Templum (Latin), a temple. Temples appear to have existed in Greece from the earliest times; they were separated from the profane land around them, and the entrances were much decorated as architecture advanced. Tenacity, that quality of bodies by which they resist tension or tearing asunder

Tender, the carriage which is attached to a locomotive engine, and contains the supply of water and coke Tenon, in carpentry, the square end of a piece of wood or metal diminished by one-third of its thickness, to be received into a hole in another piece, called the mortise, for the jointing or fastening of the two together

Tension, a force pulling or stretching

a body, as a rod. Animals sustain and move themselves by the tension of their muscles and nerves. A chord, or string, gives an acuter or deeper sound as it is in a greater or less degree of tension, that is, more or less stretched or tightened. Tension-rod, an iron rod applied to

strengthen timber or metal framing, roofs, &c., by its tensile resistance Term, a piece of carved work placed

under each end of the taffrail of a ship, at the side timbers of the stern, and extended down as low as the foot-rail of the balcony Terra cotta, in the arts, baked earth, bricks, tiles, &c.

Terra di Sienna, or Raw Sienna

Earth, a ferruginous native pigment, which appears to be an iron ore, and which may be considered as a crude natural yellow lake, firm in substance, of a glossy fracture, and very absorbent. It is in many respects a valuable pigment, of rather an impure yellow colour, but has more body and transparency than the ochres; and being little liable to change by the action of either light, time, or im. pure air, it may be safely used, according to its powers, either in oil or water, and in all the modes of

practice. By burning, it becomes deeper orange, and more transparent and drying. Terre-verte, an ochre of a bluishgreen colour; in substance moderately hard, and smooth in texture. It is variously a bluish or gray coaly clay, combined with yellow oxide of iron, or yellow ochre. Although not a bright, it is a very durable pigment, being unaffected by strong light and impure air, and combining with other colours without injury. It has not much body, is semi-transparent, and dries well in oil. There are varieties of this pigment; but the green earths which have copper for their colouring matter are, though generally of brighter colours, inferior in their other qualities, and are not true terre-vertes. Tesselated, in the arts, variegated by

squares; exemplified in the beautiful pavements of the ancients Tessera, small cubical pieces of brick,

stone, or composition, forming part of an ancient Roman mosaic or tesselated pavement

Testaceous, consisting of shells; made of baked earth, or of tiles or bricks Tetragon, a quadrangle, or a figure having four angles

Tetrahedron, in geometry, one of the five regular bodies of solids comprehended under four equilateral and equal triangles. It may be conceived as a triangular pyramid of four equal faces. Tetrants, the four equal parts into

which the area of a circle is divided by two diameters drawn at right angles to each other Tetrastyle, a portico, &c. consisting of four columns. A cavædium was called tetrastyle when the beams of the compluvium were supported by columns placed over against the four angles of a court. Thatch, straw or reeds employed for covering the roofs of buildings; particularly used for cottages Thaughts or Thwarts, in navigation, the benches or seats in a boat

Theatres, edifices of various but principally of large dimensions, for dramatic exhibitions Theatrum, a theatre. The Athenians,

before the time of Eschylus, had only a wooden scaffolding on which their dramas were performed. It was merely erected for the time of the Dionysiac festival, and was afterwards pulled down. Theodolite, in surveying, a mathematical instrument for measuring heights and distances. (See Heather's work on Instruments.) Theory, a doctrine which terminates

in the sole speculation or consideration of its object, without any view to the practice or application of it. To be learned is an art, and the theory is sufficient; to be master of it, both the theory and practice are requisite. Machines often promise very well in theory, but fail in practice. A remarkable circumstance may be instanced of a gentleman of British North America selling his estate and leaving his home to give practical effect to a theory he had, as he considered, beautifully worked out in figures, for an important improvement in steam machinery. His theory, however, wholly failed on its first application in practice. Theory, mathematical, the algebraic elucidation of the principles of any physical system, where assumptions are made, in the absence of positive data: the calculated results are expressed in formulæ, which are easily convertible into arithmetical rules. Among others, the Theory of the Steam Engine,' by the Count de Pambour, has been found to be most useful for practice; and the following is an explanation of his mathematical investigation, designed for persons not familiar with the algebraic signs, and intended to render clear and easy the use of the formulæ contained in the abovementioned work, and which may be said to have reference to all mathematical works.

Among persons engaged in the construction or working of steam engines, there is a great number to whom the algebraic terms are little familiar, and who usually give up the reading of a book as soon as they perceive that it steps beyond the simple notions of arithmetic. When it is intended to make a work profitable to those persons, the usual practice is to annex to each of the definitive formulæ an explanation, in full words, of the arithmetical operations which it represents.

The want of such explanation may be very advantageously supplied, by giving the signification of every sign employed in the formulaæ; by explaining what are the arithmetical operations represented by those signs. With the help of a very few rules on this subject, persons will find that the reading of the formulæ is quite as easy in algebraic signs as if they were written in words; since, after all, it is but an abridged way of expressing the same things, and, moreover, the operations to be performed, in order to attain the result, are much more clear, and more easy for the mind to seize. Again, a perfect acquaintance with the signification of the signs in common use can require but a few hours of attention, and when once a person shall have made himself master of them, he will be capable of reading the formulæ of all works.

....

A, B,... a, b,... l, m, n,.. .. a, B,.. &c. The letters are an abridged manner of writing the numbers which those letters represent. Thus, when the stroke of the piston has been measured, and found, for instance, to be 17 inches, it would be inconvenient to write in all the formulæ the number 17. But if the length of stroke, whatever it might be, has been represented by a letter, as 1, for instance, then, every time the letter 7 occurs, there needs only to recollect that it represents the num

It would be the same if we were to find one fraction divided by another. Each of them should be first reduced to a single number by finding the quotient they represent, and then the one of these quotients divided by the other.

() or [ ] or { }.... Paren theses indicate that the different quantities contained between them are to be reduced to a single number before performing the other operations indicated in the formula. Thus, for instance, if we find in a formula the expression

(1 + 8)v,

this means, that it is the expression (18) entire, which is to be multiplied by v. The sum then of 1+ is first to be formed, and afterwards multiplied by the number v; whereas, had we only

1 + δυ,

this would mean that the product dv is first to be formed, and afterwards the number 1 added to it.

There may occur several parentheses comprised one within the other, but their signification is always the same. The expression

002415 [(1+8) r + ƒ]

denotes that the sum of 1 + 8 is to be formed first, this to be multiplied by r, and the product added to the quantity f, which gives the number represented by the outer parenthesis; and finally, that this number is to be multiplied by ⚫002415.

Lastly, when there occurs in the formulæ a letter with a small figure or exponent above it, it is the same thing as writing that letter as many times successively as there are units in the figure or exponent.

For instance, the expression

v2

is equivalent to the expression

THE

=

These short explanations are all that is necessary, in order to read and perfectly understand all practical formulæ. Replacing each of the signs that are met with in a formula, by the periphrasis which the sign represents, you read the formula such as it ought to be expressed; and effecting the arithmetical operations indicated by those signs, you attain the result sought. A formula is, then, nothing more than an abridged manner of writing the series of operations to be performed, in order to arrive at the result which we want to obtain.

We will subjoin to this explanation some examples, taken from the practical formulæ of highpressure engines.

&=

I. Suppose we have the formula

a 6.6075002415 [(1+8) r + ƒ]'

which is intended to determine the unknown value of v; and let it be supposed that we know, besides, that the other letters comprised in this formula have the following value:

THE

indicated by the outer parenthesis, viz.

[(1 + d) r+ƒ]=3154.

Now multiply this sum by the number 002415, and the product will evidently be

·002415 [(1+8) r+ƒ] =·002415 × 3154 7.6170.

Add to this last result the number 6.6075, and you obtain 6.6075+.002415 [(1 + d) r +ƒ]=

6.6075+7.6170=14.2245.

This is then the denominator of the fraction which forms the second member of the formula. Performing the division of the number 10000 by the number just obtained, the quotient will be

Finally, then, multiplying this latter quotient by that obtained immediately above, you have definitively

S

10000

a 6.6075002415 [(1+8)r+f] ='4268 × 703.04=300.

Thus it is clear that by effecting successively the series of calculations indicated by the few signs which are explained, and proceeding gradually from the most simple terms to the more compounded ones, we arrive without difficulty at the definitive result.

We will give some other examples of these calculations; but, instead of effecting the operations, we will merely express in words