April 27, 1871] 
519 

Statik” (1866), who had not only treated this particular matter 
ina freer manner, but applied his methods to a much wider range 
of subject. Prof. Henrici further illustrated the subject of the 
communication by a very simple and ingenious construction, — 
Prof. Cayley, V.P , followed with a brief sketch of the contents 
of his third memoir on ‘‘ Quartic Surfaces.” 
Institution of Civil Engineers, April 18.—Mr. Charles 
B. Vignoles, F.R.S., president, in the chair.—‘‘On the 
Archimedean Screw Propeller, or Helix, of Maximum Work,” 
by Sir F. C. Knowles, Bart. In considering the construction 
and action of the Griffiths’ Screw Propeller, the author of this 
memoir was struck by the fact that the blades worked in great 
partin the lateral streams of the water, and had no action in 
the dead water behind the sternpost, where power applied ought 
to be the most efficient. Again, in the common screw propeller 
at all points near the axis, the power was almost wholly em- 
ployed in churning the water, and in producing vibration by 
alternately lifting and depressing the stem, which no doubt in- 
duced Mr, Griffiths to limit the extent of his blades to points 
without that space. These considerations led to an endeavour 
to devise some form of blade which should be free from that im- 
perfection, and yet on the whole possess the feathering property 
of the Griffiths’ screw. But no particular form presenting itself 
which on principle could be pronounced preferable to any other 
form, the author decided upon proceeding to an a rior solution 
of the question, and assuming the existence of some best form, 
he was ultimately led to propose this problem: ‘‘ What is the 
form of the surface of the -screw propeller of which the ‘work 
done’ is the greatest possible?” The complete solution of this 
problem was the subject of the paper, and the following was an 
outline of the methods employed, and of the results obtained. 
Referring the required surface to three rectangular co-ordinates 
x, y, and z, one in the axis of rotation, the other two in the 
plane of rotation, the author first obtained a general expression 
for the total ‘“‘ work done” by the blade in propelling the ship, 
in the form of a double integral in terms of the co-ordinates + 
and y and of the partial differentials of z with respect to each of 
them, of the speed of rotation of the blade, and lastly of the 
speed of the ship. As this integral was to be a maximum for all 
points of the surface sought, it must be treated by the known 
methods of the Calculus of Variations. This done, an equation 
of condition was obtained, which, by the performance of the 
operations indicated by the symbols, led to an equation involving 
two factors, each factor being a partial differential, equation 
between the three co-ordinates of the surface. The first of these 
being integrated gave for its solution the whole family of ordinary 
helices which were the surfaces of ast work. The second factor 
was the differential equation of the required surface, the treat- 
ment of which was given in the paper 7 extenso. It led at once, 
and very simply, to an equation analogous to that of the common 
a tan. @ 
a tan. 2a 
3 
From this it was at once deducible, that the surface of the blade 
at the axis cut the plane of rotation at an angle of 45°, while 
the common helix cut it at 90°, and therefore acted powerfully 
in the dead water to propel the ship, just where the common 
helix had no propulsive power. It was proposed to call this 
surface the hemi-helix, or hemi-angular helix.—The paper then 
proceeded to determine the pressure of this blade upon the 
vessel in the direction of the keel, and thence the whole circum- 
stances of the ship’s motion. It was found that there was what 
was called ‘‘a slip,” as in the case of the common helix, The 
author objected to this term, as involving a fallacious theory of 
the action of the screw,—in effect a denial of the equality of 
action and reaction. In order fully to expose the fallacy, the 
motion of a ship impelled by the common helix as a case of 
variable motion in a resisting medium was investigated, and, 
from the identity of the conditions and of their algebraical expres- 
sions it was proved that what was called ‘‘slip” of the screw was 
neither more nor less than ‘‘ the ratio of the difference between 
the velocity which the ship would have in anon-resisting medium 
and its actual terminal velocity in the water to the former 
velocity.” It was proposed, therefore, to substitute for this 
objectionable expression the term ‘‘ ratio of resistance,” or 
‘relative resistance,” as accurately representing the real phe- 
nomena, and measuring the efficiency of the given screw in pro- 
pelling the given vessel, The author was thus further enabled 
to explain what had been called “‘negative slip,” and to assign 
its origin to the joint action of wind and steam, it being impos- 
helix (ton. a namely, tan. °@ = 



sible in the case of steam alone. In the course of the discussion, 
objection was taken to the fundamental principles enunciated in 
the paper ; although those principles used to be almost universal y 
promulgated in mathematical treatises of reputed authority, and 
were commonly even now relied on as the basis of mathematical 
reasoning, by those whose investigations and experimental rc- 
searches had not obliged them to detect their unsatisfact ary 
character, Reference was made, in the first place, to what 
might be called the very foundation of the author’s deductive 
process,—-the proposition that when a plane moved obliquely 
| through a fluid at a given velocity, the normal pressure on its 
surface was as the square of the sine of the angle of obliquity. 
In the second place, to the hypothesis that when the true law of 
pressure on a plane thus moving had been in any way deter- 
mined, the local pressure on each unit of surface of a curved 
surface moving through a fluid could also be determined, by 
applying that law to the unit in virtue of the angle presented by 
its tangent plane to the line of motion. And thirdly to what 
appeared to be a misconception of the dynamical relations, or 
inherent conditions of the slip of the propeller. 
Zoological Society, April 18.—Dr. E. Hamilton in the 
chair. The Secretary read a report on the additions that had 
been made to the society’s collection during the month of March, 
1871. Amongst these particular attention was called to a young 
male specimen of the Cape hunting dog (Zycaon pictus), a species 
which had been deficient to the society’s collection since 1855.— 
Mr. H. E. Dresser exhibited a specimen of the American yellow- 
billed cuckoo (Coccyzus americanus), recently killed in England, 
and Sir Victor Brooke a specimen of the Esquimaux curlew 
(Numenius borealis), lately killed in Ireland.—Prof. Owen, 
F.R.S., read a paper on the dodo (Didus ineptus), containing 
notes on an articulated skeleton of this extinct bird, recently 
prepared from bones exhumed by Mr. Clark in the Mauritius, 
and now exhibited in the Omithological Gallery of the British 
Museum,—A paper was read by Mr. Thomas Davidson, F.R.S. 
(communicated by Mr. J. Gwyn Jeffreys), containing a revised 
account of the recent Brachiopoda dredged by Mr. Arthur 
Adams in the Japanese Seas.—Messrs. Sharpe and Dresser 
pointed out the characters of a new form of long-tailed titmouse, 
which occurs in Southern Spain and in Italy, and which they 
proposed to call Acredula irbit.—Mr. R. B. Sharpe read the 
second part of his ‘‘ Contributions to the Ornithology of Mada- 
gascar,” in which was given an account of a collection of birds 
recently made by Mr. Crossley in that island. Among these 
were a specimen of a new swift proposed to be called Cypselus 
gracilis.—A communication was read from Dr. A. Giinther, 
F.R.S., containing the description of a new form of percoid 
fishes from the Macquarie River, Australia, which he proposed 
to call Ctenolates macquariensis.—A communication was read 
from Dr. James C. Cox, containing descriptions of some 
new species of Jand and marine shells, from Australia and 
the Southern Pacific.—Two communications were read from 
Mr. J. Brazier. The first contained descriptions of some 
new land-shells from New South Wales—the second notes on 
some species of shells recently described by other authors from 
the Australian region. 
Chemical Society, April 20.—Prof. Odling, F.R.S., vice- 
president, in the chair. The following gentlemen were elected 
fellows : C. C. Grundy, J. B. Lee, G. Sutcliffe, W. Ward. Mr. 
C. Haughton Gill read a paper on some saline compounds of 
cane sugar. The author having succeeded in obtaining a 
crystalline compound of sodic chloride with cane sugar, mixed a 
number of sugar solutions with different salts and set them to 
crystallise spontaneously, or when no crystals were obtained by 
these means a more rapid evaporation was tried. The salts 
employed were the chlorides of potassium, sodium, lithium, and 
ammonium ; the bromides of potassium and sodium, and the 
iodides of potassium, sodium, lithium, and ammonium. None 
of the potassium salts gave compounds of a definite composition. 
The sodium salts gave much better results; there were two 
varieties of sodic chloride compounds formed, constituted re- 
spectively 2 (CysH,.0,,) . 3 NaCl. 4 H,O and C,,H4.0;, . 
Na Cl. 2 H,O; the solutions containing sodic bromide gave 
crystals of the composition C,,H,.0,,. Na Br. 14 H,O, they 
were probably not quite pure ; the sodic iodide combination, 
2 (CypH.0,,) . 3 Nal . 3 HO, formed very fine crystals. Tle 
mixture containing lithium gave only crystals of pure cane 
sugar. ‘The constitution of the sodic iodide compound makes 
it seem probable that the true molecular weight of cane sugar 
