 
Science, which containsan elaborate article by Prof. Underwood, 
headed ‘‘ The Royal Botanic Gardens at Kew,” in which the 
features of the garden and its position as a scientific institution 
—‘‘its beautiful lawns, its delightful shade, its historic asso- 
ciations, its immense collections of cultivated plants, and_its 
wonderful activity in the direction of botanical research ”—are 
described and discussed with critical appreciation apropos the 
recent establishment of the Botanic Garden of New York and 
its capability to become ‘‘even more influential in democratic 
America than. Kew has become throughout the length and 
breadth of the Queen’s dominions.” It is gratifying to have 
this acknowledgment of the work of Kew ; and the tribute paid 
to the versatility and ability of Sir William Thiselton-Dyer in 
promoting its development and widening its influence will be 
everywhere endorsed. There are some blots on the escutcheon 
in the eyes of Prof. Underwood, but we imagine there are many 
who will not see with him in all the instances he mentions. 
The crowding of the museum collections he notes isan apparent 
blemish, and one we may hope to see removed by the provision 
of increased room for the exhibition of the specimens. A some- 
what jealous comparison of Kew and Berlin as centres of 
botanical work is a jarring note in the article; and Prof. 
Underwood allows, we fear, German bias to weigh with him in 
making it, for instance, when he writes, ‘‘ the principles of plant 
distribution are not so thoroughly grasped at Kew as they have 
been brought out at the German Botanical Garden through the 
skill of Prof. Engler and his associates.” Yet Kew is the home 
of Sir Joseph Hooker ! 
