PROBLEM XIII.

TO GAUGE A CASK OF THE FIRST FORM.

There are four different forms of cafks, being diftinguished from each other according to the greater or lefs curvature of their fides; namely, firft, that which refembles the middle fruftum of a spheroid, whose sides have a greater swell than those of any other form. Secondly, that which resembles the middle fruftum of a parabolic fpindle, whofe fides have not so great a swell as those of the former; and whose length is lefs in proportion to its diameter. Thirdly, that which refembles the two equal fruftums of a paraboloid; and whose fides fwell the leaft of all. Fourthly, that which resembles the two equal fruftums of a cone, and whose fides have no curve, but run straight from each end to the middle of the cafk, where they form a very obtuse angle.

To find the contents of a cafk of the first form, regard must be had to that scale on the rule which is marked firft variety ; then, having the length of the cask, which fuppofe to be 40 inches, and diameters at the head, and bung, 24, and 32 inches; fet 40 on the line C to the ale gauge 32.82 on D, and against

24 on D stands

32 on D ftands

21.3

on C

38.0 on C

Again, fet 40 on C to the wine gauge 29.7 on D, and

PROBLEM XIV.

TO FIND THE CONTENT OF A CASK OF THE SECOND FORM.

Let the length, and head, and bung diameters be the fame as in the laft Problem: then, having fet 40 on C to 32.82 on D, against 8 on D stands 2.4 on C, of which is 0.96. This, fubtracted from 97.3, the contents of the last form, leaves 96.34 ale gallons.

Again, having fet 40 on C to 29.7 on D, against 8 on D ftands 2.9 on C, of which is 1.16, which, taken from 119.1, in the laft form, leaves 117.94 wine gallons.

1

PROBLEM XV.

TO FIND THE CONTENT OF A CASK OF THE THIRD FORM.

The dimensions being the fame as in the foregoing Problems, fet 40 on C to 26.8 on D, then against

Again, fet 40 on C to 24.25 on D: then against

TO FIND THE CONTENT OF A CASK OF THE FOURTH FORM.

The dimenfions being the fame as before, fet 40 on C to 65.64 on D, then against

Again, fet 40 on C to 59.41 on D; then against

TO FIND THE CONTENT OF A CASK BY THE DIAGONAL ROD.

Apply the rod within the cafk, from the bung-hole to the end of the oppofite stave; then take the length of the diagonal, or the measure of the rule from the middle of the bung. hole to the end of the faid ftave, which fuppofe to be 34-4 inches; then to 34.4 inches on the rod correfpond 90 ale gallons, or 111 wine gallons, the content required *.

PROBLEM XVIII.

TO FIND THE ULLAGE OF A CASK BY THE RULE.

By one of the foregoing Problems find the whole content of the cafk; then set the length on N to 100, on S S for a fegment standing, or fet the bung diameter on N to 100, on SL for a fegment lying; and then against the wet inches on N is a number on SS or SL to be reserved.

* The contents thus found by the rod give the true contents of the moft common form of cafks only; that is, fuch as fall between the second and third forms; of this form are those chiefly used by the London brewers,

Next, fet 100 on B to the referved number on A, and against the whole content on B will be found the ullage on A.

There are many folid figures befides the foregoing, the contents of which cannot be found by any actual dimenfions taken on the figure, fuch as ftatues, &c. The contents of fuch bodies are found by immerfing them in water, and meafuring the rife of the water occafioned by such immersion.

SECT. V.

A VIEW OF THE FIVE ORDERS OF ARCHITECTURE.

The origin of architecture is almoft contemporary with that of civil fociety. When mankind felt the inclemencies of the weather, and, confequently, found the neceffity of erecting habitations for shelter, eafe and convenience foon improved itself into ornament and grandeur. A few trees perhaps growing round in a circle, and leaning together at the top, afforded the first habitations, being interwoven with twigs, and plastered over with mud. This gave rise, in after-ages, to the idea of columns.

It is probable that the inconvenience of these habitations rendered their owners defirous of inventing such as should anfwer every purpose of the former fort, and poffefs feveral advantages above thofe: this improvement naturally gave rife to the invention of the cross beams to fupport the roof; for this purpose, they had, no doubt, recourfe to the trunks of trees: thus columns were at once introduced."

VOLI.

3*

The

The Egyptians were the first people from whom the Greeks derived all their knowledge of architecture; as ap pears from thofe ancient remains, the pyramids; and from the ruins of a magnificent temple at Luxor, the ancient Thebes, of which there remain more than 130 columus, all of confiderable magnitude; fome 10 feet in diameter, with elegant sculpture: and feveral other remains in the neighbourhood of the fame place.

The fertile genius of the Greeks foon improved upon the ponderous architecture of Egypt, whose ignorance in constructing the arch made it necessary for the columns to stand very thick, with large and ftrong architraves.

The Tufcans (or Etrufcans) were also very skilful in building; from whom the Romans received great help in architecture, in all their large works: the temple of Jupiter Capitolinus, the Cloaca Maxima, &c. are the works of Tuscan artists.

To produce the authority for every species of ornament in each of the five orders, would be impoffible, at the present day; I fhall, therefore, point out the more general parts, with the origin of their introduction.

1. The PLINTH was, no doubt, at first a square stone, or tile, placed under the tree or primitive column, only to prevent its rotting by the conftant moisture of the earth, and also to serve as a folid footing to the column.

2. The TORUS is the fwell above the plinth, and originated, no doubt, from the form of the tree, being thicker at the bottom than the part above, by which means it was fixed more firmly on the plinth: by fome it was conjectured to have been a rope or bandage only, round the trunk, to prevent its splitting.

3. The CAPITAL had its origin from the parts of the tree where the arms were cut off: the fwell of the arms gave the idea of the fwell of the capital, which is attended with this advantage, by being broader at the top, it is better formed for fuftaining the works above.

4. The