of lime in solution as bicarbonate, is decomposed and carbonate of lime precipitated.  You can at once imagine, then, what takes place in your steam boilers when such water is used, and how incrustations are formed.  Let us now inquire as to the precise nature of the waste and injury caused by hard and impure waters.  Let us also take, as an example, those most commonly occurring injurious constituents, the magnesian and calcareous impurities.  Hard water only produces a lather with soap when that soap has effected the softening of the water, and not till then.  In that process the soap is entirely wasted, and the fatty acids in it form, with the lime and magnesia, insoluble compounds called lime and magnesia soaps, which are sticky, greasy, adhesive bodies, that precipitate and fix some colouring matters like a mordant.  We have in such cases, then, a kind of double mischief—­(i) waste of soap, (ii) injury to colours and dyes on the fabrics.  But this is not all, for colours are precipitated as lakes, and mordants also are precipitated, and thus wasted, in much the same sense as the soaps are.  Now by taking a soap solution, formed by dissolving a known weight of soap in a known volume of water, and adding this gradually to hard water until a permanent lather is just produced, we can directly determine the consumption of soap by such a water, and ascertain the hardness.  Such a method is called Clark’s process of determination or testing, or Clark’s soap test.  We hear a great deal just now of soaps that will wash well in hard water, and do wonders under any conditions; but mark this fact, none of them will begin to perform effective duty until such hard water has been rendered soft at the expense of the soap.  Soaps made of some oils, such as cocoa-nut oil, for example, are more soluble in water than when made of tallow, etc., and so they more quickly soften a hard water and yield lather, but they are wasted, as far as consumption is concerned, to just the same extent as any other soaps.  They do not, however, waste so much time and trouble in effecting the end in view, and, as you know, “Time is money” in these days of work and competition.  After making a soap test as described above, and knowing the quantity of water used, it is, of course, easy to calculate the annual loss of soap caused by the hardness of the water.  The monthly consumption of soap in London is 1,000,000 kilograms (about 1000 tons), and it is estimated that the hardness of the Thames water means the use of 230,000 kilograms (nearly 230 tons) more soap per month than would be necessary if soft water were used.  Of course the soap manufacturers around London would not state that fact on their advertising placards, but rather dwell on the victorious onslaught their particular brand will make on the dirt in articles to be washed, in the teeth of circumstances that would be hopeless for any other brand of soap!  I have referred to the sticky and adhesive character of the