Jan. 24. 1852.] 



NOTES AND QUERIES. 



85 



my own experiments, is, that the astonished spec- 

 tators at the Polytechnic Institution, while intently 

 watching, as they believed, the rotation of the earth 

 made visible, were watching merely a weight sus- 

 pended by a cord, which, disturbed from the plane 

 m which it was set to oscillate, was describing a 

 series of ellipses on the table, very pretty to look 

 at, but having no more to do with the rotation of 

 the earth than the benches on which they were 

 sitting. 



At the same time, however, that I assert the 

 inefficacy of any experiments with the pendulum 

 as tending to show the earth's rotation, I admit 

 that, provided a pendulum could be made to pre- 

 serve its plane of oscillation for twenty-four hours, 

 it would oscillate independently of the rotation of 

 the earth, and actually describe a circle round a 

 fixed table in that interval. The mathematical proof 

 of this proposition is of a most abstruse nature ; so 

 much so, indeed, that it is understood to have 

 been relinquished by one of our ablest mathema- 

 ticians. But that it is likely to be true, and one 

 not difficult to comprehend, I think I can show to 

 A. E. B.'s satisfaction in a few lines. 



If a pendulum be placed at one of the poles of 

 the earth, it is obvious, that while it swings in one 

 plane, the revolution of the earth beneath it will 

 cause it to appear to describe a complete circle in 

 twenty-four hours. This position is simple enough, 

 but it is true also in any latitude, excepting near 

 the equator. For there is no doubt, that, as gravity 

 acts on the pendulum, only in the line which joins 

 the point of suspension and the centre of the earth 

 (thereby merely drawing the " bobs " towards 

 that line) it can have no effect on the plane of 

 oscillation ; for the line of gravitation remains 

 unchanged with respect to the pendulum, during 

 a whole i*evolution of the earth on its axis. Take 

 a map of a hemisphere, and on any parallel, say 

 60° of latitude, draw three pendulums, extended 

 as in motion, with their centres of gravity directed 

 toward the earth's centre, one on each extremity 

 of the parallel of latitude, and one midway be- 

 tween the two ; extend the " bobs" of the first two 

 north and south, and those of the middle one east 

 and west. Number them 1, 2, and 3, from the 

 westward. It will then be observed that the plane 

 of oscillation of the three pendulums, thus placed, 

 is one and the same — that of the plane of the 

 paper; and moreover, that the lower "bob," 

 which is south at No. 1., is west at No. 2., and 

 north at No. 3. By this it will be evident, that 

 the revolution of the pendulum will be through 

 the whole circle, or 360^ in twenty-four hours, at 

 all points of the earth's surface, excepting near the 

 equator; the line joining the ^^bobs" remaining in 

 a parallel plane. 



I say, excepting near the equator ; for it will be 

 seen on looking closely at the above illustration 

 (which would be better on a globe) that the three 



pendulums are not strictly in the same, or even a 

 parallel plane ; inasmuch as the plane of oscilla- 

 tion must pass through the point of suspension, 

 and the centre of the earth. But still the pendulum 

 has a tendency to remain in a parallel plane, as 

 nearly as the figure of the earth will allow, — the' 

 chord of the arc of oscillation remaining in a 

 plane parallel to itself. It will be seen that, as 

 we approach the equator, the plane of oscillation 

 is forced from its parallelism more and more, until, 

 on the equator, it has no tendency to return, as 

 all planes are there the same with reference to the 

 centre of the earth. 



I may add that there is a variation of the above 

 theory, which has found many advocates, viz. that 

 the pendulum will make the complete revolution 

 in a period varying from twenty -four hours at the 

 poles, to infinity at the equator ; varying, that is^ 

 as the sine of the latitude. This seems, d priori^ 

 not so likely as the former, while it equally wants, 

 mathematical proof H. C. K^ 



Rectory, Hereford. 



THE CROSS AND THE CRUCIFIX. 



(Vol. v., p. 39.) 



Your space precludes controversy : but the 

 communication in Number 115. from W. Dn. 

 requires an explanation from me ; which I give 

 the more readily as it may perhaps serve to throw 

 further light on a curious inquiry. A correspon- 

 dent in a former Number (Vol. iv., p. 422.) ques- 

 tioned the correctness of an assertion by the Hon. 

 Mr. Curzon, that " the crucifix was not known 

 before the fourth or fifth century, though the cross 

 was always the emblem of the Christian faith." 

 I ventured to sustain Mr. Curzon's view (Vol. iv., 

 p. 485.) by referring to authorities for the fact, 

 that the idea of ignominy associated with that 

 peculiar form of execution had long prevented the 

 cross from being adopted as a symbol of Christ's 

 passion ; that the actual representation of the 

 crucifixion itself was still more repulsive, and 

 much later in its admission into the early churches ; 

 that allegory was in consequence resorted to, in 

 order to evade the literal delineation of the 

 Saviour's death, which was typified by a lamb 

 bleeding at the foot of a cross ; and that when 

 invention had become exhausted, and inert in the 

 production of these emblems, the Church, in the 

 seventh century at the Quini-sextile, or Council in 

 Trullo, had "ordered that fiction and allegory 

 should cease, and the real figure of the Saviour he 

 depicted on the tree" (The words in Italics are 

 my own, and were not given as a quotation.) 



W. Dn. in Number 115. (Vol. v., p. 39.) 

 does not question the main conclusion sought to 

 be established, but takes exception to my refer- 

 ence to the Council in Trullo as irrelevant, and 



