A. There is a criterion of solvability of a quintic which can be put under the form F¿(cfg)—¿F¿(eƒ9) (?!) (ek) (f!)=0. B. The pair of equations F(efg)=0, Fa(efg)(?!)(ch)(f!)=0 conducts us to De Moivre's form, i. e. to or C. Either of the pairs F¡(efg)=0, F;(efg)(C!)(ch)(fg)=0, Fμ(efg)=0, Fμ(efg)(o!)(ch)(fg)=0 leads to Euler's form, i. e. to B2=0, 5B4-52В3+53Â ̧В1B=0. D. The general equation of A leads to a resultant in which P enters to twenty-four dimensions. E. The functions Fa satisfying the equation Fa(efg)=F;a(efg) (?!), the general relation of A takes the form Consequently, the interchanges being independent, the factors of the general resultant occur in pairs, which we may represent by F-3F, F-19F3, or F-G, G-3F. F. The decomposition of the general resultant of the twentyfourth degree into biquadratic factors depends upon an equation of the sixth degree. 33. Judging from the analogies afforded by Mr. Jerrard's discussion of De Moivre's form, we shall, prior to inquiring into the possibility of solving this equation of the sixth degree, have to take into consideration the forms of the functions denoted by t, u and v. Into this somewhat laborious and complicated inquiry I am not at present prepared to enter, and it may well form the subject of a separate investigation. 76 Cambridge Terrace, Hyde Park, February 24, 1857. LI. On the Chemical Composition of the Silurian and Cambrian Limestones. By DAVID FORBES, F.G.S., A.I.C.E.* OUR UR information as to the chemical composition of the lower stratified rocks, particularly of England, is so imperfect that it is uncertain whether even a single analysis is recorded. It seemed therefore desirable that this deficiency should be supplied; and the more particularly, as it is of geological importance to know whether these rocks differed from, or were analogous to, their higher equivalents in chemical composition. The analyses of limestones here brought forward are intended to form part of a series of analyses of the various lower rocks; but as from uncontrollable circumstances some time is likely to elapse before this investigation can be pursued further, it is considered best to communicate the results hitherto obtained. The mode of analysis adopted was as follows, subject to some slight variations in particular cases :-A known weight was decomposed by hydrochloric acid in a previously tared carbonic acid apparatus, and the loss estimated as carbonic acid; the insoluble matter filtered from the solution was dried at 300° F., weighed, and then ignited to a red heat and reweighed; the last weight was considered as insoluble matter, and the difference of the two weights as organic matter. The filtrate was boiled with a little nitric acid and precipitated by ammonia, which threw down the sesquioxide of iron, alumina, and any phosphoric acid present in the limestone; this was collected, ignited and weighed, and then dissolved in hydrochloric acid and molybdate of ammonia with excess of nitric acid added: the characteristic yellow phosphomolybdate of ammonia precipitated was, after standing some time, filtered off, washed with dilute nitric acid, dissolved off the filter by ammonia, and precipitated by a magnesian salt as usual. The amount of phosphoric acid deducted from that of the precipitate gave the quantity of iron and alumina present, which were not separated. Some part of the iron was evidently present as protoxide, which makes a slight error in the amounts given in the tabulated analyses. The lime was precipitated as oxalate, and determined as usual with the precaution of reheating with some carbonate of ammonia. In one case the lime contained some manganese, which was separated by weak acetic acid and determined. The magnesia was precipitated from the solution, from which the oxalate of lime had been filtered, by phosphate of soda and ammonia and determined as usual. In one case the lime was determined as sulphate instead of * Communicated by the Author. carbonate, and in two cases the amount of water present in the limestone was determined by heating a known weight to 300° F. and considering the loss sustained as water. 1. Upper Silurian.-Wenlock limestone, Dudley; very fossiliferous. The most crystalline part, free from fossils, chosen for analysis. Specific gravity 2.70 at 60° F. 26.08 grs. were employed for analysis, and furnished-insoluble matter, 1·35 gr.`; alumina, sesquioxide of iron and phosphoric acid, 0.72; phosphate of magnesia from phosphoric acid determination, 0·195; ditto from magnesia determination, 0.73; sulphate of lime, 31.95. The analysis will therefore stand as follows: The insoluble matter appeared to be nothing more than Wenlock shale entangled in the limestone. As this limestone is very largely employed in Staffordshire in the blast-furnaces for smelting iron, the amount of phosphoric acid here present is most important in a metallurgical point of view, and of course highly injurious to the quality of the iron produced. 2. Lower Silurian.-Bala limestone*, Ysputty Evan, North Wales. The specimen analysed did not contain any fossils, and was extremely impure; it could hardly be termed a true limestone, being rather a shale interlaminated with irregular depositions of calcareous matter, crystalline in texture. On dissolving in acids, the insoluble residue was argillaceous, as might be expected. 50-18 grs. gave 26.23 insoluble, and 0.37 organic matter; 2-43 sesquioxide of iron and alumina with phosphoric acid; 0-12 phosphate of magnesia from phosphoric acid determination, and 1.34 from the magnesia present; and the mean of two determinations gave 19.84 carbonate of lime. 48.31 grs., heated to 300° F., lost 0.26 estimated as water. The analysis when tabulated stands as follows: *I have here to thank Mr. Salter and Mr. Bristow of the Ordnance Geological Survey, for their kindness in furnishing me with a number of specimens of limestone from various localities for the purpose of analysis. 3. Lower Silurian.-Bala limestone, Rhiwlas, Wales. The specimen was fossiliferous and very impure, being more strictly an indurated marl than a limestone. The carbonate of lime present appeared to be disseminated through the mass as crystalline particles. The residue, after dissolving in acids, appeared to be a clay. The specific gravity was found to be 2.78 at 60° F. 28.84 grs. were examined, and yielded 5.66 grs. carbonic acid as loss; 21.08 insoluble, and 0.94 organic matter; 0.39 sesquioxide of iron and alumina with phosphoric acid; 0.06 phosphate of magnesia from phosphoric acid determination, and 0.53 gr. from the estimation of magnesia. The analysis when tabulated will be 4. Lower Silurian.-Limestone from Dinover Park near Llandeilo. Specimen very fossiliferous, containing abundance of Ogygia Buchii; it had a compact appearance, and dark bluishgray colour. The specific gravity was 2.70 at 60° F. The analysis was executed upon 23.07 grs., and gave carbonic acid, 18.57 grs.; insoluble, 4.12; organic matter, 0·13; sesquioxide of iron and alumina with phosphoric acid, 0:32; phosphate of magnesia from phosphoric acid determination, 0'21; ditto from determination of magnesia, 0.30. These results afford the following per-centage composition: 5. Cambrian.-Limestone from Church Stretton, Longmynd. In a cursory examination of this district last winter, I found a thin bed of limestone probably from 4 to 6 inches in thickness, rather irregular, and occurring imbedded in the brownish-gray clay-slates immediately in the village of Church Stretton. Owing to the weather and untoward circumstances it was but perficially examined. very su This limestone is not marked upon the Ordnance Geological Survey Sections of this district (Nos. 34 and 36), nor on the Map (61 S.W.), and, as far as I am aware, has not previously been noticed. It is of a bluish-gray colour, compact, and slightly crystalline; in parts it is often very pure, frequently much more so than the specimen analysed. No This limestone must probably be at present considered as the lowest known limestone whose geological position can be correctly determined; and by comparison with the Ordnance Geological Survey Section (No. 36), it must be situated more than 23,000 feet below the base of the Llandeilo or Bala beds. traces of fossils were observed; but when dissolved in acids, the piece analysed left a siliceous cast, very similar to what might be expected when dissolving a coralline limestone where the interstices of the coral had subsequently been filled up by siliceous matter. The specific gravity was found to be 2.33 at 60° F. The quantity operated upon was 23.61 grs., which afforded 6:37 insoluble skeleton, 0·08 organic matter, 2.14 sesquioxide of iron and alumina with phosphoric acid, 0.20 phosphate of magnesia from estimating the phosphoric acid, and 0.39 ditto from the magnesia present; also 14.90 carbonate of lime. The analysis when tabulated will stand as follows: |