TRANSACTIONS OF THE SECTIONS. 189 
Some Facts on the Flow of Water through Circular Pipes. 
By J. NEvIcce. 
On the Submarine Electric Telegraph Cable. By A. BALESTRINI. 
On the Principle of the Transformation of Structures. 
By W. J. Macauorn Rankine, LL.D., F.RS. L. and E. 
This paper consists of an explanation of some of the practical applications of a 
_ principle first communicated by the author to the Royal Society in 1856, viz.—if a 
_ structure of a given figure be stable under a system of forces represented by given 
lines, every structure whose figure is a parallel projection of the given figure is stable 
_ under a system of forces represented by the corresponding parallel projections of the 
given lines. 
(Two figures are said to be parallel projections of each other when every pair of 
parallel and equal lines in one figure corresponds to a pair of parallel and equal lines 
in the other. Thus all circles and ellipses are parallel projections of each other; so 
also are all spheres and ellipsoids.) 
This principle enables the design for a bridge with a sloping extrados and a distorted 
semi-elliptical arch to be deduced from the design for a bridge with a horizontal 
extrados and a semicircular arch. In like manner, from the figure of an equilibrated 
arch for sustaining the pressure of a fluid, which is equal horizontally and vertically, 
can be deduced the figure of an equilibrated arch for sustaining the pressure of earth, 
which is less horizontally than vertically in a given ratio; and various analogous 
roblems can be solved with ease by the principle of the transformation of structures, 
whose solution by a direct process would be very tedious and difficult. 
ad eee 
Continuation of Experiments to determine the Resistances of Screw-Propellers 
when revolving in Water at different Depths and Velocities. By 
GeorceE Renniz, F.R.S., Sc. 
My former experiments exhibited some curious phenomena on the effects produced 
on the resistances of screw-propellers when revolving in water at high velocities and 
at different depths. ‘The first idea of driving screw propellers at high velocities and 
immersed at different depths was stated to be due to Mr. Joseph Apsey, an engineer 
of Broad Wall, in the parish of Christ Church, Surrey, but from the experiments 
_ having been made in a close boiler, objections were made to them at Glasgow as being 
fallacious; and it was only after similar experiments had been made by me in the 
open water in the river Thames that they were confirmed. Those results were given 
_ in my last paper, published in the ‘ Transactions of the British Association’ in 1856, 
__ Both series of experiments proved that the influence of velocity was much greater 
than that of depth, but that the joint action of velocity and depth was very remark- 
able. The present paper contains the results of experiments made on differently 
formed propellers, for the purpose of ascertaining, first, the effects of screw-propellers 
when confined in tubes of a conical form; secondly, the effects of form of propellers 
working alone and not in tubes. 
The common two-bladed screw, 13 inches diameter, 
_ pitch 20 inches, 600 revolutions per minute, when working 
in a depth of 12 inches above top of screw, gave a pressure 
: : ft. in, 
a ; 1 5% diameter, Jarge end. 
of 69 Ibs, in a conical tbe} 1 23 Pe small end. 
ae 1 7 in length, 
The same two-bladed screw, when immersed and work- 
n a depth of 12 inches above top of screw, gave a 
ure of 144 lbs., or more than double of the pressure 
when confined by the tube. 
Without working in a tube.—Effects produced by a three-bladed 
ew-propeller of similar diameter, 134 inches and pitch 20 inches, 
a of circle 1 square foot to the two-bladed, screw and moved 
he same velocity of 600 revolutions per minute, and immersion 
2 inches above the level of the screw without a tube,—157 lbs. 
