(_b_) Permanent Hardness.--200 _c.c._ are measured into a beaker and boiled for 15 minutes with 40 _c.c._ decinormal sodic carbonate. The mixture is then allowed to cool and made up to 250 _c.c._; or the flask and its contents may be weighed before boiling and made up again to the same weight. It is then filtered, and 60 _c.c._ representing 50 _c.c._ of the original water, is twice titrated with decinormal acid and the result added. If the water were pure, exactly 10 _c.c._ should be required to neutralise the 10 _c.c._ of sodic carbonate, but if there be permanent hardness a part of the sodic carbonate will be already neutralised with the acids of the lime and magnesia salts, which have been precipitated as carbonates together with the carbonates of these bases originally present in the water. The hardness will therefore be represented by the loss, i. e. the number of _c.c._ of acid used for 100 _c.c._ of the original water must be subtracted from 20 and the remainder calculated as before, or if calculated as sulphates, each _c.c._ represents 6·8 parts of CaSO_{4} or 6 parts of MgSO_{4} per 100,000. If, as is sometimes the case, more acid is required than is needed for the sodic carbonate used, the excess corresponds to sodic carbonate originally present in the water. In this case there can be no permanent hardness. _Chlorine in Water._--If silver nitrate be added to a solution of any chloride, the silver is precipitated as white curdy insoluble silver chloride. As indicator, a few drops of neutral potassic chromate are used. So long as any chloride is present the red silver chromate which forms is at once decomposed, and the silver converted into white chloride. But as soon as all the chloride is exhausted, the red chromate becomes permanent. To prepare a standard decinormal solution of silver, 17 _grm._ of pure recrystallised silver nitrate are dissolved in 1 _litre_ of distilled water. To perform the estimation 50 _c.c._ of water are measured into a beaker, 2 or 3 drops of strong solution of pure yellow potassic chromate are added, and then silver nitrate from the burette till a permanent red is formed. This is repeated, and the results are added together, representing 100 _c.c._ of water. Each _c.c._ of silver nitrate used represents 3·55 parts of chlorine, or 5·85 parts of sodic chloride per 100,000. If more than 10 _c.c._ of silver solution are required to 50 _c.c._, it is advisable to use a smaller quantity of water. If the process be applied to other liquids than natural water, it must be borne in mind that the solution must not contain free acids or alkalies except carbonic acid. If this is not the case the liquid may be rendered faintly alkaline, with lime-water free from chlorides, and the excess of lime removed by passing carbonic acid through it; or it may be slightly acidified with sulphuric acid, and shaken with a little pure precipitated calcic or baric carbonate.