The foregoing Table contains the lengths of all the radii, to three places of decimals, and will be of use for volutes upon a large scale. And instead of constructing a scale for every different spiral, the sector nifty be used, which is an universal scale to any distance within its reach.
But no instrument can be more easily or more accurately applied, than the proportional compasses; for if the slider be so shifted, that the two long legs may be to the two short legs in the ratio of the two first radii, then all the remaining radii may be found by extending the points of the long legs to the shortest radius, which will give the length of the next shorter radius between the points of the short legs ; and by proceeding in this manner till all the points are found, the curve may be drawn as before directed.
Plate volute drawn according to the preceding principles, consisting of three spirals; the numbers affixed round the outer spiral are supposed to be minutes, and con sequently no other scale will be required than that of the order itself; but in drawing the two interior spirals, two new scales must be'formed ; or the scale of the order might be made to answer the purpose, by setting the proportional com passes in the ratio of the two radii, then taking the length of the radii from the scale with the long legs, and transferring the distances between the short legs to the spiral, and draw ing the curve; so that the whole may be completed as before.
The volute in this Plate is similar to that of the Ionic temple at Athens, the temple of Bticellus at Teos, and that of _Minerva Polias Prieue in Ionia.
Plate III. Figure 1.—A volute in imitation of that of the temple of Ereehthens, at Athens, drawn according to the preceding principles. It consists of eleven spirals. which may be all drawn front the scale of the order by the assist ance of a pair of propuitional compasses. But if this useful
instrument is not in the hands of the delineator, the eleven scales are here exhibited at Figure 2, for drawing the same number of spirals.
An universal scale may be made, as in Figure 3, thus: describe an equilateral triangle, c A n, upon c a, equal to the greatest radius; divide c a into twenty equal parts, and greatest straight lines from the points of division to A; produce c a to b, and make equal to one of the equal parts; divide b into ten equal parts, and draw lines to A ; then make A D and A E each equal to the first radius, and draw the line E n, which produce to meet A b at d; then E D d will give the scale for drawing the spiral required E D being the scale of units, and D d that of tenths; and thus any other radius may • be divided at once.
Figure 4, is another method of obtaining an universal scale, by means of a right-angled triangle, A a c, right-angled at c, making c a and c A equal to each other : but there is no method so exact and expeditious as the proportional com passes, and one scale, which may either be that of the order or not, and consequently any scale divided into units and tenths will answer the purpose, if this instrument be used.
Plate 1V. shows a design for the capital and base of an Ionic column, with the details of capital and volute.
Figure 1.—Front view of the capital.
Figure 2.—Plan of the same.
Figure 3.—Profile or section through the front.
Figure 4.—Section through the flank.
Figures 5, 6, and 7.—Parts of the capital enlarged. Figure 5.-1Ialf of the front, showing the sections through the volute and through the front.
Figure 6.—Elevation of the flank.
Figure 7.—Section through the front.
Figure S.—Elevation of the base of the column to the same scale as Figure 1.