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# Introduction

Water bells are formed when an obstacle is placed in the path of a jet of water. Depending on the type, shape and size of the object, a wide variety of water bells can be created very easily. The easiest one to make is to (in my case, quite accidentally) allow the water in ones sink to run on the top of a closed milk jug. While the size of the object and thus the form of the water bell are not quite what Taylor studied, the bell is formed and can be modified by simply adjusting the flow rate out of the faucet.

Interest in the study of the phenomenon of water bells goes well before Taylor's paper on the subject. Savart first studied water bells in 1833 using experiments to try and deduce the equation of motions. In the 1850s, Boussinesq theoretically explained Savart's shapes. Then, some time later in 1934, Bond quite successfully used experiments and theory to measure the surface tension of water. With the simplified problem quite well established, people turned to more advanced twists of the problem. In 1951, using experiments Hopwood looked at situations where there was a difference in the pressure in and outside the bell. In 1953, Lance and Perry solved Boussinesq's original equations numerically.

It was after this point that Taylor entered the theory of thin sheets of water with a series of three papers, the first being in the area of water bells. In this paper, published in 1959, he essentially non-dimensionalized the equations and repeated Boussinesq's solution in a slightly different form. In addition to this, he also tried to deduce the effect of air drag on the shape of the bell. However, the bulk of that work was done by Howarth and published in the appendix of this paper. Thus, Taylor's contributions to the area of water bells seems fairly small.

However, throughout the ground breaking work of the next two papers in the series which pertain to waves on fluid sheets and the break-up of fluid sheets, the length scale found in the water bells paper appears again and again. While the work in the water bell area seems to be a mere foot note compared to that of Savart and Boussinesq, it is in the nondimensionalization of the equations that Taylor finds this length scale which crops up in all of the work with thin sheets making the contribution much more significant than earlier believed.

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brenner@math.mit.edu