The best way of making this subject clear is probably to resort to facts which have been ascertained by experiment. The sole force which operates to produce motion in the water is the force of gravity. This force operates most strongly on bodies which are called the heaviest, and by so operating it may even cause lighter bodies to rise. Thus the light weight in the scale of a balance rises, because the heavier weight in the other scale is more strongly acted upon by the force of gravity. A cork rises from the bottom to the top of water because a corresponding bulk of water is heavier - that is, is more strongly acted upon by the force of gravity than the cork. Both cork and water are pulled downwards, but the water (that fills the same bulk) is pulled more strongly, and therefore the pull upon the water overcomes the pull upon the cork - the water sinks, and the cork rises. In precisely the same way if a portion of water is more dense - that is, heavier than another portion - it will be pulled down, and the lighter portions will be forced up by the heavier taking its place. Now, as heat causes water to expand, or to become less dense, a given bulk of cold water is heavier than the same bulk of warm water; the cold water is therefore pulled down, and forces the hot to rise.

It is important to understand this, because people are apt to speak incorrectly of heat causing water to rise. It does nothing of the sort. From 32° to 39°.2 the action of heat causes water to contract, or to become heavier, and, therefore, if a portion of water is warmed to any degree below 39°.2, it will sink instead of rising in the midst of water - that is, if a lower temperature. Above 39.2°, however, heat causes water to expand or become lighter, and then it will rise, because the colder and heavier water falls lowest and forces it up.

The amount of expansion in water corresponds inversely with the weight of equal bulk or the specific gravity, and it has been very carefully measured by men of science. The following table gives the mean results obtained by the latest observations. 1 have thought it sufficient to set down the figures for increments of 18°, which corresponds to 10° C.*:-

 Temp. Fahr. Vol. of water (at 32° = 1). Sp. gr. of water(at 32° = 1). 32° 1.000000 1.000000 (39°.2) .999871 1.000129 60° 1.000124 .999876 68° 1.001615 .998388 86° 1.004123 .995894 104° 1.00757 .99248
 Temp. Fahr. Vol. of water (at 32° = 1). Sp. gr. of water (at32O = l ) 122° 1.01181 .98833 140° 1.01677 .98351 158° 1.02243 .97807 176° 1.02874 .97206 194° 1.03554 .96568 212° 1.04300 .95878

It will be seen from this table that water does not expand in equal proportion for different increments of heat. Thus from 50° to 68° it expands about 15 parts in 10,000, from 122° to 140° it expands about 50 parts in 10,000, and from 176° to 194° it expands about 78 parts in 10,000. This fact will be found to have some importance in considering questions of circulation in pipes.

In dealing with the effect of gravity on water, it must be kept in mind that we have to consider only the height and not the bulk in other directions. This is a law of hydrostatics, a familiar example of which is that water will stand at exactly the same height in a small pipe communicating with a big barrel as it does in the barrel itself when it is of the same temperature in both. But, 1st, if the pipe communicates with the barrel only at its bottom, and we heat the water in one but not in the other, the level of the hot water will stand a little higher than that of the cold, because it takes a greater height of the hot water to balance the denser and heavier cold water. And, 2d, if the pipe communicates with the barrel both at bottom and top, and we heat the water in the barrel or the pipe, but not in both, a circulation will be set up, because now the water in both stands at the same level, but the column of cold water is heavier than the column of hot; the cold is, therefore, carried down by the superior force of gravity, and compels the hot to rise. The amount of force exercised appears from the table given above.

Thus if the water be 3 feet deep, and its temperature in the pipe be 50°, and in the barrel 194°, then the weight of the water in the pipe is 3 X .999876 = 2.999628 (in grains, ounces, or any other denomination), while the weight of a corresponding column in the barrel is, in the same denomination, 3 X .96568 = 2.89704. Hence if the water in the pipe weighs 2.9 oz., the corresponding amount of water in the barrel weighs about 2.8 oz., and necessarily the 2.9 oz. goes down and the 2.8 oz. goes up. When the water has been so far transfused as to have become of the same temperature throughout, the motion necessarily ceases, because it is all of equal weight.

* Fuller tables may be found in any of the treatises on heat.

Therefore the way to ascertain whether water will circulate in a given arrangement of boilers and pipes, is to take the weight of all which we wish to ascend, and the weight of all which we wish to descend, and to ascertain if the weight of the latter exceeds that of the former. If it does, the circulation will be as we wish; if the opposite is the case, the circulation will be reversed; and if the weights are equal, there will be no circulation at all. We get the relative weights by multiplying the specific gravity of each portion by the perpendicular weight of that portion, and we get the specific gravity from the temperature. It is not quite exact to take the mean temperature of each portion, but the errors nearly balance themselves, and may be disregarded. We need pay no attention to the portions which are on a level; and in portions which are sloping we take only the perpendicular height. Thus, if we suppose the subjoined figure to represent the section of a system of pipes, a being the boiler, b the "flow," and m the "return," then we intend the water to ascend in the portions a, b, d, h, and m, and to descend in / and k.