440 
Synopsis OF GRANTS OF MONEY appropriated to Scientific 
Purposes by the General Committee at the Liverpool Meeting 
in September 1870. The names of the members who would 
be entitled to call on the General Treasurer for the respective 
Grants are prefixed : 
Kew Observatory 
REIS? 2, 
The Council. —Maintaining the Establishment of 
Kew Observatory . ‘ 600 0 O 
Mathematics and Physics 
*Brooke, Mr.—British Rainfall 50 0 O 
*Thomson, Professor Sir W.— —Underground ‘Tem- 
perature . : 150 0 0 
*Tait, Professor. Thermal “Conductivity of Iron 
and other Metals . : 20 0 0 
*Thomson, Professor Sir W. Tidal Observ ations | ~ 19070) 0 
*Glaisher, Mr.—Luminous Meteors. =) 30: OO 
Crossley, Mr.— Observations of Lunar Objects 5) BOO. OD 
Herschel, Sir J.—Recomputation of the Gaussian 
Constants for 1839 . 50 0 O 
Stewart, Professor B Standard Measures of 
Electrical Capacity . = 20) 10) (0 
Hockin, Mr.—Standard Electrodynamometer 20 70 fo 
Thomson, Professor Sir W.—Standard Potential 
Gauge . : r * ‘ . 5 fas 20 40) (0 
Chemistry 
Williamson, Professor.—Reports of the Progress | 
of Chemistry . . 3 100 0 0 
Brown, Professor Crum. —Thermal Equiv alents of 
the Oxides of Chlorine . 25 00 
Geology 
*Lyell, Sir C., Bart.—Kent’s-Cavern Exploration. 150 0 © 
*Duncan, Dr. *p. M.—British Fossil Corals . « 25 20"\0 
*Symonds, Rev. W. S.—Sedimentary Deposits in 
the River Onny i 10 0 O 
*Mitchell, Mr. W. S. —Leaf- beds of the Lower 
Bagshot series. . 20 0 0 
Thomson, Mr. James. ~Sections of Fossil Corals. 20 0 0 
Scott, Mr. R. H.—Mesozoic Deposits of Omenak, 
North Greenland. | 50) Ono 
Woodward, Mr. H. —British Fossil Crustacea 25 G O 
Busk, Mr.—Fossil Elephants of Malta 25) Gn 0 
Biology 
*Carruthers, Mr.—Fossil Flora of Britain. 22° 6-0 
*Sharpey, Dr.—Physiological Action of Methyl 
Compounds. 25,0 16 
*Sclater, Mr.—Record of the Progress of Zoology Too 6 6 
*Foster, Professor M.—Heat Generated in the 
Arterialisation of Blood . I5 0 0 
Balfour, Professor.—Effect of the Denudation of 
Timber on the Rainfall in North Britain . 7 420)0) 0 
Geography 
Murchison, Sir R. J., Bart.—Exploration of the 
Country of Moab 5 F i00 0 O 
Statistics and Economic Scieice. 
“Bowring, Sir J.—Metrical Committee . é 25 00 
£1840 0 0 
SECTIONAL PROCEEDINGS 
SEcTION A.—MATHEMATICAL AND PHYSICAL SCIENCE 
Abstract of an Investigation of the Mathematical Theorv of 
Combined Streams. — Professor W. J. M. Rankine, F.R.S, 
The object of the investigation of which this is an abstract 
is to extend to combinations of any number of streams of 
fluid, whether liquid, vaporous, or gaseous, the principles 
which have been applied to combinations of two streams by 
previous authors, and especially by Professor Zeuner, in his 
treatise entitled ‘‘das Locomotiven-Blasrohr” (Ziirich, 1863). 
Several component streams of fluid, each coming through its 
own supply-tube and nozzle, are led in directions parallel to 
each other, into one end of a cylindrical space called the junction- 
* Re-appointed. 
NATURE 
| end and at the throat end of the chamber respectively. 
[ Sept. 29, 1870 
~ 
chamber, in which they mingle so as to form a resultant stream 5 — 
and that resultant stream escapes from the other end of the 
junction chamber through an orifice called the throat. The 
dynamical principle upon which the motion depends is that of 
the equaiity of impulse and momentum. The aggregate mo- 
mentum per second of the component streams is found by 
multiplying the mass of fluid which comes from each nozzle in a 
second by its velocity, and adding together the products. The 
momentum of the resultant stream is the product of the mass ot 
fluid discharged from the throat in a second, into the velocity at 
the throat. The difference of these two momenta is equal to 
the impulse per second exerted in the junction-chamber, which 
impulse is found by multiplying the area of the throat by the 
difference between the intensities of the pressure at the nozzle 
If there — 
be a gain of momentum, the pressure at the throat is less than _ 
at the nozzles ; if there be a loss of momentum, the pressure at A 
the throat is greater than at the nozzles. j 
There is always a loss of energy, which is expended in pro- — 
ducing eddies; unless the velocities of the component and 
resultant streams are all equal to each other. The amount ot 
that loss can be calculated in any given case, by the help of the 
principle already stated ; and that principle being expressed in 
the form of an equation, and taken together with another — 
equation expressing the equality of the mass discharged at the — 
| throat to the sum of the masses which come through the nozzles, 
: 
affords the means of solving various problems as to combined — 
streams, 
Abstract of a Paper on the Thermo-dynamic Acceleration and 
Retardation of Streams.—Professor W. J. M. Rankine, F.R.S.* 
The object of this paper is to state in a more general and 
comprehensive form than has hitherto been done to my 
knowledge, a thermo-dynamic and hydro-dynamic principle of 
which many particular cases are well known and understood. 
That principle may be stated as follows :— 
In a steady stream of any fluid, the abstraction of heat at and y 
near places of minimum pressure, and the addition of heat at and 
near places of maximum pressure, tend lo produce acceleration ; 
the addition of heat at and near places of minimum pressure, and 
the abstraction of heat al and near places of maximum pressure, 
tend to produce retardation ; ina circulating stream, the quantity 
of energy of flow gained or lost in each complete circuit ts equal to 
the quantity of energy lost or gained in the form of heat; and in \ 
the absence of fr ‘ction, the ratios borne by that quantity to the heat | 
added and the heat abstracted (of which it is the difference) are | 
regulated by the absolute temperatures at which heat is added and — 
abstracted, agreeably to the second law of thermo-dynamics. 
- Amongst particular cases of the thermo-dypamie acceleration 
and retardation of streams, the following e specified :— 
Acceleration by the addition of heat at and near a place of 
maximum pressure; the draught of a furnace; and the pro- 
duction of disturbances in the atmosphere in regions where the 
ground is hotter than the air, 
Retardation by the abstraction of heat at and near a place of 
maximum pressure ; the dying away of atmospheric disturbances 
in regions where the ground is colder than the air. 
Acceleration by the abstraction of heat at and near a place of 
minimum pressure ; the injector for feeding boilers, in°which a 
jet of stream, being liquefied by the abstraction of heat, is en- 
abled not only to force its way back into the boiler, but to sweep 
a current of additional water along with it ; also, to a certain ex- | 
tent, the ejector-condenser. | 
The conduction of heat from the parts of a stream where 
the pressure and temperature are highest, to the parts of the 
same stream where the pressure and temperature are lowest, pro- 
duces, according to the foregoing principles, a gradual and per- . 
manent retardation of the stream, independently of the agency of 
friction; and this is accompanied by the production of heat to 
an amount equivalent to the lost energy of flow. 
Srecrion B.—CHEMICAL SCIENCE 
On the Weldon Process for the Manufacture of Chlorjne.—Mx. 
W. Weldon, F€,S., the author, said the process was one for 
the manufacture of chlorine by means of a perpetually-regene- 
rated reagent consisting mainly of a compound containing the 
elements of peroxide of manganese and lime, and which was 
previously unknown. He had described the process last year at 
* Printed in full in the ‘‘ Philosophical Magazine ” for October, 1870. 
