TRANSACTIONS OF THE SECTIONS. 207 
On an Instrument for describing Spirals. 
By the Rev. James Bootnu, LL.D., F.R.S. 
This is the invention of Mr. Henry Johnson of Crutched Friars, and is called by 
him a yolutor, with reference to its practical use. 
It admits of several varieties ; and the earliest form affords a simple illustration of 
the principle of the spiral line,—that is, of a line revolving round a point at one end, 
as round a centre, while a marking point travels, during the revolution, from the 
inner end or centre to the outer end of the line. It consists of a vertical axis resting 
on a horizontal plane, and retained on it by a metal point to prevent slipping or 
lateral motion. To this upright axis is attached one extremity of the horizontal 
arm or bar. The vertical axis passes through the extreme end of the horizontal 
arm, or a block attached to the end of it, in such a way that the horizontal arm 
may freely revolve round the vertical axis. The remote extremity of the horizontal 
bar is furnished with a drum or pulley, over which a chain or band passes. 
One end of this band is fixed to the centre upon a level with the pulley; and 
the other end of the chain or band, after passing over the pulley at the outer end of 
the horizontal rod, returns and is fastened to a slide upon the horizontal bar, 
which carries a pencil or pen, and is placed at the inner extremity of the bar, close to 
the vertical axis. 
The horizontal bar is caused to revolve; and the band is thus wound round the 
centre, and the slide, with its pencil, is drawn along the bar from the centre towards 
the pulley,—the spiral curve traced upon the horizontal plane by the pencil being 
the result of the compound motion of the point travelling along the revolving line. 
The form of the centre, if cylindrical, would lead to a regular increase in the radius 
of the spiral; but by the substitution of grooved cones, any required ratio of increase 
may be obtained. 
A recent form of the instrument is even more simple than the one described,—the 
slide being dispensed with, and the pencil being attached to the horizontal bar, 
which glides through a horizontal tube fixed to the lower part of the vertical centre. 
The upper part of the vertical centre being a cone, with its handle is held stationary 
by the hand, while motion is given to the lower part with the horizontal tube by a 
small winch handle fixed on a wire descending through the cone and its handle. 
The end of the bar bearing the marking pencil recedes from the centre as the outer 
end is drawn towards the centre by the band wound round the vertical axis. 
To the horizontal tube and to the outer end of the bar are attached series of 
pulleys ; and a variety of curves may be obtained by passing the band over two or 
more pulleys, and thus dividing among several lines the effect of the band wound 
round the centre. 
On the Roof of the New Town Hall at Leeds. By C. Bropricx, Architect. 
The principal points which are worthy of notice in this roof are the absence of tie 
beams, which allows of the ceiling of the hall being brought nearer to the exterior 
of the roof than is usually the case. The roof consists of eight sets of principals 
framed together. Each principal consists of a semicircular laminated rib, formed of 
twelve 11-inch planks, 9 inches wide, nailed together and fastened with wrought iron 
bolts and straps. They are placed in couples, and stand immediately over each of 
the columns in the hall. They are respectively 4 feet and 18 feet apart, The width 
of the room is 71 feet, and the springing of the ribs 53 feet from the ground. The 
entire height to the top of the roof is 99 feet, the hall being 73 feet high in the clere. 
This system of roofs has been adopted more frequently in France than in England, the 
only one with which Mr. B. was acquainted of any considerable size being the station of 
the Great Northern Railway, at King’s Cross, The laminated rib is the invention of a 
French engineer. It was at first suggested for a bridge over the Rhine, in the year 1811, 
Several years later, M. Emy constructed several roofs on this plan; but all his roofs, 
as well as the one at King’s Cross, being very near to the ground at their springing, 
and without ceilings, are consequently much more manageable than the roof of the 
Town Hall, which has a very elaborate plaster ceiling attached to it, and the spring- 
ing is at aconsiderable distance from the ground: he had taken the precaution to in- 
sert several additional struts and braces as a preventive against any change of form 
