Now if we suppose the height of each of these portions to be that set against it in the following table (the height of the slope d being reckoned only as the perpendicular dotted line d'), and if we calculate from the length of the level portions that the water will gradually cool down to the mean temperature set against each, then by multiplying the mean temperature by its corresponding height, we get the relative weight stated in the fourth column.

 Pipes Ascending. Height. Temp. Sp. Gr. Weight. Total weight Ascending. a 2 194° .96568 4.82810 b d 3 176° .97206 2.91608 h 6 122o .98833 5.92998 m 4 86° .99589 3.98356 17.65812 Descending. Total weight Descending. f 6 158° .97807 5.86842 k 12 104° .99248 11.90976 17.77818 Excess of weight of descending water, • • • .12006

Here, then, we see that there is a clear turn of the balance in favour of the descending water, and therefore, under the conditions proposed, there will be a circulation, in spite of the dips at g and I. But now, if we suppose the boiler raised to the level of c, we shall have no b pipe at all, but only the height of the boiler 2 feet, while m will be 10 feet instead of 4: the result will be that the weight of the ascending water would be 20.73646, which would be more than the weight of the descending water, and consequently there would be no circulation. It would, indeed, commence, but by the time the heated water reached/, an equilibrium would be established, and there would be no motive power to force it in either direction. If, again, the boiler were supposed to remain, as shown on the diagram, but without any rise at d, then the height of k would be only 9 feet, and yet the water would still circulate, if the temperatures were as stated in the last table; but if the range of pipes were shortened so as to make the temperature of the water at k 140° instead of 104°, the circulation would cease, for calculation would then show that the water intended to ascend would weigh 14.74194, while that intended to descend would be only 14.72001. In short, if in any arrangement we obtain the temperatures and the heights of the several ascents and descents, we can calculate to a certainty whether the water will circulate or not.

A few words may now, in conclusion, be said on some questions that have been raised in the controversy.

1st. Water is an exceedingly bad conductor of heat; but this must be understood of it strictly when not in motion. When at liberty to move, its particles become, by what is called convection - i.e., by successive contact - capable of very rapidly transmitting heat.

2d. The rapidity of circulation cannot be reduced to any useful rule, because it is so greatly affected by friction, and still more by alteration of direction, in bends of the pipes.

3d. Water in a pipe that leaves the boiler perpendicularly cannot have any back currents, but if the pipe leaves the boiler horizontally, there may at first be a back current. It will, however, in most cases quickly disappear, because the opposing currents will cause a certain amount of mixture, and then the much colder water in the return-pipe will force the whole water in the flow-pipe to advance. Any inconvenience from the water in the bottom of the pipe being colder than the top may be obviated by inserting a short piece of sheet-iron, twisted to half a turn of a spiral, which will reverse the top and bottom water as it passes, and so compel it to mingle.

4th. There may, in certain cases, be a distinct advantage in the proposal made (originally, I think, by Mr Connell) to carry the flow-pipe as soon as possible to the summit level. This arises from the increments of expansion being greatest at the higher degrees of heat, and may be tested by calculations in different circumstances.

5th. Care must always be taken to have no lodgment of air in any part of the pipes, else the most certain circulation may be checked or stopped. Probably this was the cause of failure of J. S. W.'s apparatus, for in small-bore pipes a bubble of air often fills the pipe like a plug, and, owing to capillary attraction, resists even considerable pressure to move it. J. B. K.