{ "id": "5e5f8f0be90496854e3f98e7668050677226f4e6", "text": "IV. An account of some Experiments made on the 27th day of April, 1719, to find how much the Resistance of the Air retards falling Bodies. By J. T. Desaguliers, LL. D. &c F. R. S.\n\nI Took 12 Balls (six of which were solid Leaden Globes of about 2 Inches Diameter; three hollow Glass Balls of about 5 Inches Diameter; and three light Pastboard hollow Globes of about the same Diameter) and having carried them to the upper Gallery in the Lanthorn, on the Dome of St. Paul's Church, I caused them to fall down by two at a time, in the following manner;\n\nFirst, a Leaden Ball and a Glass Ball.\nSecondly, a Leaden Ball and a Glass Ball.\nThirdly, a Leaden Ball and a Glass Ball.\nThen I let fall in the same manner the three other Leaden Balls, each with a Pastboard Ball.\n\nAfter that, having the Leaden and Pastboard Balls brought up again, I repeated the Experiment twice more with a Leaden and Pastboard Ball: then I made the Experiment twice more with a Pastboard Ball alone, to see how long it would be in falling.\n\nUpon the whole it appeared that the Leaden Balls were a very little longer than $4\\frac{1}{2}$ Seconds in falling; the two largest of the Glass Balls 6 Seconds, and the Pastboard Balls $6\\frac{1}{2}$ Seconds.\n\nThe height of the Gallery, from whence the Bodies fell, was 272 Foot above the Pavement of the Church (then cover'd with Boards) upon which they fell.\n\nThe times of the Falls were taken two ways above, viz. with a Wheel-Chronometer, which measures a\nsmall part of Time accurately, nearer than to a quarter of a Second (made and contriv'd by Mr. George Graham, an ingenious Clock-maker) and with an $\\frac{1}{2}$ Second Pendulum: And the differences of Time between the fall of the Leaden Balls and the other Balls were taken below by the President, Martin Folkes Esq; F.R.S. and another Person, who all agreed in their Observations of the Time, which they made each with an half Second Pendulum.\n\nThe following Table gives the Marks, Weights, and Diameters of the several Balls, in three Columns.\n\n| Leaden Balls | Troy Weight. | Diameters in Inches and Decimals |\n|--------------|-------------|---------------------------------|\n| | l. oz. d. | |\n| 1c | 2 : 1 : $\\frac{1}{2}$ | 2 , 1 |\n| 2c | 1 : 11 : 4 | 1 , 99 |\n| 3c | 1 : 11 : 12 | 2 , 0 |\n| 4c | 1 : 11 : 12 | 2 , 0 |\n| 5c | 1 : 11 : 12 | 2 , 0 |\n| 6c | 1 : 10 : 0 | 1 , 98 |\n\n| Pastboard Balls. | | |\n|------------------|--|--|\n| A | 0 : 3 : 6 | 5 , 5 |\n| B | 0 : 1 : 14| 5 , 1 |\n| C | 0 : 1 : 17| 5 , 1 |\n\n| Glass Balls. | | |\n|--------------|--|--|\n| D | 0 : 3 : 13 | 3 , 9 |\n| E | 0 : 5 : 3 | 5 , 42 |\n| F | 0 : 6 : 0 | 5 , 55 |\n\nN.B. The Polar and Equatorial Diameters of the Glass Balls being different, I have set down a Mean Diameter for each of them; the true Diameters are thus, of D 4 & 3,8. of E 5, 6 and 5,25. of F 5, 7 & 5,4 Inches.\nThe particular Experiments are as follows.\n\nExperiment I. Fall of 1c and D.\nc fell by the Pendulum in $4\\frac{1}{2}$\".\nThe Fall of D was so near it, that the Difference was not taken either above or below.\n\nExperiments II. Fall of 2c and E.\n2c fell by the Chronometer in 5\", by the Pendulum in $4\\frac{1}{2}$\".\nTime of the fall of E not taken above.\nThe Difference taken below $1\\frac{3}{4}$\".\n\nExperiment III. Fall of 3c and F.\n3c fell by Chronometer in $4\\frac{1}{2}$\", by Pendulum in $4\\frac{1}{2}$\".\nF fell in Six Seconds.\nDifference taken below was $1\\frac{1}{2}$\".\n\nExperiment IV. Fall of 4c and A.\n4c fell by Chronometer in $4\\frac{3}{4}$, by Pendulum in $4\\frac{1}{2}$.\nA fell in $6\\frac{1}{2}$ Seconds.\nDifference taken below = 2\".\n\nExperiment V. Fall of 5c and B.\nWe made no Observation above nor below.\n\nExperiment VI. Fall of 6c and C.\n6c fell by Chronometer in $4\\frac{3}{4}$\", by Pendulum in $4\\frac{1}{2}$\".\nC not taken above.\nDifference below = $2\\frac{1}{2}$\".\n\nExperiment VII. Fall 1c and B.\n1c fell by Chronometer in $4\\frac{3}{4}$\", by Pendulum in $4\\frac{1}{2}$\".\nB not taken above.\nDifference taken below $2\\frac{3}{4}$\".\nExperiment VIII. Fall of 5c and A.\n5c fell by Pendulum in $4\\frac{3}{4}$\".\nA fell foul and so was not observ'd at all.\nDifference taken below 2\".\n\nExperiment IX. Fall of B alone.\nby the Chronometer in $6\\frac{1}{2}$\", by the Pendulum in $6\\frac{1}{2}$\".\n\nExperiment X. Fall of C alone\nby the Chronometer in $6\\frac{1}{2}$\" by the Pendulum in $6\\frac{1}{2}$\".\n\nBy Galileo's Theory the Lead, which was $4\\frac{1}{2}$\" in falling, must fall 4 Foot the first $\\frac{1}{2}$\", or 16 Feet the first Second, which amounts to 324 Feet in $4\\frac{1}{2}$\". But as the Sound of the Ball (as it struck the Bottom) by which we reckon'd our Time, had 272 Feet to move, we must abate a $\\frac{1}{4}$ of a Second nearly, (supposing Sound to move one Mile in $4\\frac{1}{2}$\") which will take away 35 Feet, that the Body must have fallen in the last $\\frac{1}{4}$ of a Second, and reduce the number of Feet to 289: so that the Lead will have only fallen 17 Feet short of the Theory, which must be attributed to the Resistance of the Air.\n\nThe large Glass Ball in the 6 Seconds of its Fall, wou'd in a Vacuum go thro' 576 Feet: but taking away the last $\\frac{1}{4}$ of a Second or 47 Feet, for motion of Sound, it must only fall 529 Feet in Vacuum. Now since it fell but 272, there have been 257 Feet taken off from the Fall by the Air's Resistance.\n\nLikewise the Pasteboard Ball in $6\\frac{1}{2}$ Seconds must have fallen 676 Feet: but deducting the last quarter of a Second or 51 Feet for the motion of the Sound, there remains only 625 Feet for its fall in Vacuum. But as it fell only 272 Feet, we must allow a Retardment of 353 Feet for the Resistance of the Air.\nAt a mean we may call the weight of the Glass Ball 5 oz. Troy, and its Diameter 5 Inches and $\\frac{1}{2}$; and the weight of the Pasteboard Ball 2 Ounces Troy, and a little more than 5 Inches Diameter.\n\nThe Lead Balls all fell within near a Foot of one another, and made an impression in the Boards of about $\\frac{1}{2}$ of their Depth.\n\nThe Barometer stood at 30, 1 Inches, and the Mercury was very Convex, and therefore inclined to rise still.\n\nA further Account of Experiments made for the same purpose, upon the 27th Day of July last. By the same.\n\nHaving found by our former Experiments, that thin Glass Balls, and even Balls of pasted Paper, were too heavy to make so considerable a Difference between the time of their Fall and the fall of Leaden Balls, that it might be easily Observ'd; I contrived a way to make dried Hogs Bladders perfectly round, by blowing them (when moist) within a strong Spherical Box of Lignum Vitæ, and letting them dry in the said Box before I took them out: which I did by opening the Box that screw'd in the middle, and had a hole in the Pole of one of its Hemispheres to let the Bladder pass thro', in order to tye it after blowing; and some few small holes all over the Box, that in blowing no Air might be confin'd between the inside of the Box and the Bladder, so as to hinder it from putting on a Spherical Figure. Besides I took off the ends of the Ureters, the Fat and a great deal of the upper\nupper Coats of the Bladders, before I blowed them in\nthe Box, to render them still lighter.\n\nThe Bladders I used were some of the thinnest I\ncou'd find ready blown at a Druggists, which I moist-\nened in Water, taking care to leave none in the inside.\nI chose those rather than Green ones, which in drying\nwou'd have stuck so fast to the inside of the Box, that\nit wou'd scarce have been possible to have got them out\nwithout tearing.\n\nHaving prepared five Bladders in the manner afore-\nsaid, (which I have described the more fully to direct\nany body else that shou'd be willing to try the like\nExperiments) I took them up to the upper Gallery in\nthe Lantern on the Top of the Cupola in St. Pauls\nChurch; and there by a Contrivance, which I shall\njust now describe, I let them fall by one at a time,\ntogether with a Leaden Ball of about 2 Inches Dia-\nmeter, and weighing 2 l. Troy: and I took notice of the\ntime of the Fall of each Bladder, knowing by former\nExperiments that the Balls are about 4 \\(\\frac{1}{2}\\) Seconds, or a\nlittle longer time, in falling the same Height, which is\n272 Feet.\n\nThe following Table, consisting of five Columns,\ngives in the first, the Marks of the Bladders; in the\nnext their Diameters; in the third their Weights in\nGrains Troy; in the fourth the times of their Fall in\nSecond Minutes of time; and in the fifth, the difference\nof Time between the Falls of the Leads and of each\nBladder, taken below by the President, Dr. Halley,\nDr. Jurin, Martin Folkes Esq; and Mr. George Graham\nthe Clock-maker. The Time was taken above with\nMr. Graham's Chronometer, (formerly described); and\nbelow with the same Instrument, and three half Second\nPendulums, all which agreed very well together.\nThe Experiments having been made twice over, the Table is twice set down; and those Experiments in which the Bladders fell straight down, and the most regularly, have this Mark before them (*).\n\n| Marks | Diameters in Inches | Weight in Grains Troy | Time of the whole Fall | Diff. between the Lead and Bladder Seconds. |\n|-------|---------------------|-----------------------|------------------------|------------------------------------------|\n| A | 5.3 | 128 | 19 3/8 | 14 1/2 |\n| *B | 5.193 | 156 | 17 1/4 | 12 3/4 |\n| C | 5.33 | 137 1/2 | 18 3/4 | 14 5/6 |\n| D | 5.26 | 97 1/2 | 22 1/8 | 17 8/9 |\n| *E | 5.02 | 99 1/8 | 21 5/8 | 17 |\n| *A | | | 19\" | 14 1/2 |\n| B | | | 18 5/8 | 14 1/4 |\n| *C | | | 18 3/8 | 14 |\n| D | | | 24 | 19 1/8 |\n| E | | | 21 1/4 | 16 5/8 |\n\nThe Diameters and Weights may be relied upon, being taken the Day that the Experiments were made, and the Day after; but the Diameters and Weights taken 10 Days before, not agreeing with these, I have left them out. For the Bladders by drying had lost of their Weight, and altered their Diameters.\n\nAs the Necks of the Bladders in drying shrink, so as to open a little, they must be blown before each Experiment. And for the manner of letting them fall exactly in the same Instant of time, it is described by Figure II, in which\n\nA, A, A A, is the Hole through which the Bodies fell: 1, 2, is a Board laid over the Hole. G, D, D is another Board fixt to the first Board by the two Wood-Screws D, D, with a Pulley G at the other end of it, over the Hole. W is a two Pound Ball of Lead fastned\nfastened to a strong Thread, which going over the Pulley is stretched horizontally from G to the Nails F; to which it is fastned, so as to be about a quarter of an Inch above the Board.\n\nB is one of the Bladders, hanging with the Neck or heaviest part downwards, by means of a Loop of fine Thread as E H, which goes over the Horizontal Thread G E F. Now when with a pair of Scissors the Thread of the Lead (which in all is but one Foot long) is cut just at E, before the Loop of the Bladder, the Lead pulling away the String the Loop of the Bladder slips off the remaining Thread F E, and begins to fall exactly in the same Instant as the Lead: But if the Thread should be cut between E and F, as the Lead falls its Thread might give the Bladder an oblique Direction.\n\nHe that observes the time either with a Pendulum or Chronometer may take it very exactly, by seeing the motion of the Scissors as they cut the Thread.\n\nN. B. As the Diameters of the Bladders were taken by wrapping a Thread twice round them, and something must be allowed for the thickness of the Thread; I have here under set down the Diameters of the Bladders, as corrected by that Allowance. Viz. A 5.28 Inches; B 5.19; C 5.30; D 5 ¼; and E just 5 Inches in Diameter.\n\nThe Bladder E was rough, with several Wrinkles and inequalities, which made it be longer in falling than it ought to have been, according to its Diameter and Weight.\n\nA Pail of Water thrown down met with such a Resistance in falling 272 Foot thro' the Air, that it was all turn'd into Drops like Rain.\n\nF I N I S.\n\nERRATA. Phil. Trans. No. 357. Page 848. l. 22. lege ab b 11' 32''.\nNo. 359. p. 932. l. 17. lege t = o°, i. p. 937. l. 5, 6. lege restituatur. Et Systole Arteriarum cum Cordis Diastole duratione convenit. No. 361. p. 1005. l. 16. read, proof of the falsity of the Opinion.", "source": "olmocr", "added": "2026-01-12", "created": "2026-01-12", "metadata": { "Source-File": "/home/jic823/projects/def-jic823/royalsociety/pdfs/103362.pdf", "olmocr-version": "0.3.4", "pdf-total-pages": 10, "total-input-tokens": 15036, "total-output-tokens": 4048, "total-fallback-pages": 0 }, "attributes": { "pdf_page_numbers": [ [ 0, 0, 1 ], [ 0, 0, 2 ], [ 0, 1475, 3 ], [ 1475, 3174, 4 ], [ 3174, 4318, 5 ], [ 4318, 5967, 6 ], [ 5967, 7408, 7 ], [ 7408, 9124, 8 ], [ 9124, 11604, 9 ], [ 11604, 13430, 10 ] ], "primary_language": [ "en", "None", "en", "en", "en", "en", "en", "en", "en", "en" ], "is_rotation_valid": [ true, true, true, true, true, true, true, true, true, true ], "rotation_correction": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], "is_table": [ false, false, false, false, false, false, false, false, false, false ], "is_diagram": [ false, true, false, false, false, false, false, false, false, false ] }, "jstor_metadata": { "identifier": "jstor-103362", "title": "An Account of Some Experiments Made on the 27th Day of April, 1719. to Find How Much the Resistance of the Air Retards Falling Bodies. By J. T. Desaguliers, LL. D. & F. R. S.", "authors": "J. T. Desaguliers", "year": 1717, "volume": "30", "journal": "Philosophical Transactions (1683-1775)", "page_count": 10, "jstor_url": "https://www.jstor.org/stable/103362" } }