Desaguliers, Hogs’ bladders, and St Paul’s cathedral

John Theophilus Desaguliers

John Theophilus Desaguliers FRS (1683 – 1744) was elected to the Royal Society in 1714, with responsibility for experiments, Hooke having died in 1703. The second edition of Newton’s The Principia was published in 1713, and the third in 1726. 

The experiments overseen by Desaguliers, carried out in April and July 1719, consisted, principally, in dropping balloons from a gallery in St Paul’s Cathedral, and timing their descent. Balls of lead, of glass, and of pasteboard, and flasks of mercury, were also dropped and timed; and, for good measure, a bucketful of water was also emptied from the gallery.

Here is a photograph of the cathedral, taken by Ruth Baumberg. It looks upwards into the galleries from a point where the balls and balloons might have landed. The photograph appears in my book, but in black and white.

A similar experiment had been carried out, from a lower gallery in the cathedral, in 1710. The experiments are described, as Experiments 13 and 14 in Section 7, Book 2 in the third edition of The Principia. Desaguliers published, in The Philosophical Transactions of the Royal Society, a more detailed account of his two sets of experiments as ‘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’, and ‘A further account of experiments made for the same purpose, upon the 27th day of July last’.

Why was Newton interested in how long it would take a balloon to fall from a gallery in St. Paul’s Cathedral? In Newton’s time, Descartes’ theory that the planets were whirled around the sun in a vortex was generally accepted. Book 1 of The Principia is mainly devoted to the development of dynamics, and his theory of gravity, and showing how the motion of the planets and the moon could be explained. Book 2 is mainly concerned with the development of hydrodynamics and aerodynamics, with which he attacks the vortex theory. He produced six disproofs of the vortex theory, replacing Descartes’ observation of leaves being swirled round in a vortex by hard mathematics. It is all rather difficult, and there are great flashes of Newtonian genius, together with some errors.

One problem that Newton attacked, both theoretically and experimentally, was how the force acting on a body by a resisting fluid depends on the speed of the body through the fluid. He had no idea of turbulence. So he considers the cases where the resistance is proportional to the speed, or to the square of the speed, or when it consists of two components, one proportional to the speed, and one to the square of the speed.

He also considers the trajectory of a body moving through such a fluid, when fired like a cannon ball with a given velocity, and subject to gravity. If the resistance is proportional to the speed this is easy enough. One can consider the horizontal and vertical components of the velocity independently. But in the other cases, the horizontal and vertical components of the velocity affect the vertical and horizontal components of the resistance, and there is no simple solution.

But the first question is to decide how the resistance varies with the speed. I am told that if you go into a high-tech laboratory, the most accurate instrument in the room is likely to be the watch on your wrist. But Desaguliers timed the descent of the balloons with a pendulum, as well as with a stop watch (or stop clock); as far as I know, the first such instrument.

Measuring acceleration directly was out of the question, and the cleverest and most accurate way of determining the law of resistance, where this was possible, was to measure the rate at which the amplitude of a freely swinging pendulum decays, and Newton carried out many such experiments, with the resisting fluid being air, water, and mercury. He regretted not having used molten iron. But he also timed the fall of various objects falling in water and air.

The chief difficulty with the experiment was making the balloons. They were made of hogs’ bladders, in the words of Desaguliers, and I take ‘hog’ to be a general term for a pig. So how do you make the bladder spherical? He constructed (or had a craftsman construct) a hinged wooden box with a spherical interior, wetted the bladder, placed it in the box, and blew it up until it pressed against the box. Leave it there a while, open the box, and you have a damp but spherical balloon (incidentally, rubber balloons were invented by Michael Faraday in 1824).

The next step would be to obtain permission from the Dean and Chapter to carry out the experiment, which I imagine would be easy enough, as Christopher Wren was still alive.

Problems arose with obtaining consistent results. The balloons would sometimes twist and turn on their descent. Newton eventually worked out that you need to release the balloon with its centre of gravity directly below its centre of flotation.

Desaguliers was not only known for his distinguished scientific career, but also for his beliefs. His father was a French Protestant priest, and had to leave France on the revocation of the Edict of Nantes in 1685, one of the many Huguenots who came here. He arrived in England and was ordained into the Church of England, and sent to Guernsey. Meanwhile his son was baptised as Jean Théophile in the Protestant Temple at La Rochelle, and mother and son escaped to join the father in Guernsey.

To what extent their journey to Guernsey was a clandestine affair I do not know; but it is said that Jean was concealed in an empty wine barrel. Jean, or John as he became known, had a typical academic education, was ordained, and became chaplain to Frederick Prince of Wales. But he was renowned as a leading Freemason, and this inevitably led to some controversy. The Prince of Wales was himself a Freemason, and Desaguliers presided over his initiation. As a result of his importance as a Freemason, some of the information on the web concerning Desaguliers is based more on imagination than on hard fact. There is a tendency for Theosophists and Rosicrucians to claim Desaguliers as their own, but I have no reason to believe that he shared their more exotic beliefs.

Here is a picture of ‘The temple of the Rose Cross’ published by an artist with the pseudonym Theophilus Schweighardt Constantiens in 1618. Its connection with Desaguliers is tenuous, but it is such a striking work that it should be reproduced at the slightest excuse. The artist was probably Daniel Moegling.

Desaguliers describes his experiments with pigs’ bladders in detail, so that anyone can repeat them. So there is a challenge for you. First get the bladders. Desaguliers got his ready blown from ‘Druggists’. You might try a Morris dancing society.

Charles Leedham-Green
C.R.Leedham-Green@qmul.ac.uk

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My new translation of The Principia is published by Cambridge University Press

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