130 _.... REPORT—1852. 
pose, called the Screw Helicograph. This instrument has been elaborated into the im- 
proved form now exhibited. By simply turning round the graduated ring within the 
square frame, this instrument is enabled to draw in pencil or ink any form of the equi- 
angular spiral from the circle to the straight line; and, by alterations in the position of 
the pen, or of the centre, with respect to the guide bar, certain variations may be ob- 
tained. Also either a parallel line to the first may be drawn by a simple adjustment 
of the pen, or a duly converging line, by bringing the whole frame nearer to or farther 
from the centre. Expressing the ratio between two spiral radii at an interval of 360° 
(viz. a7) by the term ‘ spiral ratio,’ it appears that curves drawn with this instrument 
with spiral ratios less than 8 or 10 to 1 are fitted for volutes and scroll-work, and 
those which are drawn with higher ratios form the outlines of vases and other such 
figures where a gentle variation of curvature is desired. This quality is ensured from 
the property of the curve that the radius of curvature is proportional to the length of 
the are. For figures where great energy is required, curves of a different nature are 
more suitable, but no curves appear to surpass these in sweetness of sequence.” 
On some Properties of Whirling Fluids, with their application in improving 
the action of Blowing Fans, Centrifugal Pumps, and certain kinds of 
Turbines. By James Tuomsoyn, A.M, Civil Engineer, Belfast. 
The author pointed out several properties possessed by masses of fluids revolving 
in the circumstances of one of the most ordinary kinds of whirlpools, that, namely, 
which is formed when water is supplied at the circumference of a widely extended 
vessel, with a very slight rotatory motion, and is allowed to flow away by a central 
orifice in the bottom. Of these properties, the following, in which the influence of 
friction is left out of consideration, may be cited :— 
The equation of the curve whose revolution would generate the curved surface of 
the whirlpool is 
Snes! 
where y is the depth of any point of the curve below the level of the fluid taken 
at any part far away from the whirlpool, where there is no perceptible depression, 
a the distance of the point from the axis of revolution, and © a constant 
quantity. : 
Every point of the surface of the fluid moyes with the velocity which a heayy body 
would attain in falling from the level of the surface far away from the whirlpool to 
the level of the point. Also every point in the interior of the reyolying mass 
moves with the velocity of the point on the surface vertically above itself; and it 
follows, that the velocities of points at various distances from the centre are in- 
versely proportional to the distances. It follows also that the yelocity of each point 
in the mass, is the greatest that is possible without an increase of the velocity of 
every other point revolving further from the centre. 
He was led from these and other properties of whirling fluids, to find that the 
efficiency of centrifugal pumps for water, and of fans for causing blasts of air, may 
be greatly increased by the provision, outside of the circumference of the wheel, of 
a space in which the fluid may continue to revolve without any interruption after it 
has left the wheel. He mentioned also, that an apparatus termed a “‘ diffuser,”’ and 
involving the same principle, has recently been applied with good results, in turbines 
of great power constructed in America. 
On a Jet Pump, or Apparatus for drawing up Water by the Power of a Jet. 
By James Tuomson, C.Z. ; 
The purpose for which the author has designed this new pump, is to clear the 
water out of the pits of submerged water-wheels, when access to them is required for 
inspection or repairs. This pump may also be used for raising water in other cases 
where an abundant fall of water is available; as, for instance, for draining a marsh 
in the neighbourhood of a waterfall. Its action depends on two principles, One of 
these is the same as that of the steam blast used in locomotive engines, and in the 
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