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The observations made are included in the following Table:

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No. 5. MATTHIESSEN'S METHOD FOR THE DETERMINATION OF THE DENSITY OF WATER AT DIFFERENT TEMPERATURES.

THIS method consists in determining the loss of weight in water at different temperatures of a piece of glass whose mass is known. Supposing we know the rate of expansion of the glass we can thus calculate the expansion of the water.

If the glass for instance were first weighed in water at its point of maximum density and the water were then heated, the apparent weight of the glass would be found to increase. If for a moment the expansion of the glass were neglected this increase would be due to the fact that, the density of the water being less, the volume of the water which the glass displaces would have less weight, and thus a smaller fraction of the weight of the glass would be supported by the upward thrust of the water. The fact that the glass also expands tends to diminish this apparent increase of weight because it increases the volume of the water displaced. By means of the weighings we find the actual increase of the apparent weight, which is due to the excess of the effect of the expansion of water over the effect of the expansion of glass. We know already the expansion of the glass and so also its effect, and can thus find at once what is the effect of the expansion of water alone.

The reason for selecting glass for this purpose is that its expansion is very small, and thus any error in its actual value would have little effect on the accuracy of our results. It is

obvious that if we suppose the law of expansion of water known the same method enables us to find the expansion of glass or any other substance not affected by water.

For a complete explanation of the theory see the paper by Matthiessen in the Philosophical Transactions, 1866. See also Balfour Stewart's Heat.

The following is a short description and explanation of the method employed in the Cavendish Laboratory.

We shall first describe the apparatus employed there.

To begin with we have an accurate balance capable of weighing to milligrammes. This balance is supported on a shelf which is attached to a chimney. One of the scale-pans is removed, and to the arm is attached a fine German-silver wire. A piece of this wire at the lower end, part of which is always immersed in the water in which the weighing takes place, is considerably finer than the rest, being only 004 of an inch in diameter. The wire is led through a hole in the floor of the balance, continued through the shelf on which the balance stands. To the end of the wire is attached, by means of a groove near one end, the piece of glass whose weight in water is to be determined. This piece of glass is of a cylindrical form, its length being large compared with its diameter. The length of the wire is such that when the arm of the balance is horizontal and weighing is going on the piece of glass does not touch the bottom of the vessel containing the water in which it is weighed. This vessel is a glass cylinder, whose height is such that when it is nearly full of water the swinging of the balance will not pull any part of the piece of glass above the surface of the water; while at the same time only a very short length of the German-silver wire is immersed. This glass cylinder is placed inside a jacketed copper vessel. The interior of the copper vessel is filled with water to such a height as to immerse the glass cylinder as far as may safely be done without risking its being floated about. Water is also put inside the jacket of the copper vessel, which is in shape cylindrical, and is provided with a lid. The lid consists of two semicircular separate pieces, which can be put off or on at pleasure. They also are jacketed, and can by means of tubing have their

interiors connected with the jacket of the copper cylinder, so that any steam formed in it can circulate also through them. When both put on, the semicircular pieces completely close in the copper vessel, save for three holes, half of each hole belonging to each semicircular piece.

The central hole is that through which hangs the Germansilver wire with its attached piece of glass. This hole is large enough to permit of its also being the means of enabling a thermometer to have its bulb immersed in the water contained in the glass cylinder while its stem projects through the lid. The thermometer is supported on a stand placed on one of the halves of the lid, and it is fixed in the stand so that its bulb is at the same level as the piece of glass immersed in the water; care being taken that the German-silver wire is quite free of the thermometer stem, of the stand supporting it, and also of the circumference of the hole.

The thermometer stem should be long enough to permit of the head of the mercury column being above the lid, while its bulb is immersed, at the various temperatures of the experiment; for it is not desirable to remove the lid more often than necessary, lest particles of dust should find their way into the water and cling to the piece of glass, altering also the temperature. Thus if the range of temperature is to be great it is best to employ two thermometers, the one for the low temperatures, the other for the high. The former of course is removed when it is found desirable, and the latter is substituted. This also obviates the evil of having a long thread of mercury in the thermometer, at an uncertain temperature, above the lid of the copper vessel, and so causing an error in the temperature readings. While if during a considerable range of temperature the head of the mercury column were below the lid there would be a continual source of error, owing to its not being possible to get the eye to the same level as the head of the mercury column without pulling the bulb of the thermometer out of the water. The actual zeros of the thermometers have been determined and their errors are known.

Of the two remaining holes in the lids, the one is for the handle of a stirrer, which carries a flat metal plate of the shape

of a crescent, which is used to stir the water surrounding the glass cylinder. The shape is such that it covers a considerable area near the glass cylinder, and so can keep the temperature of the surrounding water very uniform without any risk of its coming against the cylinder itself, which would be apt to cause the cylinder to float. This hole may also be used for enabling the water inside the glass cylinder to be stirred by a long glass rod.

The object of the third hole is to permit the steam formed inside the copper vessel to escape. It is provided with a chimney, formed of a bent tube, which is moveable and can be placed so as accurately to cover the hole. The other end of the tube is bent so as to pass into the chimney behind the balance-shelf. The only communication between the interior of the chimney and the outside is by a small hole made in a moveable wooden door which accurately fits the fireplace. It is through this small hole that the bent tube from the copper vessel passes. The chimney has a good draught, increased by means of a gas jet, and so carries off the steam which otherwise might condense on the part of the German-silver wire above the copper vessel, and so vitiate the weighings.

The copper vessel is heated from below by one or more Bunsen burners supplied with gas from the nearest main. The supply of gas may be regulated so as to cause the temperature to rise uniformly or to remain sensibly constant as the experimenter chooses.

A further requisite is a clean glass rod with which to remove any bubbles that may be formed in the glass cylinder and cling to the piece of glass. Unless the light be very good it is also desirable to have a lamp which lamp which may throw a strong light when required inside the copper vessel, so that the experimenter before weighing may be certain there are no bubbles left. The lamp and the stand for the thermometer are placed on the one half of the lid of the copper vessel, which half need never be moved. The other half should be removed as seldom as possible. There need be no occasion for doing so except immediately before each weighing when bubbles are to be looked for.

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