So is twice the height of the fluid,

To the distance which it will spout.

If the apertures be made at equal distances from the top and bottom of the vessel, (kept full of fluid), the horizontal distances to which the water will spout from these apertures will be equal; and when the orifice is made at the point bisecting the altitude of the fluid in the vessel, the fluid will spout to the greatest distance on the horizontal plane.

From experiment we may derive the following conclusions; viz.

serted in the vessel whose length is from two to four times the diameter of the orifice, then a greater quantity of water will be discharged through it than through the simple aperture, in an equal portion of time, all other circum. stances remaining the same; the quantity of the fluid discharged, in the two cases, being to eacli other as 133 to 100 nearly.

DISCHARGER, or DISCHARGING Rod, in Electricity, is a rod used for the purpose of discharging a jar or battery of its contents, with out injury or pain to the operator.

DISCOUNT, or REBATE, is an allowance made on a bill or any other debt not yet become due, in consideration of present payment. The rule for finding discount is this:

1. The quantities of fluid discharged, in equal times, from different-sized apertures, the altitude of the fluids being the same, are to each other nearly as the areas of the apertures. 2. The quantities of water dis-given rate and time charged, in equal times, by the same aperture, with different altitudes of water in the reservoir, are nearly as the square roots of the corresponding altitudes of the water in the reservoir above the centre of the aperture.

As the amount of £1. for the

3. That, in general, the quantities of water discharged, in the same time, by different apertures, and under unequal altitudes of the water in the reservoir, are to each other in a compound ratio of the areas of the apertures, and the square roots of the altitudes.

4. That on account of the fric

tion, the smallest apertures discharge proportionally less water than those that are larger and of a similar figure, the water in the re spective reservoirs being at the same height.

Is to the given sum or debt, So is the interest of £1. for the given rate and time

To the discount of the debt. So that if p be the principal or debt, r the rate of interest, and t the time;

prt

then as 1+rt:p:=: rt:
1+rt
which is the true discount. Hence
prt
also p
- is the
1+rt Irt
present worth, or sum to be re-

ceived.

Or, making a to represent the present worth, we have

@=

P
1+rt

the present value

p=a(1+rt) the sum due

2=

ar

=

the number of years

= the rate of interest.

p-a at Bankers and others who discount

5. That of several apertures whose areas are equal, that which has the smallest circumference will discharge more water than the other, the water in the reser-bills of exchange, usually charge voirs being at the same altitude, the interest. and this because there is less friction. Hence, circular apertures are most advantageous, as they have less rubbing surface under the same areas.

To this we can only add, that if instead of the orifice being pierced in a plate of tin or other thin plate, a cylindrical pipe or tube be in-J

DISCRETE, or DISJUNCT Proportion, is that in which the ratio between two or more pairs of numbers is the same, and yet the proportion is not continued, so as that the ratiò may be the same between the consequent of one pair and the antecedent of the next pair.

Thus 3: 6:5:10 is a disjunct

and the hole in it to the right and leit hand; and taking a small rod, crooked at the end, retire from the ring two or three paces; and having with one hand covered one of our eyes, to endeavour with the other to pass the crooked end of the rod through the ring. This appears very easy; and yet upon trial, perhaps once in 100 times we shall not succeed, especially if we move the rod a little quickly.

DISTANCE, in Navigation, is the number of miles or leagues that a ship has sailed from one point to another.

DIVING Bell, an apparatus used for the purpose of diving. It is most commonly made in the form of a truncated cone, the smallest end being closed and the larger one open. It is weighted with lead, and so suspended that it may be sunk full of air, with its open base downwards, and as near as may be parallel to the horizon, so as to close with the surface of the water.

nuteness of some parts of matter, A lighted candle placed on a plane will be visible two miles, and consequently fill a sphere, whose diameter is four miles, with Juminous particles, before it has lost any sensible part of its weight. And as the force of any body is directly in proportion to its quantity of matter multiplied by its velocity, and since the velocity of the particles of light is demonstrated to be at least a million of umes greater than the velocity of a cannon-ball, it is plain that if a million of these particles were round, and as big as a small grain of sand, we durst no more open our eyes to the light, than to expose to sand shot point blank from a cannon.

By help of microscopes, such objects as would otherwise escape our sight appear very large: there are some small animals scarcely visible with the best microscopes; and yet these have all the parts necessary for life, as blood and other liquors.

DIVISIBILITY, that quality of DIVISION, is one of the princi a body by which it admits of se- pal rules in Arithmetic and Algeparation into parts. The divisibi-bra; it consists in finding how often lity of quantity is a subject which a less number or quantity is conhas given rise to various argu-tained in a greater. The number ments amongst philosophers, some to be divided is called the divicontending that this separation dend, the number by which the may be carried on ad infinitum, while others maintain that it cannot be extended beyond certain limits. To the metaphysical divisibility there unquestionably is no end, but in the real division there is always a limit, though sometimes the number of parts is astonishing. Again, a whole ounce of silver may be gilt with eight grains of gold, which may be afterwards drawn into a wire 13000 feet long.

In odoriferous bodies we can still perceive a greater subtilty of parts, and even such as are actually separated from one another; several bodies scarce lose any sensible part of their weight in a long time, and yet continually fill a very large space with odoriferous particles.

division is made is the divisor; the number of times that this is contained in the former, is called the quotient, and if any thing remains, after the operation is finished, it is called the remainder. Division is either simple or compound.

Simple DIVISION, is when both the divisor and dividend are integral numbers.

Rule. Find how many times the divisor is contained in as many of the left-hand figures of the dividend as are just necessary, and place that number on the right. Multiply the divisor by this number, and place the product under the figure of the dividend above mentioned. Subtract this product from that part of the dividend under which it stands, and bring The particles of light, if light down the next figure of the divi consists of particles, furnish ano dend, or more if necessary, to the ther surprising instance of the mi-right of the remainder. Divide

this number, so increased, as hefore, and so on till the whole is finished.

Note 1. When it is necessary to bring down more than one figure to the remainder, a cipher must be placed in the quotient for every additional figure thus brought down.

Note 2. If the divisor do not exceed 12, the quotient may be written down as it arises, immediately under the dividend.

Ex. 1. How much sugar at 2. 73. 6d. per cwt. may be bought, for 301. 6s. 9d.?

2 7 6)30 8 9(12 cwt.
28 10 0

multiply by

2 7

2 7

Proof of DIVISION. Multiply the multiply by divisor and quotient together, and add to this product the remainder, which ought to be equal to the dividend if the work be right.

Sometimes, for the sake of abridg ing the operation, the successive products are omitted, and the sub. traction is made figure for figure as the work is carried on.

multiply by

2 7

2 7

Compound DIVISION, is when the dividend is a compound quantity. Rule. Divide the highest deno- multiply by mination of the dividend by the divisor, as in the former rule. Reduce the remainder, if any, to the next inferior denomination, and divide as before; reduce this remainder again, and divide as before, and so on till the whole is finished.

Note 1. If the divisor exceed 12, and be a composite number, divide by its factors successively, instead of the whole number at once.

Note 2. Both divisor and dividend may be compound quantities; but then they must be of the same kind, and the quotient either an abstract number or a quantity different from the others: thus, it may be asked, how many parcels, each containing 1 quarter 7lbs. may be made out of 5 tons; or what quantity of goods, at 5s. 9. per pound, may be purchased for 1007. In such cases, the divisor and dividend must be reduced to the same denomination; and if the quotient be such as to admit of lower deno ́minations, then the remainder must be multiplied by the number of these, in the denomination of which the price or value is given. As this case of division is not found in any of the common books on Arithmetic, two examples are subjoined

1 18 9

4

28

6)17 10 0(7 pounds
16 12 6

0 17 6

16

6)14 0 0(5 ounces
11 16 6

2 3 6
16

6)34 16 0(14 drams 335

remainder=

0

47) 124(2 roods

94

30

40

47) 1200(25 poles
1175,

25

301

47)7561(16 yards

752

43

9

47)40 (0 feet
144

47) 5832(124 inches

564

192

188

4

The quantity is 127 acres and nearly.

numbers, or by converting the repetends into their equivalent fractions, and then proceeding as in division of fractions.

DIVISION, in Algebra, is the method of finding the quotient arising from the division of one indeterminate quantity by another, which may be considered under two

cases.

Cuse 1. When the divisor and dividend are both simple quanti

ties.

Rule. Divide the co-efficients, as in arithmetic, and to the quotient annex the result arising from the division of the indeterminate quantities.

Note When the divisor and dividend have like signs, the sign of the quotient is plus +; and when they are unlike, the sign of the quotient is minus —, as in multiplication.

Case 2. When the dividend is a compound quantity, and the divisor either simple or compound.

Rule. Set the divisor on the left of the dividend, and proceed in the operation the same as in division of numbers, observing still the same rule as above with regard to the signs.

DIVISION of Fractions, is performed by the following rule. Reduce mixed numbers to improper fractions, then invert the terms Note. When there is a remainof the divisor, and multiply the der after the division, it must be numerators and the denominators written over the divisor, and antogether as in multiplication; ob-nexed as a fraction to the quotient, serving that such factors, as are DIVISION of Algebraic Fractions, common in the numerators and denominators, may be cancelled. DIVISION of Decimals, is performed the same as in the simple rule of division, observing only to point off in the quotient as many decimal places as those in the dividend exceed those in the divisor; and, if there be not so many, the defect must be supplied by prefixing ciphers.

Another way to know the place for the decimal point is this; the first figure of the quotient must be made to occupy the same place either in integers or decimals, as does that figure of the dividend that stands over the unit's place of the first product.

DIVISION of Circulating Decimals, is performed either by performing the multiplications and subtractions as directed for those

is performed the same as in the case of simple fractions; viz. reducing all mixed expressions to improper fractions, then invert the terms of the divisor, and multiply the numerators and denominators as in the rule above quoted, observing to cancel all factors that are common to the numerators and denominators.

DIVISION of Surds, is the me thod of ascertaining the quotient arising from the division of one irrational quantity by another.

Rule. Reduce the given surds to their simplest form, and the radical parts thus arising to like radicals; then divide the co-efficient of the dividend by the co-efficient of the divisor for the new co-effi cient, and one surd part by the other for the required surd, which being annexed with its proper ra