DEN 



DEN 



her 4 shews that the integer is divided 

 into four parts. So in the fraction^' b is 



the denominator. See FRACTION. 



DENOMINATOR of a ratio, is the quotient 

 arising from the division of the antece- 

 dent by the consequent. Thus 8 is the 

 denominator of the ratio 40 : 5, because 

 40 divided by 5, gives 8 for a quotient. 

 It is also called the exponent of a ratio. 

 See EXPONENT. 



DENSITY of bodies, is that property 

 directly opposite to rarity, whereby they 

 contain such a quantity of matter under 

 such a bulk. Accordingly, a body is 

 said to have double or triple the density 

 of another body, when, their bulk being 

 equal, the quantity of matter is in the 

 one double or triple the quantity of mat- 

 ter in the other. The densities and 

 bulks of bodies are the two great points 

 upon which all mechanics or laws of mo- 

 tion turn. It is an axiom, that bodies of 

 the same density contain equal masses 

 under equal bulks. If the bulks of two 

 bodies be equal, their densities are as 

 their masses : consequently, the densities 

 of equal bodies are as their gravities. If 

 two bodies have the same density, their 

 masses are as their bulks ; and as their 

 gravity is as their masses, the gravity of 

 bodies of the same density is in the ratio 

 of their bulk. Hence also bodies of the 

 same density are of the same specific 

 gaavity; and bodies of different density, 

 of different specific gravity. The quan- 

 tities of matter in two bodies are in a 

 ratio compounded of their density and 

 bulk : consequently, their gravity is in 

 the same ratio. If the masses or gravi- 

 ties of two bodies be equal, the densi- 

 ties are reciprocally as their bulks. The 

 densities of any two bodies are in * ratio 

 compounded of the direct ratio of their 

 masses, and a reciprocal one of their 

 bulks : consequently, since the gravity of 

 bodies is as their masses, the densities of 

 bodies are in a ratio compounded of the 

 direct ratio of their gravities, and a reci- 

 procal one of their bulks. 



DENSITY of the air, is a property that 

 has employed the later philosophers 

 since the discovery of the toricellian ex- 

 periment. It is demonstrated, that in the 

 same vessel, or even in vessels commu- 

 nicating with each other at the same 

 distance from the centre, the air has 

 every where the same density. The 

 density of the air, cceteris paribus, increases 

 in proportion to the compressing powers. 

 Hence the inferior air is denser than the 

 superior; the density, however, of the 



lower air is not proportional to the 

 weight of the atmosphere, on account of 

 heat and cold, and other causes, nerhaps, 

 which make great alterations in Tiensity 

 and rarity. However, from the elasticity 

 of the air, its density must be always 

 different at different heights from the 

 earth's surface ; for the lower parts 

 being pressed by the weight of those 

 above will be made to accede nearer to 

 each other, and the more so as the weight 

 of the incumbent air is greater. Hence, 

 the density of the air is greatest at the 

 earth's surface, and decreases upwards in 

 geometrical proportion to the altitudes 

 taken in arithmetical progression. 



If the air be rendered denser, the 

 weight of bodies in it is diminished; if 

 rarer, increased ; because bodies lose a 

 greater part of their weight in denser 

 than in rarer mediums. Hence, if the 

 density of the air be sensibly altered, bo- 

 dies equally heavy in a rarer air, if their 

 specific gravities be considerably differ- 

 ent, will lose their equilibrium in the 

 denser, and the specifically heavier body 

 will preponderate. See PNEUMATICS. 



DENSITY of planets. The densities of 

 bodies being proportional to their masses 

 divided by their bulks; and, when bo- \ 

 dies are nearly spherical, their bulks are 

 as the cubes of their semi-diameters; of 

 course the densities in that case are as 

 the masses divided by the cubes of the 

 semi-diameters. For greater exactness, 

 we must take that semi-diameter of a 

 planet which corresponds to the parallel, 

 the square of the sine of which is equal 

 to one-third, and which is equal to the 

 third of the sum of the radius of the pole, 

 and twice the radius of the equator. This 

 method gives us the densities of the prin. 

 cipal planets as follows, that of the sun 

 being unity : 



Earth . , . 

 Jupiter . . 

 Saturn . . 

 Herschell . 



3.93933 

 0.86014 

 0.49512 

 1.13757 



See ASTRONOMY. PLANETS, nouses of. 



DENTALIUM, tooth-shell, in natural 

 history, a genus of the Vermes Testacea. 

 Generic character: animal a terebella; 

 shell univalve, tubular straight or slightly 

 curved, with the cavity open at both 

 ends, and undivided. There are 22 spe- 

 cies, some of which are found in the fossil 

 state, in the alluvial deposit of New- 

 Jersey. 



DENT ARIA, in botany, English tooth- 

 wort, a genus of the Tetradynamia Sili- 



