Deflection of Falling Bodies

Zetetic Astronomy, by 'Parallax' (pseud. Samuel Birley Rowbotham), [1881], at sacred-texts.com

DEFLECTION OF FALLING BODIES.

"The falling of bodies from high places is a further proof of the daily rotation of the earth. By this motion everything upon the earth describes a circle, which is larger in proportion as the object is raised above the surface; and as everything moves round in the same time, the greater the elevation of the object, the faster it will travel; so that the top of a house or hill moves faster than its base. It is found then that when a body descends from a high place, say a few hundred feet, it does not fall exactly beneath the spot it left, but a little to the east .of it. This could not happen unless the earth had a motion from west to east. Were the earth stationary the body would fall immediately under the place it left."

The above "argument" for the earth's daily motion ought to be anything but satisfactory, even to its propounders; because it is the reverse of another "argument"--advanced for the same purpose, see page 63; it is not supported by uniform experimental results; the greatest

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amount of deflection which has ever been observed is a mere trifle compared with that which ought to be found according to the theory of rotation; and, lastly, because special experiment gives evidence directly against the supposition of diurnal motion.

It has been argued already that a body let fall down a coal pit, or from a high tower, does not deflect, but falls parallel to the side of the pit or tower, on account of the conjoint action of the earth's centrifugal force, and the force of gravity. It is said that at the moment it is liberated, and begins to fall by gravity, it receives an impulse at right angles to gravity, and therefore really falls in a diagonal direction. Thus what is affirmed in one place is contradicted in another! Inconsistency is ever the companion of falsehood. Again, when experiments have been tried, it has been found that a body has sometimes been out of the vertical a little to the east, sometimes to the west and north and south, and sometimes not at all. The amount, when it has been observed, has been very small, very far less than it ought to have been if it had resulted from the earth's rotation.

About the year 1843, a controversy on this subject had been going on in the "Mechanics' Magazine" for some time among persons connected with coal pits in Lancashire. To one of the letters the Editor appended the following remarks:--"Mathematically speaking, some allowance must no doubt be made for the centrifugal action of the earth; but in the height of 100 yards it is so small as to be practically inappreciable. Besides, if the question is to be considered in that light, a farther correction

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must be made for the latitude of the place at the time of the observation, the surface velocity of the earth varying between London and the equator to the extent of no less than 477 miles."

The subject became very interesting to the scientific world, and during the several following years many experiments were tried. In the Report of the British Association for the Advancement of Science for 1846 appeared "A Letter on the Deviation of Falling Bodies from the Perpendicular, to Sir John Herschel, Bart., from Professor Oerstead," from which the following is an extract:--

"The first experiments of merit upon this subject were made in the last century, I think in 1793, by Professor Guglielmani. He found in a great church an opportunity to make bodies fall from a height of 231 feet. As the earth rotates from west to east, each point in or upon her describes an arc proportional to its distance from the axis, and therefore the falling body has from the beginning of the fall a greater tendency towards east than the point of the surface which is perpendicularly below it; thus it must strike a point lying somewhat easterly from the perpendicular. Still the difference is so small, that great heights are necessary for giving only a deviation of some tenth part of an inch. The experiments of Guglielmani gave indeed such a deviation; but, at the same time, they gave a deviation to the south, which was not in accordance with the mathematical calculations. De la Place objected to these experiments, that the author had not immediately verified his perpendicular, but only some months afterwards.

"In the beginning of this century, Dr. Benzenberg undertook new experiments at Hamburgh, from a height of about 240 feet, which gave a deviation of 3·99 French lines; but they gave a

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still greater deviation to the south. Though the experiments here quoted seem to be satisfactory in point of the eastern deviation, I cannot consider them to be so in truth; for it is but right to state that these experiments have considerable discrepancies among themselves, and that their mean, therefore, cannot be of great value. In some other experiments made afterwards in a deep pit, Dr. Benzenberg obtained only the eastern deviation, but they seem not to deserve more confidence. Greater faith is to be placed in the experiments of Professor Reich, in a pit of 540 feet, at Freiberg. Here the easterly deviation was also found in good agreement with the calculated result; but a considerable southern deviation was observed. The numbers obtained were the means of experiments which differed much among themselves. After all this, there can be no doubt that our knowledge on this subject is imperfect, and that new experiments are to be desired."

"New experiments" were afterwards made, as will be seen by the following remarks by W. W. Rundell, Esq., secretary to the Royal Cornwall Polytechnic Institution, recorded in the Transactions of that society, and quoted in the "Mechanics' Magazine" for May 20, 1848

"The remarks of Professor Oerstead, at the Southampton meeting of the British Association, on the deflection to the south of falling bodies, and the variety of opinions entertained upon this subject by the most eminent men, not only in regard to its cause, but also as to its real existence, having attracted my attention, it occurred to me that the deep mines of Corn-wall would afford facilities for repeating experiments on this subject which had never before been obtained to the same extent. Professor Reich let bodies fall from a height of 540 feet, while the deep shafts of some of the Cornish mines would

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allow a fall of two and three times that amount. The man-engine shaft of the united mines was selected. It is perpendicular, and one quarter of a mile deep. . . . Besides the bullets, iron and steel plummets were used, the latter being magnetised. In form these were truncated cones, the lower and larger ends being round. These were suspended by short threads inside a cylinder, to prevent draughts of air affecting them, and, when they appeared free from oscillation, the threads. were let go. The number of bullets used was 48, and there were some of each of the following metals:--iron, copper, lead, tin, zinc, antimony, and bismuth. A plumb-line was suspended at each end of the frame, and east and west of each other; to, these were attached heavy plummets, the lower ends pointed. After they had been hanging for some hours in the shaft, a line joining their points was taken as a datum line from which to, measure the deflection. The whole of the bullets and plummets dropped south of this datum line, and so much to the south that only four of the bullets fell upon the platform placed to receive them, the others, with the plummets, falling on the steps of the man-machine, on the south side of the shaft, in situations. which precluded exact measurements of the distances being taken. The bullets which fell on the platform were from 10 to 20 inches south of the plumb-line. . . . There is a real deflection to the south of the plumb-line, and in a fall of one quarter of a mile it is of no small amount."

The above article concludes with a lengthy mathematical explanation, or attempt at an explanation, of the phenomena observed on the supposition of the earth's rotundity and diurnal motion; but it is only one out of many elaborate efforts to reconcile facts and theories which are visibly opposed to each other. Several other mathematicians

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make strenuous efforts to "explain," and one writer, after a long algebraical article, in which special formulæ are advanced, finds fault with some of the efforts of others, and concludes as follows:--

"In recapitulating, then, we find that falling bodies may have either north, south, east, or west deflection from the plumb-line, and that the first two deflections may be combined with either of the latter two, and that each may exist separately, or not at all, depending on the circumstances of height fallen through, and the weight, size, and form of the bodies used." ¹

Thus it is admitted that deflection from a height of 300 feet "is so small as to be practically inappreciable;" that "great heights are necessary for giving only a deviation of one-tenth part of an inch;" that when this amount was observed, "at the same time deviation to the south was given, which was not in accordance with the mathematical calculations;" that "the experiments have considerable discrepancies among themselves;" that "the experiments differed very much;" that "after all there can be no doubt that our knowledge on this subject is imperfect;" that on repeating the experiments with the utmost possible care down a shaft of 1320 feet in depth, the bullets did not fall easterly at all from the plummets, "but from 10 to 20 inches south of the plumb-line," and out of forty-eight bullets, forty-four fell "on the south side of the shaft, in situations which precluded exact measurements of the distances being taken;" and, finally, that puzzled mathematicians, with their ever ready ingenuity to make facts agree with the wildest of theories, even with those of a

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directly opposite character, conclude that "falling bodies may have either north, south, east, or west deflection from the plumb-line." What value can such uncertain and conflicting evidence possess in the minds of reasoning men? They are shameless logicians, indeed, who contend that, from such results, the earth is proved to have a diurnal rotation!

Footnotes

318:1 "Mechanics' Magazine" for July 1, 1848, p. 13.