PENDULUM. 



PKNSIOH. 



381 



length of the pendulum, and perhaps the only one, which is deserting 

 of full confidence. 



!ivc already pointed oat the manner in which experiment* 

 with the jndulum are used to deUnnine the figure of the earth, and 

 (tatcd that for this purpose the simple bar with a knife-edge at the 

 point of minimum oaoillation seems the moot fit. If the present 

 imperfection* can be overcome, which we aee no reason to despair of, 

 there if another research, that of the mean density of the earth, for 

 which uch an instrument is peculiarly adapted. The density which 

 has been hitherto acquiesced in, depends on the attraction of Sche- 

 hallien upon a plumb-line, observed by Maskelyne, and upon the 

 attraction of leaden balls measured by a torsion balance, according to 

 Cavendish, and more recently by Reich. Now in the Schehallien 

 experiment the whole deflection caused by the mountain was only 

 ll*-2, which, under the circumstances, might very easily be 2" or 

 even 3" wrong either way. The Cavendish experiment has been 

 repeated in this country by Mr. Baily, who from upwards of 2000 

 experiments has arrived at the result 5 <>7 as the density of our globe. 

 Still however it was desirable to adopt other modes of experiment, 

 which we now proceed to point out. 



If an invariable pendulum can be made which is only affected by 

 known causes of which the effects can be calculated, the simplicity and 

 perfection of the observation by coincidences, and the unlimited time 

 for which it can be carried on, will supply a much broader and more 

 secure base for the solution of this important problem, and one more 

 readily and universally applicable. Two attempts were made by 

 Messrs. Airy and Whewell, first by themselves, in 1826, and afterwards, 

 in 1828, with the assistance of three Cambridge friends, to deduce the 

 mean density of the earth from observing the oscillations of detached 

 pendulums at the top and bottom of Dolcoath Mine, one of the deepest 

 in Cornwall. As the first operation was less carefully planned, we 

 hall confine our account to the second, which was altogether the best 

 arranged pendulum experiment which had come to our knowledge up 

 to that time, and only failed from a cause then first discovered, namely, 

 that invariable pendulums of Kater's construction are very uncertain 

 and inaccurate instruments. We will call the two pendulums 1 and 2. 

 These were placed on their stands opposite each other, and put into 

 motion at the same arc (a board being interposed to prevent their 

 reciprocal action through pulses of the air), and the times of coinci- 

 dence observed. A few series were thus made, in which the errors of 

 observation scarcely amounted to a hundredth of a second per day.* 

 Pendulum 1 was then sent to the bottom of the mine, and and set up 

 with its clock and proper accompaniments. Pendulum 2 was 

 established with its clock in a hut at the surface. We will call the 

 observers A, B. c, D, K. A set off at six in the morning, commenced a 

 series with pendulum 2, and compared eight pocket chronometers with 

 the clock by coincident beats through a sidereal half-seconds chrono- 

 meter, t He then descended the mine and commenced a series, 

 compared his chronometers below exactly as he had done above, and 

 then sent them back to the upper station. By this time E had arrived 

 at the upper station to finish the series which A had begun, and to 

 compare the chronometers on their return. In this way the clocks 

 were compared, without a possible error of ,th of a second. After 

 finishing his first series .and commencing a second, A returned to day (in 

 the miner's language, to jrraw ). This series was completed by B, who 

 set off at 2 P.M., made a third shorter series, and commenced a fourth. 

 The night- work was taken by c or D, one of whom descended at 10 P.M., 

 finished B'S series, and commenced a fresh one ; on his return to day he 

 finished the upper series which E commenced before going to bed, and 

 started another, which was finished by A before bis next descent. In 

 this way observations were continued from Monday morning, July 11, 

 to Saturday afternoon (127 hours). On comparing the results of each 

 day, it was found that the three first days agreed extremely well, 

 showing an acceleration of about 2* per day in the lower pendulum ; 

 but the two next days, this acceleration was about double. The only 

 mode of accounting for this unexpected and very unwelcome result 

 was, that the knife-edges and agate planes were imperfect, and that the 

 time of oscillation depended on the position of the pendulum on its 

 plane. This had never been suspected before ; for confidence in the 

 accuracy of the pendulum was at that time almost an article of faith 

 among experimentalists. To ascertain this, a second series of com- 

 parisons was made between pendulum 1 and 2, taking care to place the 

 knife-edge* exactly in the same position on their planes, and that the 

 faces were turned the same way. These comparisons were necessarily 



In a series of >lx honri, tho first and last coincidences could be to observed 

 as not to admit an error of more than 2* for the whole interval, and the coin- 

 eideneea followed each other in about twenty minutes. A bright strip wo 

 nbbed off neb edge of the tail of the farther and quicker pendulum, nnd this 

 wu Illuminated by a lamp placed obliquely. The corrections for arc, barometer, 

 temperature, were the tame for each. The time was taken from an excellent 

 earooonrur. 



f The comparison of a ilnitle chronometer wu scarcely ever in error ,",th 

 of a second, generally within ^ O th. The j seconds sidereal chronometer WM com. 

 pmrtd ant sad Ut with the pendulum clock, going nearly solar time, and in 

 the interval three or fire coincidences at each pocket chronometer (which beat 

 OM solar time) were observed with the sldci cal chronometer. 



J A miner divides tbe risible world into two parts, underground and at 



hurried, as a slip had taken place in the mine near the engine-shaft, 

 which deranged the action of the pumps, and forced the experimenters 

 to repeat their operations below without delay. Pendulum 1 was 

 again sent below, and the experiment repeated exactly as described 

 above, for three days (79 hours), until the underground observers 

 were driven out by the water. Notwithstanding all the precautions 

 which had been taken,* the observations of the last day gave a different 

 result from the two first. "The conclusion therefore on which the 

 experimenters were unavoidably forced was, that even with the care 

 and attention they had used, tbe pendulum could not be trusted." 

 The pendulums were a third time compared with each other 

 ground, and the intervals of coincidence were found to vary, without 

 any assignable cause, from 20" 24* to 20 17>, and back again from 

 20~ 20* to 20" 29" ; and finally, during one wrift of oieillathnit, mtkuut 

 bring touched, or any one entering the room, the time of coincidence 

 changed from 20 25* to 20" 13', and at last to 20*> 8*. It was there- 

 fore clear that while the mode of observing was perhaps sufficient to 

 detect a difference of a hundredth of a second a day (except from the 

 effects of temperature, which might amount to a tenth of a accord), 

 the pendulums themselves, though used with the utmost skill and 

 precaution, and under the tame circutiutaneet, were liable to errors of 

 two seconds or more per day. 



In 1864 Mr. Airy repeated this experiment under more favourable 

 circumstances on the banks of the Tyne, and at the bottom of a pit of 

 Hartou colliery, one of the deepest coal-pits in this country (1260 feet 

 below the surface). Advantage was taken of electro-telegraphy to 

 moke the comparisons between the upper and lower pendulums, whinh 

 were found to differ in rate 2} seconds per day, from which it followed 

 that the gravity for that depth was increased by the w | w th part. The 

 density of the earth as deduced from this result is between six and 

 seven times that of water, but Mr. Airy imagines that he has not taken 

 full account of the hollow of the Tyne, of the basin named Jarrow- 

 slake, of the scoop indicated by the sea, and of the real and obeerved 

 specific gravity of the rocks which cover the mines of Harton. 

 Further details on this subject will be found under EARTH, M I:AX 

 DENSITY OF THE. [See also GYROSCOPE.] 



PENETRABILITY. Under IMPENETRABILITY are given a few 

 examples of the apparent penetration of one body by another ; and, 

 indeed, examples of this kind are more apparent than real. There are 

 many instances in chemistry in which a body is dissolved in water, or 

 other liquids, without visible increase in bulk. A measure of sulphuric 

 acid mixed with one of water, will give less than the sum of the two ; 

 but it is not supposed that in such cases there is any penetration of 

 matter, but only an alteration in density, and in the relation of tho 

 compound to heat, &c. 



PENITENTIARIES. [PRISONS.] 



PENITENTS. [PENANCE.] 



PENNY. [Cora; MONEY.] 



PENSION, an annual sum granted by the state to an individual. 

 The grounds upon which pensions are granted by the state ililli-r 

 according to the nature of the government. In a monarchy the ser- 

 vices rendered to the sovereign by those who surround his person will 

 recommend them as fitting objects of reward : where a mixed form of 

 government prevails, attempts will be made to establish some standard 

 of reward independent of personal bias or caprice. In this country the 

 distribution of pensions is now almost entirely subject to the control 

 of the legislature ; but the following notice will show that persevering 

 and long continued-efforts have been necessary to place it upon this 

 footing. 



Before the reign of queen Anne, the kings of England alienated or 

 encumbered their hereditary possessions at pleasure, and the courts 

 of law sustained them in the exercise of this power. In 1690-91, 

 Chief -Justice Treby, in answer to the objection that such power might 

 lead to the destruction of the revenue, said, " This might be some 

 reason to induce the making of an act of parliament to restrain the 

 king's power of alienation ; but since here the parliament has thought 

 fit to give the king such a power, we ought to acquiesce and submit to 

 it." (' State Triak,' vol. xiv., p. 30.) By the 1 Anne, c. 7, the right of 

 burdening the revenue of the crown with improvident grants, to tho 

 injury of the successors of the throne, was materially abridged. This 

 statute, after reciting that " the necessary expenses of supporting the 

 crown, or the greatest part of them, were formerly defrayed by a land 

 revenue, which hod from time to time been impaired and diminished 

 by the grants of former kings and queens of this realm," enacts that 

 no grant of manors, lands, &c., shall be made by the crown from and 



* A considerable difference was found in the temperature of tho upper and 

 lower part of the hut during the first upper ground experiment, from the heat 

 of the lamp for illuminating the disc, which was kept continually burning. 

 Before the second experiment, a side lobby was boarded off, in which the 

 observer placed the illuminating lamp a minute or two before the coincidence 

 took place. The lamp-light was thrown by a reflector on th* disc through u 

 hole in the boarding ; and when the coincidence had been observed, the lamp 

 was withdrawn and the hole stopped with flannel. Tho clock-face was illumi- 

 nated for a short time before coincidence by a lamp with a powerful reflector 

 through a hole in the front partition, which was also withdrawn and the hole 

 topped when the observer had caught the number of the beat. With these 

 precautions, the temperature was perfectly steady, and sensibly the same at all 

 altitudes and throughout the twenty-four hours. 



