45: i 



PENATES PENDULUM. 



at least once a year. It is followed by absolution. 

 according to the authority transmitted to the church, 

 and by the imposition of Mirh | CIKUHTS as are neces- 

 sary to free from the consequences of sin. The 

 council of Trent declares, in sess. xiv. c. 8, that 

 satM'.ii -lion for sin is effected only by Christ, and it 

 is left for the individual to bring forth fruits worthy 

 of repentance. Days of penance and fasting are 

 holy days, which, in certain countries, are fixed 

 annually, or after general calamities, for the purpose 

 of a general expression of penitence, or with the 

 view of appeasing the anger of the Deity. The 

 great day of fasting among the Jews is the Long 

 N:-ht. The Christians imitated these fast-days. 



IT. NATES; the private or public gods of the 

 Romans ; in tin- former sense, they resembled the 

 Lares, with whom they are often confounded. Not 

 only every house, but every city, had its Penates, 

 and the latter were the public gods. The most 

 celebrated at Rome were those that protected the 

 empire. These were brought into Italy by /Eneas, 

 together with Vesta and her eternal fire. According 

 to Varro and Macrobius, the Penates were rude 

 images of wood or stone, furnished with a spear ; 

 and generals, on their departure, and consuls, pretors, 

 and dictators, when they retired from office, sacri- 

 ficed victims before them. 



PENCIL ; an instrument used, by painters for 

 laying on their colours. Pencils are of various 

 kinds, and made of various materials ; the larger 

 sorts are made of boar's bristles, the thick ends of 

 which are bound to a stick, large or small, accord- 

 ing to the uses they are designed for ; these, when 

 large, are called brushes. The finer sorts of pencils 

 are made of camels', badgers', and squirrels' hair, 

 and of the down of swans; these are tied at the 

 upper end with a piece of strong thread, and enclosed 

 in the barrel of a quill. Good pencils, when drawn 

 between the lips, come to a fine point. 



Lead Pencils. See Plumbago. 



Pencil of Rays ; a number of rays diverging from 

 some luminous point, which, after passing through 

 a lens, converge again to a point. 



PENDANT. Two paintings or prints of equal 

 dimensions, which are attached in corresponding 

 positions to the same wall, are called pendants to 

 each other. 



PENDANT, or PENNANT; a sort of long 

 narrow banner displayed from the mast-head of a 

 ship-of-war, and usually terminatiug in two ends or 

 points, called the swallow' s-tail. It denotes that a 

 vessel is in actual service. 



Broad pendant is a kind of flag terminating in one or 

 two points, used to distinguish the chief of a squadron. 



Pendant is also a short piece of rope, fixed on 

 each side, under the shrouds, upon the heads of the 

 main and fore masts. 



PENDULUM, in dynamics, is a simple ponderous 

 body, so suspended by a flexible cord from an axis 

 of suspension, that it is at liberty to vibrate by the 

 action of its own gravity alone, when it is once raised, 

 by any external force, to the right or left of its quies- 

 cent position ; and, in demonstrating the theory of 

 its motion, mathematicians are obliged to assume, 

 that there is no rigidity in the cord, no friction at the 

 axis of suspension, no resistance to motion made by 

 the air, and no variation in the total length of the 

 cord, arising from the variable temperature or mois- 

 ture of the atmosphere ; and if these assumptions 

 were strictly correct, a pendulum, once put in mo- 

 tion, would continue to move, ad infinitum, without 

 a further accession of any external force ; but, when 

 the pendulum is applied as the regulator of a clock, 

 for which purpose it is admirably adapted, the as- 

 tumptions which we have stated, require an equal 



number of mechanical corrections, of which ttui 

 theory, simply considered, takes no notice. In horo- 

 logy, therefore., the pendulum must be considered not 

 simply as a self-moving pendulous body, without any 

 tendency to come to a state of rest, but as a body 

 whose motion is perpetuated by repeated accessions 

 of force in aid of its own gravity, and whose vibra- 

 tions are rendered isochronal by a nice adaptation of 

 mechanical contrivances, that prevent or remedy the 

 influence of all natural impediments to uniform and 

 uninterrupted motion. The first kind of pendulum 

 (the theoretical) is called a mathematical or simple 

 pendulum, the other the physical or compound pen- 

 dulum. In the mathematical pendulum, the matter 

 of the pendulous ball or bob is supposed to be col- 

 lected into one point, so that the centres of gravity 

 and of oscillation coincide. 



The doctrine of the pendulum is of the highest 

 importance, but, as it cannot be fully developed 

 without the aid of mathematics, nor rendered clear 

 without diagrams, we can state only some of the most 

 obvious properties and circumstances connected with 

 it. A pendulum, once put in motion, would never 

 cease to oscillate in arcs, were it not for the friction 

 at the point of suspension, and the resistance of the 

 air. Neither of these circumstances can ever be 

 avoided entirely, but their effect may be rendered 

 comparatively slight by giving to the weight a lenti- 

 cular shape, and suspending the rod on a sharp edge, 

 on which it plays with very little friction. The times 

 of the vibrations of a pendulum depend, 1. on the 

 magnitude of the angle of elongation, viz. that angle 

 by which the heavy body of the pendulum is removed 

 from the vertical line ; 2. upon the length of the 

 pendulum; and 3. upon the accelerating power of 

 gravity. If all these circumstances are perfectly 

 equal in the case of two pendulums, they will per- 

 form an equal number of oscillations in the same 

 time; but if there is a difference in either of the 

 circumstances, the oscillations will differ immediately. 

 Thus, if one pendulum is shorter than the other, and 

 all the other circumstances equal, the shorter pendu- 

 lum will move quicker than the longer. The law 

 which has been found to exist is, that the lengths of 

 the pendulums are in an inverse proportion to the 

 squares of their oscillations ; hence the times of the 

 oscillations are inversely as the square roots of the 

 lengths of the pendulums- Hence a pendulum 

 which is four times as long as another, will vibrate 

 with but half the rapidity, or the shorter pendulum 

 will perform two oscillations whilst the larger per- 

 forms but one. 



The pendulum does not perform its oscillations in 

 equal times in all parts of the earth. This is owing 

 to the third of the circumstances enumerated above, 

 upon which the oscillations depend. The gravity, 

 or, what is the same thing, the power of attraction 

 in the earth, does not operate every where with 

 equal force on the pendulum, which, therefore, in 

 some parts of the earth, oscillates more slowly than 

 in others. The cause of this lies in the centrifugal 

 force, or in the diminution of the power of gravity 

 caused by it. This becomes more perceptible the 

 nearer the place where the pendulum is observed is 

 to the equator. (See Earth.) At the equator, 

 therefore, a pendulum vibrating seconds must be 

 somewhat shorter than at a distance from it. The 

 length of a seconds pendulum at the equator 

 is, according to Biot, 39.011684 inches; in latitude 

 45, 39.116820, in 90, 39.221956. If the globe 

 were a perfect spheroid, the meridians would be 

 perfect ellipses, and in such case the length of 

 seconds pendulums would immediately afford a basis 

 for a calculation of the length of the degrees in the 

 various latitudes ; but actual measurements have 





