'^^m K^'^^M^y PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON. ^rj FOR THE YEAR MDCCCXLV. PART I. LONDON: PRINTED BY RICHARD AND JOHN E. TAYLOR, RED LION COURT, FLEET STREET. MDCCCXLV, ^0\ Q 41 ADVERTISEMENT. The Committee appointed by the Royal Society to direct the publication of the Philosophical Transactions, take this opportunity to acquaint the Public, that it fully appears, as well from the Council-books and Journals of the Society, as from repeated declarations which have been made in several former Transactions, that the printing of them was always, from time to time, the single act of the respective Secretaries till the Forty-seventh Volume ; the Society, as a Body, never interesting themselves any further in their publication, than by occasionally recommending the revival of them to some of their Secretaries, when, from the particular circumstances of their affairs, the Transactions had happened for any length of time to be intermitted. And this seems principally to have been done with a view to satisfy the Public, that their usual meetings were then continued, for the improvement of knowledge, and benefit of mankind, the great ends of their fii'st institution by the Royal Charters, and which they have ever since steadily pursued. But the Society being of late years greatly enlarged, and their communications more numerous, it was thought advisable that a Committee of their members should be appointed, to reconsider the papers read before them, and select out of them such as they should judge most proper for publication in the future Transactions:, which was accordingly done upon the 26th of March 1752. And the grounds of their choice are, and will continue to be, the importance and singularity of the subjects, or the advantageous manner of treating them ; without pretending to answer for the certainty of the facts, or propriety of the reasonings, contained in the sevei-al papers so published, which must still rest on the credit or judgement of their respective authors. It is likewise necessary on this occasion to remark, that it is an established rule of the Society, to which they will always adhere, never to give their opinion, as a Body, a2 [ iv ] upon any subject, either of Nature or Art, that comes before them. And therefore the thanks, which are frequently proposed from the Chair, to be given to the authors of such papers as are read at their accustomed meetings, or to the persons through whose hands they received them, are to be considered in no other light than as a matter of civility, in return for the respect shown to the Society by those communi- cations. The like also is to be said with regard to the several projects, inventions, and curiosities of various kinds, which are often exhibited to the Society ; the authors whereof, or those who exhibit them, frequently take the liberty to report and even to certify in the public newspapers, that they have met with the highest applause and approbation. And therefore it is hoped that no regard will hereafter be paid to such reports and public notices ; which in some instances have been too lightly credited, to the dishonour of the Society. The Meteorological Journal hitherto kept by the Assistant Secretary at the Apart- ments of the Royal Society, by order of the President and Council, and published in the Philosophical Transactions, has been discontinued. The Government, on the recommendation of the President and Council, has established at the Royal Obser- vatory at Greenwich, under the superintendence of the Astronomer Royal, a Magnet- ical and Meteorological Observatory, where observations are made on an extended scale, which are regularly published. These, which correspond With the gi-and scheme of observations now carrying out in different parts of the globe, supersede the necessity of a continuance of the observations made at the Apartments of the Royal Society, which could not be rendered so perfect as was desirable, on account of the imperfections of the locality and the multiplied duties of the observer. iirW. !,'• A List of Public Institutions and Individuals, entitled to receive a copy of the Philosophical Transactions of each year, on making application for the same directly or through their respective agents, within five years of the date of pub- lication. In the British Dominions^ The Queen's Library. 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The Waterville College, United States. List of Observatories, Institutions and Individuals, entitled to receive a Copy of the Magnetical and Meteorological Observations made at the Royal Observatory, Green- wich. Observatories. Algiers M. Aim^. Altona M. Schumacher. Armagh Dr. Robinson. Berlin M. Encke. Bogoslowsk Bombay G. Buist. Bornaoul M. Prang, 1st. Breda Prof. Wenchebach. Breslau Prof. Boguslowski. Brussels M. Quetelet. Cadiz M. Cerquero. Cairo M. Lambert. Cambridge Prof. Challis. Cambridge, United States . Prof. Lovering. Cape of Good Hope . . . T. Maclear, Esq. Catherineburgh M. RochkofF. ChrJstiania M. Hansteen. Cincinnati Dr. Locke. Copenhagen M. Oersted. Coimbra ~ Dorpat M. Madler. Dublin Sir W. R. Hamilton. Gotha Hammerfest Hanover Heidelberg M. Tiedemann. Helsingfors M. Nervander. Hobarton Lieut. Kay, R.N. Hudson College United States. Kasan M. SimonofF. Kew Observatory. Konigsberg M. Bessel. Kremsmiinster Prof. KoUer. Leipsic M. Weber. Lougan . . . . . ' , . Madras Lieut. Ludlow. Manheim Marburg Prof. Gerling. Marseilles Milan M. Carlini. Munich Dr. Lamont. Nertchinsk M. Prang, 2nd. NikolaiefF Dr. Knorr. Oxford M. J. Johnson, Esq. Palermo Paramatta Paris M. Arago. Pekin M. Gachk^vitche. Philadelphia Dr. Bache. Prague M. Kreil, Pulkowa M. Struve. St. Helena Lieut. Smythe. R.A. St. Petersburgh M. Kupffer. Seeberg M. Hansen. Simla Capt. J. H. Boileau. Singapore Lieut. C. M. Elliot. Sitka Messrs. Homanu and IvanofF. Stockholm Prof. Selander. Teflis M. Philadelphine. Toronto Lieut. Lefroy, R.A. Trevandrum J. Caldecott, Esq. Tubingen Upsal Prof. Svanberg. Vienna M. Littrow. Wilna Zlatoouste Institutions. Aberdeen University. Berlin Academy of Sciences. Board of Ordnance .... London. Bologna Academy. Boston Academy of Sciences. Bowden College United States. Convent of St. Bernard . . Switzerland. Dublin University. Edinburgh Astronomical Institution. Edinburgh Royal Society. Edinburgh. ...... University. Glasgow University. Gottingen University. Harvard College United States. House of Lords, Library . . London. House of Commons, Library . „ „ King's College, Librar}' . . „ „ Ley den University. Paris Academy of Sciences. Paris Board of Longitude. [ Vlll ] Paris ........ Depot de la Marine. Philadelphia Philosophical Society. Queen's Library London. Royal Cornwall Polytechnic Society Falmouth. Royal Institution .... London. Royal Society ,, „ St. Andrews University. St. Petersburgh Academy of Sciences. Savilian Library Oxford. Stockholm Academy of Sciences. Trinity College, Library . . Cambridge. Upsal Society of Sciences. Waterville College .... United States. Individvals.^ Bessel, Prof Konigsberg. Brittingham, Lieutenant, R.A. Newfoundland. Lowndes Prof, of Astronomy Cambridge. Plumian Prof, of Astronomy Cambridge. Christie, S. H., Esq. . . . Woolwich. Colebrook, Sir W New Brunswick. Dove, M Berlin. Erman, M Berlin. Fox, R. W., Esq. . Harris, W. Snow, Esq Holland, L., Esq. Howard, Luke, Esq Humboldt, Baron Kaemtz, M. . . Lawson, Henry G. Lloyd, Rev. Dr. . Loomis, Prof. Lubbock, Sir John W., Bart. MacCuUagh, James, Esq. Mahlmann, Prof. .... Melvill, J. C, Esq.. . . . Phillips, John, Esq. . . . Pickering, Captain, R.A. . . President of the Royal Society Redfield, W. C, Esq. . . . Reid, Lieutenant-Colonel Riddell, Lieut., R.A. . . . Roget, P. M., M.D. . . . Sabine, Lieut. -Col., R.A. . . Smyth, W. H., Captain R.N. South, Sir James .... Templeton, Dr Falmouth. Plymouth. Lombard-street. Tottenham. Berlin. Dorpat. Bath. University, Dublin. New York. London. University, Dublin. Berlin. East India House. York. Ceylon. London. New York. Bermuda. Woolwich. London. Woolwich. London. Ceylon. r ROYAL MEDALS. HER MAJESTY QUEEN VICTORIA, in restoring the Foundation of the Royal Medals, has been graciously pleased to approve the following regulations for the award of them : That the Royal Medals be given for such papers only as have been presented to the Royal Society, and inserted in their Transactions. That the triennial Cycle of subjects be the same as that hitherto in operation : viz. 1. Astronomy; Physiology, including the Natural History of Organized Beings. 2. Physics ; Geology or Mineralogy. 3. Mathematics ; Chemistry. That, in case no paper, coming within these stipulations, should be considered deserving of the Royal Medal, in any given year, the Council have the power of awarding such Medal to the author of any other paper on either of the several sub- jects forming the Cycle, that may have been presented to the Society and inserted in their Transactions ; preference being given to the subjects of the year immediately preceding : the award being, in such case, subject to the approbation of Her Majesty. The Council propose to give one of the Royal Medals in the year 1845 for the most important unpublished paper in Astronomy, communicated to the Royal Society for insertion in their Transactions after the termination of the Session in June 1842, and prior to the termination of the Session in June 1845. The Council propose also to give one of the Royal Medals in the year 1845 for the most important unpublished paper in Physiology, including the Natural Histoiy of b [ ^ ] Organized Beings, communicated to the Royal Society for insertion in their Trans- actions after the termination of the Session in June 1842, and prior to the termina- tion of the Session in June 1845. The Council propose to give one of the Royal Medals in the year 1846 for the most important unpublished paper in Physics, communicated to the Royal Society for insertion in their Transactions after the termination of the Session in June 1843, and prior to the termination of the Session in June 1846. The Council propose also to give one of the Royal Medals in the year 1846 for the most important unpublished paper in Geology or Mineralogy, communicated to the Royal Society for insertion in their Transactions after the termination of the Session in June 1843, and prior to the termination of the Session in June 1846. The Council propose to give one of the Royal Medals in the year 1847 for the most important unpublished paper in Mathematics, communicated to the Royal Society for insertion in their Transactions after the termination of the Session in June 1844, and prior to the termination of the Session in June 1847. The Council propose also to give one of the Royal Medals in the year 1847 for the most important unpublished paper in Chemistry, communicated to the Royal Society for insertion in their Transactions after the termination of the Session in June 1844, and prior to the termination of the Session in June 1847- The Council propose to give one of the Royal Medals in the year 1848 for the most important unpublished paper in Astronomy, communicated to the Royal Society for insertion in their Transactions after the termination of the Session in June 1845, and prior to the termination of the Session in June 1848. The Council propose also to give one of the Royal Medals in the year 1848 for the most important unpublished paper in Physiology, including the Natural History of Organized Beings, communicated to the Roj^al Society for insertion in their Trans- actions after the termination of the Session in June 1845, and prior to the termina- tion of the Session in June 1848. CONTENTS. I. Oti the Laws of the Tides on the Coasts of Ireland, as inferred from an extensive series of observations made in connection with the Ordnance Survey of Ireland. By G. B. Airy, Esq., F.R.S., Astronomer Royal page 1 II. On the Temperature of the Springs, Wells and Rivers of India and Egypt, and of the Sea and Table-lands within the Tropics. By Captain Newbold, Madras Army,F.R.S 125 III. An Account o/" Newton's Dial presented to the Royal Society by the Rev. Charles TuRNOR, in a letter addressed to the Marquis of Northampton, Pr^es. R.S., 8gc. By the Rev. Charles Turnor, F.R.S. Communicated by the President. 141 IV. ' Ajx6p 573 341 771 •970 327 334 •589 •795 •486 •269 •828 268-519 7-981 7-886 ... 147146 061146-561 477! 5-489 6-109 5-086 6-893 98-341 99-110 1-087 1-122 2-351 998 520 93117 94-314 CO r- o2+r>3 D3+D4 D4+D5 o,„ 2 ' 2 ' 2 ' 2 ' ^^- ' and the means of the numbers in this series were taken, forming Di + 2D,+D3 D2+2D3+D, D3+2D4+D5 „ 4 ' 4 ' 4 ' ^^' Then the number — ' ^ ^ was considered to be the just difference from mean for the second day in the series: it was applied to the mean of times for that day, and gave the adopted time for high or low water for that day, at the station under consideration ; and so for the succeeding days. In regard to the legitimacy of this process, it is to be observed that it does not suppress the inequalities affecting, in different degrees at different stations, the semidiurnal or diurnal tide, provided the period of such inequalities is of several days. Nor does it suppress any accidental inequality which affects the whole tide-wave coming from the Atlantic upon a large extent of coast. The only failure is, that, as D. + 2D2+D0 -r. , D,-2D2+D3 TA . 1 ,^ J v^ ' ^^^ ^=1)2+ 4^^^-'=D2+4(2nd difference) ; when the second difference of D is large, an error is introduced. So long as the tides at the different stations follow anything like similar laws, there is no fear that this error will be perceptible. The only place where there is any probability that it can become sensible is Ballycastle ; and here it will be very far below the irregularities of observation. Section III. — Theory of diurnal tide as related to observations only ; and deduction of the principal results for diurnal tide given immediately hy these observations. The remarks with which I shall immediately proceed apply equally to times and to heights, and equally to high waters and to low waters ; but, to avoid unnecessary repetitions, I shall speak only of heights at high water. Suppose then that, for any station, the heights at high water, both of the First Division and of the Second Division, have been collected and intermingled in the order of times. It is evident that the diurnal tide at any one of these heights will be found approximately by taking half the excess of that height above the mean of the two heights immediately preceding and immediately following. The number thus found will, however, be in error by one-fourth of the second difference of the semi- diurnal tide. This error may be eliminated, leaving only an error depending on fourth differences, by taking half the algebraical excess of that apparent diurnal tide above the mean of the diurnal tides next to it. The process may however be put in the following algebraical form :— Suppose the successive high waters to be affected with inequalities represented hy a.cosn—dj, c2 12 MR. AIRY ON THE LAWS OF THE TIDES a. COS n— 2 J, a. cos n—lJ, a. cos n&, a. cos n-\-\J, a.cos w+2.^, &c., where n increases by unity for each successive high water. If we take tlie 4th, the 8th, the 12th, &c. differences of these numbers, we shall have for the differences standing opposite to a.cosn&j a.cosw^X 16 sin^g"' «.cos w^X256 sin^y a .cos w^ X 4096 sini2_. Now if the inequality occupies many tides in going through its changes, that is, if 0 is small, the powers of sin ^ will be very small, and these differences will therefore become smaller and smaller till they are nearly insensible. There is one value of ^, 6 however, for which they do not become smaller, namely, that which makes sin^ nearly =1, or 0 nearly =180°, or in which the successive numbers a.cosn—\.0, a.cosnd, a.cosn-{-l.0, &c. have nearly equal magnitudes with a change of sign at every step. It is evident that this is the case of diurnal tides. Consequently, on taking the successive differences in this manner, the diurnal tide will ultimately be the only inequality sensible. If then we stop at the fourth differences, we may say that the diurnal tide fourth difference .„ , ^ ,, - ij.i. i-rn ^, j. ^ ^. ^ eighth difference _ : if we stop at the eighth difference, the diurnal tide =-^ 2 ; 16 sin*- 256 sin^j- and so on, the expressions becoming more accurate as we advance further in the order of differences. Remarking, however, that the diurnal tide goes through all its changes in not fewer than 57 high waters, and that & therefore differs from 180° by 9 1 little more than 6 , or that sin2 = cos 3° nearly =1 — — nearly, we may consider the powers of sin^ as equal to unity ; and thus we have Diurnal tide =jgX 4th difference, or =2^ X 8th difference, &c. The first of these formulae was used throughout, both for heights and for times, and at both high and low waters. Let us now consider the relation between the diurnal tide in height and that in time. Let 6 be an angle increasing uniformly with the time, and increasing by 360° in a tidal day, its origin being the time of high water in the semidiurnal tide. Let a ON THE COASTS OF IRELAND. 13 be the diurnal tide at the first high water, h that at the first low water, c the semi- range of the semidiurnal tide. And suppose a and h to be so much smaller than c that their squares, &c. may be neglected. The height of the water above its mean height, on the law of elevation usually assumed, will be a.cos^-}-A.sin^-|-c.cos2^. This quantity will be maximum or minimum, or there will be high water or low water, when — a. sin ^+6. cos ^— 2c. sin 2^=0. The first approximation to the value of 6 will be obtained by considering the large term only : from this we find 2c.sin 2^=0, from which ^=0, or =-, or =r, or =yj nearly. Substituting these values successively in the small terms, and supposing them liable to a correction x in the large term, we have, For the first high water, +i — 2c.sin (0-f-2a?)=0; or, nearly, ^--4c.r=0; whence .r=T-^ and ^=04- .r=—- For the first low water, —a— 2c. sin (5r+2.r)=0 ; or, nearly, — a+4ca?=0 ; whence ^^=4^' and ^=^+.r=|+^. For the second high water, — Z>— 2c.sin (2^-|-2jr)=0 ; or, nearly, — 6— 4ca?=0; whence ^= -J—' and &=:r-^a:=x—-r' 4c '4c For the second low water, +a— 2c.sin (3^+20:') =0 ; or, nearly, +a+4c.r=0; whence a: =^' and ^=Y~"r' It appears therefore that the diurnal equation in time at the High waters of the First Division has the same sign as, and is a certain multiple of, the diurnal equation in height at the Low waters of the First Division ; and that the diurnal equation in time at the Low waters of the First Division has the same relation to the diurnal equation in height at the High waters of the First Division ; and similarly for those of the Second Division. The factor by which the diurnal tide at low water in height is converted into diurnal tide at high water in arc is ^ ; and, observing that -x- in arc corresponds to about 12'' 24" in time, the factor for converting diurnal tide at low .... 1. 1.1 , . , . . /. .. . 744 186 J water m height into diurnal tide at high water m minutes or time is 4^=^ ; and that by which the diurnal tide at low water in minutes of time is converted into diurnal tide at high water in height is ^- The same factor applies for converting diurnal tide at high water in minutes of time into diurnal tide at low water in height. But the high and low waters of the First Division must be used together, and the high and low waters of the Second Division must be used together. This theory cannot be expected to apply with accuracy to any place far from the 14 MR. AIRY ON THE LAWS OF THE TIDES sea (as Limerick or New Ross), where the law of the height of semidiurnal tide, as depending on the time, differs sensibly from that of cos 2^. Upon investigating the magnitude of the diurnal tides, by the method detailed a short time since, it appears that, at most stations, the diurnal tide in height was given with great regularity ; but that, at the greater number of stations, the diurnal tide in time was not very regular. In order to compare the diurnal tides by means of the theory above, as well as for the purpose of ascertaining their magnitudes with some accuracy, it was necessary so to combine them that a mean of many determinations could be made available. This was done in the following manner : — First, it is to be remarked that in this and all the following investigations the high and low waters of the jfirst division only are used ; these being evidently sufficient for the complete solution of any problem of diurnal tides. Next, it is well known, or may be anticipated from the investigations of the next section, that on examining successively the diurnal tides at high water (first division) on successive days, they increase, diminish, change sign, and increase and diminish with the changed sign, in nearly the same manner as the sine of an arc increasing proportionally to the time ; and that the same remark applies to the diurnal tides at low water. The first thing to be done in investigation was therefore to ascertain when the diurnal tide vanishes. This was done by taking the five diurnal tides nearest to the estimated place of evanescence and combining them by the method of minimum squares, on the supposition that the diurnal tide ought there to alter by uniform steps ; an assumption sensibly correct. The next thing was, to take the mean of all the diurnal tides between two vanishing points. Supposing them to be expressed by the law a.sin^, the mean of all these , . Sum of the values of asin d , . , . . , i , 1 /* . 2a values IS Number of values ' which IS approximately expressed by -«/, sm^=-. and hence the coefficient a, or the maximum diurnal tide, must =0^. the mean of the diurnal tides between two vanishing points. The following results have been obtained by these methods ; — ON THE COASTS OP IRELAND. 15 Diurnal Tide in Height at High Water. First Division. Approximate time I at Kilbaha. iKUbaha. Kilrush. 1842. I June 22. 23. 24. 25. 26. 27. 28. 29. 30. July 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. August 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. hrs. 17 18 19 19 20 21 22 22 23 0 feet. feet. -0-23 .0-40 -0-29 -0-37 -0-26 -0-53 -0-50 -0-30 1-0-40 -0-30 I -0-30 -0-18; -0-24 -009 i -016 -001 -0-04 Foynes Island. feet. -0-41 -0-47 -0-41 Ivime- rick. Casleh Bay. feet. 1 -f 0-23 2 1+0-26 3 +0-21 4i+011 4 +0-07 5 +0-24 6 +0-37 7 +0-29 8+0-16 9 +0-26 +0-04 +0-17 -0-06 -012 +013 +0-28 +0-31 +0-21 +0'24 +0-31 -0-30 -0-46 -0-42 -0-36 -0-26 -0-26 -0-24 -0-13-0-24 -003; -0-28 feet. +005 + 0-09 +010 +012 +0-22 +0-42 +0-47 +0-22 +0-23 +0-28 -0-19 -002 +0-25 +0-28 +0-46 +064 +0-72 +023 +0-22 +0-16 12,-0 13-0 14 -0 -0' -0 -0 -0 11 -I 0-12 04 +0-09 03-001 12!-0-18 27 1-0-20 33-0-32 371-0-18 41 -0-36 ■42-0-34 ■42 -039 18 I -0-43 19 1-0-42 20 -0-37 20 21 22 22 23 0 1 2 3 4 5 6 6 7 8 9 10 11 12 13 14 15 16 17 18 19 19 -0-33 -0-22 -014 -009 +0-01 +011 +0-21 +0-26 +0-27 +0-20 +014 +016 +0-33 +0-31 +016 +009 -003 -0-13 -0 31 -0-32 -0-27 -0-33 -0-29 -0-28 -0-32 -0-37 -0-31 -0-40 -0-39 -0-36 -0-36 -0-25 -0-15 0-03 000 +0-11 + 0-08 +007 +0-14 +0-09 +011 +019 +0-38 +0-33 +0-16 +0-10 -0-02 +0-09-0-02 ^0-06-005 _008i+003 -0-23-0-17 -0-28-0-47 -0-35 -0-54 _0-4l -0-40 -0-41 -0-38 -0-39 -0-41 -0-38-0-38 -0-42-0-37 -0-39-0-42 -0-38; -0-38 -0-33-0-32 -0-241-0 32 -016-0-24 -0-02-007 +0-02-009 _|_007 -0-04 +0-20 +0-24 -0-22 -0-26 -0-31 -0-49 -0-38 -0-34 -0-23 -0-12 -002 +0-09 +0-20 +0-23 +016 +002 +014 +0-46 +0-22 +010 +0-27 +0-04 -0-05 -010 +0-14 +0-19 +0-28 +0-20 +0-29 +0-44 +0-35 +0-22 +0-10 +0-02 -0-12J-014 0-26 0-33 031 0-35 0-25 0-28 0-37 0-40 0-35 -023 -0-20 -0-01 -004 -0-14 -0-24 -0-23 -0-31 -0-20 +0-22 +0-22 +0-34 +0-29 +0-36 +0-49 +0-36 +019 +0-08 -0 09 -0-24 -0-36 -0-43 -0-33 ^0-40 -0-34 -0-41 -0-46 -0-45 -0-40 Galway. feet. -0-30 -0-34 -0-42 -0-40 -0-38 -0-27 -Oil -0 23 -0-13 +003 +011 +0-19 +012 +0-18 +0-32 +0-20 +0-21 +0-20 -0-09 -0-08 -0-07 Old Head. Mul- lagh- more. feet. -0-24 -0-29 -0-30 -0-37 -0 24 -0-32 -0-39 -0-41 -0-40 -0-42 -0-43 -0-38 -0-33 -0-25 -0-19 -0-10 000 +0-14 +0-25 +0-21 +0-21 +0-26 +017 +0-20 +0-45 +0-34 +0-11 -0 01 -Oil -0-21 -0-28 -0-35 -0-32 -0-39 -0-26 -0-29 -0-38 -0-38 -0-35 -0-38 -0-31 -041 -0-41 -0-39 -0 35 -0-39 -0-33 -010 -0-21 -0-23 -0-05 +005 +0-10 +0-18 +012 +0-07 +0-17 +0-14 +0-21 +0-39 +0-30 +0-10 +0-07 -001 -0-15 -0-25 -0-33 -0-32 -0-38 -0-24 -0-29 -0-35 -0-43 -0-40 -0-72 -0-64 -0-61 -0-68 -0-60 -0-40 -0-18 -014 -0-20 +009 +0-07 +0-02 +0-28 +0-21 +0-20 +0-55 +0-42 +0-34 +0-47 +0-29 +0-21 +0-15 -0-20 -0-50 -0-27 -0-37 -0-57 -0 55 -0-50 -0-50 -0-59 -0-57 -0-45 -0-45 -0-25 -005 0-00 +0-22 +0-57 +0-54 +0-43 +0-61 +0-44 +0-54 +0-69 +0-48 +0-27 +0-11 +008 -006 -0-28 -0-67 -0-44 -0-43 -0-44 -0-38 -0-62 -0-54 -0-50 feet. Bun- crana. feet. -1-05 -0-73 -0-99 -0-99 -0-91 -1-16 -0-88 -0-61 -0-24 -0-38 -0 24 +0-05 +0-41 +0-41 +0-31 +0-76 +0-69 +0-84 +0-83 +0-82 +0-93 +0-62 +0-27 -0-01 -0.32 -0-52 -0-74 -0-79 -0-86 -0 90 -0-96 -0-87 -0-87 -0-72 -0-55 -0-50 -0-11 +0-09 +0-09 +0-10 +0-29 +0-69 +0-72 +0-68 +0-96 +0-90 +0-80 +0-72 +0-47 +0-15 -009 -0-46 -0-53 -0-69 -0-84 -0-96 -103 -0-88 -0-80 Port Rush. feet. -0-64 -0-86 -0-84 -0-71 -0-62 0-70 -0-57 -0-64 -0-56 -0-34 -0-28 -0-16 +0-16 +0-44 +0-52 +0-74 +0-51 +056 +0-45 +0-50 +0-44 +0-34 +0-27 +002 -0-29 -0-44 -0-61 -0-68 -0 73 ] -0-75 I -0-64 -0-57 -0-59 -0-49 -0-42 -0-39 -0-37 -0-30 +001 +0-08 +0-33 +0-57 +0-51 +0-81 +0-83 +0-51 +0-50 +0-42 +0-15 -001 -0-09 -0-27 -0-39 -0-61 -0-66 -0-84 -0-87 -0-70 -0-60 Carrow- keel. feet. -0-72 -0-97 -0-81 -0-58 -0-56 -0-57 -0 49 -056 -0-54 -0-28 -0-22 +001 +013 +0-46 +0-53 +0-57 +0-27 +0-43 +0-36 +0-40 +0-28 +0-29 +0-20 -0 02 -0-23 -0-41 -0-55 -0-62 -0-64 1-0-40 -0-56 0-52 -0 47 -0 33 -0-21 0-24 -0-47 -0-27 +0-08 +0-03 +0-25 +0-56 +0-44 +0-70 +0-74 +0-41 +0-41 +0-19 +0-07 -008 -003 -0-25 -0-37 -0-55 -0-59 -0-74 -0-72 -0-59 -0-55 Ballv- castle. feet. -0-51 -0-78 -0-74 -0-68 -0-66 -0-63 -0-59 -0-67 -0-61 -018 -006 -0 05 +005 +032 +0-56 +0-65 +0-25 +0-37 +0-39 +0-45 +0-25 +0-16 +0-02 -0 05 -0-28 -0-48 -0-64 -0-62 -0-74 -0-71 -0-58 -0-46 -0-37 -0-37 -0-16 -0-23 0-36 -0-32 +003 -003 +0-23 +0-63 +0-32 +0-64 +0-89 +058 +0-44 +0-15 -0 06 -0-21 -019 -0-31 -0-48 -0-63 -0-55 -0-57 -0-75 -0-55 -0-50 Glen- ann. feet. Donagh- adee. feet. Ard- glass. feet. -074 -0-53 -0-48 -0-33 +006 +0-08 +0-16 +032 +0-51 +0-51 +061 +0-26 +0-40 +0-41 +0-44 +0-27 +0-27 +0-29 +001 -0-25 -0-38 -0-50 -0-58 -0-61 -0-63 -0-59 -0-53 -0-50 -0-46 -0-33 -0-29 -0-30 -0 02 +0-31 +0-21 +0-31 +0-58 +0-45 +0-65 +0-72 +0-44 +031 +014 +0-14 +019 +0-11 -0-17 -0-31 -0-42 -0-54 -0-85 -0-77 -0 57 -0-50 -0-76 -0-83 -0-83 -0-72 -066 -0-65 -0-35 -0 32 -0 30 +0-12 +016 +0-12 +0-27 +0-38 +0-56 +0-79 +0-59 +0-79 +0-98 +0-80 +0-69 +0-56 +0-27 004 -0-23 0-28 -0-34 -043 -0-48 -0-58 -0-64 -0-65 -0-58 -0-49 -0-45 -0-22 -Oil +016 +0-35 +0-27 +0 20 +0-56 +0-53 +0-65 +0-97 +0-81 +0-87 +0-84 +0-68 +0-33 +0-12 -009 -0-22 -0 39 -0 34 -0-62 -0-75 -057 -050 -072 -0-76 -0-85 -0-78 -0-78 -0-76 0-76 -0-74 -0-71 -0-73 -0 54 -036 -0 22 +0-11 +016 +006 +022 + 0 41 +0-54 +0-72 +0-50 +0-67 +0-88 +0-71 +0-62 +0-49 +0-23 -009 -0 24 -0-28 -0-44 -0-51 -0-52 -0-62 -0-68 -0 65 -0-60 -0-58 -0-59 -034 -016 +0-10 +0-30 +0-20 +0-18 +0-52 +0-53 +0-62 +0-94 +0-80 +0-77 +0-74 +0-57 +0-27 +0-03 -015 -0-25 -041 -0-29 -0-54 -0 69 -0-63 -0-50 Clogher Head. feet. -0-71 -0-79 -0-64 -0-48 -0-32 +005 +019 +014 +021 +0-37 +0-51 +0-27 +0-34 +0-41 +0-69 +0-56 +0-49 +0-48 +0-21 I +008 -0-22! -0-42 I -0-50 ' 0-58! -0-60 -0-62 -0-69 -0-67 -0-65 -0-56 -0-50 -0-31 -0-24 -0-02 +0-16 +0-20 +0-15 +0-42 +0-54 +0-66 +0-85 +0-59 +0-56 +0-71 +0-57 +0-30 +003 -0 25 -0-39 -0-50 -0-32 -0-64 -0-71 -0-58 -0-50 Kinga- town. feet. -0-75 -063 -0-69 -0-71 -0-73 -0-78 -0-67 -0-52 I -034 j +002 +0-17 +0-17 +0-21 +017 +0-47 +0-58 +0-52 +0-56 +0-75 +0-66 +0-52 +0-33 +0-28 -004 -0-26 -036 -0-50 -0-52 -0-53 -0-66 -0-83 -0-66 -063 -0-71 -0-51 -0-18 -0-21 -004 +0-21 +0-21 +019 +0-55 +0-52 +0-49 +0-65 +0-53 +052 +0-56 +038 l>un- tnore East. feet. New PaMage Rots. West. feet. feet. -0-63 -0-69 -0-61 -0-63 i -0-72] -0-75 -0-55 ' -0-39 ! -0-25 +008 +0-16 +0-15 +0-20 +0-28 ! +0-45 +0-51 +0-39 +0-43 +0-56 +0-42 +0-37 +0-38 +0-11 -009 -0-23 -0-29 -039 -0-46 -0-54 -0-53 j -0-19! -0-49 1-0-25 -0-50-0-20 +0-20 +001 -0-14 -0-26 -041 -0-34 -0-66 -0-79 -0 66 -0-50 -0-24 -0-19 -0-13 -0-13 -0-14 -014 -009 -0-18 -014 -0-25 -0-20 -0-04 +0-01 +0-11 +0-18 +0-11 +0-03 +011 +019 +011 +016 +013 +0-13 -001 -009 -0-16 -0-20 -0-21 -0-28 -0-21 1, -0-18'. 0-00*. -0-16'. -0-17 i- -0-18|. -0-12 I- -0-12 - -0-15;. 0-16 0-16 014 0-17 0-10 0 02 .007 .0 09 Caatle Towns- end. feet. -0-13 +0-01 _ 006 i +005 +0-06 +0-11 +006 1-003 +0-08!-0K» +031 ;+0-02 +0-241+0-11 +0-111+0^06' +0-22 +0-161 +0-28 1+0-16 +0-171+0-11 +0-12-0 06 -003 1-0 01 +0-0l!-00lj -0021-006 -0-12-0-12 -0-311-018 -0-35 ' -019 -0-55 -0-54 -0-48 -0-22 -0-16 -0-14 -0-08 -0-19 -017 -0-14 +003-004 +0-24 1-0 06 +0-24 +0-21 +0-49 +0-47 +0-51 +0-69 +0-54 +0-61 +0-53 +0-55 +0-22 +004 -0-14 -0 22 -0-36 -0-26 -0-54 -066 -0-59 -0-45 +0 04 +029 +0-28 +0-15 -I-0-28 +0-29 +0-18 +0-16 +001 -003 -006 -009 -019 -0-16 -006 -019 -0-21 -0-23 -0 23 -016 -0-27 -0-33 -0 29 -0-28 -0-21 -0-26 -0 23 -0-18 -0-17 -015 -0 09 -0-06 !+002 1+0-12 +0-13 +0-22 +024 +0-34 +029 +0-16 +0-12 -003 -005 -0-07 -0-11 -0-18 -020 -0-17 -0 22 -0-28 -0-29 -0 20 ^0-19 -0-25 +0-02 -002 0-00 0-00 -004 +0-01 +0-04 +0-01 -0-14 -0-13 +0-13 +0-13 +0 04 -0 05 -008 -006 +0^03 -002 1-0-02 |-fr01 -007 -0^01 1-002 -004 -008 -012 -0-13 -010 -0-15 .024-0-12 -0-191-009 -0-16 -0 10 -0-18-0 03 -010 -001 .O03l_001 -0-05 +0-04 -006+0-01 -007i-0-01 .0-O7;_004 -004 +0-11 +0-20 +0-17 +017 +0-23 +0-22 +009 +0 03 -0-06 -002 + 012 +0-20 +011 1+0 04 +0 03 +oo;j -0 04 -0 07 -008 -0-06-0 04 -009+0 02 -010 -0-06 -0-14-009 -0-23! -0^09 -0-15 '-003 -0-17-007 -0-191 000 -0-21-0 03 -0-151 16 MR. AIRY ON THE LAWS OF THE TIDES Diurnal Tide in Height at Low Water. First Division. Approximate time ! at Kilbaha. Kilbaha. 18i2. Kilrush. Foynes Island. Lime- rick. Casleh Bay. Galway. Old Head. Mul- lagh- more. Bun- crana. Port Rush. Carrow- keel. Bally- castle. Glen- arm. Donagh- Ard- adee. glass. Clogher Head. Kings- Dun- town. H^ore East. New Ross. Passage West. June 22. 23. 25. 26. 27. 28. 29. 30. July 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ]]. 12. 13. 14. 15. 16. 17. 18, 19. 20. 21. 23. 24. 25. 26. 27. 28. 29. 30. 31. August 1. 2. 3. 4. -5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 23. hrs. 23 23 0 1 1 2 3 4 5 6 feet. feet. feet. feet. feet. feet. feet. feet. feet. feet. feet. feet. +0-52 +0-46 +0-49 -f-0-44 -fO-39 +0-39 -fO-22 +0-24 +0-20 -014 101-0-34 9 +0-64 +0-50 -1-0-44 -fO-57 -fO-50 -f040 -I-0-41 -f019 -I-0-55 -1-0-65 -1-0-51 -fO-51 -1-0-51 -I-0-32 +0-16'-i-0 23 +0-18 i-j-0-10 -0-05 -0-21 -0-40 -0-16 -0-34 -0-23 -0-60 -0-44 -0-39 -0-27 -0-20 -007 -fO-13 -f-0-26 -f-0-33 22 i-l-0-41 23 I-I-0-43 0 -j- 0-39 0 -f-0-41 +0-36 -f-0-33 -fO-35 -fO-31 -fO-28 -fO-27 -1-0-19 0-02 -015 031 -0-37 -0-51 -0-45 -0-71 -0-48 -0-34 -0-28 -0-15 -004 -1-005 -I-0-17 -fO-23 -1-0-34 -fO-35 -hO-39 -1-0-38 -I-0-42 -fO-36 -1-0-32 -0-40 -0-60 -0-71 -0-42 -0-08 -0-47 -0-29 -0-41 -0-22 -0-30 -0-09 +012 -fO-28 4-0-34 -t-0-39 -1-0-39 -1-0-35 -hO-23 -}-0-25 -1-0-30 -fO-29 -fO-36 4-0-31 -1-0-21 -I-015 +007 -0-08 -0-29 -0-39 -0-45 -0-32 -0-52 -0-51 -0-34 -0-30 -0-24 -0-14 -0-08 +0-18 +0-28 +0-37 +0-37 +0-42 +0-43 +0-34 +0-27 +0-25 -0-49 -0-74 -0-90 -0-61 -0-51 -0-58 -0 55 -0-55 -0-29 -0-16 -0 05 +0-14 +0-27 +0-36 +0-45 +0-46 +0-36 +0-40 +0-46 +0-41 +0-38 +0-37 +0-30 +0-32 +0-28 +0-09 -0-09 -0-30 -0-44 -0-60 -0-57 -0-68 -0-49 -0-34 -0-28 -0-18 -0-09 +0-04 +0-26 +0-27 +0-35 +0-40 +0-49 +0-48 +0-43 +0-37 +0-35 +1-13 +0-63 +0-75 +0-61 +0-63 +0-95 +0-47 +0-29 -0-12 -055 -0 72 -1-16 -1-37 -0-57 -0-61 -0-79 -0-53 -0-50 -0-27 -0-14 +0-05 +0-14 +0-26 +0-39 +0-40 +0-32 4-0-27 +0 31 +0-32 +0-26 +0 35 +0-55 +0-39 +0-48 +0-41 +0-10 -0-21 -0-48 -0-75 -0-70 -0-47 -0-35 -Oil -016 -0-12 -0-18 -0-19 +005 +0-40 +0-30 +0-38 +0-46 +0-56 +0-46 +0-28 +0-30 + 0-25 +0-71 '+0-57 :+0-46 +0-55 +0-50 +0-41 +0-42 +0-18 '+013 +0-16 -019 -0-45 -0 52 -0-65 -0-46 -0-46 -0 67 -0-50 -0-39 -0-27 -0-24 -0-16 +0-11 +0-28 +0-36 +0-45 +0-51 1+0-42 +0-45 +0-46 +0-45 I+0-42 +0-41 ^+0-28 +0-23 +0-18 +0-01 -014 -0-22 -0-33 -0 58 -0-49 -0-60 -0-61 -0-40 -0-29 -0-15 -0-05 +006 +0-21 +0-27 +0-41 +0-40 +0-43 +0-42 +0-42 +0-35 +0-33 +0-60 +0-58 40-49 +0-57 +0-52 +0-52 +0-45 +0-26 +0-13 +011 -0-28 -0-48 -0-61 -0-68 -0-56 -0-57 -0-68 -0 63 -0-48 -0-29 1-0-20 -0-39 +0-03 +0-25 +0-41 +0-46 +0-44 +0-33 +0-41 +0-46 + 0-41 +0-47 +0-52 +0-41 +0-29 +017 000 -0-08 -0-16 -0 02 0-00 -0-42 -0-64 -0-42 -0-41 -0-26 -0-08 -0-20 +0-10 +0-25 +0-29 +0-45 +0-38 +0-36 +0-47 4-0-47 +0-36 +0-40 +0-47 +0-64 +0-53 +0-36 +0-41 +0-33 +0-38 +0-60 +0-34 +0-25 +0-28 -0-04 -0-26 -0-27 -0-56 -062 -0-73 -0-82 -0-61 -0-55 -0-44 -037 -0-39 -0-12 +0-18 +0-33 +0-52 +0-56 + 0-48 +0-48 +0-47 +0-40 +0-34 +039 +0-35 +0-39 +0-43 +0-21 +0-01 -012 -0-36 -037 -0-49 -0-72 -0-61 -0 63 -0-57 -0-57 -0 51 -0-27 +004 +0-20 +0-39 +0-39 +0-50 +0-65 +0-38 +0-18 +025 +0-30 +014 +0-15 +005 +0-09 +0-16 +0-26 +050 +0-41 +0-28 +008 +0-17 +0-35 +0-40 +009 +0-02 -0-05 -0-46 -0-43 -0-36 -0-44 -0-44 -0-45 -0-20 -0-19 -0-25 -0-07 +001 000 -001 +005 +0-06 -003 +0-04 -005 +0-21 +0-34 +0-32 +0-27 +0-14 -0-01 -004 +0-18 -0-23 -0-17 -003 +0-02 -0-10 -0-09 -0-07 -0-04 -0 04 +002 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-0-14 -0-20 -010 -0-22 -0-43 -0-46 -0-45 +0-14 +0-14 +014 +0-09 -0-11 +0-05 +0-15 -0-04 -0 04 +006 +0 02 +0-37 +014 +0-15 +007 -0-21 -0-28 -0-30 -0-27 -0 03 -008 -0 13 -014 -019 -0-26 -0-31 -0-22 -013 -0-09 -0-04 +0-02 +011 000 -oil +0-02 000 -0-10 +006 +0-08 +015 +0-50 +0-26 +0-13 +0-07 -003 -0-03 +0-08 +0-07 +0-16 +0-09 +0-07 -001 -0-26 -0-41 -0-35 +0-65 +0-73 +0-43 +0-36 +0-40 +0-15 +0-19 +0-25 +0-19 +0-27 +0-43 +010 -017 -0-34 -0-62 -0-39 -0 51 -0-70 -0-57 -0-64 -0-39 -0-28 -0-24 -0-01 -Oil +009 +0-42 +0-45 +0-47 +0-44 +0-38 +0-31 +0-23 +0-26 +0-19 +0-20 +0-09 +0-14 +0-25 +012 -0-26 -055 -071 -1-04 -0-66 -0-53 -0-42 -0-23 -0-09 -0-02 +0-18 +0-20 +0-39 +052 +0-59 +0-59 +0-39 +0-30 +040 feet. +0-63 +0-72 +0-42 +0-39 +0-46 +0 32 +0-30 +0-34 +021 +0-32 +0-35 +001 -016 -0-39 -0 64 -0-40 -0-44 -0-63 -0-50 -0-56 -0-38 -0-23 -0-19 +0-02 +0-17 +0-31 +0-44 +0-46 +0-46 +0-44 +0-38 +0-32 +0-26 +0-28 +019 +0-19 +0-18 +017 +016 +0-02 -0-35 -0-58 -0-66 -0-88 -0-58 -0-46 -0 34 -0-19 -0 07 +003 +0-24 +0-26 +0-41 +0-50 +0-54 +0-66 +0-45 +0-28 +0-35 feet. +0-40 +0-56 +0-55 +0-35 +0-38 +0-48 +0-33 +0-30 +031 +0-18 +0-28 +0-29 -Oil -0-16 -0-20 -0-64 -0-38 -0 34 -0-58 -0-49 -0-58 -0-44 -0-26 +0-14 +008 +0-10 +0-23 +0-36 +0-36 +0-38 +0-35 +0-30 +0-30 +0-28 +0-31 +0-26 +0-27 +0-25 +0-11 +0-10 -0-12 -0-40 -0-50 -0-62 -0-82 -0-55 -0-45 -0-36 -0-19 -0 09 -001 +0-21 +0-21 +0-32 +0-38 +0-39 +0-54 +0-34 +0-21 +0-26 feet. feet. feet. feet. feet. +0-54 +0-59 +0-36 +0-41 +0-42 +0-37 +0-32 +0-38 +0-18 +0-18 -004 -017 -009 -0-37 -0-64 -0-38 -0-34 -0-66 -0-49 -0-61 -0-47 -0-14 -0-23 -003 +011 +0-26 +0-25 +0 31 +0-25 +0-21 +0-31 +0-32 +0-30 +0-35 +0-28 +0-31 +0-27 +0-12 +0 23 +0-26 -0 36 -0-42 -0-69 -0-64 -0-40 -0-41 -0-36 -0-17 -013 -003 +010 +0-10 +0-21 +0-31 +0-40 +0-54 +0-33 +0-17 +0-25 +0-59 +0-58 +0-32 +0-25 +0-04 +0-31 +0-32 +0-35 +0-22 +0-29 +016 -017 -0-18 -0-42 -064 -0-32 -0-27 -0-56 -0-42 -0-56 -0-44 -0-31 -0-21 0-00 +0-11 +0-24 +0-32 +0-29 +0-27 +0-31 +0-27 +0-27 +0-26 +0-25 +0-27 +0-27 +0-19 +0-11 +006 -0-21 -0 39 -0-43 -0-50 -0-64 -0-39 -0-41 -0-38 -0-17 -014 -0 06 +013 +0-20 +0-21 +019 +0-32 +0-49 +0-32 +0-11 +0-20 -0-18 -0-15 -0-31 -0-26 -017 -0-23 -Oil -Oil -013 +0-01 +011 +0-04 0-00 +0-05 +0-06 +0-08 +0-05 +0-09 +0-10 +0-19 +0-15 +0-16 +0-06 +0-01 -0 09 -0 06 -009 -010 -0-18 -0-20 -0-24 -015 -015 -0-28 -0-15 -006 -004 +0-06 +0-09 +0-01 -003 +0-11 +0-08 +006 +0-04 +0-08 +011 +024 +0-20 +0-10 +001 -005 0-00 -016 -0-08 -0-15 -0-25 -0-28 -0-28 +0-03 +003 -0-19 -0-10 -006 -0-17 -0-11 -010 -0 08 +0-07 +0-25 0-00 -0-05 -0-17 -0-19 +0-03 +0-23 +006 +0-19 -010 +009 +010 -007 -0-02 -007 -0-14 -0-15 -Oil -0-18 -0-13 -0-15 -0-15 -014 -0-17 -0-18 -005 +001 +0-05 +0-09 -0 04 -0 09 -0-04 -0-01 -009 +0-13 +0-12 +0-08 +0-10 +0-04 +0-04 -0-04 -0-09 -0-05 -0-13 +0-02 +0-02 -0-16 -0-18 -0-15 -0-12 -0-12 ■ 0-08 -008 -0 04 -001 -0-10 -007 +0-03 +0-11 000 -0 04 +001 000 +007 +0-38 +0-12 +0-16 +009 +0-07 +011 -0-04 -0-08 -0 02 -005 -0-07 -0-05 -Oil -Oil -0-07 -0 07 -Oil -010 -0-10 -001 000 000 000 -0 03 -0 02 +008 +0-08 +0-06 +0-02 +0-07 +0-07 +009 +0-( +0-04 -002 -0 05 -0-04 -0-06 -0-02 -0-07 -0-10 -005 -007 ON THE COASTS OF IRELAND. 17 Times of Evanescence of Diurnal Tide in Height • Kilbaha /High water. j^ Low water. d. July 1-73 4-59 d. July 14-97 17-01 d. July 30-72 31-84 d. Aug. 12-03 13-15 Kilrush 1 High water. Low water. (1-8) 15-17 4 30 17-03 31-46 32-29 12-27 13-68 Foynes Island < High water. Low water. 1-98 14-74 4-27 16-98 30-74 32-64 12-31 13-19 Limerick < High water. Low water. (1-9) 4-00 n4-7) 16-86 31-30 32-54 11-86 1305 Casleh Bay < High water. Low water. 2-34 4-10 13-98 17-21 30-82 32-41 11-55 13-10 Galway < High water. Low water. 3-83 4-24 13-71 17*50 30-77 32-56 11-99 13-04 Old Head | High water. Low water. (4-8) 5-22 15-62 18-11 31-36 33-46 12-38 14-80 Mullaghmore < High water. Low water. 4-61 (7-0) 17-63 (200) 32-53 (35-0) 14-17 (16-0) Buncrana < High water. Low water. 5-38 (7-4) 17-56 (20-0) 33-32 (35-0) 13-74 15-63 Port Rush I High water. Low water. 5-09 (7-4) 17-26 (20-0) 33-43 (35-0) 13-47 14-92 Carrowkeel < High water. Low water. 4-96 (7-4) 16-66 (20-0) 3326 (35-0) 12-69 (14-9) Ballycastle < High water. Low water. 3-80 (6-4) 17-68 (19-0) 32-37 (34-0) 14-51 (13 9) Glenarm < High water. Low water. 2-80 5-92 18-11 18-78 31-72 34-24 15-62 13-84 Donaghadee < High water. Low water. 2-82 5-34 17-91 17-92 31-85 3318 15-35 13-56 Ardglass < High water. Low water. 3-76 5-57 18-00 16-11 32-82 33-47 15-10 13-71 Clogher Head < High water. Low water. 3-51 4-82 17-46 18-23 32-48 34-34 15-05 14-60 Kingstown < High water Low water. 3-70 5-10 17-62 18-41 32-22 33-25 15-44 14-16 Dunmore East . . . . < High water Low water. 6-01 3-56 17-44 18-31 3340 32-13 12-39 15-88 New Ross < High water Low water. (6-0) (3-5) (17-4) (18-3) 33-57 (32 1) 12-95 (15-8) Passage West < High water Low water. (5-0) (2-5) (16-4) 16-91 33-76 (31-1) 12-27 14-75 Castle Townsend... . < High water Low water. (3-4) (3-5) (15-7) (17-0) (32-24) (31-5) (12-15) (13-95) MDCCCXLV. D 18 MR. AIRY ON THE LAWS OF THE TIDES The numbers inclosed in brackets are supplied by conjecture, where the irregula- rity of the tides made it difficult to discover with accuracy the times of evanescence. A small error in these will produce very little error in the result for maximum coeffi- cient. The numbers at Castle Townsend (where the diurnal tide is very small) are the means between those for the adjacent stations, Passage West and Kilbaha. Cour- town is omitted, as the peculiarity of the tides there made it impossible to take diurnal tides at high water and low water in the same manner as for the other stations. The times when the moon's declination vanished are June 28'^-89, July 12*'-14, July 26*^'18, and August 8*^50. In stating these, however, I must warn the reader that these are not the only elements on which the time of evanescence of diurnal tide depends, as will appear in the next section. Attempts were made to determine, in the same manner, the times of evanescence of diurnal tide in time. The irregularities were however so great that in most cases it was useless to attempt to assign the day : in the following instances only did the results appear at all trustworthy. Times of Evanescence of Diurnal Tide in Time. MuUaghmore Low water. d d d d July 7-19 Julj 20-76 July 31-96 Aug. 14-27 Buncrana Low water. 3-30 20-41 30-77 16-02 Port Rush Low water. 4-69 21-32 31-32 16-58 Carrowkeel Low water, j 1-37 19-01 30-50 16-39 Ballycastle Low water. 5-11 18-16 36-43 15-05 Donaghadee < High water. Low watt-r. 4-11 6-13 19-07 32-59 14-18 33-94 16-18 13-15 It will be remembered that the time of evanescence of diurnal tide in time at low water ought to coincide with that for height at high water, and vice versd. The comparison of this table with that for height is not very satisfactory. The maximum values of diurnal tide were deduced in all cases by the process ex- plained a short time since, adopting for the times of evanescence the days given in the first table (or that from heights), and using the high water evanescence in height with the low water diurnal tide in time, and vice versd. The following are the re- sults : — ON THE COASTS OF IRELAND. 19 Maximum Values of Diurnal Tide, First Division: deduced from heights. Kilbaha .... Kilrush .... Foynes Island Limerick. . . . Casleh Bay . . Galway .... Old Head . . Mullaghmore Buncrana . . Port Rush . . Carrowkeel. . Ballycastle . , Glenarm .... Donaghadee Ardglass .... Clogher Head Kingstown , Dunmore East New Ross . . Passage West Castle Townsend High water. July 1—14. ft + 0-28 + 0-20 + 0-30 -I-0-30 + 0-27 + 0-24 + 0-46 -I-0-83 + 0-64 + 0-50 + 0-44 + 050 + 0-74 + 0-64 + 0-55 + 0-64 + 0-53 -fO-17 + 0-22 + 0 08 -0-02 July 14—31. ft. -0-49 -0-38 -0-45 -0-49 -0-41 -0-42 -0-61 -0-80 -073 -0-57 -0-93 -0-66 -066 -0-74 -0-74 -0-69 -0-57 -0-24 -0-33 -0-20 -009 July 31— Aug. 12 ft. + 0-30 + 0-25 + 0-33 + 0-36 + 0-30 + 0-25 + 0-64 + 0-85 + 0-66 + 0-60 + 0-60 + 0-58 + 0-82 + 0-74 + 0-69 + 0-60 + 0-64 + 0-25 + 0-25 + 0-17 + 0-05 Low water. July 4—17. ft. -0-47 -0-52 -0-74 -0-96 -0-64 -0-77 -0-69 -0-30 + 0-05 + 0-14 + 0-17 + 0-05 -0-60 — 0-64 -0-60 —0-55 — 0-55 + 0-13 + 0-05 + 0-13 -0-16 July 17—32. ft. + 0-52 + 0-42 + 0-32 + 0-49 + 0-52 + 0-57 + 0-58 + 0-14 -0-16 -0-28 -0-19 -0-16 + 0-42 + 0-41 + 0-38 + 0-36 + 0-36 -0-22 -0-22 -0-11 -0-01 Aug. 1—13. ft. -0-50 — 0-47 — 0-58 — 0-53 — 0-55 -0-35 -0-74 -0-08 + 0-25 + 0-35 + 0-33 + 0-16 -0-35 -0-71 -0-58 -0-37 -0-52 + 0-11 + 0-05 + 0-06 -0-08 These results are on the whole satisfactory. There are, however, some general differences of magnitude among the different columns, which I am not able at pre- sent entirely to explain. I may remark that the moon was in perigee on July 9 and August 7, and in apogee on July 25. Maximum Coefficient of Diurnal Tide in Time, First Division. Kilbaha Kilrush Foynes Island. . . . Limerick Casleh Bay Galway Old Head Mullaghmore . . . . Buncrana Port Rush Carrowkeel Ballycastle Glenarm Donaghadee . . . . Ardglass Clogher Head . . Kingstown Dunmore East . . New Ross Passage West .... Castle Townsend.. Low water. July 1—14. + 5-31 + 1-34 + 4-10 + 12-23 + 2-51 + 5-03 + 2-87 + 3 93 + 10-90 + 21-43 + 17-93 + 28-28 - 1-76 004 1-72 3-80 4-32 0-54 1-76 2-71 6-57 + + + + + July 14— 31. July 31— Aug. 12. — 2-69 — 1-87 — 4-00 — 8-86 — 2-40 — 6-97 — 2-96 — 7-77 — 1-51 — 4-83 — 3-35 — 31-00 — 7-82 — 6-58 — 4-41 — 5-10 — 5-46 — 2-77 — 0-48 + 2-68 + 2-12 4-25 1-73 5-11 8-15 3-18 3-08 0-66 + 10-56 + 7-90 + 16-77 + 14-92 + 17-26 + + + + + + + D 2 409 0-57 2-70 1-86 5-65 3-31 3-45 0-96 1-26 High water. July 4—17. July 17—32. 6-22 5-92 5-63 3-91 8-73 8-73 4-32 10-48 0-42 1-88 5-60 3-42 0-66 5-27 0-07 001 4-35 3-86 2-54 0-23 2-49 Aug. 1—13. 3-70 3-70 1 70 0-69 6-06 3-64 4-13 2-06 0-34 7-28 2-71 + 18-05 2-68 1-72 4-47 2-47 0-52 0-24 2-05 0-70 1-37 -0-98 — 3-li8 -3-84 -5-63 —4-29 -4-98 + 0-26 -5-09 -1-73 -3-14 -0-68 -1-96 — 2-20 -4-.')2 —0-35 -3-10 -3-92 -240 -4-99 -0-51 -3-67 20 MR. AIRY ON THE LAWS OF THE TIDES After the statement which I have given (in the second section) of the difficulty of fixing upon times of high and low water, it will not be surprising that considerable irregularities exist among these numbers. Their agreement nevertheless is sufficient to show that the diurnal tide in time of low water is great at Limerick, and very great at all the stations from Buncrana to Ballycastle. At Mullaghmore and Bally- castle it is also great at high water. The increase in numbers at low water from Kilrush to Foynes Island and Limerick, would seem to show that diurnal tide in time at low water increases considerably in ascending a river. It would appear, however (as seems, a priori, probable), that this holds only when there is at the same time a considerable diurnal tide in height, of such a nature that a depression of height accompanies a retardation of time. This is supported entirely by the analogy of the course of low water at ordinary semidiurnal tide : where, as will appear in this paper, and as is known from other observations, and as also appears from theory*, the pro- gress of the phase of low water up a river is slower as the water is shallower at low water. At New Ross, considered with relation to Dunmore East, the diurnal tide in time of low water is not sensibly increased ; and here there is no large diurnal tide in height. The large numbers in the neighbourhood of Ballycastle do not depend on this cause. Maximum Coefficient of Diurnal Tide in Height, First Division, as inferred from Diurnal Tide in Time. Kilbaha Kilrush Foynes Island. . . , Limerick Casleh Bay Galway , Old Head Mullaghmore . . . . Buncrana Port Rush Carrowkeel Ballycastle Glenarm , Donaghadee ... Ardglass Clogher Head . , Kingstown Dunmore East . New Ross Passage West ... Castle Townsend. High water (from times of low water). July 1—14. July 14— 31. July 31— Aug.l2 ft. + 0-46 + 0-11 + 0-41 4-1-88 + 0-24 -fO-60 + 0-28 + 0-16 + 0-97 + 0-77 + 0-97 + 0-75 -0-07 4-0-06 4-0-27 + 0-45 + 0-44 + 0-04 -0-19 + 0-26 — 0-45 ft. — 0-18 — 0-14 — 0-40 -M6 -0-16 — 0-51 -0-19 — 0-42 — 0-15 — 0-13 —0-20 -0-42 — 0-31 — 0-46 — 0-40 — 0-45 — 0-40 — 0-20 -006 -fO-17 4-0-12 ft. -fO-37 4-0-12 -I-0-61 4-1-35 4-0-30 + 0-45 + 0-07 + 1-02 4 0-75 + 0-73 + 0-85 + 0-50 + 0-25 + 0-10 + 0-33 + 0-32 + 0-57 + 0-34 + 0-37 + 0-09 — 0-15 Low water (from times of high water). July 4—17. July 17—32. Aug. 1—13 ft. —059 -0-62 -0-68 —061 -0-92 —0-87 -0-40 -0-78 -0-15 — 0-14 -0-25 -0-11 + 0-05 -0-39 — 0-04 -0-03 -039 + 0-31 + 0-26 + 0-02 -0-17 ft. + 0-28 + 0-30 + 0-19 + 0-06 + 0-46 + 028 + 0-24 + 0-17 + 0-04 + 0-14 + 0-11 + 0-28 + 0-13 + 0-11 + 0-37 -0-19 + 0-46 — 0-02 -0-20 + 0-08 + 0-09 ft. — 0-13 -0-37 — 0-50 — 0-81 -0-45 -068 + 0-02 -0-33 -0-25 — 0-13 -0-08 -0-08 -0-13 -0-45 -0-11 — 0-41 — 0-38 — 0-20 — 0-43 -0-04 -0-24 These numbers ought, upon the theoretical expressions for the tides given in an earlier part ^f this section, to agree with the numbers in the first table in page 19. * Encycl. Metropol., Tides and Waves, Art. 208. ON THE COASTS OF IRELAND. 21 Upon comparing them it appears that there is a very good agreement of the numbers of the littoral stations, at both high and low waters, as far as Mullaghmore or even Buncrana; and, for high water only, as far as Ballycastle. There is then great dis- cordance till we arrive nearly at Kingstown; in a short time after this the diurnal tide becomes so small that we are less surprised at apparent discordances. From the number of the instances in which the agreement is, upon the whole, pretty good, I form my opinion that the discordance between Buncrana and Kingstown is not accidental. I have little doubt that in this channel between Ireland and Scotland (which every accurate determination shows to be a critical part for the tides), the law of diurnal tide assumes a form differing much from that supposed in the investi- gation. It is, however, practically almost impossible to trace this law from obser- vations. The results for diurnal tide used in the subsequent investigations are those in the table of pages 15 and 16 deduced from observed heights only. Section IV. — Theory of Diurnal Tide as referred to the actions of the Sun and Moon. The present section will contain little more than the account of a series of failures of investigations. But the examination of these is usually so instructive that I think it desirable to state the heads of each of the unsuccessful attempts. In order to explain the theoretical difficulties of this investigation, the following remarks may not perhaps be misplaced. It is not possible to separate the effects of the sun and moon by comparison of a mass of observed diurnal tides near one solstice with a similar mass at the opposite solstice. For, although (in consequence of the opposite state of the moon's declina- tion at a given phase of the lunation) the lunar diurnal tide is different in sign, yet the solar diurnal tide is also different in sign ; and thus the two diurnal tides are mingled in the same degree at both solstices. The same applies if the observations are at any opposite seasons of the year. It is possible to separate the two effects by comparing diurnal tides near a solstice with diurnal tides near an equinox ; as, in the latter, the solar diurnal tide vanishes. Generally, it is possible to separate them by comparing two masses of diurnal tides observed at intervals of three months ; as for the high (or low) waters corresponding to a given right ascension and declination of the moon in the two masses, the sun will have widely different positions in hour-angle, and therefore its effects at those two instants will be widely different. The proportion of the effects of the sun and the moon cannot be ascertained from a single series of observations, extending through a period so short that the sun's position may be considered invariable. This will be shown by showing that the two effects, of the sun and of the moon, in producing diurnal tide at high water, follow sensibly the same law, and when added together give a compound effect following the same law. Thus : tlie time of high water bears a nearly invariable relation to the 22 MR. AIRY ON THE LAWS OF THE TIDES time of moon's transit ; and therefore, at high water, the lunar diurnal tide is always in nearly the same phase, and has no variation except from the variation of its coeffi- cient. The magnitude of the diurnal tide at semidiurnal high water may therefore be represented by coefficient x sin |3 ; and that at semidiurnal low water by coefficient Xcos^; where (3 is constant. This coefficient is proportional to the sine of the moon's declination at some time previous, or (nearly) proportional to the sine of the moon's right ascension for some time previous, or to the sine of the moon's hour- angle from the sun altered by a constant. For the solar diurnal tide, the coefficient is constant, but the phase varies every day. As the time of high water bears a nearly invariable relation to the time of moon's transit, the phase of solar diurnal tide at high water must depend upon the moon's hour-angle from the sun altered by a con- stant, and therefore the magnitude of solar diurnal tide will be proportional to the sine of the moon's hour-angle from the sun altered by a constant. Thus, putting ^ — O for the excess of the moon's right ascension above the sun's, the lunar diurnal tide at the time of high water will be represented by a.sin|3.sin{ c — O+A}, and the solar diurnal tide at the same time will be represented by i.sin{ a — 0-|-B}; and these, when added together, give a result of the same form, c.sin{ ^ — O -f-C}. And it is impossible to say whether this term, as given by observation, is entirely due to one or other of the two actions or to both combined ; because we have no a priori means of saying what is the coefficient a or b of either of the separate terms ; or what is the relation of the time of either high diurnal tide to the time of transit of the body which causes it, upon which A and B will depend. Everything here said with regard to semidiurnal high water applies also to semidiurnal low water; the only difference being that the angles /3 and B must be increased about 90° for semidiurnal low water. The unknown quantities in the problem of diurnal tide are the following : — The interval anterior to the time of observation for which the moon's place is to be taken as governing the diurnal tide at the time of observation ; the constant coefficient by which the sine of moon's declination for that anterior time is to be multiplied ; the moon's hour-angle at the time of lunar diurnal high water ; and the three similar quantities for the sun: in all, six unknown quantities. To determine these we have only the four following results of observation (or results equivalent to these four) : the time of evanescence of diurnal tide at semidiurnal high water; the maximum of diurnal tide in high water, and the two similar quantities for low water. These are insufficient for the determination of the six unknown quantities ; and we must try how we can reduce the latter number. First, as the sun's declination is considered constant, the anterior interval for the sun's place is unimportant. And in fact, though the sun's declination during these observations (June 22 to August 25) was not invariable, yet an alteration of one day in the time for which its declination was taken as ruling the diurnal tide would not have been important. For the moon it would be very important. Secondly, it seems probable that the moon's hour-angle at the time of lunar diurnal ON THE COASTS OF IRELAND. 23 high water does not differ much from the sun's hour-angle at the time of solar diurnal high water. The assumption of any constant difference, either =0 or having any assigned magnitude, reduces two of the unknown quantities to one. The number of unknown quantities is thus made the same as the number of data, and the solution can therefore (speaking in a strictly algebraical sense) be effected, in general. The following is the method by which the equations for the four unknown quanti- ties may most conveniently be formed : — From the ordinary facts of the tides, it seems probable that the coefficient of lunar diurnal tide may depend on the moon's declination at a few days, perhaps not exceeding five, anterior to the time of the tide. Let d^ be the moon's declination at one day preceding the time of tide, c^^ the moon's declination at three days preceding the time of tide. Then we may express the coefficient of lunar diurnal tide by />.sinrfi4-y.sin6/3; where by varying the proportions of/? and q the coefficient may be made to depend on the moon's declination at any day near them ; and by varying the magnitudes oi p and q in the same proportion, the magnitude of the coefficient will be altered in that proportion. The coefficient of solar diurnal tide may be represented with sufficient accuracy by r.sinDi, where Dj is the sun's declination one day preceding the time of tide. Let h be the solar hour of the tide. This is the same as the hour-angle of the sun to the west of the meridian. The phase of the solar diurnal tide will depend upon this angle diminished by some unknown constant s ; and the elevation of the solar diurnal tide may be represented by S.sinD^.cos A— 6-. Let t be the moon's time of transit. Then the moon's hour-angle west of the meridian is h—t. Therefore if the phase of lunar diurnal tide depended on the moon's hour-angle in the same manner in which the phase of solar diurnal tide de- pended on the sun's hour-angle, the elevation of the lunar diurnal tide would be represented by {p.%\ndy-\-q.&md^co&h—t—s. But we know by the retardation of the period of spring tides, as well as by the theory of tidal waves affected by friction*, that in semidiurnal tides the lunar wave is more advanced in its phase with regard to the moon's hour-angle than the solar wave is with regard to the sun's hour-angle. We may conjecture, by analogy, that the same holds for diurnal tide. Putting a for this difference of advance of phase, the elevation of the lunar diurnal tide will be represented by (/>.sin d^-^-q.^in d.^)cosh—t — s-\-K. And the compound effect of lunar and solar diurnal tides, expanding the cosines, will be S.sin Di.(cos h.cos .s-f-sin ^.sin s) -\-(p.sm di-\-q.s\n d^)(cos h—t-{-u.cos s-{-sm h—t-\-u.sm s). Let S.cos s=w, S.sin A=^, ^=i/,-^=z ; and the expression becomes * Encyclopaedia Metropolitana, Tides and Waves^ Art. 326. 24 MR. AIRY ON THE LAWS OF THE TIDES 8\nJyi.cosh.w-^smJ}i.smh.x+sindi.cosh---t-\-oi.wj/-{-s\ndi.s'mh — t-^o6.a:if •^smd^.cosh^t-\-oc.wz-\-s\n d2.smh—t-\-K.xz. It is to be remarked that, when w, x, y, and z, are ascertained (with an assumed value of a), the following more intelligible results will be extracted from them : — S=-y/wJ2ljr^= solar coefficient of the sine of the sun's declination, for solar diurnal tide. *=the angle determined by the equation tan5= — ; it is the constant angle which is to be subtracted from the sun's hour-angle west at the time of observation, in order to give the angle on whose cosine depends the height of solar diurnal tide at the instant of observation. Then, the lunar diurnal tide = (/? . sin ^1+5 . sin d.^ cos A — ^— *4-a=S.(y.sin c^j-fa.sin fl?3).cos A— /—a- -fa ; and, {putting / for the moon's longitude measured from the intersection of its orbit with the equator, I for the sine of its inclination, and ^ for the mean daily increase of longitude from transit to transit =13° 38'}, y.^\VLd^-\-%.^\x\dy=^\{y.^\\\.l^-\-z.'&\xil^) — 2^- sin /3+sin l^-\—~'^\xv /j— sin /^y = I(^+v.cos ^.sin 4+^— y.sin S.cos 4) ; or, if tan;7=— — tanS, this quantity becomes =I.2-f-3/.cos^.sec;7.sin /2H-'? ; or, making )j=w.^, it becomes =I.;z+3/.cosS.sec;7.sin /2+«=^+3/-cos^.sec?;.sinfl?2+«: and therefore the lunar diurnal tide =S.%+?/.co8^.sec;j.sin«/2+n-(^os A — / — *+«• M Effect of moon for eiven declination S — Effect of sun for same declination ~ ^ +^- ^^^ ° " ^^^ ^' M=S.2+i/.cos^.sec>7= lunar coefficient of the sine of the moon's declination on a certain anterior day, for lunar diurnal tide. 2+w= the time, in lunar days, earlier than the moon s Greenwich transit next preceding, for which the moon's declination is to be taken as governing the diurnal tide. This is correct for the time of high water, first division, and requires an altera- tion for other times, n is =,-^^^^-7; and tan;j=— -^-tan 13° 38'. 13 38' ' ' z-'ry s—a,— the constant angle which is to be subtracted from the moon's hour-angle, in the same manner as s from the sun's hour-angle. The factors of the unknown terms w, x, wy, wz, xy, and xz, in the algebraical ex- pression for the elevation produced by diurnal tide, were computed for high water and low water, first division, at Kilbaha, for every day throughout the observations. These computations would apply equally to the other stations, it being understood that certain constants (which the reader will easily investigate) depending on the longitude of the station and the time occupied by the passage of semidiurnal tide, are to be applied to the angles a and s. The hour-angles used for the moon were found by comparing the moon's time of transit at Greenwich with the time of Kil- ON THE COASTS OF IRELAND. 25 baha tide. The declinations were those for the times of transit at Greenwich one day and three days previous to the transit next preceding the tide in question. For the low waters of the first division, which follow the high waters of the first division by ^th of a tidal day, the right ascensions and declinations ought to be taken for tran- sit over the 6^ meridian ; this was done most conveniently by correcting the coeffi- cients when combined in groups, by the following formulae. If the computed terms containing w and x for the moon are W.ir+X.o? {W and X containing 1/ and z}, then the corrected terms as altered for the change of right ascension, are Wcos ^+Xsin^)/^4-(Xcosj— Wsin^jj'. And if the computed terms containing 3/ and z are Y.?/-f-Z.z (Y and Z containing w and x), then the corrected terms as altered for the change of declination, are ^ ^iK28 ^shr28/^+ \^ sm2S ^^lm2d/^- No notice was taken of the changes of parallax; nor were the hour-angles referred to the moon's place one or three days previous (as in strictness of theory they ought) ; but as the observations extend over two whole lunations, it was supposed that the effects of these omissions would nearly disappear. The factors of the unknown quantities were computed on the supposition that a=0, and also on two other suppositions. It is easily seen, however, that the factors for any assumed value of a can be readily formed from those which hold for a=0; and this computation is made most conveniently for the groups. The numbers for high water were divided into groups related to the changes of sign of the factors of w and x. These groups were then combined in the order lst + 2nd — 3rd — 4th + 5th + 6th— &c. to form one equation, and in the order 1st— 2nd— 3rd-|-4th+5th— &c. to form another equation. The numbers for low water were treated in the same way. In subsequent operations, the groups were formed and combined in difi^erent orders. But, in whatever way the groups were formed, they were so combined as to form four equations, each of which has the following form : A.w-\-B.x-{-C.wi/+D,wz-\-E.xi/-\-F.xz=G. To solve a system of four such equations is evidently no easy matter. Two me- thods of solution were principally relied on. The first (and easiest) was, to make trial-substitutions to a great extent. The numbers —2, —1, 0, +1. +2, were substituted for w, the same numbers were substituted for x ; the same numbers were also substituted for^ and for z ; and every possible combination of these numbers was used ; making 625 trial-substitutions in each of the four equations. And when there seemed a probability of success, the substitutions for one or two of the numbers were greatly extended. Calling the re- MDCCCXLV. B 26 MR. AIRY ON THE LAWS OF THE TIDES suits of one substitution in the four equations g, g', g", g'" (the numbers resulting from the tidal observations being G, G', G", G'"), it was then necessary that ^—^ ^_5! ^—91 g-G' g-G' g-G' By search among the quotients of the substitution, numbers were found approaching G' as near as possible to -q, &c. ; then, supposing w unaltered, the variations of the quo- tients were found, which corresponded to changes of 1 in .r, ^ and z ; from these, by solving three linear equations, the corrections to x, y and z were found ; and then a common multiplier for w and x was found by comparing the result of each corrected substitution with the tidal numbers G, G', &c. The other method was, to put the equations in the following form : M;X(A-l-C.y+D.^)+a^X(B+E.3/+F.2) = G. Between two of the equations, w and x were eliminated, and a complicated equation between y and z remained ; another equation of the same character was obtained from the other two of the original equations ; and these two equations were solved by trials. By these methods (but principally by the former) the equations were solved for a=0 and a= — 2'' for all the stations as far as Mullaghmore. Beyond that station it was found totally impracticable to solve them. Values of w, .r, y, z were some- times found which seemed nearly to satisfy the equations, but when an attempt was made to correct these values, the corrections became absurdly large, and the cor- rected values gave results much further from the truth than the original results. And for those stations at which the operation was successful, there were special re- M suits of inadmissible character. Thus, when a=0, -g was found =4-30 for Kilbaha, M and =1-45 for Mullaghmore; when a=--2*', -y- was found =3*40 for Kilbaha and =0*82 for Mullaghmore. These discordances seemed to show that a must be posi- tive; but in no case could a solution be obtained with a positive value for a. On examining carefully the numbers given by observation, I was led to the follow- ing considerations, which seemed likely to throw considerable light on the subject. On inspecting the table in page 17, it will be evident that at the first stations, as far as Old Head, the disappearance of diurnal tide at high water does not occur on the same day as the disappearance of diurnal tide at low water ; the former always occurring earlier than the latter. Biit at the stations from Glenarm to Dunmore East, the disappearance of diurnal tide at high water sometimes precedes and some- times follows that at low water; and may be said, roughly speaking, to occur on the same day. This circumstance fixes absolutely the value of a. For, when the diur- nal tide at high water and that at low water vanish at the same time, the inference is, that at that time the lunar diurnal tide and the solar diurnal tide have equal values ON THE COASTS OP IRELAND. 27 with opposite signs four times in their diurnal period. If then their phases at the first of those four times be represented by (p and -v// respectively, and their coefficients by f6 and p, we have /Asin j? 19 58 About August 14*56, the mean value is 0*00 „ „ „ 7 \^ From the regularity of the progress of the numbers in the second and third columns, it appears certain that the value 7^ 13"^ for a must be very near the truth. From the reasoning above it will appear that, in the case of simultaneous eva- nescence of diurnal tide at high water and at low water, we have no means whatever of ascertaining the values of joo and (p on that day. Or, if we take the expressions on page 22, we have for diurnal tide at high water, a.sin/3.sin{ =2' and dividing by g' we obtain the value of the mean of large intervals ; performing If the same operation from ^^^ to ^=t, we obtain the value of the mean of small in- tervals. The difference which will be found =~'m'( I+oIm/ /' ^^ the difference be- tween the 2nd and 3rd columns or between the 5th and 6th columns in page 39, ex- pressed in arc ; or, as 2'r of arc in the estimation of & and F correspond to a tidal day of 1488°*, if we put i for the number of minutes in that difference, the equation is 7r*M*V+9 AM/ /— '^1488' From this we obtain S ^x{i-Kn^)'}"^^''^y' M~"1488 S and then the maximum value of F in arc will be found *by making sin2F'=j^j and converting F' into time by the proportion stated above. Thus the following Table is formed. MDCCCXLV. 42 MR. AIRY ON THE LAWS OF THE TIDES Station. High water. Low water. Mean of values of S M* Difference of means of large intervals and small intervals. Value of S M' Maximum semimenstrual inequality ±- Difference of means of large intervals and small intervals. Value of S m" Maximum semimenstrual inequality ±. Kilbaha Kilrush Foynes Island Limerick Casleh Bay. ..... Galway Old Head Mullaghmore .... Buncrana Port Rush Carrowkeel Ballycastle Glenarm Donaghadee .... Ardglass Clogher Head. . . , Kingstown Dunmore East . . New Ross ...... Passage West .... Castle Townsend . m 48 51 45 46 51 48 35 53 66 89 69 143 35 39 41 47 46 45 41 43 47 0-32 0-34 0-30 031 0-34 0-32 0-23 0-35 0-42 0-57 0-45 0-82 0-23 0-25 0-27 0-31 0-31 0-30 0-27 0-28 0-31 TO 38-5 41 36 37 41 38-5 27 42 61 71-5 54-5 113 27 30 32 37 37 36 32 33-5 37 ni 54 52 48 62 57 58 37 46 58 75 57 104 45 47 47 47 48 47 46 43 49 0-35 0-34 0-32 0-40 0-37 0-37 0-24 0-31 0-37 0-49 0-37 0-65 0-30 0-31 0-31 0-31 0-32 0-31 0-31 0-28 0-33 42 41 38-5 48-5 44-5 44-5 28-5 37 44-5 60 44-5 83 36 37 37 37 38-5 37 37 33-5 39-5 0-34 0-34 0-31 0-35 0-36 0-34 0-24 0-33 0-39 0-53 0-41 0-74 0-26 0-28 0-29 0-31 0-31 0-31 0-29 0-28 0-32 I have stated in the Encyclopaedia Metropolitana, Tides and Waves, Art. 538, that S I consider the values of j^ deduced from the semimenstrual inequalities in time to be real and certain representations of the proportions of the sun's effect to the moon's effect in the seas in the neighbourhood of each station ; those deduced from the heights being liable to the effects of many local disturbing causes which do not affect those deduced from the times. In this view the table above deserves consideration. The littoral stations (including those in the Irish Sea) agree in giving a value of 0'32 or 0'33, nearly the same as that found at Brest by Laplace and Sir J. W. Lubbock. But at Port Rush and Ballycastle (the first stations in the North Channel) the lunar tide appears to be diminished in a far greater proportion than the solar tide. And then, after this alteration of relative magnitude has been established in the open sea of the neighbourhood, it appears to be again nearly destroyed by some local cause S affecting the heights, so that in the table of page 35^ the value of ^ is restored to its average value. As far as the observations can be trusted for accuracy, the two con- clusions which I have mentioned appear at first sight perfectly certain ; for the great- S est difference of intervals from moon's transit (on which the value of ^ in this page depends) is deduced from comparisons of the times of tides of equal vertical range, in which therefore the stream of tide in the neighbouring channels of small depth and width, &c. was the same, and therefore could not disturb the difference of times. ON THE COASTS OF IRELAND. 43 But the value in page 35 is deduced from the comparison of high and low tides, in which the stream of tides, &c. is different. The second apparent alteration can take place only where the tide has arrived at such localities that the second order of the vertical oscillation produces sensible terms. I was at first misled by the plausibility of this reasoning. Its fallacy, or rather its error, will appear from the following considerations. The semimenstrual inequality in time which theoretically is proper for giving the value S of j^ is that which depends only upon those differences of time which are caused by difference in the relative positions of the sun and moon, when the magnitudes of the tides are exactly the same. But when there also exists a difference of time caused by the difference of magnitude of the tide (having its maximum nearly at the time of evanescence of the proper semimenstrual inequality), then these two differences or inequalities are combined, forming a single inequality whose time of evanescence is different from those of both the original inequalities, and whose magnitude is greater than the magnitude of either. Thus it appears that the gross semimenstrual ine- S quality in time must not be used for estimation of j^- A correct application of these principles, and a consequent harmony of results, will be seen in Section XIV. S At every station except MuUaghmore, the value of ^ in the table above appears greater at low water than at high water. This evidently depends upon the difference in times (as affected by magnitude of tide) for low water and for high water, which is combined as above stated with the proper semimenstrual inequality. Mr. Whewell, in his invaluable memoirs on cotidal lines, stated that there were great contradictions in the accounts of the establishment of Ballycastle. The num- bers above serve in some degree to explain this. The semimenstrual inequality alone, comparing observations taken when its value was maximum positive with those taken when its value was maximum negative, would produce nearly four hours of uncer- tainty. More than half an hour (see the table in page 19) might be added by the diurnal tide. I shall now proceed with the age of tide as shown by the times. The method em- ployed was the same as for the heights, in forming the table in page 38. The times were ascertained at which the interval from moon's transit over the meridian to high water (and similarly the interval from moon's transit over the 6-hour meridian to low water), corrected for diurnal tide, agreed with the mean interval for high water (or for low water) in page 39. These times were then compared with the times at which the moon's hour-angle from the sun was 0^ 6^ 12*^ 18^ ; namely, June, 22*^9^, 30^ 20^; July, 7^ 19^ 14'' 21^ 2^ 23^ 30^ 16^ August, 6^ 4^ 13*^ 5^^ 20^1 16^ The high and low waters were treated separately. At Ballycastle low water six re- sults only were obtained ; for all the other determinations seven or eight results were compared. Thus the following Table was formed. G 2 44 MR. AIRY ON THE LAWS OF THE TIDES Age of Tide as inferred from Times. Station. High water. Low water. station. High water. Low water. d li d li d h d h Kilbaha 1 8 1 5 Ballycastle -0 11 -0 19 Kilrush 1 13 1 10 Glenarrn + 1 14 1 9 Foynes Island. . . . 1 21 2 2 Donaghadee .... 1 7 1 9 Limerick 1 22 4 1 Ardglass 1 8 1 15 Casleh Bay 1 14 0 22 Clogher Head. . . . 1 10 1 12 Galvvay 1 10 1 7 Kingstown 0 22 0 23 Old Head 2 10 2 9 Dunniore East . . 2 11 2 8 Mullaghmore .... 1 6 1 11 ' New Ross 2 20 3 11 Buncrana 1 4 1 3 1 Passage West .... 2 2 1 19 Port Rush 0 4 0 7 i Castle Townsend . . 1 12 1 6 Carrovvkeel 1 0 1 1 ! In the Tides and Waves, Art. 463 and 465, I have shown that the age of tide in- ferred from the times of higli water in a river (where spring-tide high waters pass more rapidly than neap-tide high waters) is too small, and that the age of tide in- ferred from the times of low water in a river (where spring-tide low waters pass more slowly than neap-tide low waters) is too great. These propositions, at least the second, are well illustrated at Limerick and New Ross. For the other stations I feel myself in some difficulty. With the exception only of Old Head, Dunmore East, and Passage West, all the ages of tide above are too small, for low water as well as for high water. This requires us to assume that all the phases of the tide-wave (low water as well as high water) are transmitted over the sea more rapidly in the spring- tides than in the neap-tides. I conjecture that some theory of friction may possibly explain this. It cannot be explained by supposing the second power of the small movements sensible ; for on that assumption the age of tide given by low water would be increased. It is worthy of remark that at Ballycastle the effects depending on the position of the sun and moon appear to precede their cause. Section IX. — Formation of the time of diurnal high water ; progress of the diurnal tide-wave i^ound the island; comparison of its progress and range with those of the semidiurnal tide. In page 20 I have given a table of the maximum values of diurnal tide, at high water and at low water. The diurnal tide being supposed to follow the law of sines, its maximum coefficient will be found by taking the square root of the sum of the squares of those two values, and the time after semidiurnal high water at which diurnal high water occurs will be found by taking the angle whose tangent value at low water . . , , . . i . ^ „^^r. f ^ value at high water' ^ converting that angle into time at the rate or 360 for a lunar day. The maximum diurnal tide for semidiurnal high water and that for semi- diurnal low water may be conceived to hold for any day near to the day of absolute maximum. Thus the following Table is formed. ON THE COASTS OF IRELAND. 45 Station. July 9. July 23. August 6. Coefficient of diurnal tide. Interval from semidiurnal high water, first divi- sion, to diurnal high water. Coefficient of diurnal tide. Interval from semidiurnal high water, first divi- sion, to diurnal high water. Coefficient of diurnal tide. Interval from semidiurnal high water, first divi- sion, to diurnal high water. Kilbaha Kilrush Foynes Island . . Limerick (;!asleh Bay Galway Old Head MuUaghmore .... Buncrana Port Rush Carrowkeel Ballycastle Glenarm Donaghadee .... Ardglass Clogher Head. . . . Kingstown Dunmore East . . New Ross Passage West .... Castle Townsend.. ft. 0-55 0-56 0-81 1-01 0-69 0-81 0-83 0-89 0-64 0-52 0-47 0-50 0-96 0-91 0-82 0-85 0-76 0-21 0-22 0-15 0-16 h m 20 44 20 4 20 9 19 50 20 12 19 49 20 56 i 23 25 0 19 1 5 1 28 0 24 22 8 21 44 1 21 34 : 22 2 21 38 2 37 0 51 4 2 18 3 ft. 0-71 0-57 0-69 0-69 0-66 0-71 0-85 0-82 0-76 0-63 0-95 0-68 0-79 0-85 0-84 0-79 0-67 0-33 0-40 0-22 0-09 h ra 9 5 9 0 8 14 9 11 ! 8 44 ' 8 37 ! 9 18 i 11 34 1 13 4 14 2 13 1 : 13 11 1 10 3 ! 10 16 j 10 23 10 21 10 3 15 10 14 33 14 13 12 41 ft. 0-58 0-53 0-67 0-64 0-63 0*43 0-98 0-86 0-70 0-69 0-68 0-60 0-99 1-03 0-91 0-83 0-83 0-27 0-25 0-17 0-10 h m 20 36 20 25 20 31 20 50 20 28 20 55 21 18 24 18 1 26 2 4 1 58 1 4 22 19 21 40 21 55 21 42 21 58 1 38 0 47 1 20 20 52 A glance at this table will show how different are the velocities of the diurnal tide-wave and the semidiurnal tide-wave. From Kilbaha to Port Rush, the diurnal tide travels in a direction so different, or with a velocity so small, that it loses 5^ hours in time upon the semidiurnal wave. But it passes through the North Channel with such speed that at Donaghadee it has regained about 4^ hours. Its course how- ever will be better understood by forming the actual time of high diurnal tide, or rather its interval after the moon's transit. I have treated the numbers in the fol- lowing manner: — Increasing the numbers for July 23rd by 12'' 24'", or half a tidal day (because the moon's declination then was in a direction opposite to that on July 9th and August 6th), I have three comparable intervals from semidiurnal higfi water to diurnal high water. I take the mean of these, and apply it to the mean interval from moon's transit to semidiurnal high water in the table of page 39. I also take the mean of the three coefficients. Thus the following Table is formed ; in which it is to be remembered that the coefficients are to be taken positive for July 9th and August 6th, and negative for July 23rd. 46 MR. AIRY ON THE LAWS OF THE TIDES Station. Coefficient of diurnal tide. Interval from moon's transit to diurnal high water. Station. Coefficient of diurnal tide. Interval from moon's transit to diurnal high water. Kilbaha Kilrush Foynes Island. . . . Limerick Casleh Bay Galway Old Head MuUaghmore .... Buncrana Port Rush Carrowkeel ft. 0-61 0-55 0-72 0-78 0-66 0-65 0-89 0-86 0-70 0-61 0-70 h m 0 51 0 45 1 23 2 31 0 38 0 40 1 35 4 39 6 56 8 16 8 55 Ballycastle Glenarm Donaghadee .... Ardglass Clogher Head. . . . Kingstown Dunmore East . . New Ross Passage West .... Castle Townsend.. ft. 0-59 0-91 0-93 0-86 0-82 0-75 0-27 0-29 0-18 0-12 h m 8 25 8 15 8 14 8 18 8 36 8 30 7 33 7 30 7 47 1 25 Comparing the coefficients in this table with the column of mean range of semi- diurnal tide in page 35, we can discover no analogy between them. The range of diurnal tide is not at all reduced in the North Channel, where the semidiurnal tide is so much diminished ; nor (as will also be shown hereafter) is it particularly dimi- nished between Kingstown and Dunmore East, where the semidiurnal tide is nearly or quite obliterated ; but it is much diminished at Castle Townsend, where the semi- diurnal tide is pretty large. On examining the interval from moon's transit, it appears evident that the diurnal tide comes from the south, or very nearly from the south. It appears also that it does not pass in either direction through the North Channel, but that the strait is filled simultaneously, or nearly so, at both ends. It appears also that the wave travels very quickly from south to north in the Irish Channel ; so quickly indeed that it is probable that the tide is simultaneous throughout. But between Castle Townsend and Passage West it loses more than six hours, or a quarter of a diurnal tide. I am totally unable to explain this. The case is very greatly different from that discussed in page 40, where the change of phase was almost exactly half a tide. I must leave the solution of this difficulty to some more advanced theory of waves. I may appropriately close this section with a statement, in the form commonly used by nautical persons, of the most prominent effects of the diurnal tide at the several stations. Assuming that the maximum diurnal tide, with positive sign for the semidiurnal high waters 1st division, occurred about July 9 and August 6, and with opposite sign on July 23, it appears that the maximum takes place when the moon's right ascen- sion is about 9''. This is not very accurate ; first, because the solar diurnal tide is neglected ; secondly, because the days adopted are not purely for maximum at semi- diurnal high water, but partly also refer to low water. Using however 9'', it appears from the table in page 39, that the semidiurnal high water at Kilbaha follows the moon's Greenwich transit by 4^' 47™ ; and, therefore, when the diurnal tide is great- est, the semidiurnal tide at Kilbaha occurs at 1 S^My"* Greenwich sidereal time, or - 13h 71' Kilbaha sidereal time. If this happens at noon, the sun's right ascension ON THE COASTS OF IRELAND. 47 must be 13'' 7% or the day mast be about October 12; if it happens at six in the morning, the sun's right ascension must be 19^' 7'", and the day must be about January 6. In the same way the day may be found for other hours. The coefficient may be taken from the table in page 28, doubling the mean of the quantities in the three high water columns (without regard of sign) for the difference of two tides. Thus the following Table is formed. Station. Kilbaha .... Kilrush .... Foynes Island Limerick. ... Casleh Bay . . Galway .... Old Head . . . Mullaghmore , Buncrana . . . Port Rush . . . Carrowkeel . . . Greatest difference of two high waters on same day. ft. 0-71 0-55 0-72 0-77 0-65 0-61 M4 1-65 1-37 1-11 1-31 Day when | Day when the excess of the excess of noon tide !morning tide over mid- over evening night tide is greatest. tide is greatest. Oct. 12. Oct. 14. Oct. 30. Nov. 7. Oct. 14. Oct. 17. Oct. 17. Oct. 26. Nov. 5. Nov. 14. Nov. 26. Jan. 6. Jan. 8. Jan. 22. Jan. 30. Jan. 8. Jan. 10. Jan. 10. Jan, 18. Jan. 28. Feb. 3. Feb. 18. Station. Ballycastle Glenarm Donaghadee . . . Ardglass Clogher Head. . . Kingstown Dunmore East . New Ross Passage West . , . Castle Townsend Greatest difference of two high waters on same day. ft. M6 1-48 1-41 1-32 1-29 1-16 0-44 0-53 0-30 0-08 Day when | Day when the excess of the excess of noon tide morning tide over mid- night tide is greatest. over evening tide is greatest. Nov. 24. Jan. 7- Jan. 13. Jan. 13. Jan. 16. Jan. 19. Oct. 21. Nov. 2. Oct. 21. Oct. 13. Feb. 16. April 10. April 17. April 17. April 20. April 23. Jan. 5. Jan. 24. Jan. 14. Jan. 7. Section X. — Method of expressing the height of the water, throughout evei^ individual tide, by sines and cosines of arcs, and expr^essions in this form for evert/ tide in the whole series of observations, except those at Courtown. The times of iiigh water (and similarly those of low water) having had their prin- cipal irregularities smoothed down by the operations described in Section II., and being corrected for the diurnal equation in time ascertained by the operations of Section III., present a series of times, which are liable perhaps to something like constant error from the method involuntarily adopted by the computer in fixing on the time of high water, and which are affected by the peculiar form of the tidal func- tion at each station, but which nevertheless follow at intervals equal (with very con- siderable accuracy) to the true tidal day of the place. This being understood, it will be seen that the following process entirely corrects any error of the supposed times of high or low water in its exhibition of the time of maximum of the first tidal argu- ment, and is entirely free from the effects of such error in the exhibition of other quantities. The whole number of observations, equidistant in time, made in the course of one tide, being about 150, if we divide this duration into sixteen equal parts we shall have at least nine observations in each part ; and the mean time of these nine ob- servations cannot in any case be more than 2^ minutes from the middle of that part. It appears evident here that we may use the mean of all the heights in one portion to represent (with smaller error than unavoidably occurs in the observations) the 48 MR. AIRY ON THE LAWS OF THE TIDES mean which would have been obtained if observations had been taken at infinitely small equal intervals. The same remark applies in a stronger degree if the whole duration be divided into twelve parts. Let us use the term phase for an angle proportional to the time which increases by 360° in a complete tide ; and let it be assumed that the height of the water can be expressed by the following formula : Ao+Aj sin phase -fAg sin 2 phase +A3 sin 3 phase 4-A4 sin 4 phase 4-Bi cos phase +B2 cos 2 phase +B3 cos 3 phase +B4 cos 4 phase, and suppose that the complete tide, or 360° of phase, is divided into sixteen equal parts and the mean height in each part taken. The mean height in the first part will be, AQ+-Aircos 0 — cos g j +2:^A2rcos 0— cos -^j +^A3rcos 0 — cos -^ j +^A4rcos 0 — cos -g- j +;^Bi(^sm g - sm Oj + 2^B2(^sm -g - Sin Oj +3^B3(^sm -g - sm 0 j +^B4(^sin y - sm OJ . The mean height in the second part will be, Ao+-Ai(^cosg - COS -g-j +2^A2(^cos-g - cos-g-J +3^A3(^cos^ - ^os-g j +-A4(^cos-g - cos- , 8„ / . 2?r . ttN 8 /. 47r . 29r\ 8 „ / . Gtt . SttN 8 „ / . Stt . 4t\ +;;^i(«"^ T - «^^ sj +2;^^2(sin -g- - sin -^) +3^B3(^sin ^ - sin-g j +4^64 (^sm -g- - sin ^ j, and so on. Now if we group these in the following manner, (lst+5th+9th + 13th) + (2nd+6th + 10th + 14th) — (3rd+7th + llth + 15th) --(4th4-8th+12th-f 16th), 32 the sum will be — A.. If we group them in the following manner, (lst+5th+9th + 13th) — (2nd+6th+10th + 14th) — (3rd+7th + llth+ 15th) + f4th + 8th + 12th + 16th), 32 the sum will be— B.. If we unite the adjacent means and group them thus, (1 st+2nd+9th + 10th)4-(3rd + 4th+llth + 12th) — (5th+6th + 13th+ 14th) — (7th + 8th +r5th + 16th), 32 the sum will be — A9. If we group them in this manner, (lst+2nd+9th+10th) — (3rd+4th+llth + 12th) — (5th+6th + 13th+l4th) + (7th+8th + 15th + 16th), 32 the sum will be — B,. ON THE COASTS OF IRELAND. 49 If we unite the adjacent numbers already formed by union, so as to have the sum of four adjacent means together, and combine them thus, (Ist+2nd+3rd4-4th) + (5th+6th+7th + 8th)-(9th + 10th + llth + l2th) -(13th + 14th + 15th + 16th), the sum is — A, + 7- A,. If we combine them in this manner, (lst+2nd+3rd4-4th)-(5th+6th+7th + 8th)~(9th+10th + llth+12th) -f(I3th+14th + 15th-t-16th), the sum is — Bi — ^Bo. Then if we divide the complete tide into twelve equal parts, and take the mean height in each, we shall have Mean height in the first part = Ao+^Ai(^cos 0-cos ^) +-A2(^cos 0-cos -^) +3^A3(^cos 0- cos ^) 4-|^A4(^cos 0- +^Bif^sm g-sin0j+2^B,(^sm -g--sm0j4-3^B3(^sm -_sm0j4-4^B,(^sin --smOJ, and so on. And combining these in the following manner, (lst+5th4-9th) + (2nd+6th + 10th)-(3rd + 7th + llth) — (4th + 8th + 12th), 24 4 32 the sum will be — Ao, or the sum X ^ = — Ao. And if we combine them in the following manner, (lst+5th+9th)-(2nd4-6th + 10th)- (3rd+7th + llth)4-(4th+8th + 12th), 24 4 32 the sum will be — Bo, or the sum x^= ~ B.. 32 By applying one-third of these to the expressions last found, we shall obtain — Aj 32 and — B,. - The mean of all the means, either in the division by sixteen or in that by twelve, is Ao. The whole of these operations (after taking the means of the original observations) are performed with great facility, and without the possibility of mistake, by means of a printed skeleton form, of which a specimen will be given shortly. The next thing to be considered is, how we shall correct these numbers for the effect of diurnal tide, which is included in the observations, but from which our formula for semidiurnal tide is to be freed. Suppose that the tide begins with high water, and suppose a to be the effect of diurnal tide at that high water, b the effect of diurnal tide at the low water following, or that which occurs in the middle of the tide. Then the complete effect of diurnal tide is represented by phase , , . phase a . cos ^-g ht' . sm — g— ; MDCCCXLV. ■ H 50 - MH. AIRY ON THE LAWS OF THE TIDES and the question now is, how this function can be represented, through the course of one tide, by a formula similar to Ao+Ai sin phase +A2 sin 2 phase + &c. +Bi cos phase +B2 cos 2 phase + &c. For this purpose I have taken the mean value of the function for each sixteenth part, and for each twelfth part, of the entire circle of phase, and have combined these num- bers according to the rules just laid down. The result is that 32 16 The sum —A. is increased by— X 0-3980 X«. "' O 1 ^ The sum — B. is increased by - — X 0-0392 X h. 32 16 The sum — A, is increased bv — X 0-8284 X a. 32 16 The sum — B., is increased by X0-1648X^. IS ^ ''IS 32 32 16 The sum — A, +t- Ao is increased by — X 2«. TS '■ OTS ^ "IS 32 32 16 The sum — B, - ^ B. is increased by — — X 0*8284 X b, 24 12 The sum — Ao is increased by —X 0-5360 X "^1 + 3^ A3, and —A3, are — c, —2c, —4c, and — c. The corrections must have opposite signs. In this manner (confining ourselves for a moment to the consideration of 4 phase) 32 32 we have such expressions as — A4 and — B4. And the quantity which we wish to ob- tain is A4 sin 4 phase 4-B4Cos 4 phase, which may be converted into one of this form, T //32 . \^ , /32„ \^ = 32V(tA4)+(vB4)- T» ^ K^-\-^^y, sin . 4 phase ■\-i). Since the Theory of Waves, as applied to Tides, leads us to refer every angle to that argument, and induces us to suppose that the term connected with that argument is the only one which is immediately created by the tidal forces (the others depending numerically on it almost in the same way in which the coefficients of successive multiples of anomaly depend on that of the simple anomaly)^ it appears to be proper to consider the times of high and low water thus found as the genuine times of high and low water. For the sake of distinction I call them the Analysed Times. As it is convenient to use the time of one phase only, I have, when the analysis gave the Analysed Times of two low waters, taken their mean for the Analysed Time of High Water. Now if we put phase -l-(pj=/?, ^2"~2^i=^2> ^3 — S^^^Cg, ^4 — 4^1=04, our expression for the height at every instant will be Ao+CiSinp+C2sin(2;? + C2)4-C3sin(3jo-fc3)+C4sin(4;?+ 00 K) ft -^ © cfc ++ + ■* CO CO 00 (N © <» OS »^© ++ + "* 1—1 (N „• .g- : « .2.2®®®®®ooooooooo ■g -c "-c ■■£ "-6 '-fi X 't, t '€ '-fi 'S "-H 'g c '-S oooooooooooooooo i-(0 V S ^ g S (M W-* a 5 .S .5 -5 '+C3)-|-C4sm(4/>-f-c4). Analysed time of high water, corre spending to J0°. Ao. Ci. C,. C2- C3. <^3- C4. e^. 1842. h m ft. ft. ft. ft. ft. July 23. 24. 18 21 6 18/ 15-47 5-55 0-14 152 0-05 0 226 0'02 28 24. 25. 18 32 1 6 52/ 15-58 5-47 0-20 140 0-03 128 0-03 56 25. 26. 19 5I 7 22/ 15-48 5-19 0-18 154 0-01 214 0-03 27 26. 27. 19 391 7 55/ 15-31 4-81 0-16 175 0-02 209 0-05 77 27. 28. 20 12 1 8 27/ 15-28 4-28 0-12 187 0-07 196 0-04 236 28. 29. 20 52 1 9 11/ 15-17 3-69 0-15 189 0-06 226 0-02 47 39. 21 32 15-32 3-30 0-15 149 0-09 267 0-02 66 30. 9 59 30. 22 26 15-25 2-73 0-04 204 0-05 232 0-03 158 31. 11 6 31. 23 46 15-45 2-57 0-06 182 0-05 199 0-02 338 August 1. 12 27 2. 1 8 15-75 2-90 0-03 218 0-03 76 0-02 132 2. 13 43 3. 2 18 15-38 3-62 0-01 261 0-05 240 0-06 60 3. 14 45 4. 3 11 15-45 4-55 0-07 205 0-09 215 0-11 104 4. 5. 15_34l 3 54 f 15-68 5-30 0-03 192 0-10 218 0-04 197 5. 6. 16 18i 4 42/ 15-70 6-32 0-05 135 0-08 233 0-05 0 6. 7. 17 2I 5 22/ 15-80 7-30 0-21 170 0-04 7 0-04 184 7. 8. 17 39 1 6 2/ 15-89 7-63 0-18 148 0-05 127 0-07 100 8. 9. 18 271 6 48/ 15-94 7-62 0-32 168 0-03 266 0-05 91 9. 10. 19 101 7 34 f 15-76 7-08 0-24 161 0-10 221 0-07 74 10. 11. 19 55 1 8 21/ 15-63 6-12 0-29 168 0-06 193 0-05 71 11. 12. 20 45 1 9 8/ 21 45 15-64 5-01 0-19 178 0-07 206 0-06 72 12. 15-41 4-06 0-13 227 0-13 242 0-04 159 13. 10 22 13. 22 58 15-27 3-24 0-10 244 0-11 309 0-02 180 14. 11 43 " 15. 0 27 15-27 2-79 0-12 221 0-07 269 0-01 0 15. 13 9 16. 1 50 15-41 3-16 0-06 235 0-10 268 0-02 316 16. 14 19 J 7. 2 48 15-59 3-71 0-05 238 0-05 279 0-00 51 17. 15 10 18. 3 31 15-64 4-32 0-09 203 0-05 270 0-01 24 18. 19. 15 501 4 11/ 15-76 4-76 0-08 121 0-05 178 0-02 108 19. 20. 16 291 4 43/ 15-74 5-29 0-13 165 0-09 242 0-03 189 20. 21. 16 55 1 5 11 / 15-54 5-73 0-11 177 0-06 232 0-04 163 21. 22. 17 26l 5 38/ 15-24 5-86 0-16 149 0-05 154 0-04 127 22. 23. 17 54i 6 12/ 15-58 5-80 0-15 135 0-10 222 0-04 88 66 MR. AIRY ON THE LAWS OF THE TIDES Height of the Water in ( 2ach individual tide at Kilrush, excluding diurnal tide. Analysed time of high water, corresponding to A„. Ci. c,. ca. C3. C3. C4. Ci. 1842. h m ft. 17-14 ft. 5-90 ft. 0-17 0 111 ft. 0-07 0 284 ft. 0-07 0 167 June 23.' 17 'sol 24. 6 11/ 24. 18 42 1 25. 6 52j 17-20 5-53 0-21 105 0-08 155 0-06 141 25. 19 hI 26. 7 28/ 16-62 5-47 0-12 119 0-05 261 0-11 175 26. 19 32 1 27. 7 51/ 16-29 5-18 0-20 124 0-07 231 0-10 146 27. 20 23 1 28. 8 43/ 28. 20 52 16-40 4-63 0-16 150 0-05 153 0-04 107 16-48 4-23 0-42 116 0-17 139 0-03 97 29. 9 17 29. 21 41 16-36 3-80 0-16 106 0-05 194 0-05 130 30. 10 7 30. 22 33 16-52 3-39 0-11 86 0-01 30 0-03 230 July 1. 11 4 1. 23 35 16-30 .S-12 0-10 135 0-09 186 0-00 130 2. 12 13 3. 0 50 16-74 3-22 0-10 84 0-06 208 0-01 240 3. 13 21 4. 1 52 17-25 3-75 0-16 150 0-07 201 0-02 269 4. 14 19 5. 2 45 16-51 4-50 0-12 136 0-09 237 0-01 333 5. 14 581 6. 3 26/ 16-20 5-13 0-15 314 0-17 177 0-08 23 6. 15 57 \ 7. 4 24/ 16-75 5-71 0-17 58 0-06 257 0-02 181 7. 16 521 8. 5 10 J 16-90 6-30 0-11 80 0-11 258 0-06 134 8. 17 25l 9. 5 45/ 16-63 6-87 0-20 77 0-12 155 0-05 205 9. 18 91 10. 6 33/ 16-86 7-17 0-31 99 0-09 254 0-13 184 10. 18 58l 11. 7 22/ 17-02 7-15 0-23 103 0-02 239 0-05 210 11. 19 40l 12. 8 3/ 16-70 6-82 0-17 100 0-04 76 0-05 119 12. 20 32 1 13, 8 56/ 16-35 6-13 0-24 152 0-09 161 0-01 44 13. 21 21 1 14. 9 48/ 14. 22 25 16-00 5-43 0-18 125 0-06 194 0-03 179 16-10 4-78 0-10 159 0-13 264 0-05 170 15. 10 58 15. 23 30 16-63 4-18 0-18 151 0-07 267 0-02 318 16. 12 11 17. 0 51 16-70 3-99 0-07 190 0-03 201 0-02 218 17. 13 28 18. 2 4 16-60 4-11 0-11 140 0-09 241 0-04 201 18. 14 36 19. 3 8 16-45 4-64 0-05 128 0-03 254 0-07 167 19. 15 301 20. 3 57/ 16-46 5-01 0-10 60 0-08 173 0-05 136 20. 16 24 1 21. 4 42/ 16-24 5-43 0-13 101 0-04 112 0-03 167 21. 17 3I 22. 5 19/ 16-29 5-82 0-12 100 0-04 194 0-03 144 22. 17 39 1 23. 5 56/ 16-28 6-02 0-20 111 0-04 179 0-03 193 The value C2= 314° for July 5 and 6 is correct. ON THE COASTS OF IRELAND. 57 expressed by the formula AQ+CiSin/>+C2sin(2/?+C2)H-C3sin(3/>-t-C3)+C4sin(4/)-fc4). Analysed time of high water, corresponding to \- <-!• c^. 02- C3. '•a- C4. c^. 1842. h m ft. ft. ft. ft. 0 ft. July 23. 24. 18 12\ 6 28] 16-31 6-02 0-21 120 0-09 228 0-05 205 24. 25. 18 40l 7 0/ 16-36 5-87 0-26 100 0-06 184 0-03 123 25. 26. 19 isl 7 32/ 16-21 5-69 ! 0-26 122 0-04 206 0-07 146 26. 27. 19 50 1 8 6/ 15-98 5-29 0-15 153 0'02 211 0-01 95 27. £8. 20 18l 8 33/ 15-95 4-82 0-19 129 0-07 165 0-08 146 28. 29. 29. 20 561 9 15/ 21 33 15-80 4-20 0-20 143 006 204 0-02 259 16-02 3^72 0-23 118 0-10 215 0-02 119 30. 30. 10 6 22 38 15-98 3-10 0-09 142 0-04 224 0-01 253 31. 31. 11 15 23 51 16-14 2-89 0-12 117 0-09 210 0-01 29 August 1. 2. 12 31 1 10 16-59 3-33 0-11 143 0-06 226 0-04 206 2. 3. 13 52 2 33 16-32 4-15 0-16 124 0-08 223 0-02 213 3. 4. 15 7\ 3 35/ 16-34 4-89 0-13 117 006 234 0-03 266 4. 5. 15-571 4 17/ 16-64 5-86 0-11 115 0-03 285 0-10 185 5. 6. 16 42l 5 6/ 16-68 6-87 0-22 82 0-07 195 0-06 151 6. 7. 17 30 1 5 50/ 16-80 7^59 0-25 71 0-11 219 0-06 128 7. 8. 18 9l 6 32/ 16-76 7-96 0-34 91 0-10 208 0-08 199 8. 9. 18 571 7 18/ 16-69 7-95 0-25 116 0-11 217 0-03 231 9. 10. 19 38 1 8 2/ 20 23 1 8 49/ 16-51 7-49 0-24 113 0-10 198 0-02 123 10. 11. 16-36 6-62 0'29 127 0-16 197 0-07 78 11. 12. 12. 21 121 9 35/ 22 7 16-38 16-17 5-50 4-58 0-15 0-11 138 150 0-11 0-11 183 213 0-06 0-07 116 175 13. 13. 10 41 23 14 15-98 3-76 0-13 148 0-08 240 0-07 212 14. 15. 11 59 0 43 16-07 3-29 0-12 153 0-06 235 002 284 15. 16. 13 25 2 7 16-24 3-69 0-10 148 0-05 265 0-03 190 16. 17. 14 37 3 7 16-53 4-30 0-11 117 0-03 123 0-01 231 17. 18. 15 281 3 50/ 16-39 4-70 0-15 31 0-15 208 0-08 117 18. 19. 16 10\ 4 31/ 16-55 5-33 0-14 84 0-11 170 0-01 209 19. 20. 16 54i 5 8/ 16-53 5-80 0-24 112 0-06 216 0-07 164 20. 21. 17 l6l 5 32/ 16-31 6-20 0-13 i 60 0-08 211 0*03 65 21. 22. 17 5oi 6 2/ 16-00 6-32 0-21 109 0-12 150 0-04 130 22. 23. 18 13l 6 31/ 16-42 6-36 0-18 68 0-14 176 0-08 72 MDCCCXLV. 58 MR. AIRY ON THE LAWS OF THE TIDES Height of the Water in each individual tide at Foynes Island, excluding diurnal tide, Analysed time of high water, corresponding to Ao. c,. Cj. Cj. C3. ^-s- C4. C4. p = 9Q°. 1842. h m ft. ft. ft. 0 ft. 0 ft. 0 June 25. 19 55 1 26. 8 9 J 17-57 6-38 0-36 122 0-15 160 0-08 289 26. 20 26 1 27. 8 45 / 17-05 6-01 0-49 116 0-15 166 0-06 232 27. 21 0 1 28. 9 20/ 28. 21 3i 17-21 5-52 0-42 128 0-11 168 0-04 107 17-08 5-22 0-39 116 0-12 143 0-02 274 29. 9 52 29. 22 12 17-03 4-57 0-38 107 0-08 160 0-04 71 30. 10 37 30. 23 3 17-25 4-16 0-28 113 0-06 163 0-04 152 July 1. 11 34 2. 0 4 17-14 3-91 0-34 122 0-09 146 0-03 268 2. 12 40 3. 1 16 17-43 3-88 0-39 127 0-16 192 0-04 351 3. 13 55 4. 2 33 J 8-04 4-38 0-34 126 0-13 182 0-04 331 4. 14 561 5. 3 20/ 17-37 5-00 0-21 111 0-19 189 0-03 280 5. 15 52 1 6. 4 24 / 16-88 5-81 0-43 115 0-13 185 0-02 167 6. 16 54 1 7. 5 21 / 17-48 6-50 0-41 109 0-19 163 0-03 329 7. 17 48 1 8. 6 6] 17-67 7-1? 0-34 113 0-22 165 0-11 25 8. 18 30 1 9. 6 50 / 17-40 7-68 0-54 115 0-37 165 0-07 279 9. 19 20 i 10. 7 44/ 17-38 8-03 0-50 128 0-28 199 0-15 271 10. 20 2 1 11. 8 26/ 17-70 7-94 0-60 102 0-37 179 0-02 20 11. 20 48 1 12- 9 11 / 12. 21 38 17-43 7-66 0-57 116 0-24 167 0-03 4 17-40 7-22 0-51 114 0-30 159 0-06 287 13. 9 59 13. 22 20 16-77 6-57 0-55 119 0-19 175 0-09 282 14. 10 47 14. 23 14 16-71 5-65 0-41 128 0-14 189 0-02 30 15. 11 46 16. 0 18 17-16 4-97 0-36 131 0-12 175 0-07 33 16. 12 57 17. 1 35 17-35 4-72 0-32 144 0-13 162 0-03 348 17. 14 11 18. 2 47 17-29 4-91 0-35 137 0-15 186 0-04 310 18. 15 21 1 19. 3 50 / 17-18 5-25 0-32 125 0-10 183 0-01 290 19. 16 15 1 20. 4 42/ 17-18 5-77 0-44 120 0-14 155 0-03 280 20. 17 8 1 21. 5 26 / 17-00 6-28 0-47 120 0-14 168 0-03 264 21. 17 48 1 22. 6 4 1 17-02 6-65 0-47 116 0-18 179 0-03 284 22. 18 22 1 23. 6 39/ 17-08 6-82 0-59 109 0-29 165 0-05 220 ON THE COASTS OF IRELAND. 59 expressed by the foi-mula Ao+CiSin/?+C2sin(2p+C2)+C3sin(3/>-4-C3)+C4sin(4/?+C4). Analysed time of high water, corresponding to Ao c,. c^. C.2. C3. C3. C,. C4. p = 90°. 1842. h m ft. ft. ft. ft. ft. July 23. 24, 18 55 \ 7 11/ 16-99 6-89 0-61 113 0-21 172 0-02 10 24. 25. 19 231 7 43/ 19 55 1 8 12/ 17-06 6-80 0-60 n5 0-18 159 0-04 306 25. 26. 16-93 6-50 0-61 116 0-22 160 0-02 307 26. 27. 20 25 \ 8 41 / 16-77 6-11 0-58 123 0-16 159 0-00 202 27. J 20 54 16-78 5-80 0-55 110 0-15 152 0-05 92 28. 9 11 28. 21 27 16-60 5-19 0-47 110 0-10 139 0-06 135 29. 9 47 29. 22 6 16-78 4-52 0-46 113 0-09 186 0-01 210 SO. 10 33 30. 23 0 16-68 3-86 0-35 119 0-06 173 0-04 61 31. 11 39 August 1. 0 17 16-89 3-64 0-39 127 0-13 190 0-03 335 1. 13 1 2. 1 45 17-20 4-07 0-38 137 0-12 198 0-05 304 2. 14 24 3. 3 2 1700 4-89 0-44 131 0-12 189 0-03 269 3. 4. 15 371 4 7/ 17-16 5-66 0-34 115 0-13 171 0-00 122 4. 5. 16 37 1 4 57/ 17-38 6-59 0-43 121 0-22 165 0-02 287 5. 6. 17 271 5 51/ 17-38 7-71 0-55 107 0-29 160 0-01 35 6. 7. 18 171 6 37/ 17-53 8-29 0-64 102 0-37 162 0-04 259 7. 8. 18 571 7 20/ 17-57 8-58 0-74 112 0-45 165 0-11 249 8. 9. 19 45 1 8 6/ 17-56 8-51 0-72 114 0-39 171 0-09 283 9. 10. 20 251 8 49/ 17-48 8-12 0-71 114 0-34 167 0-09 261 10. 21 7 17'13 7-56 0-64 HI 0-28 167 0-01 77 11. 9 28 11. 21 48 17-22 6*66 0-59 118 0-25 159 0-04 292 12. 10 14 12. 22 39 16-93 5-40 0-40 122 0-13 166 0-03 77 13. 11 9 13, 23 39 16-72 4-40 0-33 140 0-05 183 0-00 133 14. 12 23 15. 1 7 16-72 3-91 0-36 140 0-12 209 0-02 337 15. 13 50 16. 2 33 16-77 4-30 0-32 145 0-09 204 0-03 356 16. 17. 15 91 3 39/ 17-06 4-80 0-33 124 0-08 177 0-01 175 17. 18. 16 5 1 4 30/ 17-11 5-47 0-41 115 0-11 173 002 259 18. 19. 16 51 1 5 12/ 17-28 6-15 0-50 113 0-19 163 0-02 109 19. 20. 17 35 1 5 49/ 17-25 6-60 0-47 106 0-22 181 0-04 307 20. 21. 18 3\ 6 19/ 17'04 6-99 0-60 109 0-23 167 0-04 54 21. 22. 18 35 1 6 47/ 16-73 7-10 0-57 111 0-24 175 0-03 350 22. 23. 19 0 1 7 18/ 17-10 7-06 0-59 111 0-30 167 0-02 22 60 MR. AIRY ON THE LAWS OF THE TIDES Height of the Water in each individual tide at Limerick, excluding' diurnal tide, Analysed time of high water, corres})ondiiig to /; = 90°. C,. Cj. C3. C4. 1842. h m June 25. 26. 20 8 26. 21 27- 9 27. 28. 21 9 28. 22 29. 10 29. 22 30. 1 0 30. 23 July 1. 11 2. 0 2. 12 1 14 3 3. 3. 4, 30 44 3 17 30 46 1 19 37 59 20 50 20 56 31 16 0 5. 6. 6. 7. 1' 8. 8. 9. 9. 10. 10. 11. 11. 12. 12. 1.3. 13. 14. 14. 15. 16. 16. 17. 17. 18. 18. 19. 19. 20. 20. 21. 21. 22. 22. 23. 16 4 17 5 18 6 19 7 20 8 20 9 21 9 53/ 231 50/ 151 33/ } 22 20 10 37 22 11 23 12 0 54 19 44 14 44 13 21 1 14 3 15 4 16 5 17 5 18 6 18 58 35 11 501 20/ 48 1 36 1 56/ 21 1 37/ 58] 7 15 18-41 17-54 17-72 17-50 17-24 18-12 17-98 17-78 18-45 17-28 18-11 18-65 18-36 18-18 18-40 18-00 18-57 17-45 16-91 17-14 17-55 17-38 17-38 17-45 17-46 17-50 17-58 ft. 7-82 7-93 7-07 6-62 5-92 5 33 5-03 5-11 5-67 7-18 7-97 8-32 9-21 9-78 9-83 9-67 8-69 8-06 7-22 6-27 5-94 6-10 6-59 7-17 7-75 8-12 8-35 0-78 1-23 1-02 1-01 0-87 0-71 0-76 0-92 0-97 0-79 0-72 0-67 0-87 0-90 1-02 1-09 1-03 0-89 0-87 0-89 0-73 0-76 0-70 0-87 0-88 1-02 1-03 0 ft. 0 90 0-68 153 86 0-84 119 9Cy 0-64 129 103 0-51 124 97 0-48 129 108 0-34 142 118 0-27 151 121 0-43 146 1 ' 125 1 ! .... 0-38 172 ! 106 j 0-46 155 97 0-69 143 95 0-86 148 90 0-83 136 66 0-84 123 64 0-84 119 69 0-89 115 80 0-93 130 91 0-82 126 108 0-66 139 124 0-36 172 128 0-30 156 119 0-58 160 120 0-43 153 106 0-49 143 94 0-64 141 90 0-73 135 87 0-75 130 0-22 0-45 0-24 0-17 0-20 0-10 0-08 0-25 0-18 0-28 0-40 0-24 0-35 0-62 0-63 0-53 0-47 0-54 0-29 0-12 0-11 0-13 0-15 0-16 0-29 0-38 0-46 199 155 174 167 167 153 225 203 221 191 204 221 173 138 133 135 160 161 166 244 206 195 213 189 167 157 168 ON THE COASTS OF IRELAND. (Jl expressed by the formula Ao+CiSin/>-|-C2sin(2j»+C2)+C3sin(3j»+c2)+C4sin(4794-q). Analysed time of Iiigli water, corresponding to Ao- c,. C;. <*2- C3. <^3- C4. C4. 1842. h m ft. ft. ft. ft. ft. j July 23. 24. 19 311 7 47/ 17*55 8-40 0-99 85 0-76 0 138 0-48 163 24. 20 8 17-42 8-50 0-97 76 0-83 111 0*52 138 25. 8 23 25. 20 37 17-34 8-32 0-94 75 0-70 111 0-46 144 26. 8 51 26. 21 5 17-10 7-87 0-95 85 0-67 113 0-46 147 27. 9 18 27. 21 30 17-19 7-31 1-03 88 0-74 122 0-29 160 28. 9 43 28. 21 55 16-86 6-71 Ml 91 0-59 115 0-40 183 29. 10 14 29. 22 33 17-21 5-72 0-97 96 0-51 135 0-17 165 •SO. 10 56 30. 23 19 16-94 4-95 0-75 110 0-29 142 0-06 214 31. 11 57 August ]. 0 35 17-11 4-60 0-76 119 0 24 145 0-15 224 1. 13 31 2. 2 26 17-44 4-31 0-73 113 0-35 165 0-16 264 2. 3. 14 48\ 3 25/ 17-12 5-88 0-75 132 0-39 160 0-08 186 3. 4. 16 3l 4 38/ 17-65 6-81 0-63 105 0-49 143 0-31 185 4. 5. 17 lol 5 30/ 18-09 8-10 0-81 86 0-72 148 0-35 171 5. 6. 18 si 6 29/ 18-02 9-30 1-09 75 0-81 127 0-51 146 6. 7. 18 50l 7 10/ 18-41 962 M7 67 0-94 115 0-55 144 7. 19 45 17-99 10-38 0-99 35 0-74 101 0-64 117 8. 8 8 8. 20 30 18-05 10-36 0-93 40 0-77 100 0-66 118 . 9. 8 48 9. 21 6 18-16 9-95 0-96 52 0-91 107 0-69 122 10. 9 27 10. 21 47 17-73 9-17 0-91 64 0*90 118 0-63 129 11. 10 5 11. 22 23 17-77 8-24 0-88 85 0-89 122 0-42 152 12. 10 43 12. 23 3 17-18 6-89 0-87 107 0-62 139 0-22 146 13. 11 31 13. 23 58 16-87 5-56 0-79 130 0-37 169 0-09 201 14. 12 43 15. 1 28 16-86 4-95 0-67 134 0-28 160 0-09 210 15. 14 8 16. 2 47 16-85 5-50 0-75 125 0-39 160 0-13 204 16. 17. 15 29 \ 3 56/ 17-20 6-08 0-65 109 0-37 161 0-10 141 17. 18. 16 29 1 4 56/ 17-33 6-87 0-80 106 0-46 143 0-24 195 18. 19. 17 20l 5 41 J 17-73 7-64 0-94 9G 0-62 135 0-30 195 19. 20. 18 7l 6 21 / 17-84 8-05 1-10 89 0-79 143 0-38 172 20. 21. 18 361 6 52/ 17-58 8-49 1-03 80 0-74 1.33 0-49 150 21. 22. 19 91 7 21/ 19 35l 7 53/ 17-18 8-71 0-98 76 0-74 118 0-51 126 22. 23. 17-63 8-52 1-12 78 0-82 131 0-43 150 62 MR. AIRY ON THE LAWS OF THE TIDES Height of the Water in each individual tide at Casieh Bay, excluding diurnal tide. Analysed time of high water, corresponding to Ao. €,. C2. +C4). Analysed time of high water, corresponding to Ao- Ci. C,. Cj. C3. <*3- C4. C4. j!; = 90°. 1842. h m ft. ft. ft. ft. ft. July 23. 24. 20 461 8 58/ 17-92 2-95 0-04 231 0-17 0 197 0-03 0 230 24. 25. 21 8l 9 25/ 17-96 2-88 0-07 101 0-13 197 0-01 5 25. 21 43 17-79 2-82 0-02 342 0-10 166 0-03 75 26. 9 56 26. 22 9 17-55 2-62 0-15 316 0-08 181 0-00 218 27. 10 28 27. 22 47 17-60 2-24 0-07 266 0-09 201 0-02 255 28. 11 4 28. 23 21 17-56 1-92 0-08 307 0-08 201 0-ei 65 29. 11 44 30. 0 6 17-50 1-62 0-15 9 tM4 169 0-04 179 30. 12 42 31. 1 17 17-69 1-30 «-20 20 0-08 187 0-05 197 31. 14 15 August 1. 3 13 17-97 1-42 0-33 119 «-03 222 0-03 293 1. 2« 15 30l 3 56/ 17-98 1-67 D-25 207 0-13 156 0-05 90 2. 3. 16 sol 5 6/ 17-79 1-92 0-19 218 0-06 163 0-03 289 3. 4. 17 39 1 6. 2/ 18-22 2-52 0-U 255 ^•13 188 0-04 9 4. 5. 18 43l 7 3/ 18-39 3-07 0-14 242 0-18 202 0-03 26 5. 6. 19 lol 7 36/ 18-43 3-67 0-12 1S7 0-11 208 0-02 104 6. 7- 19 53 1 8 8/ 18-59 404 C-10 823 ^12 205 0-04 121 7- 8. 20 39 1 9 4/ 21 33 18-60 4-21 0-12 144 0-17 201 0-11 337 8. 18-42 4-16 0-22 224 0-22 202 O-04 342 9- 9 55 9. 22 17 18-23 3-80 0-16 248 0-19 227 0-13 211 10. 10 35 10. 22 52 17-79 3-32 0-10 257 0-17 215 0-82 356 11. 11 18 11. 23 44 17-76 2-65 0-15 271 0-07 193 O-07 155 12. 12 7 13. 0 29 17-62 1-95 0-12 805 O-04 201 0-03 131 13. 13 15 14. 2 1 17-52 1-54 +C2)+C3sin(3p+c.,)4-C4sin(4;?+C4). Analysed time of high water, corresponding to p = 90°. Ao. c,. c,. 02. C3. '^s- C,. C4. 1842. h m July 23. 20 28 \ 24. 8 38/ ft. 17-29 ft. 1-24 ft. 0-06 0 2 ft. 0-12 0 300 ft. 0-04 0 234 24. 20 49 1 25. 9 9/ 17-25 1-20 0-13 339 0-14 293 0-04 213 25. 21 46 26. 10 3 17-11 0-97 0-13 329 0-09 314 0-03 182 26. 22 19 27. 10 50 16-98 0-83 0-13 342 0-12 319 0-00 250 27. 23 21 28. 11 51 17-23 0-70 0-08 10 0-10 341 0-02 240 29. 0 21 29. 13 10 17-06 0-56 0-10 303 0-04 350 0-01 242 30. 2 0 30. 14 37\ 31. 3 11/ 17-17 17-11 0-63 0-78 0-12 0-13 113 192 0-04 0-07 171 153 0-03 0-01 343 109 31. 15 24I August 1. 4 12/ 17-07 0-92 0-19 263 0-05 214 0-03 63 1. 17 1I 2. 5 5/ 17-49 0-91 0-22 317 0-06 281 0-00 273 2. 17 571 3. 6 19/ 17-31 0-97 0-09 17 0-04 2 0-02 91 3. 18 22 1 4. 6 29/ 17-78 1-06 O-Il 339 0-07 293 0-07 270 4. 18 181 5. 6 31/ 18-06 1-36 0-15 315 0-08 199 0-08 227 5. 18 49 1 6. 7 6/ 17-87 1-65 0-09 280 0-13 288 0-05 242 6. 19 l6l 7. 7 20/ 18-11 1-87 0-08 274 0-17 233 0-08 189 7. 19 42I 8. 7 58/ 17-83 2-09 d-12 240 0-15 244 0-04 202 8. 20 26 1 9. 8 47/ 9. 21 48 17-88 1-89 0-10 222 0-10 249 0-04 200 17-58 1-70 0-30 301 0-16 319 0-09 239 10. 10 5 10. 22 22 17-34 1-26 0-24 303 0-18 297 0-02 23 11. 11 9 11. 23 55 17-51 0-86 0-21 316 0-13 354 0-05 151 12. 12 41 13. 1 26 17-59 0-68 0-18 J5 0-07 44 0-02 0 13. 14 40\ 14. 4 8/ 17-54 0-77 0-15 96 0-05 55 009 322 14. 16 7I 15. 4 45/ 17-28 0-97 0-07 315 0-04 311 0-03 106 15. 17 20I 16. 5 46/ 17-16 0-98 0-11 28 0-04 296 0-06 323 16. 17 46l 17. 6 0/ 17-52 1-08 0-08 15 0-04 310 0-01 291 17. 18 29I 18. 6 37/ 17-50 1-12 0-05 358 0-05 347 0-03 273 18. 18 55I 19. 6 55/ 17-77 1-26 0-05 344 0-10 304 0-01 176 19. 19 9I 20. 75/ 17-98 1-27 0-09 342 0-09 293 0-03 338 20. 19 32 1 21. 7 48/ 21. 20 20 17-38 1-34 0-13 337 0-14 288 0-04 230 17-05 1-27 0-13 316 0-09 286 0-04 230 22. 8 31 22. 20 42 17-57 1-21 0-23 316 0-11 273 0-02 137 78 MR. AIRY ON THE LAWS OF THE TIDES Height of the Water in each individual tide at Glenarm, excluding diurnal tide. Analysed time of high water, corresponding to Ao. Ci. Co. Co. C3. <^3- C4. C4. jw = 90°. 1842. h ni ft. ft. ft. o ft. 0 ft. Q .... i8-64 2-75 0-06 "74 0-05 205 0-04 318 June 23. 23 50 24. 12 5 25. 0 20 18-63 2-72 008 114 0*08 238 O-Ol 346 25. 12 38 26. 0 56 18-15 2-72 0-05 42 0*08 «37 0-05 41 26. 13 20 27. 1 44 17-48 2-61 0-08 96 0-07 260 0-01 235 27. 14 5 28. 2 26 17-87 2-51 0-12 151 0*03 261 0-03 344 28. 14 50 29. 3 13 17-58 2-55 0-14 171 0-09 256 0-03 256 29. 30. 15 271 3 511 > 17-32 ■2-42 0-04 241 0M)9 230 0-04 355 30. July 1. 16 22' 4 47 J ' 17-55 2-30 0*07 ^20 0-02 265 0-04 11 1. 2. 17 01 5 23, > 17-59 2-19 0-18 332 0*14 243 0-06 144 2. 3. 18 9l 6 42 J ' 17-71 2-20 G-13 12 0*«5 249 0-03 189 3. 4. 19 15' 7 42 J > 18-47 2-28 9-12 29 e-os 241 0-01 146 4. 5. 20 101 8 43 J > 18-31 2-42 0-19 37 O-02 294 0-05 260 5. 6. 21 91 9 35 J > 17-34 17-78 2-65 0-18 72 0-06 386 0-04 282 6. 22 3 2-64 0-12 76 0-08 215 0-02 50 7. 10 19 7- 22 36 17-99 2-88 0-15 54 0-06 200 0-03 219 8. 10 59 i 8. 23 23 17-93 2-87 0-22 75 0-07 224 0*03 306 9. 11 46 10. 0 9 18-11 2-96 0-24 76 0-15 243 O-05 280 10. 12 32 11. 0 54 18-30 3-18 0-27 51 O-ll 224 O-Ol 215 11. 13 19 12. 1 43 17-87 3-03 0-25 81 ©-lO 229 0-06 314 12. 14 9 13. 2 35 18-13 2-85 0-28 68 4-C3)+C4sm(4/)-l-cJ. Analysed time of high water, correspouding tc Aq. Ci. c.. Co- C3. ^3- C4. C4. i? = 90°. 1842. Ii m ft. ft. ft. ft. ft. July 24. 0 0 17-28 2*72 Q-06 61° Q-©5 268 0-03 171 24. 12 17 25. » 34 17-34 2-69 0-12 80 0-06 238 0-01 0 25. 12 34 26. 1 15 17-35 2-66 0-17 112 0-07 267 0-03 37 26. 13 32 27. 1 49 17-16 2-62 0*12 127 0-07 243 0-04 10 27. 14 4 28. 2 19 17-23 2-55 0-06 148 0-06 204 0-00 350 28. 14 45 29. 3 10 16-97 2-34 0-15 131 0-08 279 0-01 110 29. 30. 15 261 3 46 J - 17-07 2-30 0-15 212 0-04 189 0-03 ,65 30. 31. 15 56^ 4 29 1 . 17-34 2-25 0-12 250 0-04 271 0-03 101 SI. August 1. 17 151 5 54 J 17-48 2-14 0-12 334 0-05 240 0-03 110 1. 2. 18 32' 7 4J > 18-04 2-10 0-16 27 0-04 276 0-02 193 2. 3. 19 42' 8 21 ^ 17-86 2-31 0-20 77 0-01 347 0-03 311 3. 4. 20 54' 9 14J 21 37 ^ 18-09 2-63 0-18 86 0-05 276 0-02 290 4. 18-34 2-72 0-13 50 0-07 178 0-01 288 5. 9 56 5. 22 15 18-10 2-93 0-17 74 0-09 211 0-01 189 6. 10 35 6. 22 55 18-32 314 0-20 61 0-03 211 0-02 206 7. 11 15 7. 23 35 18-17 3-20 0-29 63 ©•13 205 0-04 271 8. 12 0 9. 0 25 18-19 3-12 0-33 74 0*09 226 0-03 321 9. 12 51 10. 1 17 18-26 3-15 0-30 75 0-09 221 0-01 1 10. 13 44 11. 2 12 18-07 2-94 0-30 105 0-13 230 . 0-03 232 11. 12. 14 361 2 58 > 18-06 3-10 0-13 136 0-07 266 0-02 72 12. 13. 15 24' 3 54 ^ 17-89 2-73 0-13 216 0-11 232 0-02 83 13. 14. 16 32' 5 7J . 17-54 2-55 0-03 214 0-04 237 0-02 106 14. 15. 17 401 6 25J . 17-45 2-12 0-06 329 0-02 307 0-01 97 15. 16. 19 61 7 43 J . 17-35 2-22 0-09 39 0-04 208 0-02 88 16. 17. 20 10' 8 40 . 17-74 2-32 0-07 64 0*02 181 0-04 169 17. 21 16 17-71 2-41 0-12 24 0-01 293 0*02 355 18. 9 34 18. 21 51 17-95 2-68 0-09 16 0-09 205 0*04 48 19. 10 12 19. 22 32 18-20 2-58 0-10 52 0-05 198 0*03 96 20. 10 48 20. 23 4 17-69 2-70 0-09 116 0-07 227 O'Ol 247 21. 11 19 21. 23 33 17-25 2-70 0-08 78 0-04 232 0-03 43 22. 11 49 23. 0 4 17-76 2-72 0-13 109 0-04 174 0*07 294 80 xMH. AIRY ON THE LAWS OF THE TIDES Height of the Water in each individual tide at Donaghadee, excluding diurnal tide. Analysed time of high water, corresponding to Ag. Ci. c,. C2. C3. ^3- C4. C4. ^ = 90°. 1842. h m ft. ft. ft. 0 ft. 0 ft. June 22. 23 23 18-22 4-78 0-14 72 0-07 161 0-01 221 23. 11 45 24. 0 7 18-70 4-90 0-06 325 0-03 221 0-02 61 24. 12 25 25. 0 43 18-78 4-86 0-06 16 0-06 245 0-03 303 25. 13 2 26. 1 21 18-34 4-76 0-06 356 0-09 240 0-07 31 26. 13 42 27. 2 2 17-56 4-51 0-09 246 0-04 251 005 65 27: 14 20 28. 2 37 18-01 4-29 0-01 260 0-04 211 0-03 322 28. 14 59 29. 3 20 17-81 3-97 0-08 200 0-04 208 0-06 31 29. 15 40 1 30. 44/ 17-69 3-77 0-04 238 0-06 241 0-03 94 30. 16 25I July 1. 4 50/ 1. 17 25l 2. 5 48/ 17-85 3-56 0-08 264 0-03 201 0-01 218 17-93 3-30 0-07 308 0-05 222 0-01 251 2. 18 22 1 3. 6 55/ 18-00 3-36 0-09 12 0-04 215 001 240 3. 19 31 1 4. 7 58/ 18-70 3-58 0-10 6 0-04 263 0-03 349 4. 20 25 1 5. 8 58/ 18-45 3-90 0-12 24 0-05 277 0-03 258 5. 21 23 1 6. 9 49/ 17-58 4-40 0-15 42 0-07 269 0-04 126 6. 22 13 18-01 4-61 0-09 60 0-01 53 0-05 208 7. 10 32 7. 22 52 18-21 5-12 0-08 40 0-04 172 0-02 297 8. 11 14 8. 23 35 18-00 5-36 0-07 66 0-04 162 0-04 43 9. 11 59 10. 0 22 18-18 5-54 0-05 101 0-10 212 0-03 271 10. 12 45 11. 1 7 18-37 5-71 0-11 17 0-06 199 006 247 11. 13 31 12. 1 55 17-93 5-49 0-15 66 0-05 193 0-06 331 12. 14 21 13. 2 47 18-16 5-22 0-09 34 0-07 175 0-03 317 13. 15 13l 14. 3 38/ 17-59 5-06 0-07 182 0-05 236 0-04 57 14. 16 71 15. 4 35/ 17-28 4-60 0-06 204 0-03 216 0-02 9 15. 17 I0I 16- 5 44/ 17-69 4-15 0-07 290 0-05 241 0-02 49 16. 18 21 1 17. 6 48/ 17-96 3-88 0-11 337 0-11 230 0-06 56 17. 19 291 18. 8 13/ 17-93 .3-85 0-11 13 0-02 312 0-03 198 18. 20 39 1 19. 95/ 19. 21 35 17-74 4-01 008 71 0-01 257 0-01 236 17-66 4-30 0-07 333 0-01 41 0-03 11 20. 9 59 20. 22 23 17-64 4-53 0-07 334 0-01 250 0-04 41 21. 10 42 21. 23 1 17-58 4-80 0-04 328 0-01 132 0-02 159 22. 11 19 22. 23 37 17-50 4-90 0-07 328 0-03 123 0-00 31 23. 11 55 ON THE COASTS OF IRELAND. 3 J expressed by the formula Aq+Cj sin/?+C2sin(2/?4-C2)+C3 sin (3/»+C3)4-C4sin(4p-|-C4), Analysed time of high water, corresponding to ;^ = 90°. Ao- Ci. c^. C-z- C3. ^3- C4. C4. 1842. h in ft. ft. ft. ft. ft. July 24. 0 12 17-54 4-91 0-03 11 0-02 163 0-03 13^ 24. 12 29 25. 0 46 17-55 4-87 0-03 104 0-05 140 0-01 151 25. 13 2 26. 1 18 17-57 4-71 0-06 110 0-01 214 0-03 61 26. 13 36 27. 1 54 17-43 4-56 0-02 157 0-02 318 0-04 314 27. 14 12 28. 2 31 17-58 4-31 0-08 118 0-02 212 0-02 74 28. 29. 14 491 3 9/ 17-28 4-08 0-09 206 0-08 233 0-05 71 29. 30. 15 26 1 3 46/ 17-39 3-72 0-08 251 0-08 246 0-04 112 30. 31. 16 18l 4 51/ 17-39 3-40 0-09 261 0-04 251 0-01 111 31. August 1. 17 221 6 l| 18 451 7 17/ 17-55 3-24 0-11 314 0-02 179 0-03 124 1. 2. 17-97 3-26 0-12 9 0-03 211 0-03 147 2. 3. 19 58 \ 8 37/ 21 8 17-78 3-69 0-12 60 0-08 69 0-02 325 3. 17-98 4-11 0-03 122 0-04 164 0-00 179 4. 9 37 4. 22- 7 18-24 4-81 0-06 6 0-04 158 0-01 117 5. 10 23 5. 22 39 17-99 5-28 0-09 99 0-02 162 0-07 321 6. 11 0 6. 23 22 18-18 5-72 0-13 52 0-05 174 0-02 104 7. 11 44 8. 0 5 17-88 5-98 0-10 68 0-06 152 0-05 319 8. 12 29 9. 0 52 18-02 6-01 0-15 67 0-07 174 0-05 3 9. 13 14 10. 1 36 18-03 5-89 0-11 51 0-06 166 0-01 135 10. 14 1 . 11. 2 25 17-93 5-46 0-14 92 0-05 196 0-06 9 11. 12. 14 471 3 9/ 17-93 5-20 0-11 221 0-03 237 0-03 28 12. 13. 15 40 1 4 8/ 17-76 4-50 0-16 224 0-03 223 0-02 82 13. 14. 16 421 5 17/ 17-50 3-92 0-06 234 0-03 232 0-03 108 14. 15. 18 0 1 6 45/ 17-46 3-45 0-08 277 0-01 99 0-02 41 15. 16. 19 22 1 7 59/ 17-35 3-42 0-05 6 0-03 286 0-03 192 16. 17. 20 33 1 9 3/ 21 29 17-81 3-77 0-06 4 0-04 218 0-01 138 . 17. 17-74 4-02 0-05 347 0-03 164 0-01 43 18. 9 51 18. 22 12 17-98 4-51 0-07 344 0-06 168 0-05 71 19. 10 31 19. 22 49 18-12 4-54 0-09 25 0-09 81 0-06 36 20. 11 5 20. 23 21 17-65 4-90 0-01 141 0-05 202 0-03 341 21. 11 37 21. 23 52 17-25 4-95 0-04 30 0-06 179 0-04 182 22. 12 6 23. 0 20 17-73 5-02 0-06 129 0-07 164 0-04 164 MDCCCXLV. M ^3t MR. AIRY ON THE LAWS OF THE TIDES Height of the Water in each individual tide at Ardglass, excluding diurnal tide. Analysed time of high •water, corresjionding to K C,. Co. ^2- C3. <^3- C4. c-i- jo = 90°. 1842. h m ft. ft. ft. ft. 0 ft. Jiane 2^. 33 30 18-35 6-30 0-20 87 ^12 175 0-«4 211 28. 11 45 24. 0 0 18-60 6>35 ©•17 73 0-12 231 0-09 188 2*6.' "i is i8-'20 €*11 «»15 *ii6 0-05 216 0-03 105 26. 13 34 27. 1 55 17-62 5-76 0-10 96 0-07 146 0-04 28 27. 14 14 28. 5 33 17-83 5-40 0-10 99 0-06 188 002 61 28. 14 54 29. 3 15 17-76 4-99 0-14 125 0-05 170 0-01 312 29. 30. 15 361 4 OJ 16 26 1 4 51/ 17-59 4-71 0-09 131 0-11 ^17 0-02 176 30. July 1. 17-71 4'S8 009 173 * • • • <)-12 138 ^11 5 0-08 190 ! ' 7. 22 56 8. 11 16 8. 23 35 17-76 7*08 0-19 90 O-05 47 0-00 208 9. 11 56 10. « 17 17-90 7-^4 0-18 *93 0-09 157 0-09 35 10. 12 41 11. 1 5 18-29 7-62 0-15 64 0-16 196 0-16 145 11. 13 30 12. 1 54 17-75 7-30 0-22 100 0-01 106 0-01 270 12. 14 18 13. 2 43 17-87 6-78 0-15 69 0-08 137 0-05 109 13. 14. 15 1\\ 3 36/ 17-54 6-53 0-16 116 0-04 128 0-05 215 14. 15. 16 9I 4 37/ 17-24 5-81 0-15 121 0-02 234 0-03 254 IS. 16. 17 131 5 47/ 1.7-52 5-10 0-05 138 •0-05 246 002 81 *17.' 18. 19 40\ 8 24/ 17-77 4-88 0-07 356 0-08 250 0-06 179 18. 19. 20 52 1 9 18/ 17-74 5-26 0-07 53 0-04 232 0-06 171 19. 21 47 17-64 5-50 O-08 60 0-04 296 0-06 124 20. 10 11 20. 22 35 ■17-60 5-SO 0-07 118 0-08 189 0-03 116 21. 10 54 21. as 12 17-54 6-18 0-11 89 0-06 187 0-04 254 22. 11 29 22. 23 46 17-46 6-39 0-11 132 0-06 143 0-01 112 .35. 12 3 . ON THE COASTS OF IRELAND, expressed by the formula Ao4-Cisinj9+C2sin(2/?+C2)-f C.}Sin(3/?- 83 C3)-fC4sin(4;?4-C4). Analysed time of high water, corres poading to Ao. c,. c^. ^2- C3. <-3- C,. ^4. p = 'JO°. 1842. h m ft. ft. ft. ft. ft. July 24. 0 20 17-48 6-40 0-10 140 0-08 144 0-03 199 24. 12 38 25. 0 55 17-48 6-34 0-16 99 0-03 174 0-03 26 25. 13 9 26. 1 24 17-52 6*18 0-15 118 0-05 144 0-07 196 26. 13 41 27. 1 58 17-40 5-85 0-21 lis O-07 148 0-02 200 27. 14 15 28. 2 33 17-47 5-48 0-20 117 003 123 0-03 157 28. 29. 14 531 3 13/ 17-29 5-07 0-16 129 009 187 0-06 213 29. 30. 15 33 1 3 53/ 17-35 4-67 0-12 148 0-04 221 0-03 155 30. 31. 16 21 1 4 54/ 17 281 6 7/ 17-34 4-15 0-12 U6 0-01 257 0-05 170 31. August 1. 17-38 3-88 0-07 198 0-02 255 0-01 77 1. 2. 18 48l 7 20/ 17-71 3-98 0-09 351 005 234 0-03 143 2. 3. 20 2\ 8 41/ 21 8 17-58 4-63 0-09 63 0-03 55 0-02 197 3. 17-85 5-25 0-13 105 004 168 0-05 209 4. 9 32 4. 21 55 18-03 6-21 0-12 137 0-08 132 0-04 165 5. 10 18 5. 22 42 17-91 6-99 0-24 99 0'02 140 0-06 146 6. 11 1 6. 23 20 18-05 7-60 0-26 78 0-03 124 0-09 127 7. 11 42 8. 0 3 17-83 8-11 0-27 89 0'12 109 0-04 327 8. 12 25 9. 0 47 17-88 8-12 0-25 95 0-07 138 0-09 79 9. 13 9 10. 1 32 17-85 7*80 0-20 87 0-07 139 0-08 57 10. 13 56 11. 2 20 17-81 7*13 0-32 91 0'04 88 0-03 68 11. 12. 14 511 3 13/ 17-88 6-64 0-18 133 0-08 173 0-07 73 12. 13. 15 46l 4 14/ 17-70 5-62 Q-14 132 0-06 193 0-10 127 13. 14. 16 5l1 5 26/ 17-42 4*81 0-10 139 0-03 186 0-01 158 14. 15. 18 71 6 52/ 17-36 4-22 0-04 172 O-02 313 001 253 15. 16. 19 38 1 8 15/ 17-30 4-29 0-06 95 0-02 84 0-02 182 16. 17. 20 46 1 9 16/ 17-71 4-75 0-13 88 0-03 253 0-04 135 17. 21 40 17-66 5-20 0-08 140 0-02 174 0-02 149 18. 10 1 18. 22 21 17-91 5-80 0-13 76 0-16 211 0-10 99 19. 10 36 19. 22 51 17-99 6-00 0-24 62 0-05 204 0-03 92 20. 11 5 20. 23 18 17-57 6-45 0-27 146 0-10 236 0-09 340 21. 11 37 21. 23 55 17-15 6-53 0-20 117 0'05 166 0-03 27 22. 12 7 23. 0 19 17-62 6-57 0-14 111 0-06 111 0-05 210 ivi 2 ^S4 MR. AHIY ON THE LAWS OF THE TIDES Height of tiie Watei* in each individual tide at Clogher Head, excluding diurnal tide, Analysed time of high water, corrci ponding to Ao- Cj. Co. C-2' ^3- <"3- C4. C4. P= 90°. 1842. h m ft. 17-9'6 ft. 6-22 ft. 0-22 126 ft. 0-07 0 '16I ft. 0-05 0 200 June 24. 0 6 24, 12 24 25. 0 42 17-93 6-16 0-25 113 0-06 166 0-03 307 25. 12 59 26. 1 16 17-48 5-99 0-23 124 0-04 202 0-05 167 26. 13 37 27. 1 57 17-15 5-58 0-27 116 0-07 145 0-02 162 27. 14 17 28. 2 36 17-35 5-30 0-16 119 0-05 120 0-04 177 28. 14 57 29. 3 18 17-29 4-79 0-21 123 0-05 153 0-03 233 29. 30. 15 391 4 3/ 17-13 4-50 0-19 137 0-02 85 0-08 178 30. July 1. 16 27l 4 52/ 17-26 4-18 0-13 149 0-10 190 0-03 116 1. 2. 17 27l 5 50/ 17-21 3-83 0-18 178 0-10 281 0-05 156 2. 3. 18 29l 7 2j 17-34 3-99 0-08 175 0-08 212 0-03 68 3. 4. 19 32l 7 59/ 17-88 4-28 0-06 336 0-10 227 0-07 205 4. 5. 20 31 1 9 4/ 17-52 4-90 0-10 141 0-06 52 0-04 126 5. 21 28 17-01 5-28 0-20 117 0-03 184 0-03 207 6. 9 53 6. 22 17 17-40 6-00 0-21 113 0-11 145 0-10 106 7. 10 37 7. 22 57 17-61 6-61 0-24 119 0-08 118 0-04 113 8. 11 21 8. 23 44 17-53 7-11 0-41 111 0-05 101 0-05 325 9. 12 7 10. 0 29 17-54 7-36 0-34 111 0-05 75 0-02 85 10. 12 54 11. 1 19 17-95 7-50 0-29 123 0-08 203 0-10 253 11. 13 43 12. 2 6 17-29 7-27 0-40 124 0-06 202 0-05 274 12. 14 31 13. 2 55 17-34 6-71 0-25 103 0-04 170 0-08 194 13. 14. 15 151 3 40/ 16-72 6-16 0-07 291 0-23 124 0-07 209 14. 15. 16 24 T 4 52/ 16-84 5-68 0-24 133 . 0-02 185 0-04 254 15. 16. 17 28l 6 2/ 17-14 5-10 0-14 113 009 226 0-03 45 16. 17. 18 32I 7 0/ 17-10 4-95 0-13 205 0-14 204 0-08 329 17. 18. 19 44I 8 28/ 17-30 4-60 0-11 288 0-16 159 0-11 336 18. 19. 21 6\ 9 32/ 21 59 17-14 5-20 0-11 195 0-07 252 0-07 187 19. 17-26 5-20 0-11 339 0-13 170 0-10 274 20. 10 23 20. 22 46 17-15 5-61 0-18 121 0-09 306 0-05 122 21. 11 3 21. 23 19 17-10 6-04 0-22 125 0-06 146 0-04 291 22. 11 37 22. 23 54 17-11 6-02 0-19 76 0-25 165 0-14 310 23. 12 13 - ON THE COASTS OF IRELAND. 85 expressed by the formula Ao+C\sin/»+C2sin(2/?+e^) + C.,sin(37?+c.^)-|-C4sin(4p+c4). Analysed time of higl , 1 1 water, corre si)onding to | Ag. C,. Co. Ca- Ca- ^3- C4. e^. P = 30°. 1 1842. li m ft. ft. ft. ft. ft. July 24. 0 32 16-97 6-07 0-04 lf 0-28 176 0-08 20 24. 12 51 25. 1 10 17-24 5-99 0-25 107 0-38 180 0-14 251 25. 13 20 26. 1 29 16-99 6-05 0-06 143 0-16 143 0-05 276 26. 13 46 27. 2 2 16-94 5-70 0-36 121 0-16 214 005 130 27. 14 20 28. 2 37 17-11 5-24 0-27 106 0-02 239 0-06 228 28. 29. 15 5 3 25 1 17-02 5-01 0-28 B& 0-16 162 0-05 244 29. 30. 15 45 4 5 1 16-94 4-60 0-27 150 0-12 77 0-06 261 30. 31. 16 41 5 14 1 16-81 3-96 0-18 227 0-12 151 0-10 238 31. August 1. 17 38 6 17 } 16-99 3-68 0-14 203 0-13 195 0-05 280 1. 2. 18 59 7 31 1 17-29 3-85 0-06 295 0-07 234 0-03 193 2. 3. 20 12 8 51 I 17-38 4-29 0-12 128 0-04 167 0-01 174 3. 4. 21 16" 9 35 [ 17-49 16-95 5-23 0-08 125 0-05 186 0-04 133 4. 22 17 6-06 0-52 230 0-15 236 0-08 106 5. 10 33 5. 22 48 17-44 6-99 0-24 108 0-08 70 0-06 130 6. 11 6 6. 23 24 17-53 7-78 0-30 102 0-06 72 0-05 135 7. 11 48 8. 0 12 17-16 8-03 0-31 123 0-07 153 0-10 178 8. 12 35 9. 0 57 17-18 8-10 0-03 113 0-17 305 0-10 345 9. 13 16 10. 1 34 17-37 7-76 0-34 109 0-11 85 0-10 113 10. 14 2 11. 2 30 17-54 6-91 0-63 87 0-19 185 0-10 327 11. 12. 14 481 3 lOj > 17-26 6-39 0-32 140 0-24 103 0-09 186 12. 13. 15 48' 4 l6j ' 17-27 5-34 0-28 88 0-19 148 0-10 339 13. 14. 16 56' 5 31 J . 17-36 4-64 0-57 103 0-14 227 0-03 41 14. 15. 18 6' 6 51 J . 17-16 3-99 0-35 122 . 0-14 135 0-05 81 15. 16. 19 46' 8 23 \ 17-11 4-21 0-28 71 0-10 253 0-05 27 16. 17. 20 53' 9 23, > 17-48 466 0-26 112 0-12 350 0-06 11 17. 21 50 17-23 4-97 0-19 142 0-03 177 0-05 266 18. 10 11 18. 22 32 , 17-50 5-70 0-18 96 0-04 121 0-12 45 19. 10 45 19. 22 57 17-70 5-92 0-43 100 0-10 183 0-08 56 20. 11 11 20. 23 24 16-85 6-20 0-19 324 0-19 178 0-04 245 21. 11 42 22. 0 0 16-76 6-27 0-22 108 0-26 171 0-07 296 22. 12 15 23. 0 29 17-16 6-59 0-18 124 0-09 325 0-02 238 86 MR. AIRY ON THE LAWS OF THE TIDES Height of the Water in each individual tide at Kingstown, excluding diurnal tide. Analysed time of high water, corres )onding to Ao. C,. C2. Cj. C3. <^3- €,. C4. jo = 90°. 1842. h m ft. ft. ft. 0 ft. ft. Jane 22. 23. 23 21\ 11 52/ 17-99 4-91 0-33 147 0-06 258 0-06 160 24. 0 11 18-14 4-70 0-35 149 0-03 39 0-01 31 24. 12 28 25. 0 45 18-12 4-69 0-31 147 O-02 129 0-05 132 25. 13 3 26. 1 21 17-72 4-56 0-38 153 G-08 351 0-03 72 26. 13 43 27. 2 4 17-35 4-19 0-33 146 0-02 253 0-03 197 27. 28. 14 281 2 40/ 15 oi 3 29/ 17-24 4-14 0-26 152 O-05 238 0-02 33 28. 29. 17-42 3-84 0-27 154 5-Q4 153 0-04 141 29. 30. 15 50l 4 15/ 17-31 3-48 0-25 83 0-06 144 0-04 8 30. July 1. 16 45l 5 10/ 17-48 3-18 0-23 178 0-03 189 0-02 89 1. 2. 17 47I 6 10/ 17-50 2-95 0-25 177 0-06 202 0-04 200 2. 3. 18 44I 7 17/ 17-60 3-04 0-17 196 0-02 273 0-00 264 3. 4. 19 511 8 18/ 18-18 3-21 0-18 195 0-04 216 0-01 40 4. 5. 20 43 1 9 16/ 17-86 3-65 0-16 182 0-01 148 0-03 184 5. 6. 21 39 \ 10 5/ 22 20 17-18 4-19 0-25 171 0-02 17 0-01 4 6. 17-55 4-66 0-31 159 o-oe 70 0-04 158 7. 10 39 7. 22 57 17-87 5-13 0-35 151 0-06 33 0-03 164 8. 11 21 8. 23 45 17-53 5-61 0-43 147 0-05 304 0-02 115 9. 12 6 10. 0 27 17-69 5-68 0-50 134 0-06 314 0-04 104 10. 12 54 11. 1 20 18-04 5-88 0-36 146 0-09 47 0-04 113 11. 13 43 12. 2 5 17-37 5-52 0-44 138 0-03 340 0-02 342 12. 14 32 13. 2 58 17-40 5-13 0-33 143 0-05 55 0-03 160 13. 14. 15 31 \ 3 56/ 17-19 4-88 0-43 143 0-04 17 0-04 229 14. 15. 16 331 5 l| 17-07 4-35 0-38 155 0-02 334 0-02 289 15. 16. 17 '381 6 12/ 17-50 3-86 0-30 164 0-02 229 0-02 196 16. 17. 18 51 1 7 21/ 19 571 8 41/ 21 9 17-70 3-66 0-27 180 0-01 312 0-03 128 17. 18. 17-70 3-63 0-27 175 0-01 337 0-03 190 18. 17-53 3-76 0-28 174 0-03 122 , 0-04 151. 19. 9 37 t ► 19. 22 5 17-58 4-08 0-28 165 0-05 214 0-05 348 20. 10 25 20. 22 45 17-34 4-32 0-35 165 0-01 211 0-02 48 21. 11 4 21. 23 23 17-34 4-59 0-37 152 0-05 269 0-03 140 22. 11 .39 22. 23 54 17-22 4-76 0-34 149 0-02 39 0-02 53 23. 12 10 ON THE COASTS OF IRELAND. expressed by the formiilaAo+CiSin/)-i-C2sio(2/?-f C2)+C3sin(3/>+ 87 c.O+C. sin (4^+04). Analysed time of high water, corresponding to Ao- Ci. C2. C.2. C3. «'3- C4. C4. jt; = 90°. 1842. h m ft. ft. ft. ft. ft. July 24. 0 26 17-27 474 0-33 145 0-05 85 0-O4 159° 24. 12 42 25. 0 58 17-17 4-66 0-36 142 0-06 8 0-05 91 25. 13 14 ! 26. 1 30 17-27 4-48 0-29 148 «H)3 88 0-05 229 26. 13 48 27. 2 6 17-23 4-28 0-32 141 0-D5 537 0«04 23 27. 14 24 28. 2 42 17-24 3-98 0-25 144 0-03 177 0-02 7 28. 29. 15 31 3 23/ 17-16 3-71 0-18 150 fl-03. 328 0'03 116 29. 30. 15 47 1 4 7/ 17-17 3-39 0-25 160 0-03 169 004 142 30. 31. 16 41 1 5 14/ 17-12 3-01 0-22 160 0-04 279 0-06 141 31. Angust 1. 17 48l 6 27/ 19 si 7 40/ 17-19 2-86 0-27 189 0-01 108 0-0.2 70 1. 2. 17-48 3-08 0-11 214 0-05 214 0-03 65 2. 3. 2« 23 1 9 2/ 21 20 17-33 3-50 0-15 175 0-04 211 0-02 185 3. 4. 17-52 - 3-91 0-19 147 0-03 101 0-02 168 9 42 4. «2, 3 17-75 4-73 0-34 141 0-03 168 O1OO 187 5. 10 26 5. 22 48 17-59 5-39 0-34 148 0-04 40 O-Ol 174 6. 11 8 6. 23 28 17-70 5-91 0-44 135 0-07 14 010 133 7. 11 47 8. 0 6 17-38 6-39 0-49 130 0-07 536 0-07 90 8. 12 29 9. 0 51 17-62 6-31 0-50 124 0-01 309 0-08 108 9. 13 15 10. 1 40 17-61 6-05 0-33 141 0-07 6 0^05 47 10. 14 3 11. 2 26 17-50 5-47 0-46 133 0-02 320 0-03 179 11. 12. 15 7\ 3 29/ 17-56 4-91 0-46 154 0-08 22 0-10 212 12. 13. 15 55I 4 23/ 17-36 4-17 0-21 141 0-09 230 0-06 128 13. 14. 17 si 5 43/ 17-17 3-58 0-26 168 0-02 343 0-02 , 152 14. 15. 18 28l 7 13/ 17-22 3-24 0-19 178 0-05 274 0-04 182 15. 16. 19 54I 8 31/ 17-13 3-25 0-19 185 0-02 215 0-02 157 16. 17. 17. 20 57 1 9 27/ 17-63 3-58 0-20 157 0-04 217 0-01 127 ; 21 55 17-49 3-69 0-27 193 0-09 255 0-01 46 18. 10 12 18. 22 28 17-67 4-30 0-25 165 0-00 357 0-01 8 ■ 19. 10 41 19. 22 53 17-64 4-49 0-34 157 0-05 24 0-04 ; 210 20. 11 9 20. 23 25 17-37 4-81 0-34 144 0-01 269 0-01 314 21. 11 44 22. 0 3 16-84 4-94 0-28 147 0-05 308 0-06 103 22. 12 15 23. 0 26 17-42 4-92 0-31 143 0-05 57 0-03 104 88 MR. AIRY ON THE LAWS OF THE TIDES Height of the Water in each individual tide at Dunuiore East, excluding dinrnal tide. Analysed time of high water, con-esponding to ;» = 90°. Ao. Ci. c,. C2- C3. ^3- C4. C4. 1842. h in ft. ft. ft. ft. ft. June 22. 23. 17 37"! 5 55/ 16-29 5-30 0-23 16 0-07 82 0-04 239 23. 24. 18 21 1 6 45/ 18 53 16-38 5-32 0-07 346 0-15 115 0-06 232 24. 16-23 5-12 0-13 321 0-14 126 0-03 263 25. 7 12 16-37 5-07 0-06 306 0-17 146 0-08 166 25. 19 31 16-25 5-16 0-11 327 0-12 89 0-03 314 26. 7 47 16-02 4-98 0-13 2 0-14 99 0-06 215 26. 20 5 15-71 4-98 0-10 340 0-17 107 0-01 158 27. 8 22 15-75 4-88 0-14 5 0-14 75 0-06 273 27. 20 36 15-69 4-62 0-07 49 0-18 97 0-05 250 28. 8 52 15-73 4-43 0-07 11 0-20 74 0-03 206 28. 21 17 15-84 4-28 0-06 17 0-17 89 0-02 320 29. 9 33 15-74 4-07 0-07 322 0-18 95 0-06 250 29. 21 50 15-88 3-98 0-08 9 0-14 80 0-02 207 30. 10 14 15-90 3-80 0-09 356 0-13 102 0-07 165 30. 22 24 15-84 3-56 0-10 341 0-07 113 0-03 267 July 1. 10 57 15-85 3-40 0-09 347 0-08 134 0-03 67 1. 23 22 15-81 3-19 0-12 345 0-08 129 0-01 142 2. 11 51 15-76 3-13 0-04 336 0-08 142 003 259 3. 0 39 16-28 3-08 0-18 13 0-08 115 0-02 131 3. 13 17 4. 1 54 16-63 3-50 0-10 28 0-09 153 0-03 213 4. 14 26 5. 2 57 16-04 3-93 0-07 67 0-02 190 0-04 194 5. 15 20 6. 3 43 15-58 16-06 4-52 5-38 0-09 0-15 360 44 0-09 0-16 114 129 0-03 0-04 244 25 'VV 8. 17 31 5 21/ 8. 9. 17 49 1 6 9/ 15-93 5-81 0-20. 3 0-15 106 0-02 268 9. 10. 18 30 ! 6 54/ 16-00 6-21 0-12 15 0-18 90 0-02 224 10. 11. 19 12/ 7 36/ 20 2l 8 25/ 20 48 16-41 6-21 0-26 10 0-18 105 0-06 208 11. 12. 15-73 6-00 0-15 16 0-22 97 0-01 32 12. 15-64 5-69 0-12 15 0-24 105 0-05 242 13. 9 12 13. 21 36 15-36 5-08 0-17 339 0-14 114 0-02 134 14. 10 4 14. 22 31 15-51 4-52 0-18 6 0-14 114 0-05 294 15. 10 56 15. 23 22 16-02 3-92^ 0-21 2 012 115 0-04 338 16. 11 58 17. 0 34 16-20 3-55 0-19 3 0-07 136 0-03 262 17. 13 15 18. 1 55 16-11 3-62 0-10 48 0-12 151 0-03 141 18. 14 29 19. 3 3 16-05 4-10 0-08 36 0-08 88 0-01 49 19. 20. 15 33/ 4 0/ 16 25/ 4 43/ 16-05 4-45 0-15 15 009 127 0-01 119 20. 21. 15-78 4-80 0-21 6 0-11 118 0-03 165 21. 22. 17 15/ 5 31/ 15-83 5-13 0-19 27 0-12 109 003 97 22. 23. 17 53/ 6 10/ 15-73 5-31 0-15 39 0-17 91 0-02 272 ON THE COASTS OF IRELAND. 89 expressed bythe formula Ao+C\sin;?+C2sin(2j[?+C2)+C3 sin (3/>4-C;j)+C4 sin (4;?-fc4). Analysed time of high water, corresponding tc Afl. c,. Co. Cj.. C3. = 90^ 1842. h m ft. ft. ft. ft. ft. July 23. 18 22' 24. 6 38 J > 15-72 5-39 0-18 13 0-14 96 0-08 0 141 24. 18 55^ 25. 7 15 > 15-82 5-35 0-13 17 0-19 76 0-05 244 25. 19 30' 26. 7 47 > 15-77 5-21 0-19 31 0-21 47 0-08 316 26. 20 2 '' 27. 8 18^ ► 15-65 15-57 4-90 0-12 339 0-15 95 0-05 284 27. 20 33' 4-62 0-14 8 0-18 91 0-03 213 28. 8 49 28. 21 5 15-54 4-22 0-20 322 0-21 93 0-02 254 29. 9 22 29. 21 39 15-66 3-86 0-10 352 0-13 84 0-05 191 30. 10 4 30. 22 28 15-51 3-33 0-18 328 0-09 116 0-04 9G 31. 11 2 31. 23 36 15-64 2-92 0-11 3 0-01 125 0-02 285 August 1. 12 22 2. 1 7 15-89 2-90 0-13 7 0-05 196 0-03 147 2. 13 50 3. 2 33 15-72 3-55 0-08 107 0-04 143 0-06 269 3. 15 71 4. 3 39 J ' 15-69 ' 15-87 4-29 0-08 50 0-11 109 0-04 52 4. 16 13' 5. 4 33 J 5-00 012 23 0-20 105 0-08 347 5. 16 571 6. 5 21 I > 15-91 5-90 0-17 10 0-12 95 0-08 176 6. 17 49 1 7. 6 9J . 15-93 6-40 0-14 22 0-16 100 0-01 133 7. 18 34" 8. 6 57 J ■ 15-86 6-60 0-10 343 0-20 68 0-10 40 8. 19 20' 9. 7 41 • 15-99 6-68 0-09 6 0-23 80 0-11 5 9. 20 4 16-00 6-51 0-10 346 0-21 108 0-01 37 10. 8 24 10. 20 44 15-68 5-92 0-14 358 0-27 107 0-04 29 11. 9 4 11. 21 24 15-72 5-33 0-22 5 0-22 93 0-02 140 12. 9 47 12. 22 10 15-53 4-46 0-02 6 0-23 101 0-02 322 13. 10 37 13. 23 3 15-39 3-64 0-18 329 0-13 128 0-01 50 14. 11 42 15. 0 21 15-56 3-06 0-14 10 0-08 137 0-01 84 15. 13 6 16. 1 51 15-57 3-23 0-09 14 0-07 167 0-02 131 16. 14 30 17. 3 9 16-00 3-80 0-10 17 0-08 108 0-03 158 17. 15 301 18. 4 OJ - 16-03 4-31 0-22 0 0-12 127 0-05 120 18. 16 221 19. 4 43 j 16-15 4-85 0-06 71 0-23 57 0-10 235 19. 17 5] 20. 5 19] 15-94 5-03 0-10 353 0-12 120 0-04 219 20. 17 40 1 21. 5 56 J 15-77 5-38 0-08 347 0-15 95 0-07 203 21. 18 161 22. 6 28/ 15-46 5-60 0-14 356 0-18 84 0-03 257 22. 18 41 1 23. 6 59/ 16-00 5-59 0-06 26 0-23 80 0-03 326 MDCCCXLV. ] V 90 MR. AIRY ON THE LAWS OF THE TIDES Height of the Water in each individual tide at New Ross, excluding- diurnal tide. Analysed time of high water, corresponding to Ao- c,. Cg. Co. Cg. ^3- Gi- Cj. jO=:90°. 1842. h m ft. ft. ft. ft. 0 ft. 0 June 22. 18 141 23. 6 36/ 17-32 5-88 0-05 350 0-31 93 0-01 259 23. 18 55 1 24. 7 23/ 17-47 5-85 0-40 350 0-34 92 017 140 24. 19 44 1 25. 7 54 / 17-47 3-65 0-29 340 0-40 108 0-04 107 25. 20 13 1 26. 8 27/ 16-80 5-61 0-61 342 0-22 100 0-05 104 26. 20 51 16-57 5-43 0-43 334 0-32 101 0-02 58 27. 9 6 27. 21 21 16-61 5-18 0-37 334 0-27 91 0-01 322 28. 9 38 28. 21 54 16-57 4-83 0-32 329 0-23 87 0-03 300 29. 10 14 29. 22 33 16-53 4-50 0-37 343 0-25 89 0-11 114 30. 10 52 30. 23 10 16-55 4-25 0-27 328 0-15 85 0-03 10 July 1. 11 39 2. 0 7 16-50 3-75 0-30 331 0-17 89 0-02 69 2. 12 42 3. I 18 16-96 3-69 0-26 354 0-19 91 0-01 222 3. 13 64 4. 2 29 17-56 3-96 0-13 327 0-13 104 0-05 25 4. 14 541 5. 3 35/ 17-19 4-34 0-25 350 0-17 99 0-03 158 5. 16 I4l 6. 4 45/ 16-30 5-00 0-33 355 0-23 107 0-05 137 6. 17 hI 7. 5 41/ 16-94 5-48 0-44 355 0-28 99 0-07 109 7. 18 3l 8. 6 21/ 17-11 5-88 0-51 341 0-39 97 0-03 106 8. 18 58 1 9. 7 18/ 9. 19 49 16-86 6-22 0-52 339 0-36 109 0-04 116 17-03 6-43 0-53 346 0-38 104 0-07 131 10. 8 8 10. 20 28 17-74 6-39 0-31 343 0-37 93 0-06 108 11. 8 54 11. 21 19 17-04 6-34 0-66 344 0-35 99 0-06 56 12. 9 43 12. 22 7 16-97 613 0-56 348 0-38 92 0-09 97 13. 10 29 13. 22 48 16-39 5-67 0-49 341 0-30 95 0-03 104 14. 11 12 14. 23 36 16-23 5-18 0-46 336 0-24 100 0-02 63 15. 12 2 16. 0 27 16-81 4-67 0-39 343 0-26 96 0-01 327 16. 12 55 17. 1 23 16-98 4-24 0-31 342 0-21 123 0-02 312 . 17. 14 6 18. 2 49 16-92 4-25 ; 0-30 ; 358 0-18 103 0-01 246 18. 15 271 19. 4 0/ 16-79 4-ei : 0-42 347 0-16 100 0-00 270 19. 16 37I 20. 5 4/ 16-79 5-08 0-40 . 3S2 0-21 104 0-02 352 20. 17 33i 21. 5 51/ 16-64 5-42 0-46 347 0-25 101 0-01 116 21. 18 I4I 22. 6 30/ 16-69 5-75 0-52 347 0*29 91 0-03 68 , 22. 18 531 23. 7 10/ 16-64 5-87 0-50 351 0-34 101 0-06 116 ON THE COASTS OF IRELAND. 91 expressed bytheforrnulaAQ-|-CiSin/?+C2sin(2/>+C2) -|-C3sm(3p-f-C3) +^'4^10(4 ^4-04). Analysed time of high water, corres p = d ponding to 0". Ao. Ci. Co. C2- C3. t-s- C4. «<• 1842. h m ft. ft. ft. ft. ft. July 23. 24. 19 271 7 43/ 16-59 5-93 0-51 351 0-31 93 0-10 109 24. 25. 19 581 8 18/ 16-59 5-92 0-54 351 0-35 89 0-07 98 25. 20 31 16-59 5-80 0-47 343 0-34 91 0-04 47 26. 8 46 26. 21 0 16-48 5-52 0-39 347 0-31 95 0-06 134 27. 9 15 27. 21 31 16-36 5-25 0-40 346 0-25 92 0-01 339 28. 9 45 28. 21 58 16-20 4-87 0-27 337 0-29 87 0-02 276 29. 10 15 29. 22 32 16-24 4-49 0-39 328 0-23 65 0-03 23 JJO. 10 51 30. 23 10 16-16 3-95 0-29 321 0-18 82 0-02 55 31. 11 41 August 1 . 0 12 16-35 3-58 0-32 329 0-13 90 0-01 242 1. 12 54 2. 1 36 16-66 3-47 0-27 14 0-15 104 0-06 159 2. 14 23 3. 3 10 16-40 4-17 0-20 6 0-13 94 0-05 227 3. 4. 15 421 4 21/ 16-50 4-90 0-30 352 0-21 97 0-02 70 4. 5. 16^4 1 5 14/ 16-82 5-61 0-43 341 0-35 85 0-02 314 5. 6. 17 57I 6 21/ 16-78 6-30 0-59 348 0-35 101 0-07 101 6. 7. 18 47I 7 7/ 17-05 6-76 0-58 351 0-39 100 0-07 90 7. 8. 19 34I 7 57/ 20 27 17-15 6-89 0-59 353 0-41 91 0-05 79 8. 17-13 6-95 0-68 348 0-42 98 0-12 92 9. 8 43 9. 20 59 17-14 6-81 0-63 349 0-49 93 0-16 113 10. 9 21 10. 21 42 16-77 6-31 0-59 342 0-39 106 0-09 85 11. 9 58 11. 22 15 16-88 5-86 0-49 340 0-39 101 0-06 132 12. 10 36 12. 22 57 16-33 5-09 0-41 336 0-26 99 0-03 66 13. 11 22 13. 23 46 16-10 4-26 0-37 323 0-17 103 0-05 34 14. 12 22 15. 0 58 16-26 3-70 0-25 343 0-17 105 0-05 301 15. 13 44 16. 2 30 16-28 3-82 0-24 347 0-14 100 0-01 122 16. 17. 15 141 3 44/ 16-52 4-20 0-27 343 0-13 122 0-04 43 17. 18. 16 I5I 4 47 J 16-63 4-91 0-35 358 0-23 80 0-09 141 18. 19. 17 111 5 32/ 16-87 5-39 0-38 348 0-28 95 0-05 164 19. 20. 17 57I 6 11/ 16-83 5-52 0-39 339 0-26 108 0-04 185 20. 21. 18 35 1 6 51/ 16-59 5-96 0-56 347 0-35 93 0-08 69 21. 22. 19 I2I 7 24/ 16-18 6-03 0-50 344 0-39 97 0-08 110 22. 23. 19 33 1 7 51/ 16-84 6-09 0-48 352 0-34 92 0-01 144 n2 92 MR. AIRY ON THE LAWS OF THE TIDES Height of the Water in each individual tide at Passage West, excluding diurnal tide, Analysed time of high water, corresponding to K €,. c,. C2- ' C3. (-3' C4. C4. jw=90°. 1842. h m ft. ft. ft. 0 ft. 0 ft. 0 June 24. 19 61 25. 7 16/ 16-13 15-52 5-37 5-02 0-36 0-31 279 290 0-06 0-12 104 80 0-03 0-03 92 68 '26." ' 20* ' 6 1 27. 8 25/ 27. 20 43 1 28. 93/ 28. 21 23 1 29. 9 40/ 15-55 4-64 0-32 289 0-11 60 0-03 122 15-53 4-30 0-31 295 0-16 70 0-01 58 29. 23 4 1 30. 10 34/ 30. 23 20 15-62 3-91 0-33 305 0-06 67 0-02 94 15-69 3-73 0-23 301 0-07 116 0-01 6 July 1. 11 33 1. 23 46 15-64 3-46 0-26 316 0-10 97 0-03 129 2. 12 23 3. 0 59 16-11 3-38 0-25 358 0-08 158 0-08 298 3. 13 32 4. 2 4 16-40 3-73 0-20 331 0-03 157 0-03 109 4. 14 34 5. 3 4 15-73 4-20 0-14 312 0-03 123 0-03 83 5. 15 361 6. 4 6/ 15-34 4-65 0-19 300 0-07 101 0-03 74 6. 16 32 1 7. 4 59/ 15-92 5-11 0-21 331 0-07 102 0-07 69 7. 17 22I 8. 5 40/ 15-76 5-70 0-28 310 0-09 92 0-01 88 8. 18 8l 9. 6 28/ 15-63 6-03 0-36 299 0-10 131 0-05 31 9- 18 52 1 10. 7 16/ 16-01 6-25 0-25 284 0-13 38 0-02 353 10. 19 36 1 11. 8 0/ 16-38 6-38 0-27 308 0-06 102 0-09 103 11. 20 28i 12. 8 51/ 12. 21 15 15-72 6-21 0-32 307 0-12 98 0-07 89 15-52 5-96 0-36 309 0-20 80 0-10 64 13. 9 39 13. 22 3 15-32 5-36 0-30 309 0-17 84 0-06 64 14. 10 31 14. 22 58 15-39 4-86 0-36 313 0-14 99 0-04 106 15. 11 28 15. 23 58 16-05 4-31 0-34 327 0-11 108 0-02 75 16. 12 32 17. 1 6 16-13 3-91 0-28 307 0-06 118 0-04 71 17. 13 45 18. 2 23 16-09 3-99 0-22 331 0-05 130 0-01 38 18. 14 57 19. 3 31 15-96 4-41 0-26 315 0-10 75 0-04 132 19. 15 591 20. 4 26/ 16-01 4-69 0-31 332 0-06 105 0-03 52 20. 16 51 1 21. 5 9/ 15-71 5-08 0-38 315 0-10 101 0-02 71 21. 17 31 1 22. 5 47/ 15-79 5-38 0-35 307 0-07 102 0-05 91 22. 18 6i 23. 6 23/ 15-68 5-53 0-33 301 0-09 72 0-01 36 ON THE COASTS OF IRELAND. 93 expressed by the formula A()+CiSinj»+C2siii(2/>H-C2)-|-C3sin(3/>+C3) +€48*111 (4/?+ cj. Analysed time of high water, corresponding to Ao. Ci. ^2* C2. C3- C3. C4. Cj. p = { )0°. 1842. h m ft. ft. ft. ft. ft. July 23. 24. 18 391 6 55/ 15-73 5-61 0-33 291 0-07 60 0-04 0 173 24. 25. 19 71 7 27/ 15-75 5-58 0-30 293 0-14 48 0-07 94 25. 26. 19 39 1 7 56/ 15-66 5-34 0-28 288 0-08 67 0-08 103 26. 27. 20 12"! 8 28/ 15-60 5-08 0-34 287 0-13 82 0-02 238 27. 28. 20 441 8 59/ 15-41 4-73 0-29 291 0-12 65 0-04 79 28. 21 18 15-54 4-48 0-26 291 0-17 51 0-04 58 29. 9 37 29. 21 55 15-57 3-98 0-28 303 0-14 73 0-00 28 30. 10 21 30. 22 46 15-45 3-53 0-29 302 0-08 104 0-02 325 31. 11 19 31. 23 51 15-65 3-25 0-25 329 0-07 108 0-03 343 August 1. 12 33 2. 1 15 15-86 3-30 0-14 357 0-07 173 0-00 262 2. 13 58 3. 2 40 15 8l 3 40/ 15-65 3-91 0-12 312 004 55 0-01 213 3. 4. 15-52 4-59 0-23 316 0-10 150 0-03 70 4. 5. 16 13 1 4 33/ 15-67 5-29 0-29 316 0-10 135 0-03 91 5. 6. 17 11 5 25/ 15-79 6-12 0-25 298 0-06 111 0-08 86 6. 7. 17 50l 6 10/ 15-79 6-62 0-21 299 0-09 106 0-09 88 7. 8. 18 341 6 57/ 15-78 689 0-30 294 0-08 110 0-06 37 8. 9. 19 191 7 40/ 15-95 6-93 0-30 275 0-04 140 0-09 34 9. 10. 20 21 8 26/ 15-89 6-63 0-29 289 0-11 75 0-04 38 10. 20 46 15-64 6-20 0-36 297 0-15 79 0-06 46 11. 9 7 11. 21 28 15-68 5-60 0-28 298 0-17 77 0-11 100 12. 9 54 12. 22 20 15-43 4-72 0-35 312 0-15 83 0-04 131 13. 10 51 13. 23 21 15-31 3-90 0-37 314 0-11 91 0-02 25 14. 12 1 15. 0 40 15-46 3-50 0-26 343 0-10 134 0-07 30 15. 13 23 16. 2 6 15-58 3-60 0-19 329 0-05 158 0-05 24 16. 14 40 17. 3 13 15-84 4-14 0-22 317 0-05 90 0-03 33 17. 18. 15 441 4 14/ 15-99 4-47 0-23 339 0-08 50 0-06 152 18. 19. 16 27I 4 48/ 16-01 5-02 0-25 312 0-11 73 0-04 99 19. 20. 17 101 5 24/ 15-80 5-30 0-34 311 0-08 96 009 69 20. 21. 17 401 5 56/ 15-65 5-60 0-27 296 0-05 44 0-08 73 21. 22. 18 I4I 6 26/ 15-31 5-80 0-33 291 0-07 64 0-08 51 22. 23. 18 40l 6 58/ 15-83 5-78 0-28 295 0-10 63 0-09 54 04 Height of the Water MR. AIRY ON THE LAWS OF THE TIDES in each individual tide at Castle Townsend, excluding diurnal tide. Analysed time of high water, corre spending to Ao. Ci. c,. Co. C3. <'3- C,. C4. v=' )0°. 1842. h m ft. ft. ft. 0 ft. ft. June 22. 23. 17 11 5 20/ 15-86 4-31 0-15 283 0-07 208 0-02 0 170 23. 24. 17 45I 6 10/ 15-77 4-49 0-17 276 0-02 77 0-05 277 24. 25. 18 36 1 6 46/ 15-72 4-21 0-27 266 0-07 259 0-03 13 25. 19 7I 7 21/ 15-41 4-15 0-21 271 0-03 239 0-03 203 26. 27. 19 4l1 8 0/ 20 20 1 8 40/ 15-21 3-98 0-23 292 0-02 18 0-02 0 0 27. 28. 15-20 3-65 0-17 277 0-04 243 0-01 309 28. 29. 21 0I 9 17/ 15-30 3-37 0-16 315 0-06 51 0-13 63 29. 30. 21 40 1 10 10/ 22 39 1 11 8/ 23 37 15-43 3-11 0-16 306 0-04 269 0-02 182 30. July 1. 15-29 2-83 0-19 317 0-05 315 0-02 147 1. 15-44 2-70 0-16 323 0-01 221 0-02 266 2. 12 6 3. 0 35 15-92 2-80 0-04 259 0-09 263 0-04 338 3. 13 12 4. 1 48 16-04 3-01 0-15 345 0-14 295 0-02 35 4. 14 15 5. 2 42 15-42 3-37 0-17 299 0-07 328 0-04 190 • 5. 15 12 6. 3 41 15-16 3-85 0-12 312 0-08 259 0-09 31 6. 16 2 7. 4 24 15-42 15-27 4-34 5-06 0-17 0-19 276 296 0-06 0-06 344 265 0-01 0-06 61 294 8. 9. 17 351 5 55/ 9- 10. 18 I0I 6 34/ 15-34 5-06 0-37 325 0-17 203 0-07 34 10. 11. 18 59I 7 23/ 15-92 5-28 0-18 280 0-04 313 0-06 309 11. 12. 19 50l 8 13/ 15-35 5-11 0-27 296 0-04 274 0-04 106 12. 13. 20 42 1 9 6/ 15-12 4-77 0-24 269 0-05 264 0-09 256 13. 14. 21 32 1 9 59/ 14-85 15-77 4-32 3*47 0-26 0-17 287 262 0-06 0-11 222 285* 0-10 0-07 30 * *16 15. 23' 29 16. 12 6 17. 0 43 15-65 3-55 0-18 1 0-13 77 0-13 108 17. 13 22 18. 2 0 15-72 3-31 0-18 295 0-06 284 0-04 154 18. 14 33 19. 3 5 15-66 3-61 0-19 307 0-03 323 0-05 202 19. 15 32 20. 3 59 15-66 3-92 0-27 316 0-07 329 0-01 337 20. 21. 16 261 4 44/ 15-47 4-16 0-25 318 0-04 52 0-04 137 21. 22. 17 2I 5 18/ 17 35 1 5 52/ 15-59 4-31 0-17 303 0-08 237 0-03 243 22. 23. 15-41 4-40 0-23 281 0-05 116 0-01 184 ON THE COASTS OF IRELAND. 95 expressed bytheformulaAo+CiSinp4-C2sin(2j94-C2)+C3sin(37?+C3)-fC4sin(4p+cJ. Analysed time of high water, corresponding to 1 Ag. Ci. c,. C2- C3. fs- C4. C4. P = ?0^ 1842. h m ft. ft. ft. ft. ft. July 23. 24. 18 5" 6 21 ^ > 15-45 4-43 0-15 279 0-13 0 125 0-06 0 67 24. 25. 18 36^ 6 56 ' 15-43 4-43 0-31 281 0-06 179 0-05 351 25. 26. 19 14' 7 31 J r 15-39 4-27 0-18 293 0-08 307 0-03 .281 26. 27. 19 46] 8 2 > 15-38 4-04 0-23 293 0-04 233 0-08 7 27. 28. 20 I9I 8 34 J > 15-20 3-71 0-23 282 0-11 271 0-03 78 28. 29. 20 571 9 16 J ^ 15-36 3-42 0-33 295 0-07 227 0-14 122 29. 30. 21 40] 10 5J . 15-31 3-02 0-19 274 0-05 281 0-04 79 30. 22 39 15-29 2-71 0-20 318 0-01 90 0-07 118 31. 11 13 31. 23 46 15-41 2-58 0-15 322 0-01 224 0-01 247 August 1. 12 27 2. 1 7 15-61 2-70 0-07 354 0-06 311 0*02 359 2. 13 44 3. 2 20 15-43 3-20 0-08 332 G-01 110 0*02 221 3. 14 50 4. 3 20 15-34 3-87 0-03 295 0-03 146 0-06 52 4. 15 -45 5. 4 9 15-40 4-49 0-15 333 0-10 285 0-04 108 5. 6. 16 411 5 5/ 15-52 5-07 0-16 263 0-09 57 0-09 300 6. 7. 17 331 5 53/ 17 561 6 19/ 15-51 5-44 0-25 32 0-06 328 0-03 100 * • 7. 8. 15-47 5-70 0-24 299 0-19 231 0-12 349 8. 9- 18 37 1 6 58/ 15-65 5-80 0-30 282 0-07 323 0-04 300 9. 10. 19 261 7 50/ 15-59 5-41 0-29 277 0-07 163 0-01 315 10. 11. 20 13"! 8 39/ 15-49 4-90 0-25 318 0-14 284 0-07 295 11. 12. 21 91 9 32/ 15-33 4-34 0-20 301 0-09 326 0-03 348 12. 13. 21 58 1 10 31/ 23 7 15-22 3-60 0-21 294 006 283 0-02 216 13. 15-19 3-18 0-26 323 0-03 24 0-02 96 14. 11 50 15. 0 33 15-23 2-85 0-20 312 0-08 333 0-07 41 15. 13 13 16. 1 53 15-33 2-90 0-12 317 0-03 230 0-05 18 16. 14 28 17. 3 2 15-58 3-30 0-16 307 0-04 321 0-00 329 17. 15 27 18. 3 52 15-74 3-72 0-17 311 0-03 3 0-10 74 18. 16 10 19. 4 28 15-61 4-04 0-18 298 0-09 259 0-04 55 19. 20. 16 491 5 3/ 15-58 4-28 0-27 306 0-05 276 0-07 268 20. 21. 17 211 5 37/ 15-43 4-42 0-29 279 0-06 217 0-06 146 21. 22. 17 50 1 6 2/ 15-19 4-67 0-23 299 0-04 28 0-05 149 22. 23. 18 131 6 31/ 15-48 4-61 0-27 283 0-04 20 0-05 330 96 MR. AIRY ON THE LAWS OF THE TIDES Section XI. — Discussion of the height of mean water deduced from the analysis of in- dividual tides ; with reference to difference of station, and to variations of the phase of the moon, and of the declination of the moon. The mean heights (Aq) for each station, in the results of last section, were divided into groups corresponding to large tides and small tides, the dividing places being the same as those in section V., page 29, or following by two days the times when the moon's hour-angle from the sun was S*", 9*", lo*", 21''. The means for each group were taken, and then the mean of those means of groups belonging to large tides, and the similar mean for small tides. The results are the following, the numbers for Courtown being taken by anticipation from section XVII. : — Station. Mean height. Mean of mean heights. Excess of mean height in large tides above mean height in small tides. Small tides. Large tides. Kilbaha Kilrush Foynes Island .... Limerick Casleh Bay Galway Old Head MuUaghmore .... Buncrana Port Rush Carrovvkeel Ballycastle Glenarra Donaghadee .... Ardglass Clogher Head. . . . Kingstown Courtown Dunmore East . . New Ross Passage West .... Castle Townsend . ft. 15-58 16-36 17-06 17-38 17-90 17-47 17-69 18-03 17-33 17-60 17-96 17-40 17-65 17-76 17-65 17-20 17-44 16-63 15-80 16-58 15-71 15-45 ft. 15-72 16-52 17-29 17-92 18-06 17-65 17-90 18-23 17-47 17-83 18-17 17-63 17-83 17-89 17-78 17-32 17-49 16-67 15-86 16-89 15-78 15-45 ft. 15-65 16-44 17-18 17-65 17-98 17-56 17-80 18-13 17-40 17-72 18-07 17-52 17-74 17-83 17-72 17-26 17-47 16-65 15-83 16-74 15-75 15-45 ft. 0-14 0-16 0-23 0-54 0-16 0-18 0-21 0-20 0-14 0-23 0-21 0-23 0-18 0-13 0-13 0-12 0-05 0-04 0-06 0-31 0-07 0-00 ON THE COASTS OF IRELAND. 97 The first column which deserves attention is the " mean of mean heights." The progress of the numbers from Kilbaha to Limerick, as well as that from Dunmore East to New Ross, show well the change of mean height in ascending a river affected by current as well as by tide. Excluding these river stations, as also Buncrana and Carrowkeel, which partake in some measure of the same character, we have a view of the comparative mean heights of the sea on different parts of the coast of Ireland. And here we have the remarkable result, to which allusion has already been made, that the mean height of the sea round the northern half of the island, as referred to the surface of stagnant water, is considerably greater than that round the southern half of the island. The amount of this difference of height is believed by the officers who directed the levelling operations to be much greater than can be explained by any allowable error in the levelling. The heights on the eastern coast are also, per- haps, a little greater than those on the western coast. I profess myself entirely unable to explain on mechanical principles this result. In every instance except that of Castle Townsend, the mean height in large tides is greater than that in small tides. Further allusion will be made to this in the examination of the next table. I shall here only remark that I imagine this to be a possible result of the shallowness of the sea, though theory has not yet reached so far. MDCCCXLV. 98 MR. AIRY ON THE LAWS OF THE TIDES For the investigation of the effect of the moon's declination^ the same process in all respects was used as in Section V., pages 32 and 33, and the following are the re- sults : — Station. Mean height with small dechnation. Mean height with large declination. Excess of mean height with large declination above mean height with small declination. Mean height with decreasing declination. Mean height with increasing declination. Excess of mean height with de- creasing dechna- tion above mean height ^vith in- creasing dechna- tion. Kilbaha Kilrush Foynes Island. . . Limerick Casleh Bay Galway Old Head Mullaghmore . . . Buncrana Port Rush Carrowkeel Bally castle Glenarm Donaghadee . . . Ardglass Clogher Head . Kingstown Courtown Dunmore East . New Ross Passage West . . . Castle Townsend, ft. 15-61 16-40 17-15 17-68 17-94 17-54 17-71 18-07 17-37 17-68 17-97 17-47 17-68 17-79 17-69 17-21 17-41 16-60 15-80 16-74 15-70 15-42 ft. 15-66 16-46 17-18 17-57 18-00 17-58 17-81 18-15 17-42 17-70 18-12 17-59 17-76 17-85 17-73 17-29 17-50 16-67 15-88 16-68 15-77 15-47 ft. -fO-05 -fO-06 -fO-03 -0-11 .fO-06 + 0-04 -fO-10 + 0-08 + 0-05 -f 0-02 -fO-15 -f 0-12 + 0-08 -J- 0-06 -f-0-04 -fO-08 + 0-09 + 0-07 -j-0-08 -0-06 + 0-07 + 0-05 ft. 15-68 16-52 17-24 17-81 18-03 17-62 17-91 18-22 17-53 17-88 18-18 17-64 17-87 17-93 17-82 17-29 17-53 16-70 15-90 16-85 15-77 15-46 ft. 15-59 16-34 17-07 17-43 17-91 17-49 17-69 18-06 17-31 17-59 17-94 17-39 17-66 17-77 17-64 17-20 17-42 16-63 15-79 16-61 15-70 15-44 ft. + 0-09 + 0-18 + 0-17 + 0-38 + 0-12 + 0-13 + 0-22 + 0-16 + 0-22 + 0-29 + 0-24 + 0-25 + 0-21 + 0-16 + 0-18 + 0-09 + 0-11 + 0-07 + 0-11 + 0-24 + 0-07 + 0-02 Upon comparing the results of this Table with those of the Table on page 96, the remarks made in page 33 must, I think, be considered to be insufficiently founded. The excess found by classifying according to the magnitude of the tide is here de- cidedly greater than that found by classifying according to the moon's declination. In the river tides (from Kilbaha to Limerick, and from Dunmore East to New Ross) the excess classified by the magnitude of tide proceeds more regularly than that classified by moon's declination. I think also that the change for the stations on the narrow channel from Port Rush to Donaghadee inclines us to the supposition that the whole is due rather to the variation of magnitude than to the variation of declina- tion. The change of declination, being very slow, would probably produce the same sensible change in the mean level of the deep (though contracted) sea of the North Channel as in that of the Atlantic Ocean : though everything which depended in any way upon the tides might be very different. Perhaps however the change for these stations is not sufficiently decided to give great force to this argument. On the whole, I regard the origin of this inequality as yet subject to some doubt. The values of Aq at any one station differ, sometimes rapidly, from day to day. In order to examine these, I have subtracted from every value of Aq at each place the ON THE COASTS OF IRELAND. 99 mean of all the values of Aq at that place, and have set down the excess as an irregu- larity in the general height of the water at that place on that day. The numbers for Courtown are taken by anticipation from Section XVII. The results are contained in the following Table. With the view of ascertaining any possible connexion of these irregularities with the cause of the winds, I have set down in the last columns the character of the winds observed at the four stations Kilbaha, Port Rush, Kingstown, and Passage West, which may be considered as nearly equidistant on the coast. 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(N eo CO © © © + + + (N © + t^ CO © + +0-31 -0-03 -0-08 -0-31 © 1 © 1 +0-06 -0-03 © + © CO © + © © i -0-29 +0-27 (N © + S.2 E (N « © 1 6 1 Pi »ts © 1 -0-50 -0-36 -0-56 -0-49 -0-63 (N © 1 © + © 1 N us © © + + 8 © + 8 © © + PI 'to ^ Pi © © + 1 I-l T)< PI ep © © 1 i © © 1 9 © 1 pi PI © © 1 1 CO © + © CO © + .©«>.©ao®oop-<©pi©it>ico56©©©'©- (N(N(N(N»«lNIN(N»^NiN»usSCto©«>.©SO -1 PH Pi Pi Pi Pi I-l vJr5eo-^-^»f5"5toto<>t^ccco© ©oopi©pi©iNpieoi: (N (N (N^(Np-»Ap >i®eopiuscous-^ *USU5totot4»>^o6 -,piPHPif-ipi«pi to US «>. US CO to CO to© t^ pi pi p^ fff n" CO 9«(N &)(N 31. August 1. 2. ©©©npiNiNCOCO" 00© Si (N(N 102 MR. AIRY ON THE LAWS OF THE TIDES Upon inspecting these numbers, one law cannot fail to occur to us, namely, that the irregularities are nearly the same in magnitude and in sign on every part of the coast of Ireland at the same time. So prevalent is this law, tiiat there are few instances in which the irregularity at one place differs from the mean of the irregularities at all the places at the same time by more than an inch. My ideas of the almost perfect fluidity of water have been very much raised by this comparison. I may remark that it embodies, in a form admitting of easy examination, the result concluded from rough inspection of observations which is made the foundation of a method for supplying deficient observations described in page 10. I may also add that it gives no small security for the general fidelity and accuracy of the observers at the different stations. I do not perceive any certain connexion between the irregularities and the course of the winds, except that the water is usually highest on all parts of the coast with a violent south-west wind. In order to ascertain the general relation of these irregularities to those of the barometer, I have compared the corrected mean height of the barometer at Green- wich for each civil day with the mean height for the year (using the numbers pub- lished in the Greenwich Magnetical and Meteorological Observations). The follow- ing are the results : — Excess of the corrected mean he ight of the barometer each day, at Greenwich, above ( the mean height for the year 1842. in. in. in. in. in. in. June 23. —0-142 July 4. -0-226 July 15. + 0-378 July 26. + 0-042 Aug. 6. -0-033 Aug. 17. + 0-132 24. -0-251 5. — 0-232 16. + 0-174 27. + 0-187 .... 18. -0-041 25. — 0-234 6. + 0-129 17. .... 28. + 0-056 8. + 0-078 19. -0-067 26. .... 7. + 0-070 18. -0-118 29. -0-069 9. + 0-017 20. + 0-032 27. -fO-218 8. -0-216 19. -0-147 30. +0-083 10. -0-263 21. • * • • 28. + 0-268 9. — 0-271 20. -0-231 31. • • • • 11. -0-029 22. -0-023 29. + 0-097 10. .... 21. -0-189 Aug. 1. + 0-310 12. + 0-313 23. -0-064 30. —0-080 11. -0-288 22, + 0-064 2. + 0-164 13. + 0-443 July 1. -0-168 12. -0-046 23. + 0-235 3. -0-016 14. .... 2. —0-105 13. + 0-226 24. .... 4. —0-092 15. + 0-242 3. 14. + 0-388 25. -0-040 5. -0-036 16. + 0-207 I have also obtained, through the kindness of Sir W. R. Hamilton, the barometrical observations at the Observatory of Dunsink, near Dublin ; and from Colonel Colby and Captain Larcom, R.E., I have received the observations made in the Phoenix Park near Dublin, and at Limerick. The following results are obtained by com- paring each day's mean with the mean for this period. Excess of the mean height of the barometer each day, at Dublin, above the mean of all • Dun- Phoenix Dun- Phoenix Dun- Phoenix Dun- Phoenix Dun- Phoenix Dun- Phoenix sink. Park. sink, Park. sink. Park. sink. Park. sink. Park. sink. Park. in. in. in. in. in. in. in. in. in. in. in. in. Jane 2.3. -0-31 -0372 July 4. -0-53 -0-547 July 15. +0-35 +0-388 July 26. +0-19 +0164 Aug. 6. -0-04 -0-070 Aug 17. +0-09 +0-059 24. -0-42 -0-454 5. -0-22 -0-281 16. +004 +0076 27.+0-31 +0-302 7. -0-112 18. +0-01 -0K)13 25. -0-4D -0-534 6. +0-06 +0-173 17. -0-196 28. +0-20 +0-182 8. -0-08 -0-097 19. -0-17 -0-210 26. +0-06 -0-098 7. -0-22 -0-227 18. -0-13 -0-153 29.1+0-20 +0-173 9. -0-10 -O-lll 20. —0-08 -0-105 27. +0-31 +0-315 8. -0-38 1-0-500 19. -0-12 -0-165 30. +0-29 +0-284 10. -0-21 -0-258 21. +0-12 +0-115 28. +0-16 +0-148 9. —0-32 !— 0-365 20. -0-11 -0-147 31. +0-365 11. -001 -0-011 22. +0-17 +0-165 29. +013 +0120 10. -0-25 -0-180 21. +001 -0-006 Aug. 1. +0-32 +0-315 12. +0-17 +0-170 23. -007 -0079 30. +002 +0-022 11. -0-43 -0-485 22. +0-22 +0-205 2. +0-09 +0072 13. +0-42 +0-418 July 1. -010 -0-126 12. -0-09 -0-074 23. +0-30 +0-304 3. +0-10 +0-089 14. +0-445 2. -0-04 -0059 13. +0-14 +0-121 24. +0-200 4. -0-09 -0-110 15. +6-37 +0-342 3. -0-25 -0-108 14. +0-45 +0-443 25. +009 +0-061 5. -0-14 -0-176 16. +0-29 +0-284 ON THE COASTS OF IRELAND. 103 Excess of the mean height of the barometer each day, at Limerick, above the mean of all. June 23. in. -0-407 July 4. in. -0-543 July 15. in. + 0-365 July 26. in. + 0-182 Aug. 6. in. — 0-062 Aug. 17. in. + 0-058 24. -0-447 5. -0-169 16. —0-059 27. + 0-324 7. -0-169 18. -0-002 25. -0-535 6. + 0-212 17. -0-320 28. + 0-295 8. -0-171 19. -0-198 26. — 0-077 7. —0-217 18. -0-208 29. + 0-220 9. —0-152 20. -0115 27. + 0-360 8. — 0-514 19. -0-178 30. + 0-337 10. -0-267 21. + 0-099 28. + 0-178 9. -0-346 20. -0-132 31. + 0-381 11. -0-053 22. + 0-190 29. + 0-178 10. -0-191 21. + 0-030 Aug. 1. + 0-323 12. + 0-122 23. -0-069 30. + 0-039 11. -0-491 22. + 0-173 2. + 0-052 13. + 0-406 July 1. -0-072 12. -0-104 23. + 0-308 3. + 0-124 14. + 0-422 2. + 0-022 13. + 0-094 24. + 0-206 4. -0-051 15. + 0-360 3. -0-116 14. + 0-440 25. + 0-074 5. -0-162 16. + 0-301 The comparison of these numbers with the irregularities in the heights of the water amply supports the law of Daussy, Whewell, and Bunt, that a negative irregularity in the height of the barometer is accompanied by a positive irregularity in the height of the sea, twelve or fourteen times as great as that of the barometer. Section XII.-- — Discussion of range of tide, or coefficient of Jirst arc in the analysis of individual tides ; and of semimenstrual inequality in range, apparent proportion of solar and lunar effects, and age of tide as deduced from range. The tides were divided into groups of large tides and small tides, separated at the same times as those particularized in pages 29 and 96. For each of these groups the mean of the values of C^ was taken, some deficient values being supplied by interpo- lation. The moon's parallax and the square of the cosine of the moon's and sun's declinations were taken for two days preceding each tide, and the means of these quantities were taken through the same groups. A general result will be obtained by forming the sum of the mean values of C^ for all the stations in each group. Thus we obtain : — Large Tides. Period. Sum of mean values of Ci at all the stations. Mean value of cos^ moon's declination. Mean value of moon's parallax. Mean value of cos^ sun's declination. July 6. July 20. Aug. 5. h h 16 to July 13. 3 9 to July 28. 9 OtoAug.ll. 16 ft. 117-43 100-11 129-11 0-8742 0-9076 0-9260 / // 59 44 54 41 60 31 0-8547 0-8815 0-9194 Small Tides. Period. Sum of mean values of Cj at all the stations. Mean value of cos^ moon's declination. Mean value of moon's parallax. Mean value of cos^ sun's declination. June 28. July 13. July 28. Aug. 11. h h 6 to July 6.16 3 to July 20. 9 9 to Aug. 5. 0 l6toAug.l8. 15 ft. 71-66 84-63 73-40 77-84 0-9427 0-9202 0-8965 0-8697 / // 55 13 58 19 55 56 67 34 0-8456 0-8666 0-9012 0-9378 104 MR. AIRY ON THE LAWS OF THE TIDES Put M for the lunar effect when the square of the cosine of the moon's declination is 0*9 and her parallax is 57' ; m for the quantity by which this is increased for every increase of 1' in parallax ; s for the mean effect of the sun (the square of the cosine of his declination being 0*9) for one-fourth of a lunation, positive in the large tides and negative in the small tides, which bears to the absolute effect of the sun a rela- tion explained in page 34. The effect of the variations of the moon's parallax and declination upon the luni-solar tide, as is well known, is nearly the same as that on the simple lunar tide ; and therefore it will be correct to refer the mean of the luni- solar tides to the mean of the moon's parallaxes and square of cosine of declinations. The variations depending on the moon's declinations are not strictly in the propor- tion of the squares of the cosines of her declination, but in the present instance, where the means of the squares of the cosines are very nearly equal, may be assumed to be so without sensible error. Forming then an equation from each of the lines in the Table above by these considerations ; reducing them to four equations by retain- ing the second, taking the mean of the first and third, the mean of the fourth and sixth, and the mean of the fifth and seventh, and combining these so as to form three favourable equations, by adding all, by subtracting the sum of the third and fourth from the sum of the others, and by subtracting the sum of the second and third from the sum of the others, we obtain the following equations: — 377-15= Mx4-024-l-mX0-33-5X0008 69-61 = -Mx0008-i-mXl-29-F*X 3-938 31-87 = — M X 0-036-l-m X 7-83 — 5X 0-026. From these we obtain M = 93-4, m=4'56, *= 16*37. The moon's effect, therefore, for the parallax 57'+'^' niay be represented by 93-4-|-4-56X?2. If the moon's hydro- dynamical effect varied as the cube of her parallax (which is the law of variation of her statical effect), the formula would be 93-4-1-4-92 X n. The result of the movement of the water has therefore been, to reduce the elliptic variation of lunar effect by 0-36 , , 3 ^T^part, or by^part. Now it is shown in the Encyclopaedia Metropolitana, Tides and Waves, Art. 448, that if the tides were created by the effect of the moon on the water in a uniform channel surrounding the earth, and if h were the earth's radius, k the depth of the water, g the acceleration produced by gravity in the unit of time, w' the moon's appa- rent angular motion round the earth (as estimated by a spectator who supposes that the earth does not revolve on an axis), and h the moon's angular motion from her 4 Tih'^h perigee ; then the elliptic variation is changed by ^ * n^'^—ak V^^'^- 1 hus we obtain 4 rJb'^h _ _ 3 ^' n'^b--gk~~''4:l Makmg - = gg' we find ^^ = — = - nearly ; and « = 3 • -7— Observmg that lib ON THE COASTS OF IRELAND. |(^ = linear velocity of a point at the equator produced by the earth's rotation, supposing the moon fixed, we easily find =13 miles nearly ; and thus our observations give Depth of the sea =^=22 miles. If the channel were supposed to be a small circle of the earth instead of a large one, the resulting depth of the sea would be diminished in the proportion of the square of its diameter. Whatever may be supposed of the error of this result, or the inapplicability of the theory by which it is obtained to the circumstances of the seas, I may remark that it agrees generally with a result deduced from Mr. Whewells discussions of the obser- vations at Bristol with reference to the moon's declinations*. Assuming however that we have correctly determined — v—V ^® "^^y proceed to remark that-j- the moon's hydrodynamical effect is represented by her statical effect multiplied by ,_^,2^2 and by constants ; and that the sun's hydrodynamical effect is represented by his statical effect multiplied by 7._^2^2 and by the same constants. w^ 15 If we consider "72=14' then the hydrodynamical effect of the moon contains the multiplier i. JL_- J_ ^ . J_ ^ gk _^~gk2 ^^' gk lo' 5 while that for the sun contains the multiplier J_ 1 _ 1 .14 . J_ 28 gk \^^~gk 5 ^^ gk 10 14*5 And therefore the proportion of the moon's statical effect to the sun's is greater than the proportion of her dynamical effect to the sun's in the ratio of 28 to 25. And as the moon's hydrodynamical effect, deduced from the values of M and s above (93-4 and 16*37), by the considerations in page 34, is nearly =i^;^x sun's hydrodynamical effect, it follows that the moon's statical effect =^7^5 X sun's statical effect =4X sun's statical effect. This conclusion differs widely from Laplace's ; yet it is formed, as I believe^ on grounds as good as Laplace's. For particular results applying to each individual station, regarding the semi- menstrual inequality in range and the apparent proportion of the solar and lunar hydrodynamical effects ; the mean value of C\ for large tides is found by taking the mean of the three values in the three periods of the last Table, and the mean value for small tides by taking the mean of the four values in the four periods of the last * Tides and Waves, Art. 553. t Ibid. Art. 448. MDCCCXLV. P 106 MR. Amy ON THE LAWS OF THE TIDES Table ; and then treating these in the same manner as in the latter part of the table on page 35. Station. Mean of Cj for large tides. Mean of Ci for small tides. Difference. Mean, or M. Difference divided by mean. Corresponding g value of -— . M ft. ft. ft. ft. Kilbaha 6-12 3-73 2-39 4-93 0-48 0-40 Kilrush 6-54 4-19 2-35 5-37 0-44 0-36 Foynes Island. . . . 7-35 4-96 2-39 6-16 0-39 0-32 Limerick 8-98 6-21 2-77 7-59 0-37 0-30 Casleh Bay 6-35 3-83 2-52 5-09 0-50 0-42 Galway 6-41 3-89 2-52 5-15 0-49 0-41 Old Head 5-59 3-43 2-16 4-51 0-48 0-40 Mullaghmore .... 5-35 3-25 2-10 4-30 0-49 0-41 Buncrana 5-84 3-37 2-47 4-61 0-54 0-46 Port Rush 2-56 1-38 1-18 1-97 0-60 0-52 Carrowkeel 3-35 1-95 1-40 2-65 0-53 0-45 Ballycastle 1-42 0-88 0-54 M5 0-47 0-39 Glenarm 2-89 2-47 0-42 2-68 0-16 0-12 Donaghadee .... 5-24 3-96 1-28 4-60 0-28 0-22 Ardglass 6-90 4-96 1-94 5-93 0-33 0-26 Clogher Head . . 6-79 4-81 1-98 5-80 0-34 0-27 Kingstown 5-26 3-69 1-57 4-48 0-35 0-28 Dunmore East . . 5-73 3-91 1-82 4-82 0-38 0-31 New Ross 6-16 4-51 1-65 5-34 0-31 0-25 Passage West ... . 5-94 4-19 1-75 5-07 0-35 0-28 Castle Townsend. . 4-79 3-33 1-46 4-06 0-36 0-29 For the age of tide as inferred from range, the times have been ascertained (by interpolating between the times in the Tables of formulee in Section X.) at which the actual value of C^ may be supposed to coincide with the mean value of C^ ; and the. times thus found have been compared with the times at which the moon's hour-angle from the- sun was 3^ 9^ 15^ 21^ namely, June 26, 6^ July 4, 16^ July 1 1, 3^ July 18, 9^ July 26, 9^ August 3, 0\ August 9, 16^ and August 16, 15^. An error is here committed alternately -f- and — , and therefore it is proper to use an even number of comparisons. Eight are used at every place except Ballycastle and Glenarm, where only six are used. [It is to be remarked that in the use of the formulae in Section X., a number opposite to a bracket is always held to correspond to the mean of the two times embraced by that bracket.] Xhe means of all the differences at each station between the times thus found from Section X. and the times corresponding to the hour-angles 3'', 9^ &c., are adopted in the following Table as the age of the tide. These* are the true ages of the tide. station. Age of tide. Station, Age of tide. Station. . Age of tide. Kilbaha Kilrush Foynes Island. . . . Limerick Casleh Bay Galway Old Head d h 1 20 1 19 1 21 2 1 1 20 1 21 1 22 Mullaghmore .... Buncrana Port Rush Carrowkeel Ballycastle Glenarm Donaghadee .... d h 2 0 1 20 1 11 1 14 1 5 2 9 2 6 Ardglass Clogher Head . . Kingstown Dunmore East . . New Ross Passage West. . . . Castle Townsend.. d h 2 2 2 2 2 0 2 2 2 2 2 1 1 23 * Tides and Waves, Art. 545. ON THE COASTS OF IRELAND. 10: Section XIII. — Estahlishment of each port, as deduced from the time of majcimum of the first periodical term in the analysis of individual tides. The preceding operations having' made it sufficiently clear that the age of the tide differs little from two days, it is proper now to refer all the phenomena of the tide to an epoch two days earlier than the observation. A process is therefore adopted in this section differing in a trifling degree from that in Section VII. The times are taken at which the moon's hour-angle fiom the sun was 0'', 6^, 12'*, 18'', and two days are added to these times : the resulting times are June 24, 9^ July 2, 20^^, July 9, 19\ July 16, 21'', July 23, 23^ August 1, 16'', August 8, 4'', August 15, 5'', August 22, 16''. These times are assumed to divide the large lunitidal intervals from the small ones. For the lunitidal intervals at the high waters of the First Division, the moon's time of Greenwich transit is taken for that transit which precedes the high water by two days and a few hours ; for the high waters of the Second Division the moon's time of Greenwich lower transit is interpolated. Comparing these times of transit with the times of high water in the formulae of Section X., the lunitidal intervals correspond- ing to lunar transits two days earlier are found. The means of these are taken for the groui>s separated by the times specified above. Then, the means of the large and the small lunitidal intervals being adopted as the mean interval, a correction of !'» 41°' is applied subtractively, to reduce the interval after moon's transit two days pre- vious, to the interval after moon's transit on the same day as the tide (l'' 41™ being the difference between two solar days and two lunar days). The result is contained in the following Table. Station. Kilbaha Kilrush Foynes Island. , . Limerick Casleh Bay Gahvay Old Head Mullaghmore . . . Buncrana Port Rush Carrowkeel Ballycastle Glenarm Donagliadee . . . Ardglass Cloglier Head . Kingstown Dunmore East . New Ross Passage West . . . Castle Townsend Mean of large intervals from transit two days previous. m 53 6 49 8 19 7 3 8 19 39 27 4 48 4 7 7 7 8 9 9 10 12 53 13 10 13 14 13 21 13 26 7 14 8 5 26 3 Mean of small intervals from transit two days previous. 55 7 54 27 3 9 23 37 21 50 8 44 9 2 12 3 12 16 12 16 12 24 12 30 16 11 31 5 Mean of all the intervals from transit two days previous. True establishment in Greenwich time. h 6 6 7 7 6 6 6 7 7 8 9 9 12 28 12 43 12 45 12 52 12 58 6 45 7 38 6 58 6 34 24 36 21 53 33 38 51 8 54 27 16 33 43 55 40 12 52 57 10 27 6 13 6 46 7 35 7 52 10 47 11 2 11 4 11 11 11 17 5 4 57 17 53 p2 jioa MR. AIRY ON THE LAWS OF THE TIDES Section XIV. — Semimenstrual inequality in time, proportion of solar and lunar effects from times, and apparent age of tide as shown hy times ; deduced from the time of maximum of the first periodical term in the analysis of individual tides. Taking the difference of the means of large intervals and small intervals in the last S Table, we deduce from them the value of y^ by the same formula as that employed in page 42. The results are as follows : — station. Difference of means of large intervals and small intervals. Value of S M' Station. Difference of means of large intervals and small intervals. Value of S M" Kilbaha . „ Kilrush Foynes Island. . . . Limerick Casleh Bay Galway Old Head Mullaghmore .... Buncrana , Port Rush Carrowkeel m 58 59 55 52 60 59 56 62 66 74 64 0-37 0-38 0-36 0-34 0-39 0-38 0-36 0-40 0-42 0-48 0-41 Ballycastle Glenarm ........ Donaghadee .... Ardglass Clogher Head . . Kingstown ...... Dunmore East . . New Ross Passage West Castle Townsend.. m 62 50 54 58 57 56 58 54 55 58 0-40 0-33 0-35 0-37 0-37 0-36 0-37 0-35 0-36 0-37 These are the true values of j^*, supposing that the process for finding them has been correctly followed. 1 omit here all deductions as to the absolute maximum of semimenstrual inequality in time at each station, for a reason that will be explained in Section XV. To obtain the apparent age of tide as shown by times, a process was used analogous to that in page 43 or that in page 106. The times were ascertained (by interpolating between the times in the Tables of formulae in Section X.) at which the actual interval of analysed high water from moon's transit two days previous coincided with the mean interval in the Table of page 107. These times were then compared with the times at which the moon's hour-angle from the sun was 0^, 6^', 12^ IS** ; namely, June 22, 9^ June 30, 20^^ July 7, l9^ July 14, 21^ July 21, 23^ July 30, 16^ August 6, 4'', August 13, 5^ August 20, IQ^. The difference was considered to be the appa- rent age of the tide as given by the times. The following are the results : — Station. Apparent age of tide from times. Station. Apparent age of tide from times. Station. Apparent age of tide from times. Kilbaha Kilrush Foynes Island. . . . Limerick Casleh Bay Galway Old Head d h 1 7 1 10 1 22 2 7 1 4 1 3 1 6 Mullaghmore .... Buncrana Port Rush Carrowkeel Ballycastle Glenarm Donaghadee .... d h 0 23 1 4 0 9 + 1 0 -0 14 + 1 12 1 13 Ardglass Clogher Head. . .. Kingstown Dunmore East . . New Ross Passage West .... Castle Townsend.. d h 1 11 1 11 1 3 2 7 2 18 1 23 1 11 * Tides and Waves, Art. 538. ON THE COASTS OF IRELAND. 109 The apparent age from times is at every littoral station, except Dunmore, consider- ably less than the age from range. At Port Rush the apparent age is small ; and at Ballycastle, the diminution proceeds so far as to change the sign of the apparent age. I cannot entirely explain this difference. It indicates that large tides arrive earlier (with reference to the hour-angles of the sun and moon) than small ones ; but I know not why this should happen. Section XV. — Comparison of the results as to mean height , range, semimenstrual in- equality in height, age of tide obtained from height, establishment, semimenstrual inequality in time, and age of tide obtained from times, deduced from high and low waters only, in Sections V., VI., VII., VIII., with those deduced from the ana- lysis of individual tides in Sections XL, XII., XIII., XIV. With regard to the mean heights, we have to compare the results in Section V. with those in Section XI. And first for the mean height on the whole series of observa- tions. The stations which appear best adapted to enable us to decide on the adop- tion of Mean Heights or Apparent Mean Heights as our standard (that is, as most nearly related to the height of water unaffected by tides) are those upon the Shannon. And these leave no doubt that the Mean Heights (deduced from the analysis) ought to be adopted. In a current river, it is inconceivable that the height at a lower station (as Foynes Island) should be equal to that at the highest station (Limerick), as it would be if we relied on apparent mean heights. These are the only stations which throw much light on this subject, for at Dunmore East and New Ross (river stations) the two results agree ; and, at the littoral stations, there is on the whole no difference of a critical kind. At the two quasi-river-stations of Buncrana and Car- rowkeel, we have on both systems discordant results, one giving a mean level higher and the other lower than that of the more exposed stations. The extreme diminution of the range of tide between Port Rush and Glenarm causes no sensible alteration of the mean level, in either system of results. The greater elevation of the mean level at the northern part of the island is equally well-marked in both. For the variation of mean height under different circumstances of large and small tides, large and small declinations of the moon, and increasing and decreasing declinations of the moon, the comparison of the numbers on the two systems gives little subject for remark, except that the difference between large and small tides in the Shannon sta- tions seems to be more strongly marked in the mean heights than in the apparent mean heights. This however does not well accord with the idea of a standard height. It will be remarked that at Limerick the difference between the mean height and the apparent mean height is nearly a foot. With regard to the range of the tide, we have to compare the " Mean Range" in the 8th column of the Table in page 35 with the double of " Mean or M" in the 5th column of the Table on page 106. Neglecting the differences of 0*01, we may assert that, at all the stations except Mullaghmore and Dunmore East, the apparent range 110 . MR. AIRY Om THE LAWS OF THE TIDES is greater than 2 Cj in the formulae of Section X. ; and that in the river-stations the difference is considerable. Without accounting for the two exceptions, I may remark that this shows that the departure from the pure form of tide depending on a single sine is, at all the other stations, similar in some important points of its character to that in a river tide. The nature of the tide at each station will be examined more accurately in Section XVI. With regard to the semimenstrual inequality in height and the apparent value of yF, we have to compcire the two last columns of the Table on page 105 with the two similar columns of the Table on page 35. The numbers are so nearly equal that we S cannot assert that there is any certain difference. The large value of i^ at Port Rush, the small value at Glenarm, and the general smallness from Donaghadee to Castle Townsend (like that in the river station Limerick) are equally marked in both. With regard to the age of the tide as obtained from heights or ranges (which, as I have stated before, is the true age of the tide), we must compare the results on page 105 with those on page 38. They agree, on the whole, very well; though the ages deduced from the analysis appear to be somewhat smaller than those deduced from high and low waters. The ages deduced from the analysis also agree better among themselves. The diminution however from Port Rush to Ballycastle is remarkable. The general result seems to be that on the south-western coast of Ireland the age of the tide is about one day twenty hours. For the establishment, we must compare the Table of page 106 with that of page 39. Only at Limerick and New Ross is the difference considerable : at these sta- tions it amounts to about twenty minutes. For the semimenstrual inequality in time, we must compare the numbers in page 107 with those of page 42. And here it will at once be remarked that a great and S important change has been made in the resulting values of tt by the new mode of treating them. The values at Old Head and Glenarm and the following stations are increased, and those at Port Rush and Ballycastle are diminished, till they agree suf- ficiently well with the others. This change arises from two causes. First, the deter- mination of times from the analysis is vastly more accurate than that from the esti- mation of the times of high and low water. Secondly, in Section VIII. the groups for large intervals and small intervals were divided at each station from a consideration of the magnitudes of the intervals themselves, whereas in Section XIV. they were di- vided from consideration of a totally different circumstance, namely the age of the tide as shown by the time of occurrence of the mean value of range. Strange as it may appear, the former method was incorrect, and the latter is correct. The former method is affected by a circumstance which ought not to enter into the formation of this result at all, namely the change in the time of station-tide, not depending on the change in the time of sea-tide, but depending on the change which the character of the tidal for- ■ ON THE COASTS OF IRELAND. HI mula in Section X. undergoes when the magnitude of the range is altered. Thus, the maximum and minimum intervals of sea-tide (which are the objects of our search) occur at the times (corrected forage of tide) when the moon's hour-angle from the sun is 3^, 9^, &c. But from hour-angle 9^> to hour-angle 12^^ the range of tide is in- creasing: the modification of time of station-tide as related to time of sea-tide is therefore increasing; a second inequality of time is therefore combined with the first, having a different time of vanishing: the time of vanishing of the compound in- equality is therefore different from that of the first inequality, and the maximum mag- nitude of the compound inequality is different from that of the first. And this pro- duces its full effect if we make our divisions of groups with reference to the time of vanishing of the compound inequality. But if we make our divisions strictly at the times when the first inequality ought to vanish_, then^ though every individual time be affected by the second inequality, yet there are the same number of instances affected in the same way on opposite sides of our places of division, and their effect disappears in the final result. But as the full compound effect is not used for our final result, conversely we cannot from our final result infer the maximum magni- tude of the full compound effect, or the maximum value of the semimenstrual in- equality in time. These considerations appear to be deserving of the utmost attention in investi- gating the most important single result which can be deduced from the tides, namely the proportion of the hydrodynamical effects of the sun and the moon. S The mean of all the values of rj in page 108 is 0*38. It is probable that, on at- tending more scrupulously to the age of the tide at the different stations, results would have been found agreeing more closely with each other : but I think it likely that the mean would scarcely have been altered. With regard to the apparent age of tide obtained from times, we must com- pare the numbers in page 108 with those in page 44. The general result of the com- parison is, that the mean of the opposite ages deduced from high and low water agrees with that deduced from the analysis as nearly as can be expected (where a small error in the estimated time of high or low water would produce a great effect on the resulting age). They agree in giving a small apparent age at Port Rush and Ballycastle. The ages deduced from range agree also in this. Now this result* is exactly that which would follow from the supposition that a tidal wave with a large range travels more quickly over the shallow bottom than one with a small range : and that this holds not for the phase of high water or low water only, but for the zero of the angle p. Or it would follow from the supposition that a wave of short period travels more quickly than one of long period (the tidal day near conjunction being shorter than that near quadrature). Neither of these points has been esta- blished by theory ; but the former appears to be very probable. * Tides and Waves, Art. 463. 112 MR. AIRY ON THE LAWS OF THE TIDES Section XVI. — Remarks on the succeeding terms of the expressions for individual tides, as related to the magnitude of the tide, to the position on the sea-coast, to the position on the river, S^c. ; comparison with the terms given by the theory of waves ; discussion of the quarto-diurnal tide. In order to reduce to a smaller number the numerous formulae of Section X., and to render the relations of their coefficients and arguments at once accurate and di- stinct, the formulae have been divided into groups corresponding to large tides and small tides, the times of division being the same as those used in the discussions of 32 the semimenstrual inequality of height. Then, for the large tides, the numbers — Ag have been collected and their mean has been taken ; similarly, the mean of the numbers 32 — B2 has been taken ; and from these, by the treatment described in Section X., a term similar to C2 sin (2 phase + + 88 ) + 0-01.sin(4j9 + 120) Foynes Island Limerick, Large tides. Small tides. 7*35.sinjo +0-55.sin(2p + lll) + 0-26. sin (3jo + 162) + 0-03. sin (4j9 + 277) 4-96.sinjt) +0-37. sin (2/? + 124) +0-11 .sin (3jj+ 175) +0-01 .sin (4/9 + 327) Large tides. Small tides. 8-98. sin j9 +0-90.sln(2jo+ 75) +0-68. sin (3/9 + 125) +0-38. sin (4;? + 160) 6-21. s'mp +0-74.sin(2p+lll) +0-40 .sin (3j9 + 145) +0*15 .sin (4j9 + 182) Casleh Bay . Large tides. Small tides. 6-35. sin ji? +0-l6.sin(2jo+l65) +0-12. sin 3-83. sin j» +0-07. sin (2/? + 219) +0-07. sin 3JB + 214) 3/J + 238) + 0-06. sin (4j9 + 348 + 0-03. sin (4/?+ 35* Galvvay Large tides. 6-41. sin j» +0-18.sin (2j9 + 157) +0-1 8. sin (3/) + 204) +0-1 6. sin (4/9 + 349) Small tides. 3-89 . sinjo + 0*08. sin (2j» + 204) +0-12.sin(3jB + 233) +0-04. sin (4/9+ 38) Old Head { Large tides. 5-59. sin j(? +0-08. sin (2/? + 154) +0 04.sin(3p + 196) + 0-04. sin (4jo + 282) Small tides. 3-43. sin jo +0-04.sin(2/» + 2l6) +0-10.sin(3p + 257) +0-01 .sin (4p + 237) MuUaghmore { Large tides. [5-35. sinjo +0-06. sin (2/9 + 160) +0-07. sin (3/9+ 14) +0-06. sin (4/0 + 184) Small tides. '3-25. sin /; +0-04. sin (2/0 + 217) +0-03. sin (3/0+ 134) +0-02. sin (4/0 + 254) Buncrana { Large tides. |5-84.sinj9 + 0-14. sin (2/9 + l65) +0-08. sin (3/> + 262) +0-04. sin (4/0 + 295) Small tides. 3-37. sin/0 +0-04. sin (2/0 + 199) +0-04. sin (3/0 + 256) +0-01 .sin (4p + 237) Port Rush { Large tides. I2.56. sin/9 +0-08. sin (2/9 + 153) +0-1 2. sin (3/0 + 257) +0-01 .sin (4/0 + 207) Small tides. 1.38. sin/0 +0-04. sin (2/9 + 220) +0-07. sin (3^^ + 287) +0-02. sin (4/9 + 172) ^ , , fiLarge tides. 13-35. sin/0 +0-07. sin (2/0 + 238) +0-11 .sin (3/? + 205) Carrowkeei \ Small tides. 1 1*95. sinjs +0-01 .sin (2;; + 319) +0-06. sin (3/0 + 199) +0-01 .sin (4/9 + 152) Ballycastle Glenarm Donaghadee Ardglass , Clogher Head. Kingstown Dunmore East New Ross Passage West, f Large tides. 1 1-42. sin/9 +0-07.sin (2jo + 308) +0-07. sin (3/9 + 276) +0-03. sin (4/0 + 21 8) \ Small tides. 10-88. sin/9 +0-06. sin (2/? + 338) +0-03. sin (3/0 + 311) +0-01 .sin (4/9 + 293) { Large tides. 12-89. sin/0 +0-17.sin(2p+ 76) +0-07. sin (3/9 + 227) +0-01 .sin(4;> + 310) Small tides. 2-4 7. sin/0 + 0-05. sin (2/>+ 50) +0-04. sin (3/? + 237) Large tides. 5-24 . sin/0 +0-07. sin (2/?+ 56) +0-03. sin (3/9 + 174) +0-01 .sin ^4;? + 327) Small tides. 3-96. sin/0 +0-03. sin (2/9 + 318) +0-03. sin (3/o + 230) +0-01 .sin (4^+ 85) Large tides. 6-90. sin/0 +0-18. sin (2/9+ 98) +0-04. sin (3/9 + 145^ +0-03. sin(4;? + 125) Small tides. 4-96. sin/9 +0-07.sin (2/9 + 117) +0-04. sin (3/9 + 217) + 0-03. sin(4;>+ I6I) Large tides. Small tides. Castle Tovvnsend. •••{ Large tides. Small tides. Large tides. Small tides. Large tides. Small tides. Large tides. Small tides. Large tides. Small tides. 6-79. sin/9 +0-26. sin (2/0+ 109) +0-08.sin(3/o + l66) +0-01 .sin (4^ + 233) 4-81. sin/9 +0-1 3. sin (2/0 + 143) +0-07. sin (3/9 + 180) +0-02. sin (4^ + 241) 5-26. sin/0 +0-38. sin (2/9 +143) + 0-02. sin (3/o+ 7) + 0-02. sin ^4^+ 118^ 3-69. sin/0 +0-23. sin (2/0 + 165) +0-01 .sin (3/0 + 225) +0-02.sin(4/> + l71) 5-73. sin» +0-14.sin(2/9+ 12) + 0-15.sin(3/o+ 94) +0-01 .sin (4/> + 288) 3-91 .sin/0 +0-11. sin (2/9+ 3) +0-08. sin (3/0 + 1 03) +0-01 .sm (4;? + 198) 6-16. sin» +0-47. sin (2/0 + 348) + 0-26. sin(3/o + 101) +0-03.sin(4/> + ll6) 4-51.sin}> +0-30. sin (2p+ 346) +0-l6.sin(3/o+ 95) +0-01 .sm (4^+63) 5-94.sin;j +0-29. sin (2^^ + 298) + 0-09- sin (3/o+ 87) +0-04. sin (4;?+ 73) 4-19. sin}? +0-24.sin(2/9 + 3l6) +0-07.siii(3;?+ 95) +0-02. sin (4p+ 43) 4-79. sin » +0-21. sin (2/0 + 297) +0-04. sin (3;? + 259) + 0-02. sin ^4;? + 331) 3-33. sin^ +0-l6.sin(2^ + 310) +0-03. sin (3^9 + 302) +0-03. sin (4;?+ 73) MDCCCXLV. •114 MR. AIRY ON THE LAWS OF THE TIDES In order to institute a companson of these numerical results with the formula given by theory, it may be convenient to premise the following expressions : — If the tide were created in a uniform channel, forming a great circle round the earth, the expression for the height of the water would have the form A.sin/?+B.sin2jo+90°, where B would have the same sign as A if the velocity of the tide-wave were greater than \/^, h being the depth of the channel. If the tide at the mouth of a gulf be a pure tide, or one in which the elevation is expressed by a . sin;?, then the elevation at any point in the bay will be expressed by the formula A . sin ;? +B . sin -Jjo -f 90°, where (in the case of a gulf sufficiently long to have a tidal node) A and B have dif- ferent signs from the mouth of the gulf to the node, and afterwards have similar signs. If the tide at the mouth of an indefinitely long river bs a pure tide, then the eleva- tion at any point in the river will be expressed by the formula A.sinp-1-B.sin2/?, where B has the same sign as A if the section of the river be a parallelogram, but may have the opposite sign if the section expand very much at the top. ^ „ B . ' n 1 I vertical oscillation of the water In all cases ^ is a quantity of the same order as depth of the water I shall now proceed to examine the results deducible from the last Table. The stations Kilbaha, Casleh Bay, Old Head, Mullaghmore, may fairly be consi- dered as littoral stations on the open Atlantic ocean. And their formulae agree among themselves almost absolutely to the second term, and in a great measure to the third term. They show clearly that the Atlantic tide there is not a pure tide. But the form of the argument does not agree with either of the two first formulae just cited^ which alone can apply to it. At Castle Townsend, which is nearly as much exposed, but on a different side of the island, the formula agrees pretty well with the first of those above, supposing the depth of the sea very great. At Dunmore East the tide has nearly assumed the form of a river tide. Proceeding from Kingstown (where the character of the tide is similar to that at Kilbaha, &c.) to Clogher Head, Ardglass, and Donaghadee, the argument of the second term undergoes a progressive change, its phase being less advanced. As the epoch of the first term is absolutely the same at these stations (the tide being simul- taneous at all of them), it appears that the wave represented by the second term is progressive. It seems therefore that it does not originate in the peculiarities of a gulf-tide (contained in the second formula just cited), but that it has been created either on the open sea or in the shallower water between Ireland and Cornwall, and now travels on as an independent wave. ON THE COASTS OF IRELAND. 115 From Mullaghmore to Port Rush, the second wave appears to travel with the same speed as the principal wave. In passing through the narrow channel to Glen- arm, its phases appear to increase much more rapidly than those of the principal wave; or, it appears to travel more slowly, or in the opposite direction. This how- ever is probably only an instance of the forced progression of the phases of wave in the channel connecting two tidal seas. The general relations however of the waves depending on 2p at the different littoral stations will be seen more clearly from the following process : — Take the establish- ment of each station from Section XII I., and convert it into degrees at the rate of 1440° for a tidal day, and subtract the angle thus found from the angle added to 2p. It is evident now that our phase j»' at every station is referred to the same origin, namely to the time of the moon's transit at Greenwich. The expressions thus ob- tained for the quarto-diurnal waves are the following: — Station. Large tides. Kilbaha .... Casleh Bay . . Galway .... Old Head . . Mullaghmore Port Rush . . Bally castle . . Glenarm .... |ft. 0-l6.sin(2y + 0- 16. sin (2/)' + 0-18. sin (2/?' + 0-08.sin(2/>' + 0-06. sin (2/ + 0-08. sin (2/j' + 0-07. sin (2y + 0- 17. sin (2/ + 244) 235) 223) 208) Small tides. Station. ft. 0-08 0-07 0-08, 0-04, 198)|0-04. 113)0-04. 203)0-06, 156)0-05, .sin(2y + 295) sin(2/>' + 296): sin(2/>'4-277)j sin (2/ + 278) sin(2j9' + 263): sin(2jo' + 190) sin (2/ + 245)1 sin (2/+ 147) Donaghadee . . Ardglass ClogherHead. . Kingstown .... Dunmore East . Passage West . . Castle Townsend Large tides. Small tides. ft. , ft. 0-07.sin(2/>'+ 122) 0-03, 0-18.sin(2jo' + l63)|007 0-26.sin(2y + l67)|0-13 0-38.sin(2/9'+ 195) 0-23 0-14.sin(2y+ 72)0-11 0-29. sin (2/ +344)10-24 0-21. sin (2/)'+ 7)'0-l6 sin sin sin (2/+ 41) (2^+199) .o..i(2/ + 218) .sin(2jo' + 235) .sin(2/>'+ 71) .sin(2jo'+ 10) .sin(2/?'+ 27) The expressions for Courtown, the station intermediate between Kingstown and Dunmore East, are (as I remark by anticipation from the next section) intermediate between those for Kingstown and Dunmore East, but nearly coinciding with the former. The variations in the values of the constants attached to 2/? in the Table of page 113, seem to make it impossible for us to attribute this term to the local circum- stances of each port, and the consideration of the Courtown tides in the next section will confirm this. The order of the numbers attached to 2// in the last Table shows that it may be considered as a progressive wave, beginning at Kingstown nearly, and travelling both ways round the coast as far as Donaghadee. But whether such a thing is mechanically possible, or whether it can be true that the quarto-diurnal wave (which necessarily is created by the semidiurnal wave flowing over the shallower seas between Ireland and Cornwall) can show itself as a great swell opposite Kings- town, and can then be propagated even opposite to the semidiurnal wave and round the island, are points which I cannot explain. On the whole, I am not able to pronounce with any confidence on the origin of this wave, but I have no doubt that, having been created, it travels along indepen- dently, and therefore that its existence is not due to the local circumstances of the several stations. q2 116 MR. AIRY ON THE LAWS OF THE TIDES In regard to the river stations, I may remark that the Shannon does, in conse- quence of the barriers to the tide at Limerick, resemble a gulf in its tidal character ; and the second of the formulae above ought therefore to apply to it ; and, as will easily be seen, it does apply with considerable approximation. The river Barrow, upon which New Ross is situated, is not obstructed in the same manner, and there- fore we might expect the third formula to apply, and it does apply very nearly. I omit discussion of the third and fourth terms, because theory, in a shape appli- cable to cases of nature, has not yet been extended sufficiently far. I may however observe that, as I have shown with regard to the tide at Deptford*, and to those at Southampton and Ipswich -f, so also at Limerick, and in some measure at Foynes Island and New Ross, the third term is almost as important as the second, and the fourth is one of considerable magnitude. I may also call the attention of the wave-theorist to this circumstance, that the difference between the coefficients for large tides and for small tides does not appear sufficiently great in relation to the difference between the coefficients of the first term for large tides and small tides. The coefficient of the first term being considered as of the first order, that of the second term would consist of a series whose leading term was of the second order, &c. The departure from the proportions given by this consideration may depend upon the succeeding terms of the series. It is also to be remarked that there is an undoubted difference between the argu- ments for large tides and for small tides. This seems to show that each sine is ac- companied by a cosine, and that their coefficients have, for their leading terms, terms of different orders in respect of the first coefficient of semi-range. Section XVII. — Separate discussion of the tidal observations made at Courtown. The observers at Courtown soon discovered that it was impossible to adhere to the instructions sketched in Section I. The tide was sometimes apparent as a semi- diurnal tide, but with considerable irregularity ; at other times, the character of semidiurnal tide was (to common observation) completely lost, and in its stead Uiere was a small tide four times a day ; in all cases the tide was small. In this state of things, the course which they adopted was, to observe continuously whenever the semidiurnal tide was not distinctly marked, and to follow the usual rule (with some extension of observations) when it was well-marked. In this manner a tolerably complete and very important set of observations has been secured. In several cases the observations have been interrupted by the discharge of water from the sluices for scouring the harbour of Courtown ; in some instances there has been no difficulty in filling up the observations by conjecture, in others I have been obliged to adopt the limits of the tide (in the form of analysis) to these interruptions. In order to apply the method of analysis explained in Section X., it was necessary to fix upon precise limits for each tide. But as no limits could be obtained at Cour- ♦ Philosophical Transactions, 1842, p. 4. f Ibid. 1843, pp. 49 and 53. ON THE COASTS OF IRELAND. 117 town (as at other stations) from the observations themselves, it was necessary to take them from another station. The station selected for this purpose was Ardglass. The limits and the divisions into twelfths and sixteenths for Ardglass were therefore adopted for Courtown, as far as the continuity of observations permitted. Where (as is just mentioned) it was necessary to change the limits, this was done if possible by altering the limits and all the divisions by three or six of the twelfths (correspond- ing to four or eight of the sixteenths) ; in other cases they were all altered by a defi- nite time. Then the means of the heights in these observations were treated in the usual way. A correction for diurnal tide was indispensable (the diurnal tide being, at some times, as large as the semidiurnal). For obtaining this from the observations there were two means. One was, by means of the investigations connected with tertio- diurnal tide to be detailed in the next section. These gave the diurnal tide for the beginning and the fourth parts of each of the whole day's group used there. These were the diurnal coefficients proper to be used in the semidiurnal groups composing each day's group. But the corresponding diurnal coefficient applicable at the times of any Ardglass high or low water was easily deduced from them by taking the sum of the products of the coefficients next it by the cosines of their respective distances from it (considering 360° as corresponding to a tidal day). Another method was, to select from the observed heights those which corresponded to the times of Ardglass high water and Ardglass low water, and to treat them by the method of fourth differ- ences explained in Section III. ; as these heights ought (in relation to each other) to be perfectly free from the effect of semidiurnal tide and of all tides occurring at por- tions of a semidiurnal tide. Using then these two methods, and adopting the mean of their results when both could be applied, a number of diurnal coefficients were obtained from the observations themselves. On comparing these with the diurnal coefficients at the neighbouring stations, it was found that the coefficients at Courtown might very well be represented by the mean of those for Kingstown and Dunmore East at the same time. Accordingly, for all the times for which no diurnal tide could be safely extracted from the observations, the mean of coefficients for Kings- town and Dunmore East was used ; and from these, when necessary, the coefficients for other times were deduced by the operation described above. The process then pursued was exactly the same as in other cases, except that no correction was at- tempted for rise of water. The results are the following, which differ in form from preceding results only in this circumstance, that the origin of phase is the time of mean water at Ardglass preceding high water, and that therefore an angle expressed by a number of degrees must be added to the phase to form the argutnent of the first variable term. 118 Mil. AIRY ON THE LAWS OF THE TIDES Height of the water in each individual tide at Courtown, excluding diurnal tide, where the origin oi p is at the same time as at Ardglass (p. 82 and 83), Analysed time of high water, corres ponding t 0 Afl. Ci. Ci- C2. Co. C3. <^3- C4. Ci. P + Cl- = 90. 1842. h m ft. ft. 0 ft. 0 ft. 0 ft. June 22. 20 13 16-93 0-74 109 0-43 170 0-03 320 0-02 103 23. 8 30 23. 20 46 17-30 0-74 91 0-36 133 0-05 93 0-02 265 24. 9 25 24. 22 4 17-55 0-50 73 0-36 102 0-04 180 0-04 20 25. 10 11 25. 22 18 17-03 0-78 83 0-33 127 0-08 253 0-05 337 2^. 10 13 } 16-55 26. 27. 22 9 10 21 0-46 107 0-33 122 0-03 178 0-04 200 27. 28. 22 5 10 30 1 16-58 0-38 125 0-29 128 0-04 160 0-04 152 28. 29. 29. 30. 30. July 1. 1. 2. 22 39 11 24 22 42 9 29 21 3 8 50 21 14 9 21 } 16-66 0-17 133 0-22 130 0-03 238 0-03 298 r 16-64 0-25 112 0-05 130 0-05 106 0-01 217 r 16-71 0-17 199 0-24 130 0-03 275 0-02 314 - 16-59 0-18 199 0-28 148 0-03 164 0-03 60 16-69 0-36 251 0-19 126 0-02 59 0-03 237 16-65 0-23 239 0-19 138 0-04 164 0-04 527 16-66 0-28 256 0-23 128 0-03 280 0-03 333 2. 3. 16 7 4 42 j 16-88 0-09 58 0-18 83 0-03 296 0-05 137 3. 4. 17 2Q 5 51 } 17-59 } 17-40 0-13 51 0-15 106 0-04 127 0-05 200 4. 5. 22 34 11 4 0-12 291 0-21 143 0-12 114 0-04 358 6. 6. 18 38 7 8 j 16-32 0-51 74 0-29 134 0-05 50 0-04 350 6. 7. 19 52 8 12 1 17-21 0-37 63 0-52 120 0-11 207 0-05 43 8. 9. 2042 9 12 1 16-65 1-29 81 0-44 132 0-10 138 0-05 260 9. 21 32 16-62 1-57 82 0-37 134 0-11 87 0-07 231 10. 9 58 10. 22 25 17-62 1-18 77 0-16 ^Q 0-09 101 0-08 m 11. 10 40 11. 22 56 16-48 1-26 82 0-34 116 0-10 100 0-06 202 12. 11 24 12. 23 51 16-59 0-93 86 0-42 127 0-01 1 0-03 199 (13. 9 59; ) .... .... > • • • • • . • .... (13. 20 7. ) .... .... • • . • • • • • .... (14. 6 15, ) .... .... • ■ • « • • • « .... .... 16 23; ) .... . • . • .... • . • • 15. 2 31 16-08 \ 16-58 0-27 58 0-43 121 0-04 282 0-07 345 15. 16. 17 56' 6 26 0-04 339 0-24 136 0-06 329 0-02 192 16. 20 45 17-05 0-26 288 0-33 106 0-08 101 0-11 178 17. 9 36 17-11 0-09 278 0-15 150 0-11 328 0-10 358 17. 22 4 16-89 0-10 283 0-38 135 0-01 160 0-03 164 18. 18. 2 39. 15 45j 16-90 0-01 155 0-35 115 0-17 106 0-08 231 19. 19. 5 igj 16-81 0-18 130 0-37 142 0-10 40 0-12 113 19 5i 16-82 0-17 93 0-29 115 0-16 304 0-06 304 20. 7 58] 16-70 0-21 53 0-35 125 0-14 122 0-10 131 20. 19 41< 16-80 0-58 68 0-22 151 0-04 294 0-03 341 21. 7 35^ 16-61 0-57 93 0-36 138 0-05 169 0-05 233 21. 22. 20 2 8 22 [ 16-47 0-74 , 91 0-28 141 0-04 131 0-01 12 ON THE COASTS OF IRELAND. 119 expressed by the formula Ao+CiSin(/?+Ci) + C2Sm(2;?-|-C2)-|-C3sin(3;?+C3)-fC4sin(4/>+c4), and p increases by 360° during one complete tide at Ardglass. Analysed time of high ■water, corres ponding to Ag. c,. Cj. c,. C2. C3. '"a- C4. Ca, P + Cy-- = 90°. V 1842. h m ft. ft. o ft. ft. ft. July 22. 20 40 16-32 0-80 89 0-34 135 0-05 152 0-01 158 23. 8 54 23. 21 9 16-32 0-89 ^^ 0-37 145 0-06 79 0-07 158 24. 9 18 24. 21 28 16-51 0-74 103 0-23 125 0-12 211 0-05 198 25. 9 41 25. 26. 26. 27. 27. 28. 28. 29. 29. 30. 30. 31. 31. 21 54 10 17 22 25 10 35 23 13 11 7\ 22 37 10 2 21 25 8 42 20 35 8 38 20 55^ \ 16-37 16-36 16-41 0-73 105 0-35 128 0-07 248 0-02 270 0-80 0-60 102 111 0-21 0-27 155 124 0-12 0-06 106 168 0-02 lb 16-34 0-61 106 0-25 129 0-04 130 16-42 0-39 108 0-30 117 0-04 155 0-0*3 zli 16-37 0-35 109 0-10 127 0-06 171 0-04 161 16-44 0-32 158 0-23 128 0-07 148 0-01 222 16-36 0-24 163 0-22 132 0-04 254 0-05 341 16-38 • 0-25 208 0-24 109 0-02 61 0-03 43 16-31 0-25 233 0-24 134 0-05 10 0-05 0 ' 16-25 16-21 0-41 247 0-18 116 0-01 105 0-03 245 0-43 259 0-19 150 0-01 249 0-02 18 August 1. 9 8 16-37 0-48 266 0-27 118 0-02 87 0-02 107 1. 21 6 16-53 0-34 287 0-21 148 0-02 46 0-02 36 2. 9 20 16-57 0-36 305 0-25 149 0-01 226 0-02 78 2. 19 45 16-42 0-09 9 0-26 150 0-05 30 0-03 122 3. 7 36 16-32 0-22 31 0-31 159 0-02 63 0-02 39 3. 18 27 16-48 0-35 83 0-20 148 0-06 110 0-03 177 4. 6 44 16-47 0-60 82 0-26 170 0-09 45 0-09 131 4. 19 17 16-76 0-88 79 0-35 152 0-04 274 0-07 27 5. 8 1 16-73 1-13 Q9 0-41 1.56 0-04 216 0-05 80 6. 20 0 16-58 1-23 80 0-33 140 0-09 53 0-08 55 6. 8 18 6. 20 36 16-65 1-53 78 0-41 110 0-11 128 0-05 3 7. 9 5 7. 21 34 16-46 1-89 75 0-45 141 0-03 169 0-06 127 8. 9 56 8. 22 18 16-64 1-70 74 0-52 127 0-07 118 0-01 225 9. 10 4 9. 21 50 17-31 1-60 114 0-28 225 0-21 48 0-09 226 10. 10 45 10. 23 40 16-56 1-32 82 0-33 127 0-11 ' 269 0-09 215 11. 11 57 12. 0 14 16-62 0-59 88 0-41 142 0-02 329 003 141 12. 13 15 16-63 0-58 72 0-22 120 0-05 222 0-03 59 12. 23 49 16-26 0-09 125 0-29 120 0-06 356 .... 13. 9 26, 16-29 0-11 209 0-31 123 0-11 29 0-01 247 13. 20 54^ 16-20 0-25 274 0-27 117 0-07 88 0-11 187 14. 8 41: 16-29 0-34 260 0-39 150 0-05 354 0-01 218 14. 21 8: 16-32 0-34 287 0-35 126 0-06 243 0-03 235 15. 9 33 16-35 0-39 277 0-21 130 0-04 27 0-02 208 15. 16. 16. 21 50 10 6 22 50< 16-55 0-13 307 0-17 148 0-03 157 0-02 350 16-31 0-25 300 0-24 113 0-08 94- 0-05 178 17. 6 30 16-78 0-21 78 0-14 122 0-05 169 0-02 47 17. 18 41 16-58 0-19 84 0-28 120 0-07 250 0-08 325 18. 7 24 18. 20 7 17-07 0-17 64 0-30 122 0-05 76 0-04 90 *20. 20 20 16-57 0-92 "89 0-23 1*23 0-04* V24 0-02 *267 120 MR. AIRY ON THE LAWS OF THE TIDES Upon inspecting the numbers in the column headed Cj, it will be perfectly evi- dent that there is an error on August 9. The semidiurnal tide on that day is (com- paratively) large, its whole range exceeding three feet ; and there is no instance throughout all the observations of an irregularity equal to that which corresponds to an anomaly of 30° with that range. I have no doubt that all tlie observations are recorded too early by one hour, an error which would easily be committed at begin- ning, and which, where the observations are entered on forms ready prepared, would be retained to the end. Correcting on this supposition, the three successive times of high water would be August 9*^ 10^^ 34'", August 9^ 22^' 50'", and August 10^ 1 1^ IS-" ; and the values of q, Cg, C3, C4, for August 9'^ 22i» 50'" would be nearly 84°, 165°, 218°, and 106°. Next I would remark that there is undoubtedly an error of the same kind in the tide of July 4-5 ; but as the tide is then very small, I have not ventured to state pre- cisely the alteration which I would propose. Thirdly, observing that where the tide is very small, the hours on successive days occur earlier, in each of the instances where the order is well-marked (as from June 27 to July 3, from July 27 to July 31, and from August 12 to August 14), there can be no doubt that the same thing must hold during the interruption of observations about July 13 and 14 ; and thus it will be seen that there are certainly four high waters lost at that time. I have inserted four numbers by simple interpolation, to show, within two or three hours, the times of the lost high waters. It is also to be remembered that nothing can be inferred from such tides as those of July 15-16 and July 18, where the coefficients are 0*04 and 001. Bearing these remarks in mind, and giving particular attention to the second half of the observations, which, both for the regularity of the system pursued by the ob- servers and for the agreement of the results, is greatly superior to the first, we arrive at the following conclusions : — ■ The angle c^ increases continually, and its increase amounts to 360° in about four- teen days. When its value is not far from 360°, its increase is extremely rapid. One of these jumps occurs between August 2^ 9'' and August 2'^ 19'', and one between August 16^ 22^^ and August 17'^ 6^' ; one also between July 2*^ 9'' and July 2^ \6^ ; another takes place between July 17*^ 22^' and July 19^1 5^ but (the results being at that time somewhat irregular) the time cannot be precisely pointed out. It is evi- dent from this that the Courtown tides are more numerous than the Ardglass tides by one tide in fourteen days nearly. The mean solar time of high water does not increase constantly as at other stations, but oscillates backwards and forwards. Thus, from July 19 to August 18 (in which period the tides at other stations have gradually retarded by twenty-four hours), the evening tides always occur between 5'' 18'" and 13^' 15"^, and the morning tides always occur betv/een 18'' 27'" and 24^' 14'", each time having twice oscillated be-' tween its extreme limits in that period. ON THE COASTS OF IRELAND. 121 From these circumstances it is plain that the time of high water (confining our remarks to the term C^ sin (p+Cj)) respects mainly the time of the sun's transit and not that of the moon's transit ; and therefore, at Courtown, the solar tide is greater than the lunar tide. This is, I believe, the only place on the earth in which such a result has been distinctly obtained. The observations of Sir Edward Belcher* show that at Otaheite the solar tide is as nearly as possible equal to the lunar tide. The times following lunar syzygy by two days were June 24, 9\ July 9, 19^, July 23, 23^ August 8, 4^ August 22, 16^^; and about these times the luni-solar tide is greatest at all the other stations. About these times also the soli-lunar tide at Cour- town is greatest. The solar hour of high water at Kingstown, at the highest tides, is about 12'' 30", that at Dunmore East is about 6'' 40"*. These are the two stations nearest to Cour- town on the north and south sides. The solar hour of high water at Courtown at the same times is about 9'* 30'". At these times the effects of the sun and the moon are simultaneous as to phase, so that we may treat the result as if there were only a single wave. It would seem then that the transition from a tide of elevation at Dunmore East to one of simultaneous depression at Kingstown, and vice versa, is not effected entirely by a node dividing the elevated wave from the depressed wave. It appears that there is also a small progressive wave. The geometrical representation appears to be this ; that there is a large stationary wave, having a node near Courtown, and making high water simultaneous in all parts of the inland sea or Irish Sea, and syn- chronic with low water in the exterior sea ; and that there is mingled with it a very small progressive wave. As to the mechanical explanation of it, I can offer nothing positive. But I would suggest for the consideration of wave-theorists, whether, in the case of a gulf (as the Irish Sea) having a small outlet (like the North Channel), it be possible that tiie fluctuation may be represented correctly on mechanical prin- ciples by a combination of the stationary wave peculiar to a gulf with the progressive wave peculiar to the channel. Returning now to the consideration of the magnitude of the tide, it is evident that the coefficient of the lunar tide has been diminished in a far greater degree than that of the solar tide. There is one explanation of this which is very plausible, and which I have no doubt is the true one, namely that the node for the lunar tide and the node for the solar tide do not coincide (which, on account of the difference of the pei'iods of these tides, we should expect a priori), and that the node for the lunar tide is much nearer to Courtown than is the node for the solar tide. It is clearly possible that, by varying our choice of stations, we might vary the proportion of the two effects in any degree whatever. Nay, by choosing a station between the two nodes, we might have the solar and lunar effects to conspire when they are opposed at other places, and vice versa ; and thus a station would be found where the spring tides occur at the same time as neap tides at other places. This does not occur at * Philosophical Transactions, 1843, p. 55, &c. MDCCCXLV. R 122 MR. AIRY ON THE LAWS OF THE TIDES Courtown ; but the reader, in reflecting on this, will see the importance of our com- parison of the time of the largest tides at Courtown with the time of the largest tides at the other stations. We shall now proceed to examine the second periodical term ; which will be found not less remarkable than the first. On glancing over the values of c^ (first correcting that on August 9 as I have sug- gested), the reader cannot fail to be struck with the general uniformity of the num- bei*s. It is quite evident that this term has no respect to the sun's transit, but that it respects only the moon's transit, or the commencement of the luni-solar tide. If we look also to the coefficient C^, we find that its magnitude is considerable, some- times exceeding that of the first term. It is clear therefore that this term does not originate as a derivative from the first term, produced by the local circumstances of the port. It does not change greatly, but nevertheless has on the whole larger values about the times of large tides than about the times of small tides. If we divide the observations into two groups, one corresponding to large tides and the other to small tides (the limits being the same as those for the other stations) ; and if we correct as before for the establishment at Ardglass (to which station the Courtown tides have been referred) ; and if we collect the expressions for the second periodic term at the three stations, Dunmore East, Courtown and Kingstown ; we have this sequence of expressions. Kingstown. Courtown. Dunmore East. Large tides ft. 0-38. sin (2j9' + 195) ft. 0-35. sin (2p'+l 96) ft- 0-14. sin (2/+ 72) Small tides 0-23. sin (2/ + 235) 0-26. sin (2/ + 202) 0-11 .sin(2/>' + 7l) It appeal's here quite evident that this term at Courtown is only the representation of the same quarto-diurnal tide which shows itself along the whole coast. This wave (whatever its origin may be) appears to have its greatest range and its beginning of phases at Kingstown, and tospread both ways, diminishing in range as it goes. The succeeding terms at Courtown are insignificant. We have now a clear representation of the apparently confused phenomena of the tides at Courtown. Both the semidiurnal tides are very much diminished, the lunar so much that its range is rather less than that of the solar tide. The quarto-diurnal tide exists in nearly its greatest magnitude. The geometrical representation is per- fect ; the mechanical explanation is not complete. In both respects, as regards what is reduced to law and what is yet incomplete, the Courtown tides must be regarded as the most remarkable that have ever been examined. Section XVIII. — Exarmnation into the question of tertio-diurnal tide. The observations at Courtown, as has been mentioned, and as appears from the Table in pages 118 and 119, WQve continued without interruption, day and night, for ON THE COASTS OF IRELAND. 123 a considerable time. The obsei'vations at Dunmore East, as appears from the begin- ning of the Table in page 88, were also continued without interruption for several days. These circumstances appeared to me to offer a convenient opportunity of exa- mining whether the tide occurring three times in the lunar day, which is pointed out by theory, is sensible in the seas around Ireland. The calculations for this purpose were made in the same manner as the other cal- culations described in Section X. The means for the twelfth parts of semidiurnal tide, or for the twenty-fourth parts of diurnal tide, having been already found for the operations in Section X., the means of the first and second, of the third and fourth, of the fifth and sixth, &c. were taken ; and these were evidently the same as the means for the twelfth parts of diurnal tide. They were then treated by the use of the printed skeleton form shown in Section X., in the same manner as the means for the twelfth parts of semidiurnal tide. Thus the diurnal tide and tertio-diurnal tide were obtained; and a consideration of the principles on which that process is founded will show that the result is in no way affected by the semidiurnal or quarto-diurnal tide. The constants additive to the phase, at Courtown, were corrected where necessary to adapt them to the supposition that the phases are measured from the mean water preceding High Water, First Division, at Ardglass ; those at Dunmore East are re- ferred to the same state of tide at Dunmore East. The angle jo in the following Table increases by 360° in a tidal day. The day which is set down is that whose astrono- mical commencement occurs in the tidal day (the limits of the tidal day will be seen in Section X.). Courtown. Dav. Diurnal tide. June 29. 30. July 1. 17. 18. 19.' 20. 26.' 27.' 28.' 29.' 30J 31. 2.' 3. 4J I2J 13. 14. 15.i 16J Aug. ft. 0-57 0-31 0-43 0-20 0-05 0-24 0-36 0-38 0-43 0-49 0-29 0-25 6-15 0-16 0-10 0-38 0-53 0-34 0-11 0-09 0-05 0-26 .sin (jo + 250 • sin (jo + 253 . sin (p+ 264 . sin(jo+350 . sin(/)+201 . sin (p+ 265 . sin (p+ 261 • sin (p+ 256 .sin (p+253 . sin(j(?+240 .sin (p+248 . sin (p+ 276 . sin(p+287 . sin(p+ 10 . sin (p-t 105 . sin (p+ 1(J6 .sin(p+ 87 .s'm(p+ 57 .s'm(p+357 , sin (p+ 46 .sin(p+286 . sin(/)+286 Tertio-diurnal tide. ft. 0-08 0-04 0-02 0-14 0-06 0-05 0-23 0-06 0-05 0-06, 0-08, 0-08. 0-10, 0-01 , 0-08. 0-02, 0-11 , 0-12, 0-07. 0-11 . 0-07. 0-04. sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin (Sp+lSS) (Sp+ 86) (3/>+l77) (3JO + 207) (3/> + 236) (3/?+ 279) (3/? + 187) (3/J + 179) (3;? + 132) (3/>+158) (3p+ 84) (3p+ 87) (3p+ 98) (3^0 + 306) (3/? + 315) (3p+ 3) (3;) + 328) (3/7 + 346) (3/? + 238) (3;> + 211) (3yo + 264) (3p+ 70) Dunmore East. Day. June July 24. 25. 26. 27. 28. 29. 1. 2. Diurnal tide. Tertio-diurnal tide. ft. 0-33 0-35 0-20 0-27 0-33 0-32 0-19 0-17 n (jo + 208) n(p + 207) n(p+192) n(jO + l70) n(p+\6l) n(p+150) n(/> + 187) n(;9 + l78) ft- 0-16. sin (3/7 + 253) 0-08. sin (3/7 + 304) 0-11 .sin (3/7 + 220) 0-10. sin (3/7 + 210) 0-09. sin (3/7+ 182) 0-00 0-07. sin (3/) + 349) 0-03 . sin (3/7 + 99) r2 124 MR. AIRY ON THE LAWS OF THE TIDES ON THE COASTS OF IRELAND. The diurnal tide is here shown pretty well, and the times of its changes of sign agree well with those found in Section III. But the numbers for tertio-diurnal tide appear to me perfectly lawless. I think that they must be regarded as principally the effects of accident. On the whole, I am inclined to believe that, as far as evidence goes, the tertio- diurnal tide is not sensible on the coast of Ireland. [ 125 J II. On the Temperature of the Springs, Wells and Rivers of India and Egypt and of the Sea and Tablelands within the Tropics. By Captain Newbold, Madras Army, F.R.S. Received January 1, 1842, — Read February 22, 1844*. Professor Jameson, in his chapter on the hydrography of India, justly remarks, " Although India, like other great tracts of country, contains many springs, these have hitherto attracted but little attention. The temperature of but few of them is known ; their magnitudes and geognostical situations are scarcely ever mentioned ; and their chemical composition, excepting in a very few instances, has been neglected. The most important feature in the natural history of common or perennial springs, namely their temperature, is rarely noticed, although a knowledge of this fact is illus- trative, not only of the mean temperature of the climate, but also of the elevations of the land above the level of the sea; and our information in regard to their chemical nature is equally meagre -{-." Since the publication of these remarks, much has been done by Prinsep and others in these branches of Indian hydrography, but more remains to be effected before this reproach can be wiped out. The heat of springs having a temperature little above the mean of that of the surrounding country has been rarely noticed, though I feel convinced many such exist in India. That of springs of high temperature, more attractive to the casual observer, has been more remarked. My own observations, and the few inferences I have ventured to draw from some of them, are not offered as sufficient data for the establishment of laws, but merely as a contributory mite to knowledge ; in the view of courting inquiry and observation by others more competent and better situated for continued research than myself. The thermometric observations have been snatched generally on the line of march, or during hasty travel : since my return to England, through the kindness of Mr. Roberton, they have been adjusted to the indications given by the standard ther- mometer of the Royal Society. The observations extend at irregular intervals from Alexandria to Malacca, or from 31° 13' of north latitude to within 2° 14' north from the equator ; and between the meridians of 27° and 103° of east longitude. I had continued those on the tem- perature of the sea as far as the Bosphorus and Black Sea, but have judged them * This paper having unfortunately been mislaid after its receipt hj the late Assistant Secretary, the reading of it was thus necessarily delayed. — S.H.C. t Ed. Cab. Cyc. No. 8. p. 287. 126 CAFf. NEWBOLD ON THE TEMPERATURE OF THE SPRINGS, WELLS superfluous in a paper limited almost to the subject of intertropical tempera- ture. In the columns of the registers, the latitude and longitude, the approximate height above the sea, the nature of the surrounding formation, the depth to the surface of the water and depth of water, the temperature of the air, the month during which each observation was taken, and the approximate annual mean of the climate in which the wells, &c. occur, are specified as far as practicable. In the column of re- marks will be found a few observations on the chemical nature of the water, and on the size of the wells and springs*. Those were selected which contained water all the year round ; though all were, more or less, subject to fluctuation during the wet and dry seasons. The wells in Egypt differ from the " bouries" of India in being less open and exposed to atmospheric influence. Those in the valley of the Nile are mere shafts sunk through the black alluvium to an impervious marly and sandy bed, to depths varying, according to the distance from the river, from ten to forty feet. Their circumferences, like those of the Indian " pot wells," are from nine to twelve yards. They mainly depend on the river for water, which is supplied by infiltration through the soil, — a circumstance to be taken into consideration in all indications afforded of their temperature. The wells in the deserts of Egypt, like those of Ajmir and the western deserts of India, are frequently of great depth, lying under strata of sand, gravel, and a calcareous sandstone, on an argillaceous or marly bed, some- times at a depth of 300 feet below the surface of the surrounding country. In the granitic districts of Upper Egypt, in the Thebaid desert, however, I have observed springs rising through the almost vertical strata to the surface. In India, most of the wells marked as occurring in granite, trap, limestone and sandstone, result from springs, and are consequently not so much influenced in tem- perature by the monsoon rains as those in lateritic rocks, which, from their porous structure, admit of the percolation of rain water to a considerable extent. The temperature was generally taken at about 10 a.m., a time when I found it to approximate nearest the diurnal mean ; and, whenever practicable, at the depth of about ten feet from the surface. The following are the general results of many hundred observations : — 1st. In low latitudes the temperature of the deepest wells and springs is a little higher than the mean temperature of the air. Exceptions occur : for example, the temperature of a deep well at Gadigandr, on the banks of the Toombuddra, between the 15th and 16th parallels of north latitude, at an elevation of about 1200 feet from the sea, was so low as 72°*5 (the temperature of the air in the shade, at the time of observation, 80°*5), while that of the springs and river in the vicinity was from 77° to 79°'5. Ranges of hills, attaining an altitude of 1500 feet above the plain, rose at no great distance ; a circumstance suggesting the probability that the cold spring had its * The observations of others will be denoted in the column of remarks by the names of the observers. The scale throughout is that of Faheenheit. AND RIVERS OF INDIA AND EGYPT, ETC. ISf source at an elevation having a mean temperature lower than that of the plain where the water appears on the surface. 2nd. The temperature of strongly saline and sulphureous springs is, on the average, higher than those of pure water. 3rd. Both saline and cold springs are seen to occur within a few feet from thermal and freshwater springs; a fact to be ascribed probably to their rising through different seams of the subjacent stmta (often highly inclined), and to the different depths and heights from which the supply of water is derived. 4th. The temperature of wells, particularly those with a small area, much used for purposes of irrigation, is thereby artificially increased. 5th. The temperature of shallow exposed wells, springs and rivers, especially such as have sandy beds, is subject to great diurnal fluctuation, conforming, though to a less extent, to that of the superincumbent atmosphere. The surface water of deep wells partakes of this fluctuation, to a depth varying according to the transparency of the water, extent of surface, degree of exposure, and clearness of the sky. In muddy water the surface is heated to a greater extent, but a foot or two deep is less affected by the calorific action of the solar rays than clear water. The transparent water of a large well at Bellary, lat. 15° 5' N. and long. 76° 59' E., situate on a table-land elevated 1600 feet above the sea's level, and containing sixteen feet of water, I found, at the depth of nine feet from the surface, to vary but one degree during the day, from sunrise to sunset, and this in several hundred experi- ments. The minimum, 79°*5, took place a little after sunrise, and the maximum, 80°-5, at 3 P.M. following those of the air. The diurnal variation of the water an inch below the surface amounted to 12°. During the commencement of the dry weather, as the heat increased, the water gradually decreased, and the diurnal fluctuations became greater, and increased at a greater rate than that of the decrease of the water. Thermal Springs. — The thermal springs, both of India, the peninsula of Sinai and Egypt, are, with few exceptions, either mineral or gaseous. Those near the shores of the Red Sea are sulphureous ; and strictly speaking, perhaps, should not be classed as thermal springs, from the great probability of their being connected with the vol- canic belt that passes under the bed of the Red Sea, and bursting up from its watery fetters appears in the semi-dormant volcano of Gebel Teer, and in the lavas of Aden, beyond the straits of Babel-Mandel. The highest known temperature of the thermal springs is 102°, viz. that of El Kasr in the Oasis of Dakhleh ; in the peninsula of Sinai, 91°6, that of the Hum mam Musa, hot-baths of Moses (Wells of Elim ?) near Tor, It is probable, from reports given me by the Arabs, that the Humm^m Pharaon, hot-baths of Pharaoh, about eighty-five miles northerly from Tor, are of higher temperature. The maximum attained by the thermal springs of India is 1 94° at Jumnotri in North Hindostan (lat. 30° 52' N.) ; a temperature almost equivalent, at that elevation — 10849 feet above the sea's level — to the boiling point of water, and 18° higher than that of the hottest known thermal spring of Europe unconnected with present active vol- 128 CAPT. NEWBOLD ON THE TEMPERATURE OF THE SPRINGS, WELLS canos, namely, 176° Fahr., that of Chaudes Aigues in Auvergne. The temperature of the hottest known thermal spring in the world, according to M. Arago, is that of Las Trincheras in Venezuela, stated, on the authority of Humboldt and Boussingault, to have increased 11° since 1806 to February 1823, viz. from 195° to 206° Fahr. Had M. Arago stated its elevation above the sea, a better comparison between its temperature and that of Jumnotri might have been formed. It would be interesting to observe whether any similar increment of heat takes place in the chain of thermal springs that rise abundantly along the great line of dislocation at the southern base of the Himalaya chain, or whether the temperature falls, as in some thermal springs among the East Pyrenees. It is certain that the majority of the springs strictly termed thermal, occur in India at or near lines of great faults occasioned by the upheaving of plutonic rocks, a fact that speaks intelligibly as to the great depth at which the earth's crust has been broken up. Hot springs were found by Burnes in the salt districts of the Punjaub. In Thibet, M. CsoMA DE KoROs uicntions the occurrence of hot springs between U and Ts'ang. They are numerous in the mountains lying east from the Ma-p'-ham lake, especially at one place, where there is a hole out of which vapour continually issues, and at certain intervals, as in Iceland, hot water is ejected with great noise to the height of twelve feet. The water of the hot springs of Assam was found by Mr. J. Prinsep to contain bitumen and sulphuretted hydrogen. One held in solution a portion of muriate of soda. Many other warm springs are known to occur, besides those mentioned in the register, regarding the temperature and chemical composi- tion of which further information is desirable. For instance, those of Humm^m Phardon on the east shore of the Red Sea ; of Vizrabhaee, forty-eight miles north of Bombay; at Mohr on the Bancoot river, about seventy-five miles south of Bombay; of Soonup Deo, and Oonup Deo among the Satpoora hills in Khand^sh ; of Rish'i- kiinda in Rajmahal; of Muktinath and Bhadrinath in North Hindustan ; ofTooee, near Ruttenpore on the Mhye river, in Guzerat ; of Lawsoondra, eighteen miles W.N.W. from Tooee; of Uteer, about thirty miles from Pooreanear Korachi, on the Indus ; of the diamond district at Punnah, in Bundelcund ; of Oetha-gur, and Ban- nassa, near the sources of the Jumna ; of the rivulet of Loland Khad near the Sut- ledge; of those near the confluence of the Soar and Elgie rivers with the Ganges; of many known to exist in the Birman empire and Malayan peninsula, and of Bhotan. The last-mentioned springs throw up spheroids of silex, which are brought to Al- morah and there sold by the native merchants for duck shot*. These spheroids re- semble those of the springs of Carlsbad in Bohemia, and of the Geysers. The silex composing them has doubtless been held in solution by the water ; but it remains yet to be shown whether it contains, or not, that peculiar combination of silica and soda, which, according to Mr. Faraday, characterizes the water of the Geysers-f~; a combination ceasing to exist when the water is evaporated : the silica being then de- * M'Lelland. f Bakbow's Visit to Iceland, pp. 209, 211. AND RIVERS OF INDIA AND EGYPT, ETC. 129 posited in an insoluble condition, while the alkali, probably by the agency of the carbonic acid of the atmosphere, is set free, and remains dissolved in the water in considerable quantity. In Southern India many thermal springs, hitherto entirely unnoticed, are suspected to occur ; Colonel Sykes states that he has been informed of their existence in Canara : I have heard of one among the Raidrtig hills in the Ceded districts, — in the Koondahs on the west coast, — and discovered another at the base of the hills south of Cuddapah having a temperature of 88°, as noted in the re- gister. A spring near Salem in South India is probably thermal, having a tempera- ture of 84°, ascertained for me by Mr. G. Fischer. Temperature of Rivers. — The supposition that the temperature of rivers is lower, from the influence of evaporation, radiation, and the elevation at which they rise, than that of the country through which they flow, appears subject to some modifica- tion as regards great streams whose course lies chiefly through equinoctial regions. Many, like the Nile, derive the great bulk of their water from the rains that fall pe- riodically near the equator when the sun is nearly vertical, and evaporation reduced to its minimum from the saturated state of the atmosphere. The fallen waters de- rive additional heat in overspreading the wide extent of sand and alluvium that form and skirt the channels through which they roll on towards the ocean ; and which, duiing great part of the year, have been left dry and freely exposed to the rays of a scorching sun. The beds of the most considerable rivers of South India present in many parts of their course, during the dry season, dreary wastes of arid sands, through which the river, reduced to a slender thread, barely finds its way to the sea. The mean of more than 200 observations, taken day and night, on the tempe- rature of the Nile, in July, between Cairo and Thebes, I found to exceed the mean annual temperature of the air at Cairo (72°4) by 7°"1- The temperature of the river was increased, at the commencement of the inundation in June, by the freshes from Abyssinia from 79° to 80°*5. The observations were taken at Thebes, immediately preceding, and immediately after, the appearance of the turbid milky hue that an- nounces the periodical arrival of Egypt's great benefactor. The Ganges, though having its source amid the snows of the Himalaya, and pur- suing an opposite course to the Nile, that is, a course from northerly latitudes towards the equator, has a mean temperature, as it approaches the ocean, higher than that of the country on its banks. Its mean, between Calcutta and the sea, obtained from a great number of observations by Mr. G. Prinsep, is stated not to be less than 81° Fahr. ! while that of Calcutta does not exceed 78°. The Ganges, it is well known, is little indebted to the melting of the snows near its sources, but derives its waters chiefly from the periodical rains that fall near the borders of, and within, the tropics, between 30° and 22° N. lat. During the inundation, its waters in the lower parts of Bengal are spread over a superficies of alluvial soil and sand, more than 100 miles in breadth, the greater part of which has been parched by the droughts prevalent be- tween the monsoons. MDCCCXLV. s 130 CAPT. NEWBOLD ON THE TEMPERATURE OF THE SPRINGS, WELLS' In order to obtain a better idea of the degree of heat absorbed and given out by the alluvium of the Nile, the sands and rocks in the beds of the rivers of India, I made the following observations. In July 1840, a thermometer placed on the dark alluvium, then quite dry, of the Nile opposite the pyramid of Meydtin at 12j p.m., having its bulb covered 0*1 of an inch with the same alluvium, stood at 136°-5. With, and on, the sand of the desert on the verge of the inundation line, at the same hour, it stood at 12l°*5. The tempe- rature o/ the air at the time, five feet above the surface of the dark alluvium, was 105°-5 : the same height above that of the desert, it was 103°*5 ; sky unclouded. Although the surface of the sands during the clear serene nights of Egypt is cooled considerably by radiation, still a little below the surface they retain a great portion of the solar heat. In July, at sunrise, the surface of the sandy desert, on the banks of the Nile at Thebes, lat. 25° 26' N., which during the heat of the day indicated a temperature of 130°, had cooled down to 69°-5, while the thermometer a foot helow the surface stood at 83° : temperature of the air 7^°. The temperature of the granite rocks in the beds of the Toombuddra and the Kistnah, during the months of May and June, at 2 p.m., I found from 118° to 120°: during the night they cooled down usually to 83°. The temperature of the surface sands in these rivers was slightly higher than that of the granite. The temperature of rivers whose supply, like those in South India, depends more on the periodical rains than oh springs, is consequently influenced by the tempera- ture of the former. That of the monsoon showers, which fell on the western coast near Mangalore during the months of May and June, varied from 73° to 79°, afford- ing a mean of 76°. The rains falling on the elevated table-land of the Ceded districts, from June to December, ranged from 71°'5 to 79°'5, giving the mean 75°'5. The mean general height of the plain, between lat. 13° and 17° N., is 1300 feet above the sea's level. The temperature of the showers was invariably modified by the conditions affecting that of rain water in extra-tropical countries, namely, the elevation at which condensed, and the temperature of the atmospheric strata through which the showers fell. The temperature of the Brahmaputra river at Sadya in Assam, was found in September by Mr. Griffiths to range from 63° to 70°. That of the air above the river, from 68° to 100°. That of the Indus, by Gerard, in March, near Attock, was 32°. Temperature of the Ocean on the Equator and between the Tropics. — The influence of the trade-winds, cold currents from high latitudes, frequent showers, evaporation, &c., contribute to cool the air and surface of the ocean at the equator. The ex- tremes of the temperature of the latter, at great distances from land, have been pretty correctly stated by M. Arago at 80°' 8 and 84°'2. On crossing the line in the Atlantic Ocean (in long. 20°7 W.) I found the temperature of the sea 84°'5 ; air in the shade, 87° : in the Indian Ocean (long. 58°-54 E.) 81°-5 ; air in the shade 82°-5. In the AND RIVERS OF INDIA AND EGYFr, ETC. 131 same oceans, near the land, and in narrow seas, the range between the extremes is much greater than 3°-4. In the Red Sea, from the Straits of Babeiniandel to the tropic of Cancer, I found it, in the month of May, to be 6^ viz. from 82° to 88°; and in the Indian Ocean, from lat. 12° to 19°, so much as 8°'5, viz. from 78° to 87°-5. In the Straits of Malacca, in lat. 2° N., it ranged from 80° to 85°'2. On some parts of the west coast of India (where 123J inches of rain falls during the year), during the monsoon, the surface of the sea is considerably cooled by the freshes from the numerous rivers and streamlets that descend from the lofty mountains of the Ghauts. Off Honawer, lat. 14° 16' N., the temperature of the sea during the dry season was 85°-5. During the monsoon it fell to 79°; average temperature of rain water at the time, 75°7 ; of rivers, 7^°- From its inferior specific gravity, the fresh muddy water from the hills floats on the surface of the sea to considerable distances, without being intimately blended. In the depth o^ the monsoon, near Mangalore, in 1839, the water was observed to be nearly fresh a mile off the coast; and I have seen the Mediterranean discoloured by the turbid inundation of the Nile to a distance of nearly forty miles from the Damietta embouchure. Meaii Temperature in India. — Colonel Svkes, in his statistics of the Deccan, has already noted one remarkable feature touching the mean temperature of places at elevations on 4;he table-land of India, namely, that it is much higher than the mean for the same places, calculated agreeably to Mayer's formula. To the instances he has cited of this fact, of places on the plateau of the Deccan, may be added the fol- lowing, occm-ring on the table-land of South India. Places. Feet above sea. Lat.N. Observed mean. Calculated mean. DifFereuce. Hydrabad .. Nagpore .... Bellary Bangalore . . Seringapatam J 720 1101 1600 3000 2412 o / 17 15 21 10 15 5 12 57 12 25 0 80 80 80-5 74-39 77-06 74-72 74-26 76-l« 73-05 74-93 5°-28 5-74 4-38 1-34 2-13 Among the principal causes of this differential height of temperature, — a difference more remarkable when compared with the indications afforded by the improved for- mulae of Brewster, D'Aubuisson and Atkinson, — may be enumerated the physical aspect and extent of the elevated plains on which these places stand, — the rapidity with which the drainage water passes off, and consequent little evaporation, — the comparatively fiat, or gently undulating surface, — its bareness of vegetation during great part of the year, — the non-influence of alternations of land and sea breezes, by which places near the sea are cooled, — the partial influence of the monsoon and scantiness of rain, — the favourable conditions of the atmosphere for irradiation, and the capacity of the soil for imbibing and giving out the solar heat. The temperature of the granitic soil in the vicinity of Bellary, at 2 p.m., in May, reached 121°; that of the Regur, or black soil, 122°-5 : the temperature of the air in the shade, 95°-5 : at midnight the temperature of the black soil was still so high as 86°; temperature of the ' s2 132 CAPT. NEWBOLD ON THE TEMPERATURE OF THE SPRINGS, WELLS air 80°. That of a bare rock of granite, the same locality, at 2 p.m., was 120°*5 ; of black basaltic rock 122°. The temperature of the granite at midnight was 86°'5. Both Bellary and Hydrabad are situated under the shade almost of bare granitic masses, in the midst of plains covered with sheets of the granitic and black regur soils just alluded to, whose almost treeless extent during the hot months is shrunk up and in- tersected by deep and countless fissures. The climate of the former station is nearly as dry as that of Egypt. In 1 838 only 1 1*25 inches of rain fell during the year. The atmosphere is remarkable for transparency and freedom from clouds. The foregoing views appear to be strengthened by the fact, that the observed mean temperature of the elevated stations of Ootacamund (7221 feet above the sea's level), Merc^ra (4500 feet), and Candy in Ceylon (1680 feet), are lower than their calculated mean temperatures. The calculated mean of Ootacamund is 61°*64, observed mean 55°*8; of Mercara 68°-99, observed mean 65°-58 ; and of Candy 78°-58, observed mean 73°-3. Now all these places are surrounded by an irregular surface of hill and valley, generally clothed with eternal forest, presenting an extensive radiating and evapo- rating surface, and shading the drainage of heavy monsoons that lingers in their swampy hollows. The humidity of the atmosphere at these stations is very great ; at Mercara, during nearly half the year, its hygromctric condition closely approaches saturation. Hence, favoured by the alternations of land and sea breezes, even close to the sea's level, the low temperatures of some places near the equator, viz. Singa- pore, lat. 1° 15' N., mean temperature 80°-7; Malacca, lat. 2° 14' N., mean tempe- rature 80°*4 ; Penang, lat. 5° N., mean temperature 80°-5 ; Province Wei lesley, lat. 5° 20' N., mean temperature 79°*5. The monsoons are distributed over these forest- clad regions of the equator in an almost daily succession of refreshing showers throughout the year. May not the vital functions of the plants, covering large tracts of country, particularly those concerned in their respiration and nutrition, exert an influence in cooling over-heated states of the atmosphere ? It may be further stated, in corroboration of the high temperature of table-lands being mainly produced by the causes referred to above, that the temperature of isolated peaks and summits of ridges, rising with a rapid ascent and confined super- ficies from their elevated level, appears to diminish in a greater ratio than 1° Fahr. for every 352 feet of ascent ; when, perhaps, that of the aggregate height from the sea's level is in strict accordance with this rule. The mean of a month's observa- tions by Lieut. Campbell, at the summit and base of the rock of Raya-Cottah on the table-land of Mysore, above which it is elevated 500 feet, gave a decrease of tem- perature amounting to 3°-35. The diurnal mean difference between the temperature of the summit of a mountain on the table-land of Bellary, and that of the plain at its base, I found so great as 7°-5 for the 1500 feet of elevation which separates them. This table-land has a mean temperature of nearly 4°-5 above its calculated mean. The difference of temperature of two wells, one at the summit of Mount Sinai, and the other 2000 feet below, amounted to 6°, a result closely approximating that of the comparative observations at Geneva and St. Bernard. I AND RIVERS OF INDIA AND EGYPT, ETC. 133 The highest known mean temperature of any place in India is that of Pondicherry, which, though this city stands only a little more than a degree to the south of Madras, is stated to reach 85°-28. That of Madras, in lat. 13° 5' N., is 80''-42, and of Co- lumbo, more than 5° nearer the equator than Pondicherry, only 80°75. I am not aware that any reason has been assigned for this extraordinarily high mean tem- perature; the lower temperature of some wells in the vicinity of Pondicherry leads me to doubt its correctness. Boussingault's Mode of ascei'taining the Mean Temperature of Tropical Countries. — An expeditious mode for ascertaining the approximate mean temperature of equinoc- tial regions has been proposed by M. Boussingault, and recommended to travellers, on occasions where time and opportunity do not admit of the usual means. I hardly need remark, that this method is grounded on the hypothesis, that between the tropics the temperature of the earth's crust is constant at the depth of about a foot (one-third of a metre) beneath its surface, and consists in sinking a thermometer in the soil perforated to this depth, under sheds, huts of natives, or other spots sheltered from direct warmth produced by absorption of the solar heat, from nocturnal radia- tion, and from the infiltration of rain water. The result of my own experiments in India indicates that the soil at the depth of a foot is subject to an annual, and, in light soils, taa diurnal fluctuation, varying according to the intensity of the sun's rays on the soil surrounding the sheltered spots where the experiments were con- ducted ; and radiation modified by the dry and open, moist and close nature of the soil. During cloudy weather these fluctuations were consequently found at their minimum. The maximum of diurnal fluctuation observed was at Bellary, on the centre of the table-land of peninsular India, in lat. 15° 5' N., and 1600 feet above the sea's level; mean temperature about 80°-5. The experiments were made in the hot month of May, sky unclouded ; the soil was reddish and light in texture, and completely sheltered by a thatched roof. Every precaution enjoined by M. Boussin- gault was carefully attended to, and fresh holes bored every day. Experiment. — First Day. Earth. Air in Shade. Sunrise . . . 86°5 o 81 2 P.M. . . . . 91-3 Second Day. 96-5 Sunrise . . . 85 78 2 P.M. . . , . 89 Third Day. 92 Sunrise . , . . 85-5 78-5 2 P.M. . . . . 90 Fourth Day. 95 Sunrise . . . . 87 75 2 P.M. . . . . 89 92 134 CAPT. NEWBOLD ON THE TEMPERATURE OF THE SPRINGS, WELLS At Cassergode, on the west coast, lat.N. 12° 29', whose mean temperature is about 80°, the diurnal fluctuation amounted to only 1°'5 in cloudy weather. At Mangalore, on the same coast, lat. N. 12° 53', it amounted on a clear day to 2°-75. The last ex- periment was made, at my request, by my friend Mr. B. G. Maurice, Madras Medical Service. In stiff clayey soils, at the depth of four feet from the surface, and sheltered to the distance of six yards radius from the spot perforated, the temperature fluctuated but little, and gave a tolerably correct mean of the air. In light sandy soils a greater d^pth is necessary ; and at all times it is advisable to observe the temperature of the perforation in the soil at the coldest and hottest periods of the day, which, with an unclouded sky, will be found to occur at, or just before, sunrise, and from 2 to 3 p.m. Such observations should, if possible, be compared with the temperature of a spring or well of moderate depth, at from six to ten feet below the surface, bearing in mind what has already been stated regarding the causes affecting the temperature of wells and springs. AND RIVERS OF INDIA AND EGYPT, ETC. 135 o . oo oo © © ©© u> © ©IQ ©(M©00 © "* © © eci f 00 00 00 00U5 3» «>. (M © 1-1 »« «0 © © N ;5 ;=; i* © irj i-( (N >* «o ffi ;0 CO ^ ■* «* «2^P © © © US CO f-( O CO ©« ifl ©■* «o si a a Q> o o .-tj •a O 3 i#^ a> u .«>. *<• ** CO Ui (M.^ >^^ S'-C g (U g 4J a " V e # WJ © "5 © .ifl (N IN CO t>. UJ °G0 CO «>. t>. »» CO ^(M to lO © (N S 3 o •" *^ ^11 .22 'C .52 „ oj a; 4J o c -c c c «; 5. So •28 © © © © © QO ^^ © CO CO 00 OS CO i>.^ 00 CO -* qIN M' -^ ■* 5 >« Its «o t-»oo s <1 J OSvS s W W M M ^ S O 3 c o © E o S cd 0) CO es .£ U OS OPLiO OPS H ~ S " s ^ g ^ s ^ in .2 o .a o s C p< OS c ^ ^ AND RIVERS OP INDIA AND EGYPT, ETC. 137 © .J 5 S CC 4) s S ■< o n r: o (4 3 60 O OS tT '^ -3 < CO "O ^ " « a ns " <: M KfQ >i > Cm So r& CM(k4 B S £ d g 3 & 5 -3 US ^1 S ooooo© © © ©©2 © © 2 ®® CO QO ^ o> a> © © Tt CO 00 © © •* © is< -^ji =y -<*< -. 05 --< m ^o?o t>. © -« t^eo 00 CO 00 "^ © « " s ■5 ll O fli S § 8 8 Ofl ©I «>• §? ^^ T3 '^ '^ "^ '^ '^ 'Ti '^ 'C '^ '^ '^ c gggccc « a gcco 3 So so ^ ^ s s § 00 © © ^ »«! 0.a . S bOrS tfSBfeS^*"— esaJ.SLNNN «fljf-'?> .s n MDCCCXLV. 138 CAPT. NEWBOLD ON THE TEMPERATURE OF THE SPRINGS, WELLS Comparative Register of the Temperature of the Air (in the shade) and of the Sea, from Bombay to Suez. The indications of thermometer are adjusted to those given by the standard of the Royal Society. Noon. Midnight. - Month. Lat. N. Long. £. Remarks. Air. Water. Air. Water. May 1. o 18 36 7°l 1 41 o o No obs. No obs. ~] 2. 18 5 69 38 87-5 85-5 86-5 84-5 V3 3. 17 30 67 28 87 86-5 87 No obs. 4. 16 57 69 12 86 84 86-5 No obs. m 5. 15 29 63 5 87-5 85-5 85 85 i 6. 15 52 60 53 87 85-5 85 84-5 1 7. 15 19 58 40 85 83 86 84-5 >^ 8. 14 56 56 17 85-5 82-5 85-5 82-5 -c 9. 14- 27 53 56 85-5 84-5 83-5 84 03 10. 13 43 51 39 86-5 83-5 84-5 84-5 C 11. 13 32 48 43 88 85-2 87 85 "5 12. 12 46 45 53 89 86-6 87 85-5 JB Off coast of Arabia. 13. Aden. Ad en. 89-5 87-8 86-5 86 J Back Bay, at anchor. | 14. 12 49 43 21 88-7 86 85-5 84-5 " 15. 15 14 41 55 88 86 84 84 . In sounding, off volcano of Gevel Teer. 16. 17 28 40 20 87-5 87 87 84-5 % Sun's rays 115° 2 p.m. 17. 19 55 38 52 90 88 85 85-5 >^ Sun's rays 120'''5 2 p.m. 18. 22 23 37 21 86 84-5 85-5 82 ^3 •/ 19. 24 38 36 13 84-2 80-5 82 79 20. 26 38 34 45 84 80-5 89-5 82 Suez, hot khamsin set in about 10 p.m. Memoranda supplied by the kindness of a friend from the register kept on board the Honourable East India Company's Steamer Cleopatra, from Bombay to Suez. A.M. P.M. Lat N Long. E. Remarks. Air. Water. Air. Water. April 2. o 89 o 84 8°1 o 78 3. 84 83 80 78 4. 84 84 81 83 5. 81 83 81 83 6. 80 82 80 82 7. No entry. No entry. 8. No entry. No entry. 9. No entry. No entry. 10. No entry. No entry. At Aden. 11. No entry. No entry. Passed Straits of Babelmandel. 12. 86 84 86 5 84 13.' 87 84 81 82 14.1 79 82 79 80 15. No entry. No entry. 16. 84 76 73 1 71 17. 75 82 No entry. Passed Island of Shadvvan. 18.1 i No entry. No entry. Suez Bay. N.B. The latitude and longitude have been omitted in the above register ; but after making allowance for the more rapid run of the Cleopatra than that of the vessel in which I left India, and calculating from Bombay to the Straits of Babel- mandel, and thence to Suez, an approximation may be made to the vessel's situation at the time of taking the observations. The indications could not be adjusted to the standard thermometer of the Society. AND RIVERS OP INDIA AND EGYPT, ETC. 139 Note on the Thermal Springs of the Peninsula of India. Since my arrival here my friend Mr. Malcolmson has put into my hands the first volume of the Bombay Medical and Physical Transactions, where I find, p. 257, a few notes on the thermal springs in the Konkan, by A. Duncan, Esq. The geographical distribution of these springs corroborates the remark in my paper under the head of thermal springs, viz. " that the majority of the springs termed thermal occur in India at or near lines of great faults." The thermal springs mentioned by Mr. Duncan lie at the base of the Western Ghaut elevation, intermediate between the mountains and the sea, generally from sixteen to twenty-four miles, or thereabout, inland from the latter. The line of springs follows pretty nearly that of the mountains, viz. nearly north and south, and extends from the vicinity of Surat, or about 21° N. lat. to South Rajapore : they are supposed to exist still further south, following at irregular inter- vals the line of West Ghauts to Ceylon. Not less than twelve are known to exist between Dasgaun and South Rajapore, viz. — 1 at Oonale in the taluk of Viziadroog. 3 in the Rutnaghirry taluk, at Rajwaree, Tooril and Sungmairy. 1 at Arowlee in the Konedree taluk. 1 at Mat, Hatkumbee Mahal. 1 at Oonale, in the Natoe Pali van Mahal, Severndroog. 3 at Oonale, Jaffrabad Mahal. 1 at Savi, in the Ryghur taluk, Bhar Nergannah. 1 at Oonale, Sankse taluk, Mahal Palee. 12 total. Oonale is the native term for a hot spring. The temperature of all the springs examined exceeded, with a single exception, 100° Fahr., and amounted to 109°. That of Tooril, which unfortunately was not thermometrically ascertained, appeared to Mr. Duncan to be almost at the boiling-point. The water was not found to be mineral, though impregnated with sulphuretted hydrogen. A little higher up, on the hill where the thermal spring No. 1 occurs, is a singular intermittent cold spring, over which a temple has been built. It is resorted to by crowds of Hindus during the season when the fountain periodically flows, viz. during the hot months. A more minute analysis of the water, and a more continued series of thermometric observa- tions, are a great desideratum. The temperature of a hot spring of Oonye in the jungle between Bansda and Boharee is asserted by the Brahmins to diminish annually at the time of the full moon in April, so as to admit of persons bathing in it at this period, when the natives assemble there in great numbers for that purpose. This assertion was contradicted by the late Dr. White, but the question, I see, has again been raised by the observations of Mr. J. S. Law, of the Civil Service, who found the temperature of the hottest part of the spring to have diminished at this period from 124° to 94° Fahr. It is probable however that future observations on this supposed singular annual variation will set the matter at rest. Bombay, July 15, 1842. T 2 I [ HI ] III. An Account of Newton's Dial presented to the Royal Society by the Rev. Charles Turnor, in a letter addressed to the Marquis of Northampton, Pres. R.S., &;c. By the Rev. Charles Turnor, F.R.S. Communicated by the President. Received May 25, 1844,— Read June 13, 1844. My Lord, Your Lordship having been pleased to express a wish to Captain Smyth that I should furnish a detailed account of the Newtonian Dial which I have had the honour of presenting to the Royal Society, I beg to submit to your Lordship the fol- lowing particulars. The dial was taken down in the early part of the present year from the south wall of the Manor House at Woolsthorpe*, a hamlet to Colsterworth in the county of Lincoln, the birthplace of Newton. The house is built of stone, and the dial, now in the possession of the Royal So- ciety, was marked on a large stone in the south wall at the angle of the building, and about six feet from the ground, and which was reduced to its present dimensions for the convenience of carriage. The name of Newton, with the exception of the first two letters, which have been obliterated by the hand of time, will, on close in- spection, appear to have been inscribed under the dial in rude and capital letters. There is also another dial marked on the wall, suialler than the former, and not in such good preservation. The above are the only dials about the house which I have been able to discover, nor can I find by inquiry on the spot that more ever existed, though some of Newton's biographers assert that there were several. An opinion has always prevailed that the dials now in being were executed by Newton's own hand when a boy, which appears probable from the well-known fact, that at a very early period of his life he discovered a genius for mechanical contrivances, evinced more particularly by the construction of a windmill of his own invention, and a clock to go by water applied to its machinery. Finding, however, this latter contrivance (however ingenious) to fail in keeping accurate time, it is not improbable, that with a view to secure that object, he formed with his own hands the two dials in question ; and very probably the dial now remaining in the wall of the house, from its inferiority in point of construction to that now in the possession of the Royal Society, was his first attempt in dial-making. The gnomons of these dials have un- fortunately disappeared many years, but as they are described in some of the printed * See Woodcut in the next page. 142 MR. TURNOR'S ACCOUNT OF NEWTON'S DIAL. accounts as clumsy performances, it may be concluded that they were not the work of a professed mechanic, but were probably formed and applied by Newton himself when he constructed the dials. I trust your Lordship will allow me to express the high satisfaction I feel in seeing this very interesting relic in the possession of that Society of which Newton was so distinguished an ornament, and over which he presided more than twenty years. I must beg your Lordship's permission to add, that for the gratification which I ex- perience on this occasion, I am greatly indebted to my nephew, Christopher Turnor, Esq., of Stoke, Rochford, to whom the manor-house and landed property of Newton now belong, and who not only permitted, but kindly encouraged me to offer this valuable relic to that Society, which he, as well as myself, consider as its fittest and most appropriate depository. I have the honour to be, my Lord, Your Lordship's obedient humble Servant, Spa Buildings, Cheltenham, Charles Turnor. May 24, 1844. MANOR-HOUSE, WOOLSTHORPE; THE BIRTH-PLACE OP SIR ISAAC NEWTON, P.R.S., SHOWING THE SOLAR DIALS WHICH HE MADE WHEN A BOY. [ 143 ] IV. 'A^opcjyioTa, No. I. — On a Case of Superficial Colour presented by a homogeneous liquid internally colourless. By Sir John Frederick William Herschel, Bart., K.H., F.R.S., 8^c. 8^c. Received January 28, 1845, — Read February 13, 1845. A CERTAIN variety of fluor spar, of a green colour, from Alston Moor, is well known to mineralogists by its curious property of exhibiting a superficial colour, differing much from its transmitted tint, being a fine blue of a peculiar and delicate aspect like the bloom on a plum, and like that bloom might perhaps be referred to a peculiar texture of the surface, the result of crystallization, were it not that it appears equally on a surface artificially cut and polished. Glasses also are manufac- tured which, by the agency of a delicate superficial film, consisting apparently of a dull green-coloured powder, and reflecting (or rather dispersing) a green light, ex- hibit a brownish red tint by transmission ; chloride of sulphur, and the infusion of lignum nephriticum are particularized in some books as exhibiting different colours by transmitted and reflected light. As respects the chloride of sulphur, the state- ment is incorrect, and has originated in a misapprehension of its scale of absorbent action, which (as is the case with many dichromatic media) causes its hue to change from green to red by mere increase of thickness. In the infusion of lignum nephri- ticum, and in one other instance which has occurred to my notice, the reflected tint arises from suspended particles too minute, or too nearly of the specific gravity of the liquid, to be separated by subsidence*, the transmitted colour being that of the trans- parent liquid in which they float, and the particles themselves being opake. The case which I am about to describe is not precisely parallel to any of these, though far more striking than either. That of the fluor spar presents the closest analogy to it, though from what we know of the impracticability of obliterating the internal structure of mother-of-pearl by any artificial polish, the diflference between the solid and fluid states of aggregation precludes any argument from that pheno- menon to the one in question. The sulphate of quinine is well known to be of extremely sparing solubility in water. It is however easily and copiously soluble in tartaric acid. Equal weights of the sulphate and of crystallised tartaric acidf , rubbed up together with addition of a very little water, dissolve entirely and immediately. It is this solution, largely diluted, which exhibits the optical phenomenon in question. Though perfectly trans- * I write from recollection of an experiment made nearly twenty years ago, and which I cannot repeat for want of a specimen of the wood. I think the filtered liquid did not exhibit the double colour, t Citric acid answers equally well. 144 SIR J. F. W. HERSCHEL ON THE parent and colourless when held between the eye and the light, or a white object, it yet exhibits in certain aspects, and under certain incidences of the light, an extremely vivid and beautiful celestial blue colour, which, from the circumstances of its occur- rence, would seem to originate in those strata which the light first penetrates in entering the liquid, and which, if not strictly superficial, at least exert their peculiar power of analysing the incident rays and dispersing those which compose the tint in question, only through a very small depth within the medium. To see the colour in question to advantage, all that is requisite is to dissolve the two ingredients above mentioned in equal proportions, in about a hundred times their joint weight of water, and having filtered the solution, pour it into a tall narrow cylindrical glass vessel or test tube, which is to be set upright on a dark-coloured substance before an open window exposed to strong daylight or sunshine, but with no cross lights, or any strong reflected light from behind. If we look down perpen- dicularly into the vessel so that the visual ray shall graze the internal surface of the glass through a great part of its depth, the whole of that surface of the liquid on which the light first strikes will appear of a lively blue, which as the situation of the eye changes is either fore-shortened into a vivid concave gleam, or opens out into a paler and broader band, as the visual line is more or less oblique to the glass surface. If the liquid be poured out into another vessel, the descending stream gleams in- ternally from all its undulating inequalities with the same lively yet delicate blue colour, thus clearly demonstrating that contact with a denser medium has no share in producing this singular phenomenon. The thinnest film of the liquid seems quite as effective in producing this superficial colour as a considerable thickness. For instance, if in pouring it from one glass into another, it be made to trickle down the internal surface of the receiving glass towards the light, or if instead of falling in drops from a filter, the end of the funnel be made to touch the internal surface of the vessel well moistened, so as to spread the de- scending stream over an extensive surface, the intensity of the colour is such that it is almost impossible to avoid supposing that we have a highly coloured liquid under our view. By candlelight the gleam is less vivid, and verges more to violet. Analysed by a prism the red rays are found to be almost entirely absent. No signs of polarization were perceived in it, on viewing it through a tourmaline plate turned round in its own plane. As this phenomenon in all its circumstances is (so far as I am aware) unique in physical optics, I have thought no apology necessary for simply describing, without attempting to pursue it further, which present circumstances do not permit. It would be interesting to know whether the property in question is characteristic of quinine, or is participated in by cinchonine, salicine, or any of the other vegetable alkaloids, which I have not been able to decide for want of specimens. J. F. W. Herschel. Collwgwoody Jan, 25> 1845. EPIPOLIC DISPERSION OF LIGHT. 145 Received February 20, 1845. P.S. — Having been obligingly favoured by Professor Daniell with specimens of very pure cinciionine and salicine, I am enabled to state that they do not possess in the smallest appreciable degree the curious property above shown to belong to qui- nine. As regards the latter alkaloid, all the acids I have tried appear to produce the same effect, though not all in an equal degree. The muriatic seems least efficacious ; the sulphuric and acetic decidedly the most so. The intensity of the superficial colour produced when either of the latter acids (very dilute) is used, is really sur- prising. Only acid solutions succeed. After precipitating by excess of potash a solution of quinine, the liquid filtered was very bitter, and of course contained quinine. It however exhibited no trace of superficial colour; but on dropping powdered tartaric acid into the test glass the blue colour was instantly developed, and seen to follow the course of the descending acid. J. F. W. H. Feb. 16, 1845. MDCCCXLV. U [ 147 ] V. 'Aiii6p(j)cjTa, No. II. — On the Epipblic Dispersion of Light, heing a Supplement to a paper entitled, " On a Case of Superficial Colour presented ly a homogeneous liquid internally colourlessV By Sir J. F. W. Herschel, Bart., KM., F.R.S., §c. Received March 6, — Read April 3, 1845. In reasoning- on the peculiar coloured dispersion operated on a portion of a beam of white light intromitted into a solution of sulphate of quinine, it occurred to me as a subject well worthy of inquiry whether the rays so selected for dispersion and thus singularly separated from the rest, were disting-uished by any other pecu- liarity ; whether in effect an analysis of the incident light into two distinct species qualitatively different had been performed, or merely a simple subdivision, such as takes place, for instance, in partial reflexion, as in the phenomena of the colours of thin plates. Another interesting subject of inquiry presents itself in the laws which regulate this singular mode of dispersion itself, which, for brevity, I shall venture to call (at least provisionally) epipblic, from eTriTroXi), a surface, the seat of the dispersion being at or very near the intromitting surface. As regards the question of analysis, two modes of examination present them- selves, viz. either, — I, by subjecting the dispersed portion of the light to experiment, or, 2, the residual portion, which, having escaped dispersion, preserves the unity of its direction ; and on that account, as well as by reason of its vastly superior intensity, offers itself more readily to experimental inquiry. The colour of the dispersed portion being blue, that of the residual beam ought, of course, to verge towards orange. But owing to the large excess of undecom- posed white light present, this tendency is inappreciable ; and the regularly trans- mitted beam is not to be distinguished by the eye from white light. Another reason is, that some portion of the dispersed necessarily mingles with the regularly trans- mitted beam, the medium being equally permeable to both ; so that in viewing an extensive white surface (the cloudy sky for instance, or a piece of white paper), the regularly transmitted ray reaching the eye in any given direction, that is, from any one point in the luminous surface, has, intermingled with it, a dispersed ray from every other point of that surface, the totality of which goes to restore to it some material portion of the blue light which it lost by dispersion at its intromission. In the ordinary production of colour in liquids by absorption of the comple- mentary tint, the smallest preference of one over the other coloured rays may be magnified and brought into evidence as a cause of coloration by increasing the thickness of the transmitting medium, or by passing the light successively through u2 148 SIR J. F. W. HERSCHEL ON THE many vessels filled with it. Accordingly it might be supposed that by passing the same incident beam successively through many such dispersive surfaces, the whole of the blue rays would at length be separated from it, and an orange, or red residual beam be left. But this is not the case, the reason of which is to be found in a very remarkable peculiarity in the transmitted light, which may be thus announced. An epipolized beam of light (meaning thereby a beam wliich has been once trans- mitted through a quiniferous solution and undergone its dispersing action) is inca- pahie of further undergoing epipolic dispersion. In proof of this, the following experiments may be adduced. Exp. 1. A glass jar being filled with a quiniferous solution'*, a piece of plate-glass was immersed in it vertically, so as to be entirely covered and to present one face directly to the incident light. In this situation, when viewed by an eye almost per- pendicularly over it, so as to graze either surface very obliquely, neither the anterior nor posterior face showed the slightest trace of epipolic colour. Now the light, at its egress from the immersed glass, entered the liquid under precisely the same cir- cumstances as that which, when traversing the anterior surface of the glass jar, un- derwent epipolic dispersion on first entering the liquid. It had therefore lost a pro- perty which it originally possessed, and could not therefore be considered, qualita- tively, the same light. Exp. 2. The epipolic tint is developed only on the surface of incidence. When the solution is exposed to light in a glass vessel, the posterior surface, whether viewed internally or externally, is quite colourless. Here again, since ingress and egress into and out of a medium are, optically speaking, convertible, a qualitative analysis at the surface of incidence would appear to be indicated. Exp. 3. A test cylinder filled to the height of two or three inches with the so- lution was set upright on black velvet, its bottom being also shaded to the depth of half an inch (to prevent reflected light from the bottom from reaching the eye). The epipolic tint being now fully developed, a hollow parallelopiped of plate glass, filled with the same solution, was interposed between the test cylinder and the inci- dent light, side light being at the same time obstructed by screens duly placed. Immediately the epipolic colour in the interior of the cylinder vanished altogether. The transmitting vessel was now emptied of its contents and filled with pure water, * The solution here used and subsequently referred to (except when otherwise expressed) is formed by add- ing to sulphuric acid, diluted to such an extent as just to bear being swallowed without pain, about one two- hundredth part of its weight, (the weight, i. e. of the diluted acid) of sulphate of quinine. When of this strength it is difficult to believe that a bottle half-filled with it contains a colourless liquid. When shaken, it tinges the glass vividly blue : lively blue gleams are reflected from the interior, and from the capillary ring at the surface level, &c. I may mention that in one instance a rose-coloured solution was formed, which I have never been able to reproduce. The ingredients were taken from the very same parcels which gave the usual colourless solution, and the mixture made in the identical vessel which had just recently served for the same experiments, and which had not even been washed, and from which a colourless solution had just been emptied. If owing to any foreign ingredient accidentally present, the quantity must have been inconceivably minute. EPIPOLIC DISPERSION OF LIGHT. 149 from which its former contents were in no way distinguishable by an eye situated behind it. Being then replaced as before, so as to intercept the light incident on the test cylinder, the epipolic colour was produced, exactly as if nothing had been interposed ; a trifling difference of intensity only excepted, which arose from the glass used not being wholly devoid of colour. Exp. 4. This experiment was varied so as to present a result disengaged from this slight source of uncertainty, and perfectly decisive. A cylindrical jar was coated exter- nally with black paper round three-fourths of its circumference, as was also its bottom, and a ring of the same paper was carried round the cylinder at the bottom so as to cut off light from being internally reflected on its base. In it was set upright a test cylinder of the solution, and the jar was then filled with pure water rising considerably above the solution in the cylinder. When exposed to light as usual, the epipolic tint was finely seen. But on emptying out the water, and introducing in its stead an equal quantity of the quiniferous solution, the tint in question was completely destroyed, whether the surface of the cylinder was viewed from within or from without, proving evidently that no rays susceptible of epipolic dispersion had reached its surface. This result was rendered the more remarkable by an effect of contrast. The external, upper portion of the cylinder, above its liquid contents, but below the level of the liquid in the jar, reflected to the eye (or rather the air within it reflected) a pretty strong blue gleam, being no other than the epipolically dispersed light of the anterior surface of the liquid in the jar ; while all below (being glass in contact with the liquid on both sides and so deprived of reflective power on both surfaces) was com- pletely dark and almost invisible. When the interior test cylinder was sloped backwards from the incident light at an angle of about 70° to the horizon, a beautiful and instructive feature was deve- loped. In this situation of things, the interior liquid being as usual the quinine solu- tion, and the exterior pure water ; to an eye perpendicularly over the surface, the whole anterior portion of the cylinder from below upwards to the surface of the interior liquid, appeared coated as it were internally with a most delicate and beautiful blue film of extreme tenuity and perfect transparency, presenting a singular ghost-like appear- ance, easier produced than described. This being seen through the cylinder, by an eye situated externally to its prolongation, affords a proof that the epipolic dispersion takes place in all directions : but except in this mode of viewing it the rays dispersed outwards cannot reach the eye, or not in abundance (for which a very oblique inci- dence is required), being at such an incidence internally and totally reflected by the outer surface of the glass. To see this to advantage an eye-tube internally blackened should be used to guard the eye from extraneous light. Such a tube indeed is ge- nerally advantageous in all these experiments. If, instead of water, the test cylinder be plunged into a solution of quinine, all else remaining as before, the blue film in question totally disappears. I tried a great many other liquids, all in fact which I had at hand in sufficient quantity and colour- 150 SIR J. F. W. HERSCHEL ON THE less, or but little coloured, in hopes of discovering something which might elucidate the subject. Strong alcohol, solution of corrosive sublimate, ammonia, &c. acted as water ; allowing the blue film to be seen externally at a perpendicular incidence of the visual ray to the surface of the liquid. With strong sulphuric acid, and with muriate of lime so concentrated as to be syrupy, this was not possible, but the film became visible, and of its full intensity, on moving the eye forward (i. e. towards the incident light). When sulphate of manganese was used, its delicate pale rose-co- lour no way prevented a fine exhibition of the blue film (a point to which I shall have occasion to revert). On the other band, the lemon yellow-colour of nitrate of ura- nium (a much fuller tint) materially enfeebled, though it did not prevent the forma- tion of the film. This last effect did however appear to be produced by two liquids, viz, pyroxylic spirit in a small degree, and oil of turpentine in a much greater ; the effect in this case being very obviously much more than could justly be attributed to a trifling tinge of yellow in the oil (which was not fresh), as I satisfied myself by a comparative experiment with water purposely coloured to a similar tint of greater intensity. Neither of these liquids however was found on trial in the test cylinder, or otherwise, to possess in the smallest degree the property of epipolic dispersion; nor have I found any other liquid which does so. Exp. 5. Among solids the only one I am acquainted with possessed of a simi- lar property, is the green fluor of Alston Moor, which exhibits by superficial dispersion a fine deep blue colour, very different from the inherent or absorptive colour of the mineral. This is strictly an epipolic tint, as the following experiment will show, and at the same time affords another, and not a little striking confirmation of the general proposition announced in p. 148. I should premise that to see the epipolic colour of the fluor in perfection, it must be laid on black velvet, or the re- flexion of light from its posterior surfaces must be destroyed by roughening and coating them with black sealing-wax. In this state, if exposed to daylight at a window, and viewed through a blackened eye-tube, it is seen not as a green, but as a fine deep blue crystal. If a piece of fluor so prepared be placed in water in a glass standing on black velvet, the blue epipolic colour is seen greatly heightened. But if the water be exchanged for a solution of quinine, this colour is completely destroyed and the surface appears simply black. To make the experiment successfully, the greatest care must be taken to cut off all lateral or reflected light. The arrangement I adopted was, to coat a fluor as above described, and fastening it with black sealing-wax to a wire, to lower it into the coated jar described in Exp. 4, filled alternately with a solution of quinine and with pure water. Using the eye-tube for further precaution, the destruction of the epipolic tint by the solution was quite as complete as if instead of the fluor a test glass full of the quiniferous solution had been used. It would certainly appear from these experiments that the residual beam after un- dergoing epipolic dispersion had lost some constituent portion, or otherwise under- EPIPOLIC DISPERSION OF LIGHT. 151 gone some qualitative modification which might be considered as rendering it spe- cifically difFeient from the incident beam. It cannot be the mere tinge of colour which the loss of so small a portion of blue light has given to it. There is still plenty of blue light left, and the experiment on sulphate of manganese proves that a mere absorption of a much larger proportion of the blue rays has not the same effect. Moreover the portion of light dispersed traverses the solution of quinine with perfect facility, proving that no peculiar absorptive power is exercised by that medium on these rays ; nor indeed would the separation of such rays by dispersion at the surface in any way tinge the medium itself with a complementary tint, but only the residual beam. I come now to the examination of the dispersed portion of the light. As just remarked, when once dispersed it is freely transmitted. The epipolic colour is seen as well, in a long test-cylinder filled with the solution, at the bottom of the tube as at the top, when viewed by an eye situated in its axis, supposed vertical. If all light be cut off from the tube by a sheet of black paper rolled round it, except from the lowest inch of its length, that inch is seen to gleam with quite as intense a colour as when the uppermost inch only is so exposed. I have already had occasion to remark that the epipolic tint is a compound one. To obtain a pure ray for prismatic analysis, a cylindrical glass jar with perpendicular sides was partly filled with the quiniferous liquid and placed in a strong light, the whole anterior side being coated with black paper rising somewhat above the level of the liquid. The eye was then placed in such a position, below that level, that the visual ray proceeding from it would suffer total reflexion at the under surface. For comparison, a similar vessel of water, similarly shaded, was placed beside it. The surface of this, so viewed from below, was of course perfectly black, no ray from above being able so to penetrate it as to reach the eye. Not so the quiniferous solu- tion. In this the under surface was wholly visible, of a fine blue colour, considerably deeper in tint than in the ordinary mode of viewing it, though not of so rich and saturated a character as the epipolic blue of the fluor. It was, however, much more luminous, and being thus completely purified from all possible admixture of regularly refracted or reflected light, was well-adapted for prismatic analysis. By raising the eye exactly to the horizontal level of the surface of the liquid, the whole of that surface became of course foreshortened into a narrow blue line. And in this situation it became perfectly evident that this line was not a mere elon- gated ellipse, the perspective representation of the circular area of the surface, but a very narrow parallelogram, having a breadth of about a fiftieth of an inch, of a vivid and nearly uniform blue colour over its whole breadth. This proves that the epipolic dispersion takes place within the liquid, and almost wholly within a distance not exceeding one-fiftieth of an inch from the surface. I say almost wholly ; for when a sunbeam was directed downwards on the surface, by total reflexion from the base of a prism, a feeble blue gleam was observed to extend downwards below this vivid 152 SIR J. F. W. HERSCHEL ON THE line to nearly half an inch from the surface, thus leaving it doubtful whether some small amount of dispersion may not be effected in the interior of the medium at ap- preciable depths. The narrow blue line above described was viewed through a Fraunhofer flint prism. The spectrum was deficient at the red end by the totality of the purer and less refrangible red, nearly the whole orange, and all the yellow. A rich and broad band of fine green ligiit slightly fringed with red on the less refrangible side, passed suddenly, on the more refrangible, to a copious indigo and violet without any inter- mediately graduating blue. Either from want of sufficient brightness, or from some other cause, no black lines were seen ; as far as mere illumination went, the spectrum developed appeared continuous. It appears from this that no one prismatic ray in particular is selected for epi- polic dispersion, but that a certain small per-centage of rays extending over a great range of refrangibility are subject to be so affected, the less refrangible extreme being however wholly excluded, as well as the majority of all below a mean refrangibility. The epipolic colour is more intense the more oblique the visual ray is to the dispersing surface. This, which would be inexplicable on the supposition of the dispersion being effected rigorously at the geometrical surface of the medium, is a necessary consequence of its taking place within a superficial stratum of very small, but appreciable thickness, or according to a law of intensity decreasing with great rapidity as the depth within the medium increases. It has been already shown that the dispersion is not confined to the interior of the liquid, but that a large portion of the dispersed light is directed outwards, Exp. 4. The more oblique portions of this (which are also the more intense) require, as is there shown, peculiar management to render them visible. Those whose inclination to the dispersive surface is greater, may also be subjected to ocular inspection, by carefully destroying all regularly re- flected or accidental light. Thus, if on a surface of black paper two blots be made, the one of water, the other of a solution of quinine, and if these be laid before a window and viewed through a blackened tube in any direction but that of regular reflexion, the water will appear perfectly black, the quinine feebly blue. But however oblique to the surface the visual ray may be in this case, no great accession of inten- sity takes place in the epipolic tint, for this obvious reason, that the dispersing stratum being ivithin the medium, no ray dispersed by it can penetrate the surface, which has not an inclination thereto exceeding 41° 22', at which angle, therefore, it must cut the stratum, and cannot therefore traverse any great extent of it bodily. Hence, moreover, on the other hand, the internally dispersed light, at great obli- quities to the surface (supposed in contact with air), will be reinforced by all that portion which would have penetrated the surface and gone into the air but for the law of total reflexion ; all the dispersed rays, that is to say, whose inclination to the surface is less than 41° 22'. This consideration helps to explain the great comparative intensity which the dispersed beam possesses under such circumstances. EPIPOLIC DISPERSION OF LIGHT. 153 As it has been clearly shown that a beam of white light from which certain rays have been separated by epipolic dispersion is no longer susceptible of producing the epipolic phenomena, it would seem a natural and almost a necessary conclu- sion, that the rays so separated ought to be ivholly, or in a very high degree, so dispersed when incident on an epipolizing surface. But the whole history of physical optics is one continued warning against such seeming logical conclusions ; and in this case also the conclusion is not borne out by fact. Thus in Exp. 2 and 4, abun- dance of rays internally dispersed must of necessity have been incident on the new surface presented to them, yet no fresh dispersion whatever took place. I may add too that in experiments made with considerable care to exclude all other light from incidence on a quiniferous surface, but such as had originated in epipolic dispersion, I have not succeeded in obtaining any indication of their susceptibility of being a second time so dispersed. Though from the obscurity of such rays as compared with direct light, these trials can hardly be considered as proving a negative, yet they certaiidy go very far towards proving the absence of any peculiar susceptibility in those rays to this particular affection. J. F. W. Herschel. Collingivoodi March 1,1845. Note added during the Printing. — Professor Graham has had the kindness to transmit to me a specimen of an alkaloid, extracted from the brown coat of the seed of the chestnut, to which the name Esculine has been given, which possesses in per- fection the property of epipolic dispersion when in dilute solution, in which state it precisely resembles quinine. The same eminent chemist refers also to a peculiar oil called Colophene, formed by the regulated action of sulphuric acid on oil of tur- pentine, which by his description of its phenomena, must also be an epipolizing liquid of a similar character. J. F. W. H. May 12, 1845. MDCCCXLV. C 155 ] VI. On the Liquefaction and Solidification of Bodies generally existing as Gases. By Michael Faraday, Esq., D.C.L. F.R.S., Fullerian Prof. Chem. Royal Institution, Foreign Associate of the Acad. Sciences, Paris, Corr. Memb. Royal and Imp. Acadd. of Sciences, Petershurgh, Florence, Copenhagen, Berlin, Gottingen, Modena, Stockholm, 6^c. 8fc. Received December 19, 1844, — Read January 9, 1845. 1 HE experiments formerly made on the liquefaction of gases*, and the results which from time to time have been added to this branch of knowledge, especially by M. Thilorier-j-, have left a constant desire on my mind to renew the investigation. This, with considerations arising out of the apparent simplicity and unity of the molecular constitution of all bodies when in the gaseous or vaporous state, which may be expected, according to the indications given by the experiments of M. Cagniard de LA Tour, to pass by some simple law into their liquid state, and also the hope of seeing nitrogen, oxygen, and hydrogen, either as liquid or solid bodies, and the latter probably as a metal, have lately induced me to make many experiments on the subject ; and though my success has not been equal to my desire, still I hope some of the results obtained, and the means of obtaining them, may have an interest for the Royal Society; more especially as the application of the latter may be carried much further than I as yet have had opportunity of applying them. My object, like that of some others, was to subject the gases to considerable pressure with considerable depression of tempera- ture. To obtain the pressure, I used mechanical force, applied by two air-pumps fixed to a table. The first pump had a piston of an inch in diameter, and the second a piston of only half an inch in diameter ; and these were so associated by a connecting pipe, that the first pump forced the gas into and through the valves of the second, and then the second could be employed to throw forward this gas, already condensed to ten, fifteen, or twenty atmospheres, into its final recipient at a much higher pressure. The gases to be experimented with were either prepared and retained in gas holders or gas jars, or else, when the pumps were dispensed with, were evolved in strong glass vessels, and sent under pressure into the condensing tubes. When the gases were over water, or likely to contain water, they passed, in their way from the air-holder to the pump, through a coil of thin glass tube retained in a vessel filled with a good mixture of ice and salt, and therefore at the temperature of 0° Fahr. ; the water that was condensed here was all deposited in the first two inches of the coil. * Philosophical Transactions, 1823, pp. 160, 189. f Annales de Chimie, 1835, Ix. 427, 432. x2 156 DR. FARADAY ON THE LIQUEFACTION AND SOLIDIFICATION OF The condensing tubes were of green bottle glass, being from Jth to Jth of an inch external diameter, and from ^^-6 to ^th of an inch in thickness. They were chiefly of two kinds, about eleven and nine inches in length ; the one, when horizontal, having a curve downward near one end to dip into a cold bath, and the other, being in form like an inverted siphon, could have the bend cooled also in the same manner when necessary. Into the straight part of the horizontal tube, and the longest leg of the siphon tube, pressure gauges were introduced when required. Fig. I. Fig. 2. iiro Caps, stop-cocks and connecting pieces were employed to attach the glass tubes to the pumps, and these, being of brass, were of the usual character of those employed for operations with gas, except that they were small and carefully made. The caps were of such size that the ends of the glass tubes entered freely into them, and had rings or a female screw worm cut in the interior, against which the cement was to adhere. The ends of the glass tubes were roughened by a file, and when a cap was to be fastened on, both it and the end of the tube were made so warm that the cement*, when applied, was thoroughly melted in contact with these parts, before the tube and cap were brought together and finally adjusted to each other. These junctions bore a pressure of thirty, forty, and fifty atmospheres, with only one failure, in above one hundred instances ; and that produced no complete separation of parts, but simply a small leak. The caps, stop-cocks, and connectors, screwed one into the other, having one com- mon screw thread, so as to be combined in any necessary manner. There were also screw plugs, some solid, with a male screw to close the openings or ends of caps, &c., others with a female screw to cover and close the ends of stop-cocks. All these screw joints were made tight by leaden washers ; and by having these of different thickness, equal to from f th to -g-th of the distance between one turn of the screw thread and the next, it was easy at once to select the washer which should allow a sufficient compression in screwing up to make all air-tight, and also bring every part of the apparatus into its right position. * Five parts of resin, one part of yellow bees'-wax, and one part of red ochre, by weight, melted together. BODIES GENERALLY EXISTING AS GASES. 157 I have often put a pressure of fifty atmospheres into these tubes, and have had no accident or failure (except the one mentioned). With the assistance of Mr. Addams I have tried their strength by a hydrostatic press, and obtained the following results : — A tube having an external diameter of 0-24 of an inch and a thickness of 0*0175 of an inch, burst with a pressure of sixty-seven atmospheres, reckoning one atmosphere as 1 5 lb. on the square inch. A tube which had been used, of the shape of fig. 1, its external diameter being 0-225 of an inch, and its thickness about 0'03 of an inch, sustained a pressure of 118 atmospheres without breaking, or any failure of the caps or cement, and was then removed for further use. A tube such as I have employed for generating gases under pressure, having an external diameter of 0*6 of an inch, and a thickness of 0035 of an inch, burst at twenty-five atmospheres. Having these data, it was easy to select tubes abundantly suflScient in strength to sustain any force which was likely to be exerted within them in any given experi- ment. The gauge used to estimate the degree of pressure to which the gas within the con- densing tube was subjected was of the same kind as those formerly described*, being a small tube of glass closed at one end with a cylinder of mercury moving in it. So the expression of ten or twenty atmospheres, means a force which is able to compress a given portion of air into -r^th or Yo^h of its bulk at the pressure of one atmosphere of thirty inches of mercury. These gauges had their graduation marked on them with a black varnish, and also with Indian ink : — there are several of the gases which, when condensed, cause the varnish to liquefy, but then the Indian ink stood. For further precaution, an exact copy of the gauge was taken on paper, to be applied on the outside of the condensing tube. In most cases, when the experiment was over, the pressure was removed from the interior of the apparatus, to ascertain whether the mercury in the gauge would return back to its first or starting-place. For the application of cold to these tubes a bath of Thilorier's mixture of solid carbonic acid and ether was used. An earthenware dish of the capacity of four cubic inches or more was fitted into a similar dish somewhat larger, with three or four folds of dry flannel intervening, and then the bath mixture was made in the inner dish. Such a beith will easily continue for twenty or thirty minutes, retaining solid carbonic acid the whole time ; and the glass tubes used would sustain sudden immersion in it without breaking. But as my hopes of any success beyond that heretofore obtained depended more upon depression of temperature than on the pressure which I could employ in these tubes, I endeavoured to obtain a still greater degree of cold. There are, in fact, some results producible by cold which no pressure may be able to effect. Thus, solidification has not as yet been conferred on a fluid by any degree of pressure. Again, that beautiful condition which Cagniard de la Tour has made known, and * Philosophical Transaction?, 1823, p. 192. 158 DR. FARADAY ON THE LIQUEFACTION AND SOLIDIFICATION OF which comes on with liquids at a certain heat, may have its point of temperature for some of the bodies to be experimented with, as oxygen, hydrogen, nitrogen, &c., below that belonging to the bath of carbonic acid and ether ; and, in that case, no pressure which any apparatus could bear would be able to bring them into the liquid or solid state. To procure this lower degree of cold, the bath of carbonic acid and ether was put into an air-pump, and the air and gaseous carbonic acid rapidly removed. In this way the temperature fell so low, that the vapour of carbonic acid given off by the bath, instead of having a pressure of one atmosphere, had only a pressure of -g^th of an atmosphere, or 1*2 inch of mercury; for the air-pump barometer could be kept at 28'2 inches when the ordinary barometer was at 29*4. At this low temperature the carbonic acid mixed with the ether was not more volatile than water at the temperature of 86°, or alcohol at ordinary temperatures. In order to obtain some idea of this temperature, I had an alcohol thermometer made, of which the graduation was carried below 32° Fahr., by degrees equal in capacity to those between 32° and 212°. When this thermometer was put into the bath of carbonic acid and ether surrounded by the air, but covered over with paper, it gave the temperature of 106° below 0°. When it was introduced into the bath under the air-pump, it sank to the temperature of 166^^ below 0°; or 60° below the temperature of the same bath at the pressure of one atmosphere, /. e. in the air. In this state the ether was very fluid, and the bath could be kept in good order for a quarter of an hour at a tim.e. As the exhaustion proceeded I observed the temperature of the bath and the corre- sponding pressure, at certain other points, of which the following maybe recorded: — The external barometer was 29*4 inches : inch. Fahr, o when the mercury in the air-pump barometer was 1 the bath temperature was— 106, 10 20 22 24 26 27 28 28-2 -112i, — 121, — 125, — 131, -139, — 146, — 160, — 166; but as the thermometer takes some time to acquire the temperature of the bath, and the latter was continually falling in degree ; as also the alcohol thickens considerably at the lower temperature, there is no doubt that the degrees expressed are not so low as they ought to be, perhaps even by 5° or 6° in most cases. With dry carbonic acid under the air-pump receiver I could raise the pump baro- meter to twenty-nine inches when the external barometer was at thirty inches. BODIES GENERALLY EXISTING AS GASES. 159 The arrangement by which this cooling power was combined in its effect on gases with the pressure of the pumps, was very simple in principle. An air-pump receiver open at the top was employed ; the brass plate which closed the aperture had a small brass tube about six inches long, passing through it air-tight by means of a stufSng- box, so as to move easily up and down in a vertical direction. One of the glass con- densing siphon tubes, already described, fig. 1, was screwed on to the lower end of the sliding tube, and the upper end of the latter was connected with a communi- cating tube in two lengths, reaching from it to the condensing pumps ; this tube was small, of brass, and Qj feet in length ; it passed six inches horizontally from the condensing pumps, then rose vertically for two feet, afterwards proceeded horizontally for seven feet, and finally turned down and was immediately connected with the sliding tube. By this means the latter could be raised and lowered vertically, without any strain upon the connexions, and the condensing tube lowered into the cold bath in vacuo, or raised to have its contents examined at pleasure. The capa- city of the connecting tubes beyond the last condensing pump was only two cubic inches. When experimenting with any particular gas, the apparatus was put together fast and tight, except the solid terminal screw-plug at the short end of the condensing tube, which being the very extremity of the apparatus, was left a little loose. Then, by the condensing pumps, abundance of gas was passed through the apparatus to sweep out every portion of air, after which the terminal plug was screwed up, the cold bath arranged, and the combined effects of cold and pressure brought to unite upon the gas. There are many gases which condense at less than the pressure of one atmosphere when submitted to the cold of a carbonic acid bath in air (which latter can upon occasions be brought considerably below —106° Fahr.). These it was easy, therefore, to reduce, by sending them through small conducting tubes into tubular receivers placed in the cold bath. When the receivers had previously been softened in a spirit lamp flame, and narrow necks formed on them, it was not difficult by a little further management, hermetically to seal up these substances in their condensed state. In this manner chlorine, cyanogen, ammonia, sulphuretted hydrogen, arseniuretted hy- drogen, hydriodic acid, hydrobromic acid, and even carbonic acid, were obtained, sealed up in tubes in the liquid state; and euchlorine was also secured in a tube receiver with a cap and screw-plug. By using a carbonic acid bath, first cooled in vacuo, there is no doubt other condensed gases could be secured in the same way. The fluid carbonic acid was supplied to me by Mr. Addams, in his perfect apparatus, in portions of about 220 cubic inches each. The solid carbonic acid, when produced from it, was preserved in a glass ; itself retained in the middle of three concentric glass jars, separated from each other by dry jackets of woollen cloth. So eflfectual was this arrangement, that I have frequently worked for a whole day of twelve and fourteen hours, having solid carbonic acid in the reservoir, and enough for all 160 DR. FARADAY ON THE LIQUEFACTION AND SOLIDIFICATION OF the baths I required during the whole time, produced by one supply of 220 cubic inches^. By the apparatus, and in the manner, now described, all the gases before condensed were very easily reduced, and some new results were obtained. When a gas was liquefied, it was easy to close the stop-cock, and then remove the condensing tube with the fluid from the rest of the apparatus. But in order to preserve the liquid from escaping as gas, a further precaution was necessary ; namely, to cover over the exposed end of the stop-cock by a blank female screw-cap and leaden washer, and also to tighten perfectly the screw of the stop-cock plug. With these precautions I have kept carbonic acid, nitrous oxide, fluosilicon, &c. for several days. Even with gases which could be condensed by the carbonic acid bath in air, this apparatus in the air-pump had, in one respect, the advantage ; for when the conden- sing tube was lifted out of the batli into the air, it immediately became covered with hoar frost, obscuring the view of that which was within ; but in vacuo this was not the case, and the contents of the tube could be very well examined by the eye. Olefiant gas. — This gas condensed into a clear, colourless, transparent fluid, but did not become solid even in the carbonic acid bath in vacuo ; whether this was because the temperature was not low enough, or for other reasons referred to in the account of euchlorine, is uncertain. The pressure of the vapour of this substance at the temperature of the carbonic acid bath in air (— 103°Fahr.) appeared singularly uncertain, being on different occasions, and with different specimens, 3'7j ^'7, 5 and 6 atmospheres. The Table below shows the tension of vapour for certain degrees below 0° Fahr., with two dif- ferent specimens obtained at d liferent times, and it will illustrate t Fahr. Atmospheres 3. Atmospheres. — 100 . . . 4-60 . 9-30 - 90 . . . 5-68 10-26 - 80 . . . 6-92 11-33 - 70 . . . 8-32 . 12-52 - 60 . . . 9-88 13-86 -50 . . . 1172 , 15-36 - 40 . . . 13-94 17*05 - 30 . , . 16-56 . 18-98 — 20 . . . 19-58 . 21-23 — 10 . . . 23-89 0 . . . 27-18 10 . . . 31-70 20 . . . 36-80 30 . . . 42-50 * On one occasion the solid carbonic acid was exceedingly electric, but I could not produce the effect again : it was probably connected with the presence of oil which was in the carbonic acid box ; neither it nor the fila- BODIES GENERALLY EXISTING AS GASES. 161 I have not yet resolved this irregulanty, but believe there are two or more sub- stances, physically, and perhaps occasionally chemically different, in olefiant gas ; and varying in proportion with the circumstances of heat, proportions of ingredients, &c. attending the preparation. The fluid affected the resin of the gauge graduation, and probably also the resin of the cap cement, though slowly. Hydriodic acid. — This substance was prepared from the iodide of phosphorus by heating it with a very little water. It is easily condensable by the temperature of a carbonic acid bath : it was redistilled, and thus obtained perfectly pure. The acid may be obtained either in the solid or liquid, or (of course) in the gaseous state. As a solid it is perfectly clear, transparent, and colourless ; having fissures or cracks in it resembling those that run through ice. Its solidifying temperature is nearly —60° Fahr., and then its vapour has not the pressure of one atmosphere ; at a point a little higher it becomes a clear liquid, and this point is close upon that which corresponds to a vaporous pressure of one atmosphere. The acid dissolves the cap cement and the bitumen of the gauge graduation ; and appears also to dissolve and act on fat, for it leaked by the plug of the stop-cock with remarkable facility. It acts on the brass of the apparatus, and also on the mercury in the gauge. Hence the following results as to pressures and temperatures are not to be considered more than approximations : — At 0° Fahr. pressure was 2*9 atmospheres. At 32° Fahr. pressure was 3*97 atmospheres. At 60° Fahr. pressure was 5-86 atmospheres. Hydrohi^omic acid. — This acid was prepared by adding to perbromide of phos- phorus* about one-third of its bulk of water in a proper distillatory apparatus formed of glass tube, and then applying heat to distil off the gaseous acid. This being sent into a very cold receiver, was condensed into a liquid, which being rec- tified by a second distillation, was then experimented with. Hydrobromic acid condenses into a clear colourless liquid at 100° below 0°, or lower, and has not the pressure of one atmosphere at the temperature of the carbonic acid bath in air. It soon obstructs arid renders the motion of the mercury in the air- gauge irregular, so that I did not obtain a measure of its elastic force ; but it is less than that of muriatic acid. At and below the temperature of —124° Fahr. it is a ments of ice which formed on it in the air conducted, for when touched it preserved its electric state. Believing as yet that the account I have given of the cause of the electric state of an issuing jet of steam and water (Phil. Trans. 1843, p. 17) is the true one, I conclude that this also was a case of the production of electricity simply by friction, and unconnected with vaporization. * The bromides of phosphorus are easily made without risk of explosion. If a glass tube be bent so as to have two depressions, phosphorus placed in one and bromine in the other ; then by incHning the tube, the vapour of bromine can be made to flow gradually on to, and combine with, the phosphorus. The fluid proto- bromide is first formed, and this is afterwards converted into solid perbromide. The excess of bromine may be dissipated by the careful application of heat. MDCCCXLV. Y 162 DR. FARADAY ON THE LIQUEFACTION AND SOLIDIFICATION OF solid, transparent, crystalline body. It does not freeze until reduced much lower than this temperature ; but being frozen by the carbonic acid bath in vacuo, it re- mains a solid until the temperature in rising attains to —124°. Fluosilicon. — I found that this substance in the gaseous state might be brought in contact with the oil and metal of the pumps, without causing injury to them, for a time sufficiently long to apply the joint process of condensation already described. The substance liquefied under a pressure of about nine atmospheres at the lowest tem- perature, or at 160° below 0°; and was then clear, transparent, colourless, and very fluid like hot ether. It did not solidify at any temperature to which I could submit it. I was able to preserve it in the tube until the next day. Some leakage had then taken place (for it ultimately acted on the lubricating fat of the stop-cock), and there was no liquid in the tube at comqion temperatures ; but when the bend of the tube was cooled to 32° by a little ice, fluid appeared : a bath of ice and salt caused a still more abundant condensation. The pressure appeared then to be above thirty at- mospheres, but the motion of the mercury in the gauge had become obstructed through the action of the fluosilicon, and no confidence could be reposed in its indications. Phosphuretted /n/droge?i. —This gas was prepared by boiling phosphorus in a strong pure solution of caustic potassa, and the gas was preserved over water in a dark room for several days to cause the deposition of any mere vapour of phosphorus which it might contain. It was then subjected to high pressure in a tube cooled by a carbonic acid bath, which had itself been cooled under the receiver of the air-pump. The gas in its way to the pumps passed through a long spiral of thin narrow glass tube im- mersed in a mixture of ice and salt at 0°, to remove as much water from it as possible. By these means the phosphuretted hydrogen was liquefied ; for a pure, clear, colour- less, transparent and very limpid fluid appeared, which could not be solidified by any temperature applied, and which when the pressure was taken oflf immediately rose again in the form of gas. Still the whole of the gas was not condensable into this fluid. By working the pumps the pressure would rise up to twenty-five atmospheres at this very low temperature, and yet at the pressure of two or three atmospheres and ^ the same temperature, liquid would remain. There can be no doubt that phosphu- retted hydrogen condensed, but neither can there be a doubt that some other gas, not so condensable, was also present, which perhaps may be either another phosphu- retted hydrogen or hydrogen itself. Fluohoron. — This substance was prepared from fluor spar, fused boracic acid and strong sulphuric acid, in a tube generator such as that already described, and con- ducted into a condensing tube under the generating pressure. The ordinary car- bonic acid bath did not condense it, but the application of one cooled under the air- pump caused its liquefaction, and fluoboron then appeared as a very limpid, colour- less, clear fluid, showing no signs of solidification, but when at the lowest tempe- rature mobile as hot ether. When the pressure was taken oft', or the temperature raised, it returned into the state of gas. BODIES GENERALLY EXISTING AS GASES. 163 The following are some results of pressure, all that I could obtain with the liquid in my possession ; for, as the liquid is light and the gas heavy, the former rapidly disappears in producing the latter. They make no pretensions to accuracy, and are given only for general information. Fahr. / atmospheres. Fahr. Atmospheres. Fahh. Atmospheres — 100 . . . 4-61 -72 . . . 9-23 o — 62 . . . 11-54. — 82 . • . 7-5 -66 . . . 10-00 The preceding are, as far as I am aware, new results of the liquefaction and solidi- fication of gases. I will now briefly add such other information respecting solidifi- cation, pressure, &c., as I have obtained with gaseous bodies previously condensed. As to pressure, considerable irregularity often occurred, which I cannot always refer to its true cause; sometimes a little of the compressed gas would creep by the mer- cury in the gauge, and increase the volume of inclosed air ; and this varied with different substances, probably by some tendency which the glass had to favour the condensation of one (by something analogous to hygrometric action) more than another. But even when the mercury returned to its place in the gauge, there were anomalies which seemed to imply, that a substance, supposed to be one, might be a mixture of two or more. It is, of course, essential that the gauge be preserved at the same temperature throughout the observations. Muriatic acid. — This substance did not freeze at the lowest temperature to which I could attain. Liquid muriatic acid dissolves bitumen ; the solution, liberated from pressure, boils, giving off muriatic acid vapour, and the bitumen is left in a solid frothy state, and probably altered, in some degree, chemically. The acid unites with and softens the resinous cap cement, but leaves it when the pressure is dimi- nished. The following are certain pressures and temperatures which, I believe, are not vei-y far from truth ; the marked numbers are from experiment. Fahr. Atmospheres. Fahr. Atmospheres. Fahr. Atmospheres ^ — 100 . . 1-80 ^ - 5°3 . . . 5-83 v^- 5 . . . 13-88 w__ 92 . . 2-28 -50 . . 6-30 - 0 . . . 15-04 - 90 . . . 2-38 42 . . . 7*40 10 . . . 1774 ^— 83 . . . 2-90 — 40 . . . 7-68 20 . . . 21-09 - 80 . . . 312 V--33 . . . 8-53 - 25 . . . 23-08 — 11 . . 3-37 — 30 . . . 9-22 30 . . . 25-32 - 70 . . . 4-02 v^__22 . . . 10-66 - 32 . . . 26-20 Q1 . . . 4-26 -20 . . . 10-92 40 . . . 30-67 — 60 . . . 5-08 — 10 . . . 12-82 The result formerly obtained* was forty atmospheres at the temperature of 50° Fahr. * Philosophical Transactions, 1823, p. 198. v2 . 164 DR. FARADAY ON THE LIQUEFACTION AND SOLIDIFICATION OF Sulphurous acid. — When liquid, it dissolves bitumen. It becomes a crystalline, transparent, colourless, solid body, at —105° Fahr. ; when partly frozen the crystals are well-formed. The solid sulphurous acid is heavier than the liquid, and sinks freely in it. The following is a table of pressures in atmospheres of 30 inches mer- cury, of which the marked results are from many observations, the others are in- terpolated. They differ considerably from the results obtained by Bunsen*, but agree with my first and only result. Fahr. Atmospheres. Fahk. Atmospheres. Fahr. Atmospheres c 0 . . . 0725 40 . . 178 76-8 . . 3-50 10 . . . 0-92 46-5 . . 2-00 85 . . . 4-00 -14 . . . 1-00 -48 . . 2-06 - 90 . . . 4-35 -19 . . . 1-12 -56 . . 2-42 93 . . . 4-50 -23 . . 1-23 58 . . 2-50 98 . . . 500 -26 . . 1-33 -64 . . 276 -100 . . 5-16 31-5. . 1-50 68 . . . 3-00 104 . . . 5-50 -32 . . . 1-53 -73-5 . . . 3-28 110 . . . 6-00 -33 . . 1-57 • Sulphuretted hydrogen. — This substance solidifies at 122° Fahr. below 0°, and is then a white crystalline translucent substance, not remaining clear and transparent in the solid state like water, carbonic acid, nitrous oxide, &c., but forming a mass of confused crystals like common salt or nitrate of ammonia, solidified from the melted state. As it fuses at temperatures above —122°, the solid part sinks freely in the fluid, indicating that it is considerably heavier. At this temperature the press- ure of its vapour is less than one atmosphere, not more, probably, than 0*8 of an atmo- sphere, so that the liquid allowed to evaporate in the air would not solidify as car- bonic acid does. The following is a table of the tension of its vapour, the marked numbers being close to experimental results, and the rest interpolated. The curve resulting from these numbers, though coming out nearly identical in different series of experiments, is apparently so different in its character from that of water or carbonic acid, as to leave doubts on my mind respecting it, or else of the identity of every portion of the fluid obtained, yet the crystallization and other characters of the latter seemed to show that it was a pure substance. * Bibliotheque Universelle, 1839, xxiii, p. 185. BODIES GENERALLY EXISTING AS GASES. 165 Fahr, Atmospheres. Fahr. Atmospheres. Fahk. Atmospheres. — 100 . . 1-02 — 50 . . . 2-35 b . . . 610 -— 94 . . . 1-09 - — 45 . . . 2-59 10 . . . 7-21 -— 90 . . . 1-15 --40 . . 2-86 20 . . . 8-44 -'- 83 . . . 1-27 -30 . . 3-49 -26 . . . 9-36 — 80 . . . 1-33 24 . . . 3-95 30 . . . 9-94 ^— 74 . . . 1-50 - — 20 . . . 4-24 40 . . . 11-84 - 70 . . . 1-59 --16 . . . 4-60 -48 . . . 1370 68 . . . 1-67 -10 . . . 5-11 50 . . . 14-14 — 60 . . . 1-93 -— 2 . . 5-90 -52 . . . 14-60 -— 58 . . . 2-00 Carbonic acid. — The solidification of carbonic acid by M. Thilorier is one of the most beautiful expenraental results of modern times. He obtained the substance, as is well known, in the form of a concrete white mass like fine snow, aggregated. When it is melted and resolidified by a bath of low temperature, it then appears as a clear, transparent, crystalline, colourless body, like ice ; so clear, indeed, that at times it was doubtful to the eye whether anything was in the tube, yet at the same time the part was filled with solid carbonic acid. It melts at the temperature of —70° or —72° Fahr., and the solid carbonic acid is heavier than the fluid bathing it. The solid or liquid carbonic acid at this temperature has a pressure of 5*33 atmospheres nearly. Hence it is easy to understand the readiness with which liquid carbonic acid, when allowed to escape into the air, exerting only a pressure of one atmosphere, freezes a part of itself by the evaporation of another part. Thilorier gives —100° Cor — 148° Fahr. as the temperature at which carbonic acid becomes solid. This however is rather the temperature to which solid carbonic acid can sink by further evaporation in the air, and is a temperature belonging to a press- ure, not only lower than that of 5-33 atmospheres, but even much below that of one atmosphere. This cooling eflfect to temperatures below the boiling-point often ap- pears. A bath of carbonic acid and ether exposed to the air will cool a tube con- taining condensed solid carbonic acid, until the pressure within the tube is less than one atmosphere ; yet, if the same bath be covered up so as to have the pressure of one atmosphere of carbonic acid vapour over it, then the temperature is such as to produce a pressure of 2*5 atmospheres by the vapour of the solid carbonic acid within the tube. The estimates of the pressure of carbonic acid vapour are sadly at variance ; thus, Thilorier* says it has a pressure of 26 atmospheres at —4° Fahr., whilst Addams-}- says that for that pressure it requires a temperature of 30°. Addams gives the press- ure about 27^ atmospheres at 32°, but Thilorier and myself :{: give it as 36 atmo- spheres at the same temperature. At 50° Brunel§ estimates the pressure as 60 * Annales de Chimie, 1835, Ix. 427, 432. J Philosophical Transactions, 1823, p. 193. t Report of British Association, 1838, p. 70. § Royal Institution Journal, xxi. 132. 166 DR. FARADAY ON THE LIQUEFACTION AND SOLIDIFICATION OF atmospheres, whilst Addams makes it only 34*67 atmospheres. At 86° Thilorier finds the pressure to be 73 atmospheres; at 4° more, or 90°, Brunel makes it 120 atmospheres ; aud at 10° more, or 100°, Addams makes it less than Thilorier at 86°, and only 62*32 atmospheres; even at 150° the pressure with him is not quite 100 atmospheres. I am inclined to think that at about 90° Cagniard de la Tour's state comes on with carbonic acid. From Thilorier's data we may obtain the specific gravity of the liquid and the vapour over it at the temperature of 86° Fahr., and the former is little more than twice that of the latter ; hence a few degrees more of temperature would bring them together, and Brunel's result seems to imply that the state was then on, but in that case Addams's results could only be accounted for by supposing that there was a deficiency of carbonic acid. The following are the pressures which I have recently obtained : — Fahr. ^— lii — 110 V— 107 — 100 v'— 95 — 90 ^— 83 — 80 ^— 75 — 70 Atmospheres. •14 •17 •36 •85 •28 •77 •60 •93 •60 •33 Fahr. Atmospheres. Fahr. Atmospheres -60 . . . 6^97 0 -— 4 . . . 21-48 ^ — 56 . . . . 7-70 0 . . . 22-84 -50 . . . 8^88 - 5 . . . 24-75 —40 . . iro7 ^ 10 . . . 26^82 - — 34 . . . 12-50 « 15 . . . 29-09 — 30 . . . , 1354 20 . , . . 30-65 v^ — 23 . . 1545 ^ 23 . . . 33-15 -20 . . 16-30 30 . , . 37-19 "^—15 . . 17'80 ^ 32 . . . 38-50 — 10 . . . 19-38 Carbonic acid is remarkable amongst bodies for the high tension of the vapour which it gives off whilst in the solid or glacial state. There is no other substance which at all comes near it in this respect, and it causes an inversion of what in all other cases is the natural order of events. Thus, if, as is the case with water, ether, mercury or any other fluid, that temperature at which carbonic acid gives off vapour equal in elastic force to one atmosphere, be called its boiling-point ; or, if (to pro- duce the actual effect of ebullition) the carbonic acid be plunged below the surface of alcohol or ether, then we shall perceive that the freezing and boiling-points are inverted, i. e. that the freezing-point is the hotter, and the boiling-point the colder of the two, the latter being about 50° below the former. Euchlorine. — This substance was easily converted from the gaseous state into a solid crystalline body, which, by a little increase of temperature, melted into an orange-red fluid, and by diminution of temperature again congealed; the solid euchlo- rine had the colour and general appearance of bichromate of potassa ; it was mode- rately hard, brittle and translucent; and the crystals were perfectly clear. It melted at the temperature of 75° below 0°, and the solid portion was heavier than the liquid. BODIES GENERALLY EXISTING AS GASES. 167 When in the solid state it gives off so little vapour that the eye is not sensible of its presence by any degree of colour in the air over it when looking down a tube four inches in length, at the bottom of which is the substance. Hence the pressure of its vapour at that temperature must be very small. Some hours after, wishing to solidify the same portion of euchlorine which was then in a liquid state, I placed the tube in a bath at —110°, but could not succeed either by continuance of the tube in the bath, or shaking the fluid in the tube, or opening the tube to allow the full pressure of the atmosphere ; but when the liquid euchlorine was touched by a platinum wire it instantly became solid, and exhibited all the properties before described. There are many similar instances amongst ordi- nary substances, but the effect in this case makes me hesitate in concluding that all the gases which as yet have refused to solidify at temperatures as low as 166° below 0°, cannot acquire the solid state at such a temperature. Nitrous oxide. — This substance was obtained solid by the temperature of the car- bonic acid bath in vacuo, and appeared as a beautiful clear crystalline colourless body. The temperature required for this effect must have been very nearly the lowest, per- haps about 150° below 0°. The pressure of the vapour rising from the solid nitrous oxide was less than one atmosphere. Hence it was concluded that liquid nitrous oxide could not freeze itself by evapo- ration at one atmosphere, as carbonic acid does ; and this was found to be true, for when a tube containing much liquid was freely opened, so as to allow evaporation down to one atmosphere, the liquid boiled and cooled itself, but remained a liquid. The cold produced by the evaporation was very great, and this was shown by putting the part of the tube containing the liquid nitrous oxide, into a cold bath of carbonic acid, for the latter was like a hot bath to the former, and instantly made it boil rapidly. I kept this substance for some weeks in a tube closed by stop-cocks and cemented caps. In that time there was no action on the bitumen of the graduation, nor on the cement of the caps ; these bodies remained perfectly unaltered. Hence it is probable that this substance may be used in certain cases, instead of carbonic acid, to produce degrees of cold far below those which the latter body can supply. Down to a certain temperature, that of its solidification, it would not even require ether to give contact, and below that temperature it could easily be used mingled with ether ; its vapour would do no harm to an air-pump, and there is no doubt that the substance placed in vacuo would acquire a temperature lower than any as yet known, perhaps as far below the carbonic acid bath in vacuo as that is below the same bath in air. This substance, like olefiant gas, gave very uncertain results at different times as to the pressure of its vapour ; results which can only be accounted for by supposing that there are two different bodies present, soluble in each other, but differing in the elasticity of their vapour. Four different portions gave at the same temperature. 168 DR. FARADAY ON THE LIQUEFACTION AND SOLIDIFICATION OF namely, -106° Fahr., the following great differences in pressure, 1*66; 4*4; 5*0; and 6-3 atmospheres, and this after the elastic atmosphere left in the tubes at the conclusion of the condensation had been allowed to escape, and be replaced by a por- tion of the respective liquids which then rose in vapour. The following Table gives certain results with a portion of liquid which exerted a pressure of six atmospheres at — 106°Fahr. p^HE. Atmosplieres. Atmospheres. — 40 10-20 -35 10-95 -30 ..... 11-80 -25 12-75 — 20 ..... 13-80 -15 14-95 — 10 16-20 — 5 .... . 17-55 0 .... . 19-05 24-40 5 20-70 26-08 10 22-50 27-84 15 24-45 ..... 29-68 20 .... . 26-55 ..... 31-62 25 28-85 ..... 33-66 30 ..... 35-82 35 38-10 The second column expresses the pressures given as the fluid was raised from low to higher temperatures. The third column shows the pressures given the next day with the same tube after it had attained to and continued at the atmospheric tem- perature for some hours. There is a difference of four or five atmospheres between the two, showing that in the first instance the previous low temperature had caused the solution of a more volatile part in the less volatile and liquid portion, and that the prolonged application of a higher temperature during the night had gradually raised it again in vapour. This result occurred again and again with the same spe- cimen*. Cyanogen. — This substance becomes a solid transparent crystalline body, as Bunsen has already stated-f, which raised to the temperature of — 30°Fahr. then liquefies. The solid and liquid appear to be nearly of the same specific gravity, but the solid is perhaps the denser of the two. * ITiis substance is one of those which I liquefied in 1823 (see Philosophical Transactions). Since writing the above I perceive that M. Natterer has condensed it into the liquid state by the use of pumps only (see Comptes Rendus, 1844, 18th Nov. p. 1111), and obtained the liquid in considerable quantities. The non-soli- dification of it by exposure to the air perfectly accords with my own results. t Biblioth^que Universelle, 1839, xxiii. p. 184. BODIES GENERALLY EXISTING AS GASES. 169 The mixed solid and liquid substance yields a vapour of rather less pressure than one atmosphere. In accordance with this result, if the liquid be exposed to the air, it does not freeze itself as carbonic acid does. The liquid tends to distil over and condense on the cap cement and bitumen of the gauge, but only slightly. When cyanogen is made from cyanide of mercury sealed up hermetically in a glass tube, the cyanogen distils back and condenses in the paracyanic residue of the distillation, but the pressure of the vapour at common temperatures is still as great, or very nearly so, as if the cyanogen were in a clean separate liquid state. A measured portion of liquid cyanogen was allowed to escape and expand into gas. In this way one volume of liquid at the temperature of 63°Fahr. gave 393*9 volumes of gas at the same temperature and the barometric pressure of 30*2 inches. If 100 cubic inches of the gas be admitted to weigh 55*5 grains, then a cubic inch of the liquid would weigh 218-6 grains. This gives its specific gravity as 0"866. When first condensed I estimated it as nearly 09. Cyanogen is a substance which yielded on different occasions results of vaporous tension differing much from each other, though the substance appeared always to be pure. The following are numbers in which I place some confidence, the pressures being in atmospheres of 30 inches of mercury, and the marked results experimental ='<'. Fahu. Atmospheres. Fahr. Atmospheres. Fahr. Atmospheres. 6 . 1-25 -38-5 . . . 272 0 11 . . 500 8-5 . . 1-5 -44-5 . . . 3-00 -79 . . 516 -10 . 1-53 -48 . 3-17 83 . . 5-50 15 . . . 172 -50 . 3-28 88-3 . . 6-00 -20 . 1-89 -52 . . 3-36 -93-5 . . . 6-50 22-8 . . 200 54-3 . . 3-50 -95 . . 6-64 -27 . . 2-20 -63 . . 4-00 98-4 . . . 7-00 -32 . . 2-37 -70 . 4-50 -103 . . . 7*50 34-5 . . 2-50 -74 . . . 479 Ammonia. — This body may be obtained as a solid, white, translucent, crystalline sub- stance, melting at the temperature of 103° below 0°; at which point the solid sub- stance is heavier than the liquid. In that state the pressure of its vapour must be very small. Liquid ammonia at 60° was allowed to expand into ammoniacal gas at the same temperature ; one volume of the liquid gave 1009*8 volumes of the gas, the barometer being at the pressure of 30*2 inches. If 100 cubic inches of ammoniacal gas be allowed to weigh 18-28 grains, it will give 184-6 grains as the weight of a cubic inch of liquid ammonia at 60°. Hence its specific gravity at that temperature will be 0'731. In the old experiments I found by another kind of process that its specific gravity was 0-76 at 50°. * See Bunsen's results, Biblioth^que Universelle, 1839, xxiii. p. 185. MDCCCXLV. Z • If? 170 DR. FARADAY ON THE LIQUEFACTION AND SOLIDIFICATION OF The following is a table of the pressure of ammonia vapour, the marked results, as before, being those obtained by experiment : — Atmospheres. . 7-00 . 7*50 . 7*63 . 8-00 . 8-50 . 9-00 . 9-50 . 10-00 . 10-30 Jrseniuretted Hydrogen. — This body, liquefied by Dumas and Soubeiran, did not solidify at the lowest temperature to which I could submit it, i. e. not at 166° below 0°Fahr. In the following table of the elasticity of its vapour the marked results are experimental, and the others interpolated : — Fahu. Atmospheres. Fahr. Atmospheres. Fahr -6 . . 2-48 -4°1 . . . 5-10 -61-3 0-5 . . 2-50 -44 . . . 5-36 -65-6 v-9'3 . . . 300 -45 . . . 5-45 ^Q7 -18 . . 3-50 45-8 . . . 5-50 69-4 -21 . 3-72 -49 . . . 5-83 73 25-8 . . . 4-00 -51-4 . . . 600 76^8 -26 . . . 4-04 -52 . . . 6-10 80 -32 . 4-44 -55 . 6-38 -83 -33 . . . 4-50 -56*5 . . 6-50 85 39-5 . . . 5-00 -60 . 6-90 Fahr. --7°5 -70 - — 64 — 60 - — 52 — 50 — 40 - — 36 Atmospheres. 0-94 1-08 1-26 1-40 1-73 1-80 2-28 2-50 Fahh. o — 30 --23 -20 -10 -— 5 0 3 Atmospheres . 2-84 . 3-32 . 3-51 . 4-30 . 4-74 . 5-21 . 5-56 Fahh. -10 -20 30 -32 -40 -50 -60 Atmospheres. 6-24 7*39 8-66 8-95, 10-05 11*56 13-19 The following bodies would not freeze at the very low temperature of the carbonic acid bath in fac2;i-ii!lib,mriiig Coasts ol' F.nillana md Sriilkna . ( PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON. FOR THE YEAR MDCCCXLV. PART II. LONDON: PRINTED BY RICHARD AND JOHN E. TAYLOR, RED LION COURT, FLEET STREET. MDCCCXLV. Adjudication of the Medals of the Royal Society for the year 1845 by the President and Council. The Copley Medal to Professor Thomas Schwann of Louvain, for his Physiolog^ical Researches on the development of Animal and Vegetable Textures. The Royal Medal, in the department of Astronomy, to George Biddell Airy, Esq., Astronomer Royal, for his Paper entitled " On the Laws of the Tides on the Coasts of Ireland, as inferred from an extensive series of observations made in connexion with the Ordnance Survey of Ireland," published in the Philosophical Transactions for 1845. The Royal Medal, in the department of Physiology, to Thomas Snow Beck, Esq., for his Paper entitled "On the Nerves of the Uterus," communicated to the Society in 1845, and ordered for publication in the Philosophical Transactions. The Paper appointed for the Bakerian Lecture in 1845, is Professor Daubenv's Memoir, entitled " On the Rotation of Crops." CONTENTS. VII. Memoir on the Rotation of Crops, and on the Quantity/ of Inorganic Mutters abstracted from the Soil hy various Plants under dijferent circumstances. By Charles Daubeny, M.D., F.R.S., ^c, Honorary Member of the Royal English Agricultural Society, and Professor of Rural Ecmomy in the University of Oxford page 179 VIII. An Account of the Artificial Formation of a Fegeto- Alkali. By George Fownes, Ph.D., F.R.S., Chemical Lecturer in the Middlesejc Hospital Medical School, Communicated hy Thomas Graham, Esq., F.R.S., S^c 253 IX. On Benzoline, a new Organic Salt-base from Bitter Almond Oil. By George Fownes, ^sq., Ph.D., F.R.S 2G3 X. On the Elliptic Polarization of Light by Reflexion from Metallic Surfaces. By the Rev. Baden Powell, M.A., F.R.S., F.G.S., F.R.A.S., SavilianProfessor of Geometry in the University of Oxford 269 XI. Electro-Physiological Researches.— First Memoir. The Muscular Current. By Signor Carlo Matteucci, Professor in the University of Pisa, S^c. 8^c. Commu- nicated by Michael Faraday, Esq., F.R.S., S^c. S^c 283 XII. Electro-Physiological Researches. — Second Memoir. On the proper Current of the Frog. By Signor Carlo Matteucci, Professor in the University of Pisa, 8^c. 8^c. Communicated by Michael Faraday, Esq., F.R.S., Sfc. ^c 297 XIII. ElectrO'Physiological Researches. — Third Memoir. On Induced Contractions. By Signor Carlo Matteucci, Professor in the University of Pisa, 8fc. S^c. Communicated by W. Bowman, Esq., F.R.S 303 XIV. On the Temperature of Man. By John Davy, M.D., F.R.S.L. ^ E., Inspector- General of Army Hospitals 319 XV. Contributions to the Chemistry of the Urine. On the Variations in the Alkaline and Earthy Phosphates in the Healthy State, and on the Alkalescence of the Urine from Fixed Alkalies. By Henry Bence Jones, M.A., Cantab., Fellow of the College of Physicians. Communicated by S. Hunter Christie, Esq., Sec.R.S. 335 [ viii ] XVI. On the Gas Voltaic Battery. — Voltaic Action of Phosphorus, Sulphur and Hydrocarhms. By W. R. Grove, Esq., M.A., F.R.S., VP.R.L, Prof. Exp. Phil., London Institution 351 XVII. On the Compounds of Tin and Iodine. By Thomas H. Henry, Esq. Commu- nicated by R. Phillips, Esq., F.R.S 363 Index 369 Appendix. Presents , [ ^ ] PHILOSOPHICAL TRANSACTIONS. VII. Memoir on the Rotation of Crops, and on the Quantity of Inorganic Mattei^s abstracted from the Soil hy various Plants under different circumstances. By Charles Daubeny, M.D., F.R.S., S^c, Honorary Member of the Royal English Agricultural Society, and Professor of Rural Economy in the University of Oxford. Received May 5,— Read May 22, 1845. Contents. Introduction. Part I. — On the quantity of produce obtained from the several plots of ground, each year throughout the period during which the experiments were continued. Part II. — On the chemical composition of certain crops cultivated in the Botanic Garden, and on the amount of inorganic principles abstracted by them from the soil during the period the experiments were conducted. Part III. — On the chemical composition of the soil in which the crops were grown, and on the proportion of its ingredients that was available for the purposes of vegetation. Introduction. In laying before this Society an account of certain experiments which I have under- taken with the view of elucidating the principles upon which the advantage of a ro- tation of crops in husbandry depends, it may be proper that I should in the first instance state the circumstances under which they were commenced, as well as those which led me during the course of them to deviate in some respects from my original plan of proceeding. During the prosecution of a set of researches which embraced a period of more than ten years, it might naturally be expected, that the views at first entertained would become modified, and that arrangements deemed sufficient for carrying out the original plan should appear unsatisfactory, in proportion as glimpses of other truths, than those which enlightened us at the outset, began to open upon the field of our inquiry. Thus, when first I determined to apply a portion of the ground at my disposal to experiments having reference to the rotation of crops, the scientific world was gCr MDCCCXLV. 2 B 180 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. nerally impressed in favour of a theory which the celebrated De Candolle had so ingeniously and eloquently maintained ; namely, that a soil became unfitted for sup- porting a second crop of any given plant, in consequence of the deleterious influence exerted upon it by juices excreted from the former one. My original object therefore was, — first, to detect, if possible, the chemical nature of these supposed excretions ; and secondly, to demonstrate their poisonous influence, by taking account of the expected diminution in the amount of the crop exposed to them beyond that of another in which all the circumstances were the same, except- ing the presence of the excretions in question. To accomplish these two objects, it seemed sufficient to set apart a number of plots of ground uniform as to the quality and richness of its soil, planting one-half of the number year after year with the same species of crop until the land no longer pro- duced it, and the other moiety with crops of the same description, succeeding one another in such a manner, that no one plot should receive the same twice during the period of the continuance of these experiments, or at least within a short interval of one another. By weighing the produce of each plot, reduced to the same uniform condition of dryness, when it had arrived at maturity, I hoped to obtain data for computing, how much of the expected diminution might be referred to the exhaustion of the ground, and how much to the effect of excretions which the preceding crop had given out. The influence of seasons indeed is in all these cases one of the most important elements in the calculation, yet by taking the average of a number of years, it was hoped that this source of error might be eliminated, and that whilst the mean of the crop obtained during the latter half of the period, as compared with that of the former half, might suggest the rate of exhaustion brought about by the annual demand made upon the resources of the soil, the diflference between the permanent and the shifting crop in each instance might tend to show, in what degree the excretory function of each plant contributed to the result. Assuming, therefore, on the faith of the then existing authorities, that soil would soon become deficient in the food which was required for the plants grown in it, and moreover that, even if not exhausted, it would become unsuitable to their growth, by being contatninated with the excretions from preceding crops, I conceived it unnecessary either to undertake an analysis of the soil itself at the commencement of my labours, or to inquire into the chemical constitution of the crops which I had obtained in the course of them. Supposing, as was then too hastily assumed, that the composition of each vegetable was uniform, and had been already determined with sufficient precision, it should follow, that the amount of produce ought in itself to be an index of the quantity of inorganic matter abstracted from the soil, and that the number of crops obtained before the soil became eff^ete would indicate the relative richness of the latter in those ingredients which were essential to the growth of the plant in question. DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 181 As I proceeded however in my experiments, I began to find, that both the postu- lates on which I had built were unsound, for neither was I able to detect any foreign organic matter in the soil, referable to the excretions of the crop which had grown in it*, nor did I find that uniform difference between the shifting and the permanent crop, to the disadvantage of the latter, which I should have expected upon the prin- ciples of De Candolle's theory. Moreover, the researches of Braconnot, which have since been made known to the world, tended still further to throw doubt upon the truth of the facts on which the doctrine of excretion reposed, and when no longer swayed by the authority of the distinguished author of the theory in question, I perceived more clearly the difficulty of reconciling it with many facts or opinions that seemed current amongst agricul- turists— such, for instance, as the growth of repeated crops of the most exhausting plants in certain rich alluvial, or newly settled countries ; the continuance of a plant in a state of nature for ages in the same locality ; and lastly, the views of Liebig, which went to prove, that the food of plants, so far as their organic constituents are concerned, is derived in all instances from the elements of air and of water. No sooner, therefore, had I become suspicious as to the truth of the opinion which I had previously entertained as to the excretions from the roots of plants being capable of explaining the falling off of a crop after repetition, than I felt desirous of shaping my inquiries in such a manner as to ascertain, if possible, which of the other two conceivable explanations might deserve a preference ; whether, for instance, the falling off of the crop was attributable to a failure in the soil of organic matters fitted for its nutrition, or of those inorganic materials which it equally required. * The soils that seemed to me most likely to afford indications of the presence of root excretions were those which had reared crops of poppies and of tobacco for several years in succession, the former plant containing, in morphia and meconic acid, products readily recognizable by chemical tests, and the latter one sufficiently so in nicotine. I accordingly digested sifted portions of the soils, amounting in each instance to 5 lbs., in water for several hours. The water drained off was evaporated, and then filtered. The clear solution was first treated with sugar of lead, and the precipitate which fell was collected, and then dissolved in water acidulated with sulphuric acid. Had any meconic acid existed in combination with the lead, it would have been thus separated, the metal being precipitated along with the sulphuric acid with which it forms an insoluble salt. None of the tests, however, usually employed for detecting meconic acid produced any effect, — chloride of iron dissolved in alcohol causing no red colour, and ammonio-sulphate of copper not being rendered green. The liquor remaining after the introduction of the sugar of lead might have contained morphia held in solution by acetic acid. To detect it, the lead was in the first place thrown down by sulphuretted hydrogen, after removing which, the remaining solution, after being concentrated, was treated with ammonia, which pro- duced a flocculent precipitate. This, however, proved destitute of morphia, for neither was there any blue colour as produced by chloride of iron, nor any redness by nitric acid. My attempts to detect nicotine in the soil in which tobacco had been grown proved equally ineflFectual. 2 B 2 182 DR. DAUBENY ON THE ROTATION OP CROPS, ETC. To determine this, it seemed necessary to appreciate, if possible, first, what mate- rials the soil might have contained, both before the experiments commenced, and after their termination ; and secondly, what might be the constitution of the plants themselves both in the permanent and the shifting crop, as compared with the normal condition of the same. But as the experiments which I had instituted extended to no less than sixteen different species, my object being to select at least one out of each natural family, which contained amongst the plants included under it any of those usually cultivated for farm or garden purposes in this country, it seemed necessary to limit that part of the inquiry which involved the necessity of ash analysis to a portion only of the series, and accordingly, in the autumn of 1844, I selected from the crops grown in that year the following as the subjects of chemical examination, namely. Barley, Potatoes, Turnips, Flax, Hemp, and Beans. Of each of these six plants, the shifting and permanent crops, after having been weighed in the usual manner, in order to estimate their relative amount, were reduced to ashes, so that the proportion of inorganic to organic matter might in the first instance be determined. In consequence of the largeness of the bulk, iron vessels were necessarily employed for burning away the volatilizable parts, and hence a portion of peroxide of iron was always introduced into the ashes, which, being indefinite in quantity, rendered it necessary for me, in the subsequent analyses, to regard the whole of that ingredient as extraneous, and to reject it from the calculation. The same course was also pur- sued with respect to a certain variable amount of sand and charcoal always present in the ash, the former derived evidently from the soil, the latter from the carbo- naceous matter of the vegetable, which could not be entirely removed by the combustion. Of each of these six plants it appeared necessary to analyse at least three speci- mens— the first taken from the permanent crop, the second from the shifting one, the third from a piece of ground, not belonging to the spot at wiiich the experiments were carried on, and under ordinary treatment, but corresponding as nearly as pos- sible in natural character to the soil of the experimental garden. Thus this part alone of the inquiry involved at least eighteen distinct analyses, an amount of labour, which, as I soon found, my other occupations precluded me from undertaking, and which I was glad to delegate to other hands. I therefore esteemed myself fortunate in being able to secure the services of Mr.THOMAS Way, a gentleman, who had for the last two years officiated as Assistant to Professor Graham of University College, London, and who was recommended to me by that distinguished chemist as well-qualified for the task. On him, therefore, the merit, as well as the responsibility, of this part of the inquiry must mainly devolve ; all that I can lay claim to in this part of the subject as my own, is the having considered, in conjunction with him, the method of analysis which DR. DAUBENY ON THE ROTATIOiN OF CROPS, ETC. 183 he ultimately adopted, and having made such preliminary trials on one of the crops which he afterwards analysed, as tended to satisfy me, that on those points in which the plan differs from that proposed by Dr. Will, our method deserves the preference, on the score of convenience, if not with respect to accuracy. In a case of this kind, experience alone can determine the degree of confidence which is due to the results obtained, but I ought not to withhold my own individual testimony to their fidelity, from having witnessed the manner in which they were conducted by Mr. Way, his perfect familiarity with the processes which he pursued, and the scrupulous care taken by him in repeating every step in the investigation, which presented anomalous results, or appeared from any cause open to suspicion. But to complete my design, an analysis of the soil, as well as of the crops which grew in it, was requisite, and to this subject therefore my attention was next directed. Now, when we consider the nature of a soil in an agricultural point of view, or in reference to its suitableness for the growth of various kinds of vegetables, two questions naturally come before us ; namely, what amount of ingredients capable of being assimilated in the course of time by the crops does it contain ; and secondly, what is the amount of those which are present, in a condition actually available for their purposes, at the precise moment when the examination is undertaken. Both the above points are obviously quite distinct from that of the total amount of ingredients actually existing in the soil, and hence some might be disposed to add to the labour of the two preceding investigations, that of ascertaining the whole of its constituents, whether in a state to be affected by the ordinary agents of decom- position, or not. The latter question, however, seems to me to possess, with reference to the agri- culturist, only a speculative interest, and when introduced into a Report intended for his use, may be more liable to mislead than to instruct, unless due caution be taken to point out to him, how much of each ingredient is to be regarded as inert, and how much of it as applicable to the future or present uses of the plant. Let us take the case of a natural soil, composed of certain kinds of disintegrated lava, or even of granite, in which it is evident, that an actual analysis, conducted by means of fusion with barytes, or lead, or by those other processes which chemists employ for decomposing compounds of a refractory nature, would detect the presence of a large per-centage of alkali, not improbably of a certain amount of phosphate of lime, and in short would indicate an exuberant supply of all those ingredients which plants require for their support. Nevertheless a soil of this description, in conse- quence of the close union of the elementary matters of which it consists, and of the compactness of its mechanical texture, might be as barren, and as incapable of im- parting food to plants, as an artificial soil composed of pounded glass is known to be, notwithstanding the large proportion of alkali which it contains. 184 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. Thus I have myself observed*, that the soil which covers the serpentine rock of Cornwall, a mineral consisting of — • SiHca 43-07 Magnesia 40-37 Alumina 0-25 Lime 0-50 Oxide of iron 1-17 Water 1245 — Hisinger, contains so minute a proportion of magnesia, that in an analysis of a small sample I altogether overlooked its presence, in so great a degree does the mechanical texture of the rock, and the state of combination subsisting between its ingredients, preserve it from the decomposing action of the elements which tend to set loose its treasures. Now it seems obvious, that whatever cannot be extracted from a soil by digestion in muriatic acid during four or five successive hours, must be in such a state of com- bination as will render it wholly incapable of imparting anything to a plant, for such a period of time at least as can enter into the calculations of the agriculturist ; and moreover, that all which muriatic acid extracts, but which water impregnated with carbonic acid fails in dissolving, ought to be regarded as at present contributing nothing, although it may ultimately become available to its purposes. I have therefore thought proper to distinguish between the actually available re- sources of the soil, and those ultimately applicable to the uses of the plant, designating the former as its dormant, and the latter as its active ingredients. The portion dissolved after digestion in muriatic acid will contain both the dor- mant and the active ; that taken up by water impregnated with carbonic acid will consist merely of the latter ; the difference in amount between the two will therefore indicate the dormant portion of its contents. The dormant and active portions may both be comprehended under the designation of its available constituents, whilst those which, from their state of combination in the mass, can never be expected to contribute to the growth of plants, may be denominated the passive ones. Every soil, which is capable of yielding an abundant crop of any kind of plant after fallowing, must be assumed to possess in itself an adequate supply of all the ingre- dients necessary for its support in an available condition, but it is plain that these could not have existed in an active one, or such an interval of rest would not have been required for rendering them efficient. Accordingly it is quite possible, that after ten years cropping, the soil of the expe- rimental garden might still retain plenty of alkaline salts and phosphates, although what was ready to be applied to the uses of the plant had for the most part been absorbed by the crops previously obtained. * Lecture on the Application of Science to Agriculture, from the Journal of the Royal Agricultural Society of England, vol. iii. part 1. DR. DAUBENY ON THE ROTATION OP CROPS, ETC. 185 * With a view then to this part of the inquiry, I proposed to estimate, first, the amount of ingredients severally present in the soil which might sooner or later become available for the purposes of vegetation ; and secondly, that of those principles which were in a state to be applied immediately to those uses. It would also have been instructive, to determine, by a comparative analysis of the soil, in the state in which it was before, and after the experiments had been instituted, the loss which had been occasioned by the crops in both these particulars ; but as, from the reasons assigned, I had neg- lected to examine the identical soil of the experimental garden before the researches commenced, I was obliged to content myself with obtaining an approximation to its probable constitution, by selecting for examination that taken from a portion of the garden, which was immediately contiguous, but which had recently been manured, and had borne good crops. Here also I was assisted by Mr. Way, who undertook the more laborious part of the inquiry, namely, that of determining the entire amount of the available consti- tuents present in certain of the soils, leaving to me the task of ascertaining merely the nature of those which could be extracted by water. The investigation therefore divides itself naturally into three heads ; the first re- specting the actual amount of the permanent and shifting crops each year obtained ; the second, the chemical constitution of the ashes resulting from those which had been burnt for the purpose of examination ; and the third, the nature of the actual as well as of the available ingredients of the soil in which the crops had been reared. PART I. On the quantity of produce obtained from the several plots of ground, each year throughout the period during which the experiments were continued. The following plants were made the subjects of experiment : — Spurge . . Potatoes . Barley . . Turnips Hemp . . Flax. . . Beans . . Tobacco . Poppies Buckwheat Clover . . Oats . . . Beet . . . Mint . . Endive . . Parsley . . Euphorbia lathyrls Solanum tuberosum Hordeiim sativum Brasslca rapa . Cannabis satlva . Linum usltatlsslmum from 1835 to 1838 from 1834 to 1844 from 1835 to 1844 from 1834 to 1844 from 1835 to 1844 from 1835 to 1844 Flclafaba from 1835 to 1844 Nlcotlana Tabacum . Papaver somnlferum Polyg onum fagopyrum Trlfollum pratense Avena satlva . . Beta vulgaris . . Mentha viridls Clchorlum endlvia Aplum petrosellnum from 1834 to 1844 from 1834 to 1844 from 1835 to 1844 from 1 834 to 1 844 from 1839 to 1844 from 1839 to 1844 from 1835 to 1844 from 1835 to 1844 from 1835 to 1844 186 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. As the experiments were carried on from 1834 to 1844 inclusive, it may be satis- factory to state in the first instance such of the meteorological characters of these years as may be gathered from the Register kept at the Radcliffe Observatory, rela tive to the mean temperature, or from my own observations made at the Botanic Garden, Oxford, as to the amount of rain. Year. Inches of Rain. Where observed. Variation -|- or — (above or be- low) the mean of the period. Mean temperature of the year. Variation + or — (above or be- low) the mean of the period. 1834. 1835. 1836. 1837. 1838. 1839. 1840. 1841. 1842. 1843. 1844. 21-899 26-182 24-339 21-900 20-080 32-720 18-530 35-275 23-490 25-150 22-621 Obs. Obs. Obs. B.G. B.G. B.G. B.G. B.G. B.G. B.G. B.G. — 2-845 + 1-438 — 0-365 — 2-844 — 4-664 + 7-976 — 6-214 + 10-531 — 1-254 + 0-406 — 2-123 52-8 51-5 49-9 50-0 49-9 51-2 49-9 49-8 50-8 50-3 49-6 + 2-282 + 0-982 — 0-618 -0-518 —0-618 —0-318 -0-618 -0-718 + 0-282 -0-218 —0-918 Total in eleven years. U72-186 555-7 Average of eleven years. I 24-744 50-518 The plots of ground set apart for the experiments were not exactly equal in point of size, but their square contents being known, it was easy to reduce the crops to one standard, and that of 100 square feet was selected as the most convenient. In reporting to the Society the results, I shall therefore always suppose that re- duction as being made, and shall set down what ought to have been the produce, supposing each plot to have measured exactly 100 square feet. In this statement I will begin with the only case in the whole series to which De Candolle's theory of excretions appears at all applicable ; namely, that in which the plant experimented on was a species of Spurge, the Euphorbia lathyris. In 1835 a luxuriant crop of this weed was obtained, amounting to about 18 lbs., but the next year the produce had dwindled almost to nothing, and in 1837, in which fresh plants were introduced, an equal failure took place. Nor did any new plants start up in 1838, so that in 1839 the plot was sown with flax, barley, and beans, of all of which I obtained a tolerable yield. This experiment therefore might be appealed to in support of De Candolle's views, as it would appear, that excretions had been emitted from the roots of the Euphorbia, which proved injurious to plants of the same species as those from which they had proceeded, but which exerted no such poisonous influence upon others not allied to them in organization; or, if it be objected, that during the course of 1838 the excretions might have become so far decomposed as to lose their poisonous cha- DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 187 racter, still the failure of the second and third crops of Euphorbia would seem attri- butable to some deleterious influence exerted by the excretions of the antecedent crop, rather than to the ground having become exhausted, inasmuch as the latter, without being in the meanwhile enriched with manure, proved its ability to produce tolerable crops of other vegetables. The acrid nature of the juices of the Euphorbia may possibly explain, why this plant should constitute an apparent exception to the rest, for it will be seen, that in all the other cases, the diminution in the amount of produce, consequent upon the continua- tion of the crop from year to year, was only such as might be supposed to result from a falling off in some one of those ingredients which were necessary for its develop- ment, and was not of a nature to indicate the existence of anything poisonous in the soil in which it grew*. I shall therefore now proceed to state the amount of produce obtained during the several years from each of the remaining plants above enumerated, distinguishing the crop which was repeated year after year in the same plot of ground as the permanent one, and that which was grown successively in different parts of the garden as the shifting one. 1. Solanum tuberosum. — Ground not manured since 1833. Year. Permanent crop. Weighed without having been dried, but merely cleaned from dirt. Shifting crop. 1836. 1837. 1838. 1839. Plot No. 1. — After a crop of Turnips. Tubers . . . 89-50 Tubers ... 59-5 Tubers . . . 68-0 Tubers . . . 59-0 After a crop of Papaver somniferum. Tubers . . 84*00 Afler a crop of Cannabis saliva. Tubers . . 108-0 After a crop of Cannabis sativa. Tubers . . 68-5 After a crop o^ Polygonum fagopyrum. Tubers . . 132-0 1840. In this year it occurred to me, that it might be interesting to determine what difference, as to the amount of produce, would be produced by planting in one in- stance tubers from the crop obtained the year before in the same plot, and by employ- ing in another those raised in some different locality. The difference in quantity will be seen not to be very considerable. * It can hardly, I think, be denied, that juices are excreted from the roots, as well as taken up by them ; the only question is, are these excretions injurious to the plants of the same species which grew in the soil afterwards, and if they are, are they favourable to the growth of others } The first of these positions may be countenanced by the facts detailed in the text, but the latter is little, if at all, corroborated by them. MDCCCXLV. 2 c 188 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. Year. Permanent crop, from the same No. 1.— Tubers plot planted. Permanent crop. No. 3. — Tubers from a different locality planted. Shifting crop. After Euphorbia lathyris, which had failed. After Linum usitatissimum. 1840. Tubers . . 88^ Tubers . . 90 Tubers . . 72 After Linum usitatissimum. 1841. Tubers . . 64 Tubers ..87^ Tubers . . 81^ After Vicia Faba. 1842. Tubers . . 82-5 Tubers . . 94-0 Tubers . . 110 After Vicia sativa. 1843. Tubers . . 48-6 Tubers . . 38-6 Tubers . . 48-4 After Hordeum sativum. 1844. Tubers . . 61-0 Tubers . . 57| Tubers . . 98*0 Average of nine years. Tubers . . 68-9 t 1 Average of nine years. Tubers . . 89-1 Average of the first five years. Tubers . . 72*9 Average of five years. Tubers . . 74*77 Average of the first five years. Tubers . . 92-8 The following diagram may convey a clearer idea of the differences in the amount of the crops, and the relation between the permanent and shifting one. Potatoes. 140 130 120 no 100 90 Permanent " Shifting... - 80 70 60 50 40 0 >lbs. DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 189 It is worth remarking, that the average of the shifting crops of potatoes corre- sponded very nearly to the amount obtained in the year 1844, from a bed of similar size, in a portion of the garden contiguous to that on which my experiments had been carried on, and which had been recently manured, the produce in this instance being 96*0 lbs., whilst the average of nine years in the other case was 89*1 lbs., and moreover that the produce of the last year, in which the crop succeeded one of barley, was not less than 98 lbs., thus apparently showing, that after so long a period of cropping, there was still a sufficient supply in the soil of those ingredients which were requisite for the due development of the plant. An examination of samples of potatoes from the crop of 1844 proved, that the shifting crop contained more starch, and more of the woody fibre and other organic matters which belong to this vegetable, than either of the permanent ones ; and that of the latter, the one grown in soil which had borne potatoes only five years, ap- proached in these respects more nearly to the shifting, than that taken from the soil which had been cropped during ten years. The proportion of water in the two cases was not very different, but with respect to the inorganic matters, it was found that the remark held good. Here the shifting crop yielded in a given amount of tubers the least, and the per- manent crop the largest quantity of ash, as if the. deficiency of organic matter had been made up by an increased quantity of that which was derived from inorganic sources. The nature of this latter portion will be stated when I proceed to detail the analyses performed by Mr. Way. On examining a specimen of a good mealy description of potatoe taken from a garden in the neighbourhood of Oxford, the soil of which was similar to that of the experimental garden, I found the proportion of starch much the same as in the shift- ing crop, but the quantity of water greater. '■ The following is a tabular view of the results : — Good mealy kind of potatoe from a garden near Oxford Shifting crop in experimental garden Permanent crop of five years' standing Permanent crop of nine years' standing Starch. per cent. 13-00 13-67 10-54 9-11 Fibrous matter. 5-90 9-76 11-32 9-76 Other solid matters. 5-6 5-7 4-5 Water. 75-5 71'9 73-7 72-4 2. Hordeum sativum. The next crop I shall notice is Barley, in which it will be perceived that, allowing for differences of seasons, the produce obtained during ten successive years was tole- rably uniform, there being however a considerable balance in favour of the shifting over the permanent crop. 2 c 2 190 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. The following are the results : — Year. Permanent crop. Produce in a dried state. Shifting crop. Produce in a dried state. 1835. No. 4. 29-0 After Linum usitatissimum. 35-5 1836. 29-0 After Apium petroselinum. 51-0 1837. 21-5 After Linum usitatissimum. 30-0 1838. 42-5 After Cichorium endivia. 75-0 1839. 28-0 After Brassica Rapa. 41-0 1840. 28-75 After Brassica Rapa. 54-5 1841. 28'0 After Vicia Faba. 27-4 1842. 27-5 After Solarium tuberosum. 34-2 1843. 26-5 After Papaver somniferum. 42-5 1844. 28-7 After Cannabis sativa. 30-0 Average of ten years . . Average of first five years Average of last five years Maximum in one year . Minimum in one year . 28-9 30-0 27-8 42-5 21-5 Average of ten years . . . 42*1 Average of first five years . 46-5 Average of last five years . 37*7 Maximum in one year . . 75*0 Minimum in one year . . 30-0 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. The following Table will show the curve of their growth : 191 Barley. Years. 100 1 2 3 4 -j <_. ._ 5 6 7 8 9 10^ 90 80 70 60 .' ''. / 50 ;« r \ 40 ' / A V '' /- Shifting v r \ ' ^ \ 30 I'ermanent. 20 ^ V 1 10 0 1 2 3 4 5 6 7 8 9 10 100 90 80 70 60 50 40 30 20 10 >lbs. The quantity of barley produced in a contiguous piece of ground recently manured, was 39*4 lbs., being more than the average of the shifting crops, but about equal to the produce obtained the first year from the permanent one. 3. Brassica Rapa. Next in the series are Turnips, in which the difference between the average of the shifting and permanent crop is very remarkable, namely as 176 to 100. Nevertheless it will be seen, that even the latter did not sink below a certain amount when the seasons were tolerably favourable. 192 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. The following are the results : — Year. Permanent crop. Produce in a green state. Shifting crop. 1834. No. 2. 125*0 1835. 185*0 192*0 1836. 133*0 After Linum usilatissimum. 144-0 1837. ^7-2 After Vicia Faba. 154*0 1838. 56*0 After Linum usitatissimum. 150*0 1839. 110*0 After Cichoi'ium endivia. 226*0 1840. 128-0 After Nicotiana rustica. 217-0 1841. 98*0 After Papaver somniferum. 245*0 1842. lll'O After Avena sativa. 179*0 1843. 73*5 After Solanum tuberosum. 110*0 1844. 77-0 After Helianthus annuus. 148*0 Average of ten years . . Average of first five years Average of last five years . Maximum in one year . . Minimum in one year . . 100*8 104*0 97*5 185*0 37*2 Average of ten years . . 1 76*5 Average of first five years . 1 73*0 Average of last five years . 176*5 Maximum in one year . . 245*0 Minimum in one year . . 110*0 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. The following diagram will show the variations in their yearly produce :- 193 Turnips. Years. 250 240 230 220 210 200 Shifting ... 190 Permanent . 180 170 160 150 140 130 120 - 110 100 90 80 70 60 50 40 30 In the contiguous bed recently manured the produce was 152 lbs., a quantity about intermediate between the average of the shifting and permanent crops. 4. Cannabis sativa. The next crop I shall notice, Hemp, presents a very uniform rate of produce during the whole period, nevertheless the shifting crop, which however was not grown during the years 1840 and 1841, presents a much larger produce than the permanent one, as will be seen by the following Table. 194 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. Year. Permanent crop. Dried in the sun. Shifting crop. Dried in the sun. 1836. 1837. 1838. 1839. 1840. 1841. 1842. 1843. 1844. No. 17. 46-5 27-75 34-0 34-0 20-5 33-3 23-7 30-0 21-5 Average of nine years . . 30*13 Average of first five years 32*55 Average of last four years 27*12 Maximum in one year . 46*50 Minimum in one year . . 20*50 After Trifolium pratense. 52*5 After Brassica Rapa. 22*5 After Brassica Rapa, 32*5 After Hordeum sativum. 42*5 None. None. After Beta vulgaris. 53*0 After Polygonum fagopyrum. 39*5 After Brassica Rapa. 37*6 Average of four years . . 30*0 Maximum in one year . . 52*5 Minimum in one year . . 22*5 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. The following diagram will show the variations in the yearly produce Hemp. 195 Years, c 80 1 2 3 4 5 6 7 8 9 10 ^ [——J80-j 70 60 Shifting 70 60 50 — \ ^ ■ \ 50 Permanent - _,-' 40 \ ,''' '' V \ \ 40 \ / ' — i / ' A 30 30 y/ \ \ / \ /\ \ A 20 \ / y V V k 20 10 0- 10 0 1 2 3 4 5 6 7 8 9 10 >lbs. In the contiguous bed recently manured the crop weighed 45*4 lbs., somewhat more than the average of the shifting, and considerably exceeding that of the perma- nent beds. 5. Linum usitatissimum. Flax presents a gradual, though not an uniform, rate of deterioration, the shifting crop always standing in advance of the permanent one. In this instance I tried the same experiment as in the case of the potatoes, namely, that of sowing one bed with seed from the last year's crop, and the second with seed obtained from some other source. The latter produced much the most abundant crop, but I am now inclined to attribute its superiority chiefly to its succeeding a crop of Valerian, a plant which probably draws little from the soil, and which conse- quently having grown in it for five successive years, had given time to the materials of the earth to undergo decomposition, so that an accumulation of nutritious prin- ciples may have taken place in it, nearly as would have been the case if it had been left entirely fallow. MDCCCXLV. 2d 196 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. The following are the results obtained : — Year. Permanent crop of ten years' standing. Crop dried. Permanent crop of five years, fresh seed, Crop dried. Shifting crop. Crop dried. 1835. 1836. 1837. 1838. 1839. 1840. 1841. 1842. 1843. 1844. No. 19. 12-9 167 12-0 20-0 13*75 16-5 9-0 8-4 11-7 5-2 Average often years. . . 12*6 Average of first five years 15*0 Average of last five years 10*4 Maximum in one year. . 20*0 Minimum in one year. . 5*0 Nos. 13 and 14. After Valeriana Phu. 43-5 41-0 34-0 31-0 11-5 Average of five years . . . 32-5 Maximum in one year. . 43*5 Minimum in one year . . 1 1 "5 15-8 After Polygonum fagopyrum. 17*0 After Solanum tuberosum. 19-8 After Solanum tuberosum. 25-5 After Valeriana Phu. 21-75 After Polygonumfagopyrum. 21-5 After Vicia sativa. 25-0 After Brassica Papa. 34-0 After Vicia Faba. 29-6 After Solanum tuberosum. 17-8 Average of ten years . . . 22*7 Average of first five years 19*9 Average of last five years 25*5 Maximum in one year. . 34*0 Minimum in one year . . 15*8 The following- fliagrani will show the curve of their growth : — Flax. Years. , — -A. I 2 3 4 5 6 7 /j •%'* :■ ■> Permanent five years 40 20 Shifting Permanent ten years. 10 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 197 The contiguous manured crop weighed 222, rather less than the average of the shifting crops. 6. P^icia Faha. Beans showed a considerable falling off in the case of the permanent crop, but not in tne sr Hiung, tne lollowmg being t he results obtamed : — Year. Permanent crop. Produce in a dried state. Shifting crop. Produce in a dried state. 1835. No. 23. 38-0 27-7 1836. 40-0 After Linum usitatissimum. 39-0 1837- 23-5 After Euphorbia lathyris. 31-2 1838. 28-4 After Nicotiana rustica^ 28-5 1839. 34-0 After Nicotiana rustica. 48-0 1840. 16-5 After Papaver somniferum, 26-5 1841. 24-5 After Polygonumfagopyrum. 56-0 1842. 15-8 After Papaver somniferum. ' 28-0 1843. 17-1 After Avena sativa. 28-0 1844. 9-2 After Nicotiana rustica. 24-0 Average of ten years . . . Average of first five years . Average of last five years . Maximum in one year . . Minimum in one year . . 24-7 32-8 16-6 40-0 9-2 Average of ten years . . 33*6 Average of first five years . 34*8 Average of last five years . 32*5 Maximum in one year . . 56*0 Minimum in one year . . 24*0 2 D 2 198 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. The following represents the curve of their growth : — Beans. Years. A , 10 60 50 40 Pennanent 30 Shifting 20 10 A .1 \ A r \ — ^ A / f 1 1 1 r \ 1 1 M \ — -' V 1 y \ Y /\, ^ ~-^- V V- ^ k. \ 60" 50 40 30 20 10 >"lbs 1 2 3 45678910 In the contiguous manured bed the crop was only 27' I lbs., not greatly exceeding the average of the permanent, and falling considerably short of that of the shifting crops. 7. Nicotiana rustica. Tobacco is one of the plants which most strikingly illustrates the dependence of the crop upon manuring; the first year the produce being 178 lbs., whilst it sunk in six years' time to 17 lbs. The whole of this diminution, however, must not be set down to the deficiency of inorganic matter, since in subsequent years the produce became greater, although it never recovered its former rate. In this instance the permanent presents a higher average than the shifting crop, but this seems attributable to the circumstance that in the latter instance the soil had been previously drawn upon by a crop of beans, whilst in the former it had been recently manured. The following are the results : — Year. Permanent crop. Produce nearly dry. Shifting crop. Produce nearly dry. 1834. No. 9a. 172-0 None. 1835. 83-0 None. 1836. 33-0 After Apium petroselinum. 42-0 1837. 29-0 After Papaver somniferum. 25-0 1838. 29-0 After Euphorbia laihyris, 38-0 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 199 Nicotiana ruslica (Continued). Year. Permanent crop. Produce nearly dry. Shifting crop. Produce nearly dry. 1839. No. 9a. 17-25 After Linum usitatissimum. 22-5 1840. 27-0 After Cichorium endivia. 250 1841. 30-0 After Apium petroselinum. 24-0 1842. 22-5 After Helianthus annuus. 30-0 1843. 37*8 After Brassica Rapa. 49-0 Average of ten years . . Average of first five years Average of last five years Maximum in one year . 48-0 69-2 26-9 172-0 Average of eight years . . 32*0 Average of first four years . 32-0 Average of last four years . 32*0 Maximum in one year . . 49*0 Minimum in one year . 17-2 Minimum in one year . . 22*5 The following diagram shows the variations of the crops :- Tobacco. Years. A 180 Permanent . 170 160 150 140 130 120 110 100 90 80 70 60 50 Shifting ... 40" 30 20 10 10 "\ \ \ \ \ \ \ \ \ / \ A \ / "v \ V^ y^ 71J> lbs. 10 9. Polygonum fagopy rum. Buckwheat, not being- an exhausting crop, does not vary more than can be explained by differences of seasons and other contingent causes, the results being as follow : — Year. Permanent crop. Produce in a dried state. Shifting crop. Produce in a dried state. 1835. 1836. Nq. 25. 12-8 14-0 14-8 After Mentha viridis. 11-5 1837. 6-0 ^ After Valeriana Phu. 5-7 1838. 16-0 After Papaver somniferuin. 18-0 1839. 9-25 After Vicia Faba. 12-5 1840. 11-5 After Hordeum sativum. 11-5 1841. 3-2 After Nicotiana rustica. 5-5 1842. 9-6 After Nicotiana rustica. 14-1 1843. 3-8 Mter Beta vulgaris. 6-15 1844. 5-1 After Beta vulgaris. 6'Q Average of ten years . . Average of first five years Average of last five years Maximum in one year . Minimum in one year . 9-1 11-6 8-7 16-0 3-2 Average of ten years . . Average of first five years Average of last five years Maximum in one year . Minimum in one year . 10-6 12-5 8-7 18-0 5-7 202 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. Buckwheat, Shifting ... Permanent . 10 >lbs. 10. Trifollum pratense. Red clover being a biennial, it was necessary to retain the shifting crop in the same bed for two years ; and as the produce of the second year was in general larger than that of the first, the results can best be compared by stating the sum of each two years' growth. Year. Permanent crop. Produce of two years. Shifting crop. Produce of two years. 1835. 1836. 1837. 1838. 1839. 1840. 1841. 1842. 1843. 1844. No. 12. 1^2}-^ ^^•^"144-0 30-OJ^^" 15-2/'^' ^ 17-oj-^^ After Mentha viridis. ^2-5 135-1 After Euphorbia lathyris. 31-OJ^^^ During the last four years it was not found convenient to introduce a shifting crop of clover. The following curve represents the variations of the crop in the two cases. DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 203 Clover. Years. 50 1 2 3 4 5 6 7 8 9 10 ^ 40 30 20 /v /\ \, Shifting ... 10" /' / •- N V- A N. Permanent "' 0 / V/ ■ \ 10 40 30 20 10 0. Ubs. 1 1 . Avena sativa. My trials with oats continued only for six years, and on ground already drawn upon by four crops since the period at which manure had been applied ; the plot selected for the permanent crop having borne successively flax, beans, turnips, and hemp ; that on which the corresponding crop in 1839 was raised, parsley, mint, and clover. The produce therefore of the first year was in both cases moderate, and nearly uniform, but subsequently there was a greater diminution in the permanent than in the shifting crop, as will appear from the following Table : — Year. Permanent crop. Shifting crop. 1839. 1840. 1841. 1842. 1843. 1844. No. 20. 31-0 44-0 31-7 22-5 24-4 14-6 After Trifolium pratense. 37*5 After Trifolium pratense. 49-0 After Beta vulgaris. 53-0 After Trifolium pratense 28-5 Average of six years . Maximum in one year Minimum in one year 28-0 44-0 14-6 After Polygonum fagopyrum. 24-4 After Helianthus annuus. 14'7 After Vicia sativa. 28-3 Average of six years . . . 32*4 Maximum in one year . . 49*0 Minimum in one year . . 14*7 MDCCCXLV. 2 E 204 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. The following curve will show the variations in the yearly produce. Oats. Years. r 1 2 3 4 5 6 7 8 9 10 ' 50 / /\ 4» Shifting / /\ — f — / \ . Permanent ... J \ 30 *'■•*« \ / t 20 \ \ 10 0 \ 2 3 4 5 6 7 8 9 10 50' 40 30 20 10 >lbs. \2. Beta vulgaris. In the case also of the beet, the length of time during which the ground was cropped seems insufficient to lead to any decisive results, especially as the matters extracted from the soil by this plant are, compared to its bulk, inconsiderable. The average of the shifting and permanent crops, it will be seen, does not vary materially, and what difference there is, seems in favour of the latter. Year. Permanent crop. Weighed in a green state. Shifting crop. Weighed in a green state. 1839. 1840. 1841. 1842. 1843. 1844. No. 11 b. — After Papaver somniferum. 312'0 217-0 250-0 344-0 135-0 278-0 None. After Cannabis sativa. 330-0 After Hordeum sativum. 264-0 After Avena sativa. 173-0 187-0 200-0 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. The following; diagram will show the variations in the annual produce Beet. 205 12 3 4 5 13. Cichorium endivia. 14. Mentha viridis. 15. Apium petrosel'mum. The three remaining crops, of Endive, Mint, and Parsley, were introduced into the series, from a wish to have one representative at least of the principal of those natural families, which supply us, with either plants useful for field or garden purposes, or with any of the commoner weeds which intrude themselves into our fields, it being conceived, that some interesting and useful results might be obtained, by watching the effect of their root excretions on plants of the same or of a different tribe. Had it not been with a view to this theory, I should hardly have thought it worth while to experiment upon plants, which appear to draw comparatively so little from the soil, as the three now alluded to. The following, however, were the results obtained : — 2 E 2 206 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. Cichorium endivia. Year. Permanent crop. Dried in the sun. Shifting crop. Dried in the sun. 1834. No. 15. 73-5 None. 1835. No. 16. 68-5 After Polygonum fagopyrum. 68-0 1836. No. 15 and 16. 44-4 After Nicotiana rusiica. 49-0 1837. 33-3 After Hordeum sativum. 34-0 1838. 50-0 After Vicia Faba. 46-2 1839. 48-5 After Hordeum sativum. 38-0 1840. 22-0 None. 1841. 58-5 None. 1842. 67-0 None. 1843. 50-0 None. 1844. 72-0 None. Average of ten years . . Average of first five years Average of last five years Maximum in one year . Minimum in one year . 51-5 53-9 49-2 73-0 22-0 Average of five years . . Maximum of one year . . Minimum of one year . . 47-0 68-0 34-0 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. Mentha viridis. 207 Year. Permanent crop. Produce in a dry state. Shifting crop. Produce in a dry state. No. 21. 1835. 1836. 21-9 53-0 17-0 After Apium petroselinum. 26-0 1837. 38-0 After Apium petroselinum. 9-25 1838. 18-3 36-8 1839. 26-75 None. 1840. 24-5 None. 1841. 16-8 None. 1842. 18-7 None. 1843. 12-8 None. 1844. 16-5 None. Average of ten years . . . Average of first five years . Average of last five years . Maximum in one year . Minimum in one year . . 24-7 31-5 17-8 53-0 12-8 Apium petroselinum. Year. Permanent crop. Produce in a dried state. Shifting crop. 1835. 1836. No. 27. 64-25 115-0 74-0 After Vicia Faba. 208-0 1837. 52-0 After Polygonum fag opy rum. 61-0 1838. 58-0 After Polygonum fagopyrum. 68-5 1839. 13-0 After Mentha viridis. 32-5 1840. 59-0 After Mentha viridis. 83-0 1841. 22-7 None. 1842. 9-4 None. 1843. 12-0 None. 1844. 33-0 None. Average of ten years . . 39-75 Average of first six years . 60*2 Average of last four years . 19-3 Maximum in one year . .115*0 Minimum in one year . . 9*4 Average of six years . . . Maximum in one year . . Minimum in one year . . 87*8 208-0 32*0 o X .a.SScsotj'Scs . §"=-»■"§ 0-5: :i 3 5 2 « =^? g « s^i ■^ S, a • •S =^-3 S' C 3 gOJ — «o t^ i--*C0»fli— I© eq5apb«©OJicacQpO>(SO©'j5 _S«N(N4iits6s'fiiy«-^©«b-3'Ae3 ■gt^05«>»^FHeoe>scQeO'^©t^«0 : js :> :2i3 ffC CO "^ ift "^ ^ N S "!* * eo "•" * .2 00 00 — a5 w '- S •« f»^ -H >S 3 *^'~ «>'M — SJ w^ocooacooaooooo 4J 4) a) >. ;»-. >^ >^ . ^u 4J - - 00 00 -^ >^ >^ »fa p-j gj 69 vw *v w^ fc« rt> Sl 4j -J5»p Sciodoc>bii5»r5'^05-^'^»--^»©©(J» a-^-^O --^ ^ (M — ^ —" — eo * 06 « 5o 2 S4j£D 3 53 3 53 3 « 2 ^ S g. 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DAUBENY ON THE ROTATION OP CROPS, ETC. 209 It appears then that out of the whole series, there are only four cases in which the average amount of the permanent crop was equal or superior to that of the shifting one. In the first of these, the Tobacco, the fact may be accounted for, from the condition x)f the ground being more favourable to the permanent than to the shifting crop on the year of its introduction, the former being obtained from soil which had been re- cently manured, the latter from what had been partially exhausted by preceding crops. The second, the Beet, was scarcely continued for a sufiicient length of time to lead to any certain conclusions. The two others, namely, the Endive and Mint, present results so nearly agreeing in the amount of their permanent and shifting crops, that the slight disparity may be fairly referred to contingent circumstances, and an uniformity in the products obtained may in consequence be inferred. Setting aside then the above four cases as exceptional, the general tenor of the experiments would seem to indicate a manifest advantage on the side of the shifting crops, varying from 1 to 75 per cent., but more generally approaching to the latter. Yfit it by no means follows that this difference is to be attributed to the influence of root excretions. Were such the cause, we ought to perceive a more regular, as well as a more rapid, diminution in the permanent crop than is indicated in these Tables ; we should not find, for instance, the crop of potatoes equalling in the fifth year the produce of the first ; the Turnips, after sinking to 37'0 lbs. in the third year, rising in the sixth to 128 lbs. ; not to allude to other similar instances of oscillation. If De Candolle's theory too could be carried out, we might have expected to find a more manifest improvement in the shifting crop occasionally occurring, owing to the excretions of the family of plants which had preceded it proving congenial to its constitution. But if nothing positively injurious be imparted to the soil by the crop, the gradual falling off in the amount of the latter can only be attributed to the deficiency, either of organic, or of inorganic matter fitted for its development, in the soil in which it was reared. Of the two continental writers on chemical agriculture whose works have excited the greatest interest in this country, the one would seem to favour the former, the other the latter explanation, although it may be more correct to consider them, as viewing the subject under two different aspects, rather than as laying down principles irreconcileable one with the other. LiEBiG, for instance, although he regards the presence of certain inorganic matters as the only condition essential to the existence of a plant, does not deny, that its growth may be accelerated in proportion to the ready access to it of ammonia and carbonic acid, and these, it is evident, would be supplied more abundantly by the presence in the soil of organic matter in a readily decomposable condition. Nor, on the other hand, would Boussingault deny the necessity for a supply of the * 210 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. inorganic principles, which form, as it were, the skeleton of each plant, although he attributes the peculiar benefit derived from fallow crops to their power of generating the organic matter which is required by the cereals that are to succeed them. In order to determine then in what degree the falling off of the permanent crop arose from the one or the other of these causes, it seemed necessary to obtain an analysis of the plants derived from this and from the shifting crop corresponding, and to compare the composition of both with that of a standard specimen of the same plant determined by the method pursued with respect to the two former ; and it would have been also satisfactory, not only to ascertain, whether the soil itself origi- nally contained such a store of all the principles existing in the crop, as might be sufficient to meet the demand made upon it for that purpose during the whole decen- nial period, but also whether its present composition was such, as actually indicated a deficiency in any of the principles which entered into the constitution of the plants grown in it. It is evident that the former branch of the inquiry would have been superfluous, if I could have depended on two things : — 1st. That the analyses given by Sprengel and others, of the plants to which the inquiry related, were trustworthy ; and 2ndly. That the composition of the same vegetable was at all times uniform both as to the quality and quantity of its ingredients. But with respect to the former point, I found, on turning to the analyses given of the ashes of the same plants by different authorities, many marked discrepancies, and that those of Sprengel, which are the most numerous of any we could appeal to, were regarded as inaccurate by other chemists of higher distinction. Nor, even if they had represented truly the composition of the plants which were actually examined by that analyst, could we be sure, that they would apply to those of the same species, grown in a different country, and under altered circumstances, more particularly as the recent researches of Liebig, Will, Fresenius and others, appeared to indicate, that certain ingredients admit of being substituted for others, according to laws as yet not fully made out. For all these reasons then, it became necessary for my purpose to obtain a correct analysis, both of the crops, and of the soil ; and I was the more reconciled to the ex. penditure of labour involved in this undertaking, when I reflected, that the results obtained were likely not only to lead to an explanation of the cause of the utility of a rotation of crops, but also to throw some incidental light upon certain other points connected with the chemistry of agriculture, which did not appear to be suf- ficiently elucidated ; such for instance, as the degree of variation of which a plant may admit in the quality and quantity of its inorganic ingredients, or in other words, its power of substituting one principle for another, and likewise as to the state of combination, in which the alkalies, phosphates, &c. exist with the other constituents of the soil, when in a condition to be assimilated by a plant. DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 211 I shall, therefore, next proceed to state the results of the analyses of the several crops which were made in my laboratory by Mr. Way. PART II. On the chemical composition of certain crops cultivated in the Botanic Garden, and on the amount of inorganic principles abstracted by them from the soil during the period the experiments were continued. It is only within a few years that the importance of ash analyses has been under- stood, and we were consequently much at a loss for accurate instructions as to the best method of conducting it. A valuable paper has however recently appeared in the Memoirs of the Chemical Society of London (Part IX.), by Will and Fresenius, which in a great degree sup- plies this deficiency, and which we therefore determined to adopt as the basis of our scheme of operations. One part of it, however, relating to the determination of the phosphoric acid, was soon found extremely troublesome in practice, and too tedious to be resorted to in an inquiry which involved the necessity of so large a number of analyses. In this part therefore of the process, Mr. Way suggested a method, which, as it recom- mended itself from its greater simplicity, and appeared to answer well in practice, he has adopted in all the cases, of which mention will hereafter be made. But although the plan of analysis pursued presents in other respects but little of novelty, yet as certain modifications of the scheme of the German chemists have been here and there introduced, and as some of the manipulations may admit of being more clearly explained than in the paper alluded to, it will not be amiss to set down, as briefly as possible, all the principal steps pursued for the determination of the several ingredients existing in the ash. In a few instances, as in the Cerealia, where the ashes abounded in silicates, com- plete solution in acids could not be effected, until the whole had undergone, either a previous fusion with carbonate of barytes, or evaporation with caustic potass, the former substance being employed for that portion of the ash which was to be ex- amined for alkalies, the latter for the one set apart to ascertain the other ingre- dients. But where the whole of the ash proved soluble in muriatic acid, no such prelimi- nary process was required, and we were able to proceed directly to dissolve it in this menstruum. A certain amount, however, of sand derived from the soil in which they had grown, and of charcoal, from the organic matter of the plant which had not been burnt off, was always present, and these of course would not be acted upon by this acid. There was also in every instance a variable quantity of peroxide of iron proceeding manifestly from the vessels in which the combustion had been carried on, the quantity MDCCCXLV. 2 F . * 212 DR. DAUJBENY ON THE ROTATION OF CROPS, ETC. to be burnt being too considerable to allow of its calcination in any of the platina vessels which I chanced to possess. The ashes, therefore, of which 200 grains were usually taken, had first to be treated with pure muriatic acid, and the latter to be driven off by heat, so that the silica of the ash might be rendered insoluble. Water aitd muiiatic acid were tben added to tli« dry mass, and the portion which e precipitate, we obtain that of the phosphoric acid present in the ash. This modification of the process saves some trouble, as it obviates the necessity of reducing the bulk of the solution remaining after the separation of the phosphate of iron precipitated from A. in the first process, which, owing to the number of washings necessary, becomes inconveniently large. I felt curious to ascertain whether the phosphoric acid obtained by the above me- thod was combined with two or with three atoms of base, as Will and Fresenius state, that the Cerealia generally present it in the former predicament, the Legumi- nosee in the latter. Our experiments on this point do not appear to confirm such a conclusion, showing 2 f2 214 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. rather, that the proportion of base to acid has some reference to the quantity of alkali present, and is therefore dependent in a certain degree upon the manner in which the previous calcination had been conducted. Supposing a plant to be rich in alkali, and to contain but little silex, it would seem natural to expect, that the phosphoric acid would be united with three atoms of bases. When, on the contrary, the proportion of silica was large, a strong heat would cause more of it to unite with the alkali, and hence there might be only enough of the latter remaining to form a bibasic combination with phosphoric acid. Yet even here, if a slighter heat had been applied, it might happen that a tribasic compound would be produced. Thus we found, that in all the three crops of potatoes the phosphate gave a yellow precipitate with nitrate of silver, and the same was also the case in the turnips ; but in only one sample of beans, viz. the shifting crop, and in one of barley, which was also the shifting one, did the same hold good. On the other hand, in two other samples of ash from the barley, and in two samples of that from the beans, the phosphoric acid seemed, from the precipitate afforded by nitrate of silver, to be united with two atoms only of base. It is easy to determine the amount of lime and of magnesia from either of the liquids already operated upon, oxalate of ammonia being added to separate the former, and, after neutralizing with ammonia the acid solution, phosphate of soda throwing down the magnesia. In these respects the common methods were adhered to. The solution C. was reserved for the determination of the alkalies. For this purpose it is necessary to get rid of all the earths and metallic oxides which may be present, which is accomplished by adding barytic water so long as a precipitation takes place. That reagent of course throws down the whole of the sul- phuric and phosphoric acids, the peroxide of iron, most of the magnesia, and most of the lime*. The filtered solution may however contain a little magnesia and lime, and pro- bably much barytes. To remove these, carbonate of ammonia is added in excess, and the precipitate which is thrown down removed by filtration, after being allowed to stand until it becomes heavy and granular. If this be duly performed, the remaining solution can contain only muriate of ammonia and chlorides of the fixed alkalies. The former is removed by heat, and the dry chlorides then remaining will repre- * As the entire precipitate, excepting what consists of sulphate of barytes, is soluble in muriatic acid, we may estimate the amount of sulphuric acid present, by treating it with the former acid, removing all that is soluble in water by filtration, and lastly weighing the dried residue, from which the weight of sulphuric acid may be readily deduced. DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 215 sent the weight of the alkaline salts originally present in the ash. Having ascertained this, the dry residue is dissolved in a small quantity of water, chloride of platinum added, and the whole evaporated nearly to dryness. It is then treated with dilute alcohol, which takes up the double chloride of platinum and sodium*, together with any excess of the reagent that may have been added. The undissolved residue is the double chloride of platina and potass, from which the amount of the chloride of potassium may be calculated. The difference between the weight of the latter and of the whole salt gives that of the chloride of sodium proceeding from the ash. The carbonic acid present was best ascertained by operating on a separate portion of the ash, and the common method of determining it by the loss of weight conse- quent upon the addition of a stronger acid was adopted, with the precautions usually taken -f-. The chlorine also was determined in the usual manner by nitrate of silver, a sepa- rate portion of the ash being employed for that purpose. In the analyses given, it has been usual to consider it as in combination either with sodium or with potassium. That this was the case, seemed probable from the curious relation generally found to subsist between the quantity of chlorine and of sodium detected, which in many instances approximated so nearly, that we were led to conclude, that the chlorine in these instances merely implied a corresponding amount of chloride of sodium existing in the ash. That the correspondence should not have been exact, may be more readily explained, when we consider that the only generally practicable mode of estimating soda is an indirect one, and therefore liable to some degree of uncertainty. In the few instances where the amount of chlorine was more than proportionate to that of the sodium, it was thought consistent with analogy to regard that portion of the former which was in excess, as held in combination with the vegetable alkali, or as representing an equivalent weight of chloride of potassium. This mode of stating the results may appear objectionable, as blending theory with fact, but my reason for adopting it is, that it j»oints at an important general conclu- sion, which it is hoped future inquiries will either negative or confirm, namely that the base of the soda found in plants commonly enters them in a state of combination with chlorine, being derived from the common salt, taken up, but not decomposed, by the organs of the plant. Such an inference indeed cannot be adopted by those who receive the analyses given by Sprengel as correct, for in many of these large quantities of soda are stated * This double chloride is readily decomposed, if first rubbed up with mercury, which flies off along with the chlorine in the form of calomel, when heated. t It seems a defect in the analyses reported by Sprengel, that this ingredient is never mentioned in them ; for although it may not be present as such in the crop, yet its amount in the ash probably represents that of the organic acids existing in the plant previously to its being burnt, and hence the proportion which it bears in different samples of the same species to the phosphoric and other mineral acids, may tend to indicate the rela- tion subsisting between the amount of organic and of inorganic matter, arising from the mode of culture or other circumstances. '216 DR. DAPBENY ON THE ROTATION OF CROPS, ETC. as having been detected ; but, without presuming to bring forward the analyses made in my laboratory as in themselves sufficient to justify the public in rejecting the former as inaccurate, I may be permitted to observe, that it is much more easy to conceive that the amount of soda present may have been overrated, than that it should have been estimated below its real amount, supposing anything like an equality of skill and attention on the part of the operator. To overrate it, we need only attribute to him some degree of negligence, either in not converting by means of chloride of platinum the whole amount of chloride of potassium into the sparingly soluble double chloride, or in not determining its entire quantity ; to estimate it too low, we must imagine, what is far less probable, a portion, of the readily soluble compound of chlorine with sodium, or the equally soluble double salt which the latter forms with platinum, to remain attached to the chloride of potassium and platinum, and thus to add to its weight. Our results may also appear to militate against the conclusions of a much higher authority than Sprengel, I mean Professor Liebig, who has lately represented that one alkali may be substituted for another in the organization of a plant, and that a species, which in inland spots assimilates a certain amount of potass, takes into its fmme an equivalent proportion of soda in maritime districts, where the latter alkali abounds. With the slender data before me, it would be the height of presumption to impugn the generalisations of this distinguished philosopher, but it will be seen from the analyses given below, that no difference in the nature of the alkaline ingredients could be detected between barley, taken from the neighbourhood of the sea, whether from the eastern or western coasts of this country, and from the more central region of Oxfordshire. Two ingredients mentioned by Sprengel as existing in the ashes of plants were searched for in a few of those to which this paper refers, but without success. These were alumina and manganese, the former so universally present in the soil, tlmt it may readily find admission into the ashes of the plants, unless the greatest care be taken to clean off every particle of dirt entangled by their i*oots ; the latter, as Liebig thinks, an accidental ingredient, being taken up by many plants in consi- derable quantities where the soil contains much of it, but altogether wanting in the same vegetables cultivated elsewhere. In order to ascertain the presence of alumina, the ash Wcis dissolved in muriatic acid, the solution evaporated to dryness, in order to separate the silica, and then re- dissolved in muriatic acid diluted with water. An excess of ammonia was afterwards added to the filtered liquor, and the preci- pitate which fell, after having been well-washed, was boiled with a pure solution of potass. The portion dissolved was then filtered, neutralized with muriatic acid, and treated a second time with ammonia. If any precipitate had been thrown down, the presumption would have been that it consisted of alumina, and the appropriate tests would have been applied to confirm the conjecture ; but in the only instance in which DR. DAUBENY ON THE ROTATION OP CROPS, ETC. 217 we could positively assure ourselves that no admixture of the soil had got in, namely, in the grain of barley from Ensham, nothing was thrown down by the last application of ammonia, and in one sample of ash from flax (viz. the standard crop), only a mexe trace was discoverable. Considering indeed that the soluble salts of alumina are poisonous to plants, and that the earth itself is confessedly present in very variable, sometimes very minute^ quantities, I am inclined to doubt whether it be in reality a constituent of their ashes at all. With respect to manganese, two methods were adopted for ascertaining its presence. The first, that of boiling the muriatic solution with carbonate of lime, and then, after filtering it, adding hydrosulphuret of ammonia. The second, the blow-pipe test, fusing a little of the muriatic salt with borax, when a very minute quantity of manganese would produce its characteristic colour in the bead of glass produced. By neither of these methods were any indications of manganese obtained. I next proceed to state the results of the analyses made in my laboratory by Mr. Way, of six kinds of crops grown in the experimental garden, together with those obtained from certain standard crops of the same species, grown in another part of the garden, or in other places in the vicinity of Oxford, under more natural circumstances. My original object being merely that of ascertaining the quality and quantity of the inorganic matters abstracted from the soil in these instances, the crop of barley, flax, hemp and beans, was burnt altogether without any separation of their respectivie parts having been previously made, and it was only in the case of the potatoes and the turnips that a distinct portion of the plant was selected for analysis, namely, the tubers in the former, and the bulbs in the latter. Barley. Permanent crop, ^fter ten years' repetition. 100 grains of the dried crop, including both the straw and grain, left of ash 8*7 grains. 100 grains of this ash contained as follows: — Sand and charcoal, extraneous 22*36 Peroxide of iron, chiefly extraneous . . . 212 24-48 Silica of the plant 24*60 Phosphoric acid - 7*3i Sulphuric acid 2*12 Carbonic acid 1'94 Chloride of sodium 4*73 Potass 17*33 Magnesia 4*68 Lime . , 13-91 Total . . 101-14 218 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. Barley. Grown in the same part of the garden as the last, for ten years immanured, distinguished as the shifting crop. 100 grains of the dried crop, including as before both the straw and the grain, left of ash 6-25 grains. 100 grains of this ash contained as follows:^ Sand and charcoal, extraneous 21*91 Peroxide of iron, chiefly extraneous ... 2*30 24-21 Silica of the plant 36-47 Phosphoric acid 9*30 Sulphuric acid . 2-35 Carbonic acid 1*44 Chloride of sodium 1*43 Potass 16-58 Magnesia 3-58 Lime 772 103-08 Barley. Grown in a distinct part of the garden. Soil similar, but recently manured, distinguished as the standard crop. 100 grains of the dried crop, including as before the straw and grain, gave of ash 7' 15 grains. 100 grains of this ash contained as follows : — Sand and charcoal, extraneous 16*60 Peroxide of iron, chiefly extraneous . . . 2*30 18-90 Silica of the plant . 37*27 Phosphoric acid 7'^7 Sulphuric acid 4*37 Carbonic acid 1-51 Chloride of sodium 1 -84 Potass 13*86 Magnesia 3*96 Lime 11*81 101*19 It would appear then from the above analyses, that the principal difference between the permanent crop and the two others consisted in the larger amount of soluble silica, which, together with the greater proportion of ash, may have arisen from the straw predominating in quantity over the grain. DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 219 It next appeared to me desirable, both by way of testing the accuracy of these re- sults, and likewise of ascertaining whether the third sample of barley analysed might really be adopted as a fair representative of a standard crop, to examine separately the grain and straw taken from a crop of average quality grown in the neighbourhood of Oxford. Mr. Druce of Ensham accordingly supplied me with a sample of barley from his farm, of which the following analysis was made by Mr. Way. 1000 parts of the crop of barley from a field near Ensham, situated on the Oxford clay, consisted of — Grain 575 Aulm 37 Straw 383 1000 Of the Grain. — 100 parts yielded of ash 2*04 parts, 100 grains of which consisted of— Charcoal*, extraneous . 24*51 Peroxide of iron, extraneous 2*30 26-81 Ingredients of the grain . 73-86, viz.- Total . . . 100-69 Silica Excluding extraneous matter. 24-51 or 33-2 Phosphoric acid . Sulphuric acid . . Carbonic acid . 22-97 2-48 or or 31-2 3-4 Chloride of sodium 1-48 or 2-3 Potass .... 14-10 or 191 Magnesia . . . Lime . . . . . 5-63 2-71 or or 7-6 3-6 73-86 100-4 Of the Straw. — 100 parts yielded 4*2 of ash, of which 100 parts contained — Sand and charcoal, extraneous 4-20 Peroxide of iron, extraneous . 474 Ingredients of the straw. Total ... 8-94 94-62, viz. — 103-56 Silica .... 44-72 Phosphoric acid . 1-68 Sulphuric acid . 4-38 Carbonic acid . 121 Chloride of sodium 7'85 Soda .... 0-98 Potass .... 22-98 Magnesia ... 1*67 Lime 915 Excluding extraneous matter. or 47*20 1-80 4-60 1-27 8-25 r06 or or or or or or 24-40 or 170 or 9-65 103-56 99-93 * In this instance the extraneous matter not dissolved by muriatic acid proved to consist almost wholly of MDCCCXLV. 2 G 230 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. Of the Julm, — 100 parts yielded 137 of ash, of which 100 parts contained- Charcoal and sand, extraneous 6*22 Peroxide of iron, extraneous 1*53 Ingredients of the aulm 775 90-58, viz.- < Total 98-33 Silica .... Phosphoric acid . Sulphuric acid . Carbonic acid . Chloride of sodium 073 Soda .... Potass .... Magnesia . . . Lime .... 98-33 Excluding extraneous matter. 80-96 or 89-50 1-20 or 1-30 0-89 or 0-90 a trace 0-00 I 0-73 or 0-80 0-22 or 0-24 1-23 or 1-30 0-90 or 0-99 4-50 or 5-00 100-03 According to these data the crop of barley will consist as follows :- Parts. Parts. Parts. Total. Grain .... 57500 Straw .... 38800 Aulm .... 568 96868. Yielding of ash . 1170 Yielding of ash . 1629 Yielding of ash . 77-5 3406-5 Of which the ex- "^ Of which the ex-"" Of which the ex-" traneous matter > 313 traneous matter ^ 141 traneous matter > . 5-5 459-5 amounted to Real ash . . amounted to 85 7 i Real ash . . 1488 amounted to Real ash. . 72-0 2417-0 The latter consisting of | Consisting of Consisting of Silica ... 287. Silica .... 705 Silica .... 64-50 1056-50 Phosphoric acid 270 Phosphoric acid . 26 Phosphoric acid . 0-13 296-13 Sulphuric acid . . 29 Sulphuric acid . . 70 Sulphuric acid . 0-65 99-65 Carbonic acid . . 00 Carbonic acid . . 18 Carbonic acid 0-00 18-00 Chloride of sodium 17 Chloride of sodium 122 Chloride of sodiuna I 0-57 139-57 Soda 00 Soda .... 15 Soda .... 0-14 15-14 Potass 164 Potass . . . 361 Potass .... 0-93 525-93 Magnesia. . . . 65 Magnesia . . 25 Magnesia . . . 0-65 90-65 Lime 31 863 Lime .... 143 1485 Lime .... 3-60 177-60 71-17 2419-17 Now according to this calculation, 100 parts of the mixed ash ought to contain the subjoined quantities of the ingredients below- mentioned, and by comparing these with the composition given of the ashes obtained from the three crops grown in the Botanic Garden, which I have deduced from the analysis before given, after deducting in each instance the matters regarded as extraneous, it will be seen that there is a near correspondence. charcoal, for after the first analysis had been completed, another portion of the ash was fused with potass, after which the silica obtained agreed within 0*2 with that procured in the first instance by the usual process. I am the more anxious to state "this, as it will be seen from the statement given in a subsequent page, that there is a great discrepancy between the per-centage of silica given in Mr. Way's analysis and that reported by Sprengel, a discrepancy which, without this explanation, might be attributed to a want of care on his part in not dissolviug the whole of the silica. DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 100 grains of real ash contain, — 221 Drhce's Barley and Barley-straw. Botanic Garden. | Permanent. Shifting. Standard. Silica 43-6 Phosphoric acid . . . . 12*2 Sulphuric acid .... 4'1 Carbonic acid .... 0*7 Chloride of sodium . . . 5*7 Soda 0-6 Potass 21-7 Magnesia 3*7 Lime 7*3 Total .... 99-6 Or Acids 17-00 Bases 3270 32-3 9-5 2-7 2-5 6-1 0-0 22-6 6-0 18-2 99-9 14-7 46-8 46-1 11-8 2-9 1-7 1-7 0-0 20-9 4-4 99-2 16-4 35-0 45-0 9-2 5-2 1-8 2-1 0*0 16-8 4-7 14-3 99-1 16-2 35-8 These results are interesting on two accounts ; first, as they show what the com- position of barley is when cultivated under natural circumstances, or within what limits its variation from a normal condition may be circumscribed ; secondly, as they confirm tlie general exactness of the preceding analyses, by the correspondence which is seen to exist between the composition of the shifting crop, as ascertained by experiment, and that of the sample obtained from Mr. Druce's brought out by the above method of computation. As the analyses of the ash, both in the case of the straw and of the grain, were performed by Mr. Way, whilst the proportion between the grain and straw, as well as that subsisting in each instance between the crop and its ash, was ascertained by myself, the statement which I have just submitted as to the real composition of the crop, calculated from these data, would hardly have presented so near an accordance with the analysis made of the entire crop which I had obtained in the Botanic Garden, had not both the one and the other been executed with considerable care. It was far otherwise, however, when we compared our results with those of Sprengel, in which, amongst other striking discrepancies, we observe, that the proportion of soda stated to exist in the grain exceeds that of the potass, whilst in our analyses, only so much as was equivalent to the amount of chlorine appeared to be present*. * Our analysis, of Hordeum vulgare. Sprengel's, of Hordeum distichum. Bichon's, as quoted by Will. Silica 33-2 Phosphoric acid 31-2 Sulphuric acid 3-4 Carbonic acid 0-0 Chloride of sodium 2*3 Potass 19-1 Soda 0-0 Magnesia 7*6 Lime 3-6 Alumina 0-0 100-4 Silica 50-2 Phosphoric acid 8-4 Sulphuric acid ........ 2-5 Carbonic acid 0-0 Chloride of sodium 0-0 Potass 11-80 Soda 12-30 Magnesia 7-65 Lime 4-50 Alumina 1 -50 99-95 2 G 2 Silica 21-99 Phosphoric acid 40*63 Sulphuric acid 0*26 Carbonic acid 0-00 Chloride of sodium .... O'O* Potass 3-91 Soda 16-79 Magnesia 16*05 Lime 3-.36 Alumina 0-00 97-03 222 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. This discrepancy made me desirous of learning, whether, in accordance with the observations of Will and Fresknius, any marked variation in the character of the alkaline constituent might subsist between barley cultivated in an inland county like Oxfordshire, and near the sea, and I therefore procured, through the kindness of a friend one sample from the coast of Essex, and another from that of Cardigansiiire, in South Wales. The following were the results obtained of barley from the sea coast of Essex : — 1000 grains yielded 19 grains of ash. 100 grains of this ash contains, of — Sand and charcoal, extraneous . 23*28 Peroxide of iron, extraneous . 2*44 2572 Silica 24*89, or, excluding extraneous matter 34*0 Phosphoric acid 21*84, or, excluding extraneous matter 29*7 Sulphuric acid 1 *79, or, excluding extraneous matter 2*4 Carbonic acid ...... 0*00 0*0 Chloride of sodium .... 0*00, there being no chlorine in the ash. Soda . . . . . . . . . 1*05, or, excluding extraneous matter 1*3 Potass. 15*42, or, exchiding extraneous matter 21*1 Magnesia 5*29, or, excluding extraneous matter 7'2 Lime . . 3*36, or, excluding extraneous matter 4*5 99*36 100*2 25*72 Real ingredients of plant . . 73*64 Barley-straw belonging to the same crop from Essex. 1000 grains yielded 49 grains of ash. 100 grains of these ashes contain, of — Sand and charcoal, extraneous 8*59 Peroxide of iron, extraneous . 4*26 12*85 Silica . 41*81, or, excluding extraneous matter 48*9 Phosphoric acid 4*18, or, excluding extraneous matter 4*9 Sulphuric acid ..... 0*67^ or, excluding extraneous matter 0*8 Carbonic acid 000 0*0 Chloride of sodium . . . . 9*58, or, excluding extraneous matter 11*2 Soda . 0*65, or, excluding extraneous matter 0*7 Potass 18*49, or, excluding extraneous matter 21*6 Magnesia 4*95, or, excluding extraneous matter 5*7 Lime 5*18, or, excluding extraneous matter 6*1 98*36 99*9 12-85 Real ingredients .... 85*5 1 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 223 The straw of the barley grown on the coast of Wales was not examined, but the ash of the grain from that quarter was found to contain, in 100 parts, 9*64 of potass, 1'32 of chloride of sodium, and only 0*84 of soda, the smaller proportion of potass being explained by the larger amount of extraneous matter present in the residuum left by it after calcination, than by the samples previously noticed. The small proportion of soda, however, both in this, and in the former case in which the sample was obtained from the neighbourhood of the sea, seems to militate against the general conclusion deduced by Will, from his analysis of barley taken from the interior of Germany, as compared with the same brought from the Nether- lands. Potatoes. The crop grown in a recently manured portion of the Botanic Garden, separate from the spot set apart for the experiments, proving defective in quality, I selected as my standard a good mealy sort reared in the neighbourhood of Oxford, in the same kind of subsoil. The following will give the relative composition of this, and of the two crops obtained from the ground left for ten years unmanured, which, in the case of that styled the permanent, had borne potatoes for ten years consecutively, whilst in that styled the shifting, it had only borne them in 1844, having been occu- pied with the following plants on the nine years preceding, viz. — 1835. Delphinium consolida. 1836. Trifolium pratense. 1837. Nicotiana rustica. 1838. Valeriana Phu. 1839. Valeriana Phu. 1840. Linum usitatissimum. 1841. Solanum tuberosum. 1842. Papaver somniferum. 1843. Hordeum sativum. Standard Crop. r 7"6 of ashes. Of the tubers, 1 000 grains yielded about . . . < 755-0 of water. L 236*4 solid organic matter. 1000-0 Overlooking the small amount of extraneous matter intermixed, the ash will of course represent the proportion which its inorganic constituents bear to the whole quantity. Now 100 grains of this ash consisted of — Sand and charcoal, extraneous . . . 593 Peroxide of iron, extraneous . . . . 685 12-78 Silica 5-81 Phosphoric acid 9-68 Sulphuric acid 5*23 Carbonic acid 5*84 Chloride of sodium 2-06 Chloride of potassium ^'Q7 Potass 37-99 Magnesia . 10-98 Lime ............ 2-71 99-75 12-78 Real ingredients .... 86-97 224 DR. DAT7EENY ON THE ROTATION OF CROPS, ETC. Permanent Crop of Potatoes. Tubers, 1000 grains yielded 100 grains of this ash consisted of — Sand and charcoal, extraneous Peroxide of iron, extraneous . ■ 127 of ash. 724-0 of water. 263*3 solid organic matter. 1000-0 14-40 3-30 1770 Silica 1*57 Phosphoric acid ........ 10*68 Sulphuric acid 3-74 Carbonic acid 10-68 Chloride of sodium ....... 2*79 Chloride of potassium ...... 3*09 Potass 37-47 Soda 0-00 Magnesia 7*00 Lime 364 Real ingredients . . . Shifting Crop of Potatoes. Of the tubers, 1000 grains yielded 98-24 1770 80*54 10*8 of ash. 719*0 of water. .270*2 solid organic matter. 10000 100 grains of this ash consisted of — Sand and charcoal * . . 2*16 Peroxide of iron 5*15 7*31 Silica 6*60 Phosphoric acid 15*13 Sulphuric acid 2*21 Carbonic acid 1 r03 Chloride of sodium 1-87 Chloride of potassium 0-00 Potass 46- 12 Soda 0*78 Magnesia . 6*31 Lime 2*54 Real ingredients . . 99-88 7*31 92-57 DR. DAUBENY ON THE ROTATION OP CROPS, ETC. 225 The above analyses of potatoes, it may be observed, agree more nearly with BoussiNGAULT than with Sprengel, as will appear by the following Table :— Ingredients. BoussiNGAULT, Sprengel. Way. 1 Permanent. Shifting. Standard. Silica Phosphoric acid . . . Sulphuric acid . . . Carbonic acid ... Chloride of sodium . . Chloride of potassium . Soda ...... Potass Magnesia Lime 5-6 11-3 7-1 13-4 0-0 0-0 traces. 51-5 5-4 1-8 1-0 4-8 6-5 0-0 0-0 0-0 28-5 48-2 3-9 4-0 1-95 13-30 4-66 13-30 3-43 0-00 0-00 46-60 8-70 4-54 7-150 16-200 2-370 11-900 1-950 0-000 0-840 50-00 6-85 2-70 6-67 11-15 6-00 6-70 2-30 7-60 0-00 43-80 12-65 3-10 The correspondence between the standard crop analysed by Mr. Way and the one analysed by Boussingault, is in many particulars exceedingly close ; there is indeed an excess of magnesia and some little deficiency of potass, but if the potassium present in 7*6 of chloride (which is equivalent to 4'0) be represented as potass, it will amount to 4-8, which, added to 43'8, brings up the proportion of potass to 48-6, or to more than that present in the permanent crop. Turnips. The next kind of crop which we analysed was the turnips, and the following were the results obtained : — Standard sort from the neighbourhood of Oxford, contained about 10 of water, and 1 of organic matter. 1000 grains yielded 3*18 of ashes ; 100 grains of which consisted of — Sand and charcoal . 5-28 Peroxide of iron 11-91 17*16 Silica 3-81 Phosphoric acid 1 2-63 Sulphuric acid 7*17 Carbonic acid 7*04 Chloride of sodium 4*83 Soda 2-57 Potass 31-62 Magnesia 3* 18 Lime 11'54 Real ingredients 101-55 17*16 84-39 226 DR. DAUBENY ON THE ROTATION OP CROPS, ETC. Turnips. Shifting crop. Sand and charcoal 4'01 Peroxide of iron 3*81 7*82 Silica • . 330 Phosphoric acid 10-77 Sulphuric acid 9'43 Carbonic acid 8*66 Chloride of sodium O'OO Chloride of potassium 5'40 Potass 38-46 Magnesia 5*08 Lime 10*44 99-42 7-82 Real ingredients . . . . 91-60 Permanent crop. Sand and charcoal 3*92 Peroxide of iron 2-80 6-72 Silica 2-67 Phosphoric acid 12-80 Sulphuric acid 11*07 Carbonic acid 975 Chloride of sodium 1-74 Soda 0-00 Potass 39-44 Magnesia 3-83 Lime 11*81 9973 6-72 Real ingredients .... 93-01 Here also there is a pretty near coincidence between the analysis of Mr. Way and that of BoussiNGAULT, excepting in the amount of phosphoric acid, which corre- sponds nearly to that reported by Sprengel, with whom however in other respects there is but little agreement, as will appear from the following Table : — DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 227 Way. Ingredients. Permanent. Shifting. Standard. Silica 6-4 7-8 2-87 3-60 4-5 Phosphoric acid. .• . . 6-0 14-0 13-70 11-80 14-9 Sulphuric acid . . . . 10-9 7-9 11-80 10-30 8-5 Carbonic acid . . . . 00 0-0 10-40 9-40 8-3 Chloride of sodium. . . 0-0 0-0 1-83 0-00 5-7 Chloride of potassium . . 0-0 0-0 0-00 5-90 0-0 Soda 4-1 21-0 0-00 0-00 3-1 Potass 33-7 14-0 42-40 42-00 37-4 Magnesia ...... 4-3 4-3 4-10 5-60 3-8 Lime r . 10-9 24-4 12-81 11-30 13-6 BOUSSINGAULT. Sprengel. Way. Permanent. Shifting. Standard. Potass . . . Soda Alkalies . . 33-7 4-1 21-0 14-0 42-40 1-14* 45-74t 0-00 37-40 6-l6t 37-8 35-0 43*54 45-74 43-56 Hemp. Standai'd crop grown in the Botanic Garden apart from the portion reserved for the experiments. 100 grains of the crop left 6-1 of ashes, 100 grains of which contained of — Charcoal and sand 7'48 Peroxide of iron . 2-78 10-26 Silica 5-58 Phosphoric acid 5-44 Sulphuric acid 1'09 Carbonic acid . . . 19-81 Chloride of sodium . . . . . . . 1*72 Soda 0-98 Potass 13-71 Magnesia . . . . 7'^7 Lime . . . . 34-03 100-29 10-26 Real ingredients .... 9003 * Viz. Ch. Sod. 1-83 = Soda 1-14. J Viz. Soda 310 t Viz. Potass 42-00 Ch. Sod 5-7=3-06 Ch. Pot. 5-9 = Potass 3-74 g.jg 45-74 MDCCCXLV. 2 H 228 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. Hemp. Shifting crop. 100 parts yielded 7*01 of ash, 100 parts of which consisted of-— Sand and charcoal 830 Peroxide of iron 3*78 12-08 Silica 871 Phosphoric acid 5*68 Sulphuric acid 0*73 Carbonic acid 20*10 Chloride of sodium 0*63 Chloride of potassium 0*00 Soda 0-14 Potass 7-49 Magnesia 5*19 Lime 39*00 99-75 12-08 Real ingredients .... 87*67 Hemp. Permanent crop. 100 parts yielded 6*00 of ash, 100 parts of which consisted of — Sand and charcoal 10*40 Peroxide of iron 3*94 14*34 Silica 8*39 Phosphoric acid 4*50 Sulphuric acid r09 Carbonic acid 19*78 Chloride of sodium 0-43 Soda 0-06 Potass 7-25 Magnesia , 2*18 Lime . 40*10 98*12 14*34 Real ingredients .... 83*78 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 229 The following will give a tabular view of the composition of the above three crops in 100 parts, after deducting the extraneous matters present in the ash. Ingredients. Standard. Shifting. Permanent. Silica 6-13 9-95 10-00 Phosphoric acid. . . . 6-00 6-50 5-35 Sulphuric acid . . . . 2-00 0-83 1-20 Carbonic acid . . . . 21-79 23-00 23-50 Chloride of sodium . . 1-89 0-72 0-47 Soda 1-08 0-16 0-07 Potass 15-08 8-55 8-62 Magnesia 8-43 5-95 2-62 Lime 37-40 44-60 47-60 99-80 100-26 100-00 Flax. Standard crop grown in the Botanic Garden apart from the spot reserved for the experiments. 100 grains of the crop, including the ripened seeds, yielded 10*7 of ash, of which latter 100 parts contained — Sand and charcoal 12-02 Peroxide of iron 3*42 16-44 Silica 1-77 Phosphoric acid 6*85 Sulphuric acid 5-10 Carbonic acid 15*69 Chloride of sodium 2*43 Chloride of potassium 6*04 Soda 0-00 Potass 21*73 Magnesia . . . 3*89 Lime 18*30 97*24 15*44 Real ingredients . . . . 81*80 2 H 2 ^2^0 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. Shifting crop. 100 grains of the crop yielded 8'0 of ashes, 100 grains of which consisted of- Sand and charcoal . . . . v - -i . 13*15 Peroxide of iron . . . ..... 5*41 18-56 Silica 1-82 Phosphoric acid . . , 6-77 Sulphuric acid . . . . . . . . . 4*18 Carbonic acid . ... ..... 17*38 Chloride of sodium 1*58 Soda . . . . . 1-05 Potass 20-5 1 Magnesia .......... 4*72 Lime 21*56 Real ingredients Flax. 98*13 18-56 79*57 Permanent crop. 100 grains of the crop yielded 6*675 of ash, 100 grains of which consisted of- toctuu aiiu v^iicvi vyv/ui Peroxide of iron ...... . . 8*01 15*06 Silica . . ............... 6*55 Phosphoric acid . . . . 6*56 Sulphuric acid .... . • , • 312 Carbonic acid . . . . , , . 12*20 Chloride of sodium . J ^ 1*14 Soda . , 5-87 Potass , 11*05 Magnesia .,.,.. . .. -.1 4-68 Lime • ■ 33*59 99*81 15*06 Real ingredients 84*75 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 231 The following will show the composition of the three crops of flax, after deducting the extraneous matters present in the ash. Ingredients. Standard. Shifting. Permanent. Silica 2-16 2-3 7-3 Phosphoric acid. . . '. 8-40 8-5 7-3 Sulphuric acid . . . . 6-20 5-3 3-7 Carbonic acid . . . . 19-10 21-9 14-4 Chloride of sodium. . . 2-93 2-0 1-4 Chloride of potassium . . 7-35 Soda . ... . . . 1-3 25-8 6-9 13-0 Potass 26-50 Magnesia 4-76 5-9 5-5 Lime . . .... . 22-30 27-0 40-0 99-70 100-0 99-5 Beans. Standard crop grown in a part of the Botanic Garden distinct from the poi-tion set apart for the experiments. 100 grains yielded 6'45 of ash, 100 grains of which consisted of — Sand and charcoal 12*00 Peroxide of iron 2-33 14*33 Silica 2*44 Phosphoric acid . I'll Sulphuric acid 2*95 Carbonic acid 17'38 Chloride of sodium ..... . . 2*58 Chloride of potassium .... . . 0*91 Soda . . . . . . . 0*00 Potass .. . 30*37 Magnesia ........... . . . 2*69 Lime . . . . . . . . . . .^ .^ 1717 • . ^ ^ ^ * 98-57 • ' 14-33 Real ingredients .... 84-26 • 232 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. Beans. Shifting crop. 100 parts of crop yielded 5*7 of ashes, 100 parts of which consisted of- Sand and charcoal 8*24 Peroxide of iron . 3*77 12-01 Soluble silica 3-97 Phosphoric acid 3*83 Sulphuric acid 2*49 Carbonic acid 18*45 Chloride of sodium 1*23 Soda 0-22 Potass 20-56 Magnesia 3-79 Lime 33-87 88-41 12-01 Real ingredients .... 76*40 Beans. Permanent crop. 100 parts of crop yielded 4*4 of ash, 100 parts of which consisted of — Sand and charcoal, extraneous . . . 6*13 Peroxide of iron, extraneous .... 4*24 10-37 Soluble silica 4-05 Phosphoric acid ........ 3*29 Sulphuric acid 1*96 Carbonic acid 19*87 Chloride of sodium 1 '00 Soda 7*00 Potass 12*77 Magnesia . 3*63 Lime 35*76 99-70 10-37 Real ingredients .... 89-33 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 233 The following Table will show the composition of the three crops of beans, after deducting the extraneous matters present in the ash. Ingredients. Standard. | Shifting. Permanent. Soluble silica . . Phosphoric acid. . Sulphuric acid . . Carbonic acid . . Chloride of sodium. Chloride of potassium Soda 2-90 9-25 3-50 20-70 3-17 1-08 0-00 36-10 3-20 20-30 4-48 4-32 2-80 20-85 1-38 0-00 0-24 23-20 4-28 38-20 4-50 3-68 2-19 22-20 1-12 0-00 7-80 14-20 4-06 40-00 Potass Magnesia .... Lime 100-00 99-75 99-75 Having now, with reference to the six plants above-mentioned, stated, not only the amount of every year's crop, but also the composition of the last of each which had been obtained, we seem to be in a position to calculate the amount of the several inorganic ingredients contained in them, which will have been abstracted from the ground during the time the experiments were carried on. This indeed is a question of little interest, so far as regards the acids and bases that are predominant ingredients in the soil, but in the case of the alkalies, the mag- nesia, and the phosphates, which exist there in more limited quantity, its determina- tion may afford us a clew towards the main object of our inquiry, namely, the cause of the falling off of a crop after frequent repetition. In the case of the barley, it will be seen, that the produce of the same plot of ground amounted in the course of ten years to 289*65 lbs., including straw as well as grain, and that, taking the last year's crop as the criterion, this quantity would have yielded 25*2 lbs. of ash. For as 100— 8*7— 289*65— 25*2. Now 25*2 lbs. of ash would contain nearly as follows, according to the analyses given above : — Sand and charcoal ") „ . , ^ . y extraneous . . . 6*25 Peroxide or iron J Silica 6*30 Phosphoric acid ........ 1*84 Sulphuric acid 0*53 Carbonic acid 0*47 Chloride of sodium 1*18 Potass 4-36 Magnesia 1'15 Lime 3*52 25*60 234 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. On the other hand, the shifting crops of barley, which in ten years amounted to 421 lbs., and which, taking as our criterion the amount of ash yielded the last year (1844), had drawn from the land 26*31 lbs. of inorganic matter (the sand, charcoal, and peroxide of iron, drawn from other sources having been deducted), would have abstracted from the soil in ten years, as follows : — Sand and charcoal") ^ ^ ,^r . , „ . > extraneous . . 6* 1 75 Peroxide ot iron J Silica 9-300 Phosphoric acid 2370 Sulphuric acid . 0*600 Carbonic acid 0*366 Chloride of sodium 0*364 Potass 4*220 Magnesia . . ^ 0*915 Lime 1*960 26*270 Proceeding now to the second case, that of the potatoes, we find the amount of the produce, in the case of the permanent crop, in nine years to have been 620*8 lbs., yielding 7*37 of ashes, of which, however, about 1*37 were extraneous. Consequently during that period the inorganic constituents, abstracted from the soil, and contained in 6 lbs. of real ash, would be as follows : — Silica 0*11 Phosphoric acid .... 0*80 Sulphuric acid .... 0*27 Carbonic acid .... 0*80 Chloride of sodium . . . 0*20 Chloride of potassium . . 023 Potass 2*80 Magnesia 0*52 Lime 0*27 6*00 On the other hand, we find, in the case of the shifting crop, the average of nine years' produce to be 89*1, or nearly 802 lbs. for the whole period, yielding of ashes about 7'3 lbs. from which must be deducted, as extraneous matter, about. . . . . . 0*7 Leaving for real ash . . . . 6*6 DR. DAUBENY ON THE ROTATION OP CROPS, ETC. 235 and containing the following constituents : — Silica . 0-472 Phosphoric acid . . . . r070 Sulphuric acid . . . . 0*157 Carbonic acid .... 0*785 Chloride of sodium . . . 0*130 Potass 3*300 Soda 0-055 Magnesia 0452 Lime . 0*178 6-599 In the case of the next crop, the turnips, I have not sufficient data to determine with exactness the amount of inorganic ingredients extracted from the soil, having omitted to weigh the bulbs, from which the ash, in the case both of the permanent and shifting crops, was derived. I find, however, that 1000 parts of a good sample from the neighbourhood of Oxford yielded 3-15 of ash, of which about 0*55 was extraneous, so that 2-6 grains will represent the amount of inorganic constituents really present. The bulbs obtained from the permanent crop in ten years amounted to about 1008 lbs. ; so that the inorganic constituents extracted from the soil in this instance may be reckoned at about 2*62 lbs. Now 2*62 lbs. of inorganic matter would, according to the previous data, consist of the following ingredients, viz. lbs. Silica 0-075 Phosphoric acid . . . 0-360 Sulphuric acid .... 0-310 Carbonic acid .... 0-2/3 Chloride of sodium . . 0*050 Potass 1*110 Soda 0*000 Magnesia 0-110 Lime 0332 2*620 The shifting crop of turnips in the same period yielded of bulbs 1765 lbs., which, according to the same calculation, would have produced 458 of real ash. For as 1008—262—1765—4-58. Now 4-58 lbs. of ash would contain the following proportions of inorganic consti- tuents, viz. MDCCCXLV. 2 I 236 DR. DAUBENV ON THE ROTATJON OF CROPS, ETC. Silica . . . . . . . . 0-165 Phosphoric acid . . . 0540 Sulphuric acid . . . . 0*470 Carbonic acid .... 0430 Chloride of potassium . 0*270 Potass 1*930 Magnesia . . . . . 0*255 Lime 0*520 4*580 The next crop I shall consider is hemp, of which the permanent crop, according to the statements given in the first part of this paper, would have amounted in nine years to 271*25 lbs., or 30*13 lbs. per annum, yielding of ash 16*27 lbs. For as 100--6*0— 271*25— 16*27. Now 16*27 lbs. of ash would contain of extraneous matter about 2*27 leaving 14*00 of inorganic principles belonging to the plant, which would consist of — Silica 1*30 Phosphoric acid .... 0*70 Sulphuric acid .... 0*17 Carbonic acid .... 3*07 Chloride of sodium . . . 0*06 Soda 0*08 Potass 1*10 Magnesia 1*40 Lime 6*12 14*00 Now the average of the shifting crops for seven crops was 40 lbs., and as the ash obtained was about 7 per cent, its whole amount would have been 2*8 lbs. lbs. Or in seven years (2*8x7)=l9*6 Of which the extraneous matter would be about 2*3 Leaving of inorganic principles extracted from the earth in seven years 17*3 Or, if in seven years — 17'3 — nine years . . 22*17 Now 17*3 lbs. of inorganic principles consist of 2*19 1*52 0*18 5*10 0*15 0*04 1*90 1*29 9*80 17*20 2217 Silica . . . . . . . 1*70 Phosphoric acid . . . 1-18 Sulphuric acid 0*14 Carbonic acid . . . . 3*96 Chloride of sodium . . . 0*12 Soda 0*03 Potass . 1*47 Magnesia . , . . . . 1*00 Lime 7*60 DR. DAUBENY ON THE ROTATION OP CROPS, ETC. 237 I next proceed to the flax, which in ten years produced, as we have seen, an amount of crop equal to 126 lbs., yielding of ashes 8*4 lbs. of which 1-26 was extraneous. Leaving of real ash 7*14, which would consist of — Silica 0-520 Phosphoric acid . . . 0*520 Sulphuric acid .... 0*264 Carbonic acid . . . . 1*020 Chloride of sodium . . 0*099 Soda ....... 0*490 Potass . 0*925 Magnesia 0*390 Lime . . . . ^ . . . 2*850 7*078 Now the average of ten crops of flax, cultivated in different plots of the same garden, was 22*7 lbs., yielding 1*816 of ashes, = in ten years 18*16 lbs., of which 3*36 lbs. were extraneous, leaving 14*8 lbs. of real ash, which would consist of the following ingredients : — Silica 0*34 Phosphoric acid .... 1*25 Sulphuric acid .... 0*78 Carbonic acid . . . , 3*22 Chloride of sodium . . . 0*30 Soda 0*20 Potass 3*80 Magnesia 0*87 Lime 4*00 14*76 The last of the crops made the subject of examination was the beans, where the aggregate of ten years' produce, in the case of the permanent crop, was 247 lbs., which would have yielded 10*8 lbs. of ashes. Of this, however, about 1*1 would consist of extraneous matter. Leaving 9*7 of real ash, consisting of the following ingredients : — Silica 0*44 Phosphoric acid .... 0*36 Sulphuric acid .... 0*22 Carbonic acid .... 2*13 Chloride of sodium . . . 0*12 Soda 0*76 Potass 1*37 Magnesia ...... 0*40 Lime 3*90 9*70 2 I 2 238 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. In the case of the shifting crop of beans the produce of ten years gives an aggre- gate of 336 lbs., yielding of ash 19*15 lbs., of which, however, about 2*30 was extraneous, leaving 16*85 of real ash, which would contain, of — Silica ...... 0*757 Phosphoric acid . . . 0*723 Sulphuric acid .... 0*470 Carbonic acid .... 3*500 Chloride of sodium . . 0*235 Soda 0-044 Potass 3*900 Magnesia 0*725 Lime 6*420 16-774 Diagram showing the relation between the Permanent and the Shifting Crops. The shiftiDK J Potatoes, Barley, | «^««e 1 Turnips, Hemp, > crops. ^ Ylax and Beans . . J The permanent - crops. Before we proceed to inquire, whether the difference in the average amount of pro- duce obtained under these two modes of cultivation arose from a deficiency of the organic, or of the inorganic materials present in the soil, it may be worth while to present a tabular view of the numerical relation subsisting between the permanent and shifting crops in each instance, with respect to the entire crop, to the entire amount of inorganic matter, and to the proportions of phosphoric acid and of alkalies present in each. DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 239 Total amount of produce. Inorganic constituents. Phosphoric acid. Alkalies. Permanent. Shifting. Permanent. Shifting. Permanent. Shifting. Permanent. Shifting. Barley. . . . 69-0 100-0 96-5 100-0 77-0 100-0 77-0 100-0 Potatoes . . 77-5 100-0 91-0 100-0 75-0 100-0 85-0 100-0 Turnips . . 57-0 100-0 77-0 100-0 58-0 100-0 Hemp .... 75-0 100-0 63-5 100-0 46-8 100-0 55-0 100-0 Flax 55-5 100-0 48-0 100-0 41-6 100-0 35-0 100-0 Beans .... 73-0 100-0 58-0 100-0 50-0 100-0 36-0 100-0 The results in the two first instances would seem to lead to opposite conclusions from those suggested by the three latter, inasmuch as, whilst in the barley and the potatoes, the difference between the amount of inorganic constituents in the two cases was much less than that between the permanent and shifting crop collectively taken ; in the hemp, flax and beans the contrary remark applies. If we take the phosphoric acid, we find also that in the barley, and turnips, it stands in a higher ratio to the other constituents in the permanent, than in the shifting crop, whilst in the hemp, flax and beans, it stands in a much lower one. A similar remark applies to the alkalies, so that no general conclusion, as it might seem, is deducible from these premises. It appears to me, however, that the existence of a larger relative amount of phos- phoric acid in the permanent than in the shifting crops of barley and of turnips, affords a stronger presumption in favour of a certain dependence of the produce on the organic matter, than the opposite result arrived at in the three other cases does of the reverse. If the falling-off of the crop in these instances had arisen from a deficiency of cer- tain of its inorganic principles, such for instance as the phosphates or the alkalies, at least a corresponding reduction in these latter might have been expected to have been found in the ashes of the one which proved deficient in quantity ; whilst on the other hand, if the deficiency of organic matter be supposed to have checked the develop- ment of particular parts, as, for example, of the seeds, it might thereby affect the character of the ashes obtained, and thus a smaller amount be abstracted, without any actual failure, in the supply afforded by the soil to the plants that grew in it, taking place with regard to them. I am led to this opinion, by the result of an examination, which I requested Mr. Way to institute, into the nature of the inorganic constituents present in ordinary gluten, and in starch. The first, obtained from wheat, yielded about three parts of inorganic matter in the 1000 parts, which latter contained as much as 33 per cent, of phosphoric acid com- bined with lime, and a trace of magnesia, but no carbonate of lime*. * I found also that the bran contained a larger proportion of silica than the albumen of the grain itself, and we know that the proportion of these several parts, one to the other, varies considerably in different samples of flour. 240 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. The latter, obtained from potatoes, yielded about 3*43 parts of inorganic matter in the 1000, of which only 4*77 per cent, was phosphoric acid, whilst 82*48 was car- bonate of lime. Thus, in the case of wheat, any condition of things which should check the forma- tion of gluten, would diminish the quantity of phosphoric acid present in the ashes of this plant, even thougli the soil might contain an abundant supply of that ingre- dient; and as tlie formation of gluten is promoted by the presence of manures abound- ing in ammoniacal salts*, so it may easily happen, that this principle should be deficient where such manures are too sparingly administered. In a similar way, a variation in the constituents of barley and other crops may be supposed to arise, not only from a larger or smaller supply of inorganic principles in the soil, in the manner that Liebig has so lucidly explained to us, but likewise from a more plentiful exhibition of those products of the decomposition of organic bodies, which favour the development of particular organs, or of certain of the prox- imate principles which the latter contain. Which, however, of tliese two suppositions applies to the cases now under con- sideration, will be better seen, wlien we have considered the composition of the soil in which they grew, as determined by analysis. PART III. On the chemical composition of the soil in tvhich the crops were grown, and on the proportion of its ingredients that were available for the purposes of vegetation. The chief difficulty, which occurs with respect to the analysis of a soil, relates to the determination of those ingredients which, like the phosphates and the alkalies, exist in minute proportions, and which accordingly appear to have been overlooked by Davy, and others, who first applied themselves to the subject of agricultural chemistry. It will not be necessary therefore to take up the time of this Society, by giving a detailed account of the method pursued by Mr. Way in his examination of the soils of which I wished to learn the composition ; it may be sufficient to state, that after separating the several portions, one from the other, by the mechanical method pointed out by Mr. Rham, and determining the relation which the coarser bore to the finer, the latter, which alone were supposed capable of imparting any nourishment to plants, at least within a limited period, was submitted to the usual course of examination pursued by chemists. To ascertain the phosphates however, a distinct and a much larger portion of the soil was operated upon, not less than 2000 grains being taken for the purpose, and this was digested for five hours in water acidulated with muriatic acid, the flask employed for the purpose being fitted up with a funnel attached to its neck, in the manner re- * See Hermbstadt's experiments quoted in the third of my Lectures on Agriculture, and Sir H. Davt's Lectures on Agricultural Chemistry. DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 241 comaiended by Dr. Ure, for the purpose of condensing the acid which might be dis- engaged in vapour, and restoring it to the body of the vessel*. The liquor, after being filtered, was evaporated to dryness, so as to dispel the greater part of the acid. The residuum was then treated with water, and an excess of ammonia was added, by which the iron, alumina, and phosphate of lime were thrown down. The whole was then carried to dryness, and gently ignited, by which means the greater part of the iron and of the alumina is rendered insoluble in dilute acids, which take up the phosphate of lime. The solution was then treated with ammonia so long as any precipitate was thrown down, and the latter digested with dilute alcohol mixed with sulphuric acid, by which any alumina and iron that had been precipitated were converted into soluble salts, whilst any lime in combination with phosphoric acid would remain as an insoluble sulphate, from the amount of which, when well-washed and dried, that of the phos- phate present in the soil admits of being calculated. After ammonia had thrown down the alumina, iron, and phosphate of lime, the alkalies existing in the ash would still remain in the solution. The latter was therefore again evaporated to dryness, and the ammoniacal salts driven off. The residue was then treated with water, boiled and filtered, after which a solution of carbonate of ammonia, to which a little pure ammonia had been added, was intro- duced into the liquor that came through. The remainder of the earths were thus thrown down, and nothing remained in solution except the alkalies. After the am- moniacal salts had been expelled by heat, the mixed chlorides of potassium and sodium were separated in the usual way by chloride of platinum. Such then was the method pursued for determining the nature and proportions of those ingredients, which, if not available for the purposes of vegetation at the present time, may at least be regarded as likely to prove useful to them within no very distant period, as being separable, by dilute muriatic acid, from the mass of the earth. The soil of that part of the garden, in which the experiments above detailed had been conducted, varied in depth from three to four feet, and rested upon a stiff clay, of which the subsoil in the valley of Oxford consists, wherever it is not overlaid by gravel. It was chiefly made ground, brought in to elevate the level of the garden above that to which the contiguous river rises during the winter floods, and about a year antecedent to the commencement of the experiments it had been manured with stable dung. I have already expressed my regret, that no analysis was made of it until the pre- sent year, at which time the experiments had been already brought to a close. In a neighbouring part of the garden, which appeared to be similarly circumstanced to that which had been set apart for the experiments, except that it had been recently * Journal of the Agricultural Society, vol. v. p. 617. 242 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. manured, the ingredients of the impalpable portion of the soil, which had passed through the meshes of a fine sieve, were found by Mr. Way to be as follows : — Sand and clay . 410-44 Organic matter 103-96 Silica . . . 95-06 Lime. 139-53 Peroxide of iron 98-33 Alumina . . 35-60 Carbonic acid. . 106-10 Sulphuric acid 1-82 Chlorine . . . a trace. Magnesia . . •46 Potass .... 2-58 Soda .... 1-18 Phosphate of lime . •73 995-79 JLoss 4-21 890-00 Coarse sand . . . . Stones and pebbles . • 870-00 2760-00 The soil of the garden in which the experiments had been conducted was also sub- jected to a similar examination, the plot which had grown a crop of barley for ten years without manure having been selected. The following were the results : — Sand and clay. Organic matter Silica . . . Lime. . . . Peroxide of iron Magnesia . . Alumina . . Sulphuric acid Carbonic acid . Potass . . . Soda .... Phosphate of lime Chlorine . . Loss Coarse sand . . Stones and pebbles 407*00 75*00 109-20 144-17 103-80 •85 25^00 r65 125-69 2-91 •29 •80 a trace. 3-64 1000-00 810-00 660-00 2470-00 J>R. DAUBENY ON THE ROTATION OF CROPS, ETC. 243 In another of the beds which had reared a permanent crop, viz. that of potatoes, the proportion of the phosphates, alkalies, and magnesia did not appear to vary much, the analysis of 1000 grains of the finer portion sifted, affording the following results : — Phosphate of lime . . . 0*86 Potass 157 Soda . 0*27 Magnesia 0*82 The organic matter here was 53'00 A third of the beds in the same garden, which had borne a crop of turnips for ten years, exhibited rather a remarkable anomaly, as the phosphates exceeded in quantity considerably that present in the contiguous garden, the results being as follows :-- Potass, in 1000 parts . . 0'46 Soda ....... 0*74 Phosphate of lime . . . 1*62 Organic matter . . . 1 10*80 It will be seen, that the permanent crop of turnips in ten years would have extracted from the soil only 0*36 of phosphoric acid, whilst the barley in the same time had extracted 1-84, and the potatoes .0*80 ; hence perhaps the difference in the quantity present in the soil. One only of the plots of ground, which had grown a succession of different crops for ten years without manure, was examined *", and the proportion of the above ingredients found in it appeared to be as follows, viz. — ■ Potass in 100 grains . . 1*96 Soda 1-J2 Phosphate of lime . . . 0*33 Organic matter .... 76*50 It will be seen from the table in the following page, that, taking as our standard the composition of the contiguous garden, of which the analysis is first reported, and in which the proportion of phosphoric acid would seem to be lower than it is in most of the plots of ground experimented upon, even after ten years' cropping without manure (judging from the few which were examined), a sufficient quantity of the above ingredient existed, to supply what would be necessary for nineteen crops of barley, of the same amount as the average of those obtained from the permanent bed, and of the same quality as that produced in 1844. * The crops were, barley in 1844, hemp in 1843, buckwheat in 1842, tobacco in 1841, parsley in 1840 and 1839, mint in 1838 and 1837, parsley in 1836, and beans in 1835. MDCCCXLV. 2 K 244 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. In the following Table the results are all reduced to one standard. 1000 grains of the soil. Ingredients. Contiguous garden. Permanent bed of barley. Permanent bed of potatoes. Permanent bed of turnips. Bed which had borne a succession of ten crops with- out manure. Stones and pebbles Coarse sand . . Fine sand and clay- Organic matter . Silica, soluble . Lime .... 315-000 322-000 149-000 37-600 34-400 50-500 35-500 12-800 38-400 0-660 a trace. 0-167 0-930 0-428 0-265 267-000 328-000 165-000 30-400 44-000 58-000 41-800 10-100 50-500 0-665 a trace. 0-344 1-180 0-117 0-322 21-400 0-332 0-640 0-109 0-346 44-8* 0-186 0-300 0-656 31-000 0-790 0-470 0-133 Peroxide of iron Alumina, soluble Carbonic acid . Sulphuric acid . Chlorine . . . Magnesia . . ., Potass .... Soda .... Phosphate of lime 997-650 997-428 For one cubic foot of the soil of the garden was found to weigh eighty-two lbs., from which it follows, that an area of 100 square feet to the depth of three feet (which is less than the average depth of the soil in the garden), would contain 24,600 lbs. of soil, which at TO gr. to 1 lb. of soil would give an amount of phosphoric acid equal to 3-5 lbs. Now it has been calculated (page 230) that the quantity of phosphoric acid extracted from the soil in ten years did not exceed 1-84 lb., so that the permanent bed of barley, which contains at present 0*8 of phosphate of lime, or 0-4 of phosphoric acid, would not have possessed before the cropping more than 1*26 of phosphate, or 0-63 of phos- phoric acid, in the 1000 grains. With respect to the alkalies, we shall find by the same mode of calculation that the medical garden contains in 100 square feet — lbs. Potass 6-9 Soda 2-9 And as each permanent crop of barley in the average extracted no more than of — Potass 0-436 Soda 0-064, (deduced from 1-18 of chloride of sodium) in 100 parts, there would be a supply of potass equal to fifteen crops of barley, and of soda equal to forty-five crops. * Thus we perceive that a series of ten successive crops of turnips had added more organic matter to the soil than it had abstracted. See Boussingault's late work, chap. vii. on the Rotation of Crops. DR. DAUBENY ON THE ROTATION OF CROPS, ETC. 245 Here also we have reason to believe, that the soil of the experimental garden was richer than that upon which our calculations are founded, so that the falling-off of the crop cannot be attributed to any actual deficiency either of alkali or of phos- phoric acid in the soil. The amount of magnesia in the soil was also very small, not exceeding 3*8 lbs. to the 100 square feet. This however would have been sufficient for thirty-four crops of barley, according to the estimate given (in p. 230) of the quantity taken up by the crop in ten years. When, however, we proceed to inquire into the quantity of these ingredients, which are at the particular moment in a condition to be taken up by the spongioles of the roots, we find the case very different. I have already pointed out, that, with a view of imitating nature as nearly as pos- sible, water impregnated with carbonic acid is a preferable solvent to muriatic acid, since it may be presumed, that what is not extracted from the soil by a sufficiently large amount of the former, is not in a condition to be readily assimilated by the plants that grow in it. I therefore took sifted portions, each weighing 5 lbs., of the soil, from the part of the garden contiguous to the scene of my experiments, as well as from several of the plots which had grown either the same or different crops during ten years without the addition of manure, and having introduced them into earthen pots, with a hole at the bottom covered over with a piece of wire gauze fine enough to prevent the earth from falling through, I added to each a known quantity of distilled water which had been saturated with carbonic acid gas. After a certain amount of the water had passed through, generally two quarts were taken and evaporated to dryness, after which the residuum was treated, in the first place with water, which took up the alkaline salts together with a little calcareous matter, and afterwards with muriatic acid, which dissolved the rest of the lime, whether in combination with carbonic or with phosphoric acid. Having got rid of the earthy matter from the aqueous solution by means of oxalate of ammonia, the alkalies remaining were converted into sulphates, heated and weighed, after which the nature of the alkali, combined with the sulphuric acid, was determined by the usual method. The acid solution was then treated with ammonia, and the precipitate, when well- washed and dried, was set down as phosphate of lime, iron being rarely present, and never except in minute proportions. The following results were obtained, by operating in this manner on the soils enu- merated below, and, granting that objections may be raised against the precision of the method adopted, they at least suffice to show, that the ten years' cropping had reduced very materially the amount of matter immediately available for the purposes of vegetation, however little it appear to have trenched upon the latent resources of the soil. 2 K 2 246 DR. DAUBENY ON THE ROTATION OF CROPS, ETC. a to V B CO ?= 0) -" s ai a r/) 0) 3 -1^ c Ct 0) CO .^ O O 2.. ID '^ I ■2:2 -= o a. ^ .s Cm o c V, J!,®-^ -S O o S aJ to >.-^'2 .2 .-s S ■* o o o o o o o o o o o .■a ^.s . ''t* 00 © ©I o ©* »>. Quant earthy phate squan ofs (24,601 1— < ■>* o* rf CT) ^H 05 ■»»< Oi -* ■* "* ^ *> ■-H l~( r^ ©< CO ■* CO -* CO "* t-H ^ ^Ps^ CO o luanti f eai-t alpha lb. of c «n U5 CO ©< r^ ©* "»»< oo CO ©t o o o i-^ o o t— 1 o ^ o o o , , o O o o , o o o Cro «. jj a a a; P. -1 3 — 1 c c "c Quantity of earthy phosphate per quart of water. 2 2 W3 2 lO cu cu ©< o o* »c »o lO W5 0* D- P^ "5 o CO U3 P, U3 »c »c CO o o O I— t o OS e8 ^ CO 6 o o 6 Ss CO o o "OJ ^ Ol "a - « " c e; ^ mt U c u ntity irthy phat( n up Ifl e »o a: a: o e CO o o CC o l>i t>. o M ©t CO cc o *>. Ol CO 1 §5§^ fc^« <= o 6 o o 6 o o o o o ©"s-as bo <*- J O +a'-v . o 3 o « « r-j "ti 3j a -X — K o o o o o o e o o o o o o Tj< "5 o u: IC »o ifl o o o l>. o o « a -5 go 5, g ee +j a '*!-►' 3 .a 2 i::<-.ji «« to Ci It- Oi ■<»< Oi ■"J" t~-» o^ o^ ■^ »>• 05 1 ^ 00 ch r-t ©) ©1 ©I ©^ ^H ■^ ■<»< !>. -* 1 ©•■s^"^® >>a oj'S •^ ^ «5 . • . ©1 o e* c *>. <= o cc ©t o 1 -g 5^.q:s Th ^H o r^ 1— ( r^ c ©1 ©1 e ^^ ©* 1 fe ' w <3 6 o 6 o <= <= <= a c <= o Ctw M a O '^ .■S .3 ^ "S fc O "5 o "? o »fl t>. c e »c o Quani of alka sulphi per qu of wai a- 1— 1 CO o 6 ©) o CO o ©; <= 6 6 QC »>»>»>, .a ^ q3 cc cc q= q: a o a; U a a Ol a 15 = 0 -H B B B B B B b. 0 bi D bl D t) D bj 0 bo a> 5 0 ,5 3 J a c4 0 C! 03 R c _B _C (^ .5 s a c -<- c C o E s 1 s Si E it it ^ ct <£ s n c c c o i 2 9: a (U a ]E ]£ ^ It ^ s Carbon .... 67-13 Hydrogen . . . 4*47 Nitrogen . . . 10*48 Oxygen . . . . 1792 10000 Hence it is clear that the solid substance is produced from the oil by the assimila- tion of the elements of one equivalent of ammonia, and the separation of those of three equivalents of water. Oil C,.H« 0«1 r solid CisHgNOa '15 Hg ^6 "I _ / H.N J I -fl eq. ammonia . H3N J 1 3 eq. water. . . H3 O3 CisH^NOe Ci^HgNOg The new substance belongs in fact to the class of the amides, which it resembles in many important particulars, as will be more apparent in the sequel. In the year 1841 Dr. Stenhouse-}- published an interesting paper on a peculiar oily matter, first noticed by Doebereiner, which occasionally appears in very small quantity, in the preparation of artificial formic acid from sugar or starch, oxide of manganese, and dilute sulphuric acid, and to which he gave the name of artificial oil of ants. Dr. Stenhouse, in the investigation above referred to, succeeded in pre- * It may not be amiss perhaps to mention, that in the method adopted the organic substance is strongly heated in a hard glass tube with a mixture of hydrate of soda and quicklime. The whole of the nitrogen issues thence in the form of ammonia, and being condensed into hydrochloric acid, is afterwards converted into chlo- ride of platinum and ammonium, from the weight of which that of the nitrogen is easily calculated. t Philosophical Magazine for February 1841 ; also Annalen der Chemie und Phannacie, xxxv. p. 301. 256 MR. G. FOWNES ON THE ARTIFICIAL paring this substance at will, and in sufficient quantity to serve the purposes of expe- riment ; he found it composed of carbon, hydrogen and oxygen, and, what appeared very extraordinary in such a body, the two latter elements were in the proportions to form water. The analytical results, reckoned to 100 parts, were as follows: — (1.) (2.) (3.) Carbon .... 62-59 61-87 62-55 Hydrogen . . . 4*37 4*37 4-46 Oxygen .... 3304 3376 32*99 100-00 100-00 100-00 These numbers agree very closely with those furnished by the assigned empirical formula C5 H2O2. There could be but little doubt that the oil upon which I had been experimenting was identical with the substance above described ; its properties agreed on the whole pretty well with those assigned by Dr. Stenhouse to his interesting product, with the exception of its extraordinary behaviour with ammonia, which seems to have escaped notice, probably from time being required for the production of the amide. To com- plete the identification, therefore, a small portion of oil was prepared, the process described and recommended being closely followed. 2 lbs. of oatmeal, 2 lbs. of water, and 1 lb. of oil of vitriol, were well-mixed in a small copper still, and heated until the pasty mass became thin and fluid from the conversion of the starch into dextrine ; the head was then applied and luted down, and distillation commenced. As soon as sulphurous acid began to appear, an additional lb. of water was introduced, and the distillation continued until that gas began to escape in large quantity. The liquid which came over was then rectified to one-half, the product neutralized with hydrate of lime to fix the sulphurous and formic acids, and again distilled, the first third only being collected. A small quantity of heavy yellow oil was thus procured, and an additional portion obtained by again subjecting the watery liquid to distillation. So far as could be seen, this oil corresponded in every particular with that examined by myself; when put into solution of ammonia it formed in a few hours the charac- teristic yellowish compound, identical in composition and properties with that already described. The nature of the oil so far elucidated, it will be proper to return to the subject of the amide, or ammonia-compound, the latter term being however hardly applicable. The mode of preparation of this substance has been already described ; it is always produced when ammonia and the oil are brought into contact. It is very pale yellow, approaching to white, and nearly inodorous when dry and pure ; in cold water it is insoluble ; alcohol and ether, on the other hand, dissolve it freely. It may be obtained in tufts of small, short, acicular crystals, by allowing a hot, saturated alcoholic solution to cool; or whiter and purer, by adding ammonia to a saturated aqueous solution of the oil, and allowing the mixture to stand several days. In chemical characters this amide much resembles the hydrobenzamide of M. Laurent, FORMATION OF A VEGETO-ALKAU. 257 obtained by putting pure bitter almond oil into solution of ammonia. It is slowly decomposed by boiling water, and even by boiling alcohol, into free ammonia and volatile oil, and very slowly suffers the same kind of decomposition by moisture at the common temperature of the air. When heated, it melts, inflames, and burns with a smoky light, leaving a small deposit of charcoal. Acids decompose it imme- diately ; a salt of ammonia is produced, and the original oil set free. The action of alkalies on this substance is very remarkable, and well deservei attention. When boiled with a large quantity of dilute solution of caustic potash, it dissolves without the least evolution of ammonia, and the liquid deposits, on cooling, small, white, silky needles of a second new substance, having the same composition as the amide itself, but all the properties of a stable and exceedingly energetic organic base, possessing alkalinity, and having the power of forming with acids an extensive series of well-defined, and for the most part, crystallizable salts of great beauty. Portions of the new salt-base, prepared at different operations with the greatest care, were submitted to ultimate analysis by burning with oxide of copper as before, the substance being dried in vacuo over a surface of oil of vitriol ; the following results were obtained : — (1.) (2.) (3.)* Substance employed . . 2-668 grs. 3-985 grs. 3-698 grs. Carbonic acid produ(;ed . 6*53 grs. 9-74 grs. 9*06 grs. Water produced . . . 1*12 grs. 1-63 grs. . 1-51 grs. Hence, in 100 parts, — (1.) (2.) (3.) Carbon. . . . 66-75 66-66 66-82 Hydrogen . . 4*66 4-54 4-53 Estimation of nitrogen : — (1.) (2.) Substance employed. . 3-79 grs. 3-75 grs. Platinum salt produced 6-12 grs. 6-11 grs. Per-centage of nitrogen lO'lS 10*28 The isomerism of the two substances is seen to be most complete; the numbers obtained by analysis absolutely coincide : and yet how discrepant their properties! I am inclined to think that the nature of the isomeric change which the amide undergoes in presence of the alkali consists simply in a duplication of its elements ; at least, this is the simplest view that can be taken. It is besides the only product. It will be seen from analyses of the salts formed by this substance, that the proportion of matter required to form a perfectly neutral compound with an acid, organic or inorganic, is expressed by the formula C30 H12 Ng Og, which is the double of the amide C15H6NO3 But then, as the constitution of this latter substance must be to some extent uncertain, since that of the oil is also unknown, and the amide forms no com- binations, the above view must remain merely conjectural. * This specimen was prepared from the oxalate by precipitation by ammonia. •258 MR. G. FOWNES ON THE ARTIFICIAL I pass now to a description of the properties of the new salt-base, of its principal salts yet studied, and of the best method of preparation on a considerable scale. The substance itself crystallizes from boiling water in fine, soft, white, silky needles, much resembling those of cafeine, quite permanent in the air, and even in the dry vacuum. It has but little taste, although its salts are very bitter; they are far less so however than those of morphia, or of the bark-alkalies. It is inodorous. At a temperature rather below the boiling-point of water it melts to a heavy, nearly co- lourless, oily liquid, which on cooling assumes at first the consistence of a soft resin, but eventually becomes brittle and crystalline. When strongly heated in the air, the new substance inflames, burns with a red and smoky light, and leaves but very little charcoal. It is soluble in about 135 parts of boiling water, but after cooling, scarcely a trace remains dissolved. Alcohol and ether in the cold dissolve it with the utmost facility ; the alcoholic solution deposits, on spontaneous evaporation, ex- ceedingly brilliant silky crystals ; the liquid has a great tendency to creep up the sides of the vessel. The alkaline reaction to test-paper, when dissolved in hot water or alcohol, is exceedingly strong and well-marked. Dilute acids dissolve this sub- stance with the utmost ease, becoming thereby completely neutralized, unless em- ployed in excess ; from these combinations the base is precipitated in an unchanged state, by the addition of ammonia or of a fixed alkali. A salt of the new base gives no precipitate with solutions of peroxide of iron, oxide of copper or silver, lime or baryta ; the hydrochlorate forms with Corrosive sublimate, a white, and with chloride of platinum, a bright yellow, double salt. What is rather remarkable, it is not pre- cipitated to any extent by tincture of galls. So powerful are the basic properties of this alkaloid, that when boiled with a solution of sal-ammoniac, it decomposes that salt with evolution of ammonia and formation of a hydrochlorate. The salts formed by this curious body are exceedingly numerous, and would in all probability well repay a more extended investigation ; the few yet examined are the following: — Hydrochlorate. — This is easily prepared by dissolving the alkaloid in dilute, warm hydrochloric acid, to saturation. The salt, which is perfectly neutral to test-paper, forms tufts of fine, silky, acicular crystals, like those of hydrochlorate of morphia. It is very soluble in pure water, but far less so in an excess of hydrochloric acid. The crystals retain their brilliancy when dried in vacuo over sulphuric acid. An ana- lysis of this salt gave the following results : — (Carbon and hydrogen.) (1.) Salt employed 5-855 grs. Carbonic acid produced . . 12* grs. Water produced .... 2*49 grs. (^•> Carbon. . . . 55-89 Hydrogen. . . 4-72 (2.) 5-435 grs. (3.) 6-115 grs. 11-12 grs. 12-55 grs. 227 grs. 2-56 grs. (2.) ' 55-62 (3.) 55-97 4-64 4-65 FORMATION OF A VEGETO-ALKALI. 259 6-027 grs. salt gave of chloride of silver 2*65 grs. = 10*67 per cent, chlorine. 6*68 grs. salt gave of chloride of silver 2*92 grs. = 10*60 per cent, chlorine. 6" 147 gfs. salt gave of double chloride of platinum and ammonium 8*24 grs.=8*45 per cent, nitrogen. The formula C30 H12 Ng Og, HCI+2HO, reckoned to 100 parts, gives numbers closely agreeing with the preceding ; viz. — Carbon .... 55*81 Hydrogen . . . 4*66 Nitrogen .... 8*72 Chlorine .... 10'98 Oxygen .... 19*84 100*00 When a solution of the hydrochlorate of the new base is mixed with one of bichlo- ride of platinum, an insoluble, or sparingly-soluble, bright yellow, crystalline preci- pitate falls, which is a compound of the two bodies. It is blackened and decom- posed by boiling. When heated in the dry state, it melts, blackens, and swells up to a prodigious extent, evolving fumes of sal-ammoniac ; the incineration of the char- coal is slow and difficult. Examined by analysis, the double salt gave the following results : — Salt employed 7*28 grs. Carbonic acid produced . . 10*16 grs. Water produced. . . . . . 1*97 grs. In 100 parts, — Carbon. ......... 38*06 Hydrogen 3* 16*43 grs. salt gave of metallic platinum 3*36 grs., or 20*45 per cent. The formula C3oHi2N2 0g, HCl-j-PtClg, calculated to 100 parts, gives — Carbon . . . . . 37*97 Hydrogen . . . . 2*74 Platinum .... 20*90 Nitrate. — This is a very beautiful salt ; it forms hard, transparent, colourless, and very brilliant crystals, whose form yet remains to be determined. It is freely soluble in pure water, but very sparingly soluble in excess of nitric acid. The crystals effloresce and become opake in a dry atmosphere. In this state they contain C30H12N2O6, NO5-I-HO, as shown by the result of an analysis given below. ^ Nitrate employed . . . 5*62 grs. Carbonic acid produced . 11*19 grs. Water produced . » . 2*02 grs. MDCCCXLV. 2m. 260 MR. G. FOWNES ON THE ARTIFICIAL or, in 100 parts, — Carbon 54*30 Hydrogen ....... 3*99 The theoretical quantities are — Carbon 54-35 Hydrogen 3-93 Oxalates. — The neutral oxalate is a very soluble salt, crystallizing, when the solu- tion is sufficiently concentrated, in tufts of fine needles, like the hydrochlorate. The binoxalate is very sparingly soluble in the cold, and crystallizes remarkably well when a hot saturated solution is left slowly to cool. It forms transparent plates, like those of oxalate of "urea, which have a strong acid reaction when dissolved, and re- tain their lustre in the dry vacuum. This substance gave on analysis the results stated below, leading to the formula C30 H^gNg Og, 2C2O3+2HO. Salt employed .... 4'808 grs. Carbonic acid produced 10-05 grs. Water produced ... 1*76 grs. 4-85 grs. salt gave of double chloride of platinum and ammonium 5*95 grs., or 7-74 per cent, nitrogen. Hence, in 100 parts, — Carbon 57*01 Hydrogen 4-06 Nitrogen 7*74 Oxygen 31*19 100*00 The theoretical numbers are- Carbon 56*96 Hydrogen 3-91 Nitrogen . 7*85 Oxygen 31*28 10000 The acetate is very soluble, and apparently uncrystallizable, or at least ci*ystal- lizable with great difficulty. The following is an excellent and easy method of preparing the vegeto-alkali in a state of purity and whiteness. The amide, dried in the air, or better, over oil of vitriol in the vacuum of the air-pump, is thrown into a large quantity of boiling-hot dilute solution of caustic potash contained in a capacious glass flask placed over a FORMATION OF A VEGETO-ALKALI. 261 lamp or chauffer. After ten or fifteen minutes' ebullition the change is complete, the great bulk of the new substance appearing in the form of a heavy, yellowish oil, which, on the removal of the vessel from the fire, collects at the bottom of the flask, and on cooling, solidifies, while that which had been dissolved by the liquid crystallizes out. When perfectly cold, the whole is thrown upon a cloth filter, slightly washed with cold water, and then dissolved in a large quantity of dilute boiling solution of oxalic acid, the acid being kept in considerable excess. The liquid, filtered hot, deposits on cooling a large crop of crystals of the acid oxalate of the base, dark-coloured, however, and impure. The salt may then be collected on a cloth filter, slightly washed and pressed, redissolved in boiling water, and heated for a few minutes with a little good animal charcoal, deprived of its earthy phosphates, &c., by washing with hydrochloric acid. The filtered solution now deposits the acid oxalate in a state of perfect whiteness and purity; from the pure salt the alkali may be obtained in crystals by solution in a large quantity of boiling water, addition of excess of ammo- nia, and rapid filtration at a high temperature. The crystals which form on cooling require of course washing with distilled water until all the ammoniacal and other salts are removed, and a portion of the alkaloid taken from the filter is found to leave no residue when completely burned on platinum. I am in great doubt as to the most appropriate names to be bestowed on these curious bodies, and this doubt will remain until more is known respecting the real origin of the oil. This substance has no apparent connection with formic acid, ex- cept the accidental one of contemporaneous production. It is allied in constitution to the sugar and starch series, inasmuch as it contains oxygen and hydrogen in the proportions to form water, and in properties to bitter almond oil and the essential oils in general. So far as my own experiments go, it seems to be produced most freely and in greatest abundance from bran, 1 lb. of that substance distilled with half its weight of sulphuric acid and 3 lbs. of water having yielded nearly a drachm of oil, while mere indistinct traces could be obtained from similar quantities of rice- and potatoe-starch. Under these circumstances, perhaps the name " Furfurol" (from furfur, bran, and oleum) might be applied provisionally, and I am informed that this is the name which was proposed by the party who several years ago prepared a con- siderable quantity of the oil (a portion of which came into my hands, as mentioned at the commencement of this paper), and endeavoured to discover for it economical applications. The following, therefore, will be the provisional nomenclature : — Oil produced by the action of sulphuric acid on bran, &c., termed "furfurol," ^15 Hg Og. Product of the action of ammonia on fnrfurol, or " furfurolamide," CjsHgNO.^. Vegeto-alkali, " furfarine," produced by the duplication of the elements of furfu- rolamide, CgoHigNaOg. 2 M 2 •262 MR. G FOWNES ON THE ARTIFICIAL FORMATION OF A VEGETO-ALKALI. In conclusion, I beg to direct attention to the large and promising field of investi- gation offered by the study of the action of ammonia on the volatile oils, and on other allied bodies. Middlesex Hospital, Jan. 9, 1845. Note added during the printing. Since the preceding paper was read I have received a communication from the gentleman just referred to, Mr. William Coley Jones, late of Plymouth, who has directed my attention to an article in the Polytechnic Journal, April 1840, in which he has described some of the more important properties of the oil in question, and among others, its power of generating a solid compound with ammonia, which when distilled with dilute sulphuric acid reproduced the furfurol. Mr. Jones prepared furfurol on a very extensive scale from the waste " lignin," or bran, separated from wheat in the process of starch-making ; the details of the method however are not given, and there are no analyses of the products. I feel no hesitation in expressing my opinion that the honour of the independent discovery of this most curious body is justly due to Mr. Jones, and it is much to be regretted that it did not receive greater publicity. Aug. 12, 1845. [ 263 ] IX. On Bmzoline, a new Organic Salt-base from Bittei^ Almond Oil, By George Fownes, Esq., Ph.D., F.R.S, Received May 9, — Read May 29, 1845. When pure oU of bitter almonds is left some days in contact with a strong solu- tion of ammonia, at the ordinary temperature of the air, it is slowly, but in the end completely converted into a white crystalline substance, insoluble in water, but readily soluble in hot alcohol. The solidification of the oil is complete, and there is no secondary product. This substance was examined by M. Laurent*, who con- ferred upon it the name of hydrohenzamide, and assigned to it the formula C42 Hig N2 J it is generated by the union of the elements of two equivalents of ammonia with those of three equivalents of hydruret of benzoyle, and the separation of six equivalents of water. 3 eq. bitter almond oil . C42H18 Ogj _ f Hydrohenzamide C42H18N2 2 eq. ammonia H gNa J ~ 16 eq. water ... H g Og C42 H24 Ng Og C42 H24 N2 Og Acids decompose hydrobenzamide immediately, with separation of bitter almond oil and formation of salt of ammonia ; with alkalies the case is different, solution of potash, even at a boiling heat, occasioning, as remarked by M. Laurent, no percep- tible change. I found however that when the boiling was prolonged for some hours, a change was induced resembling that undergone by furfurolamide\ under similar circumstances. A few brownish crystalline flocks appear in the solution, and after cooling, the cake of resin- like substance is found harder and less fusible than hydro- benzamide which has been melted and left to solidify. This change is unaccompanied by any notable alteration of weight, although a faint odour of bitter almond oil is disengaged during the whole course of the ebullition. The new substance is an organic salt-base, having the same composition as hydrobenzamide itself; it might perhaps with propriety be called benzoline. The salts formed by this substance are for the most part remarkable for sparing solubility, with the exception of the acetate ; the hydrochlorate, the nitrate, and the sulphate are crystallizable ; the last-named salt is exceedingly beautiful, crystallizing from an acid solution in colourless prisms resembling those of oxalic acid. Precipitated by ammonia from a cold solution of the hydrochlorate or sulphate, * Ann. Chijp, et Phys. 62, p. 23. .. , t See preceding paper. 264 MR. G. FOWNES ON BENZOLINE, A NEW ORGANIC benzoline separates in white curdy masses, which when washed and dried diminished greatly in volume ; when quite dry the powder is singularly electric ; if rubbed with a spatula its particles repel each other with violence, scattering the powder over the paper on which it lies. It is not sensibly soluble in water, but dissolves with great ease in alcohol and ether. A hot alcoholic solution left for some time deposits the base in brilliant transparent colourless crystals, which apparently have the form of square prisms with variously-terminated summits ; the alcoholic solution is strongly alkaline to test-paper. At a temperature below 212° benzoline melts, and on cooling assumes a transparent glassy state, without any tendency to crystallization. Heated in a retort, it boils and at length entirely volatilizes, with scarcely a residue of char- coal. Ammonia is disengaged during the distillation, a highly volatile oily liquid, having the odour of benzine, collects in the receiver, and a crystalline solid matter condenses in the neck of the retort. This latter substance, which seems to be the most abundant product, has been but partially examined ; it is described below under the name pyrohenzoline. The action of oxidizing agents upon benzoline is remarkable. When heated in a retort with a mixture of bichromate of potash, sulphuric acid and water, it is attacked with great energy, the mixture becomes dark green, and on distillation benzoic acid in large quantity passes over with the vapour of water. With nitric acid the same change seems to occur, but the action is not so definite and speedy. Hydro- benzamide, under similar circumstances, yields the same product, accompanied how- ever in the first part of the distillation by a little bitter almond oil. Melted hydrate of potash appears to exert no action on benzoline, unless the temperature be ex- cessive. The composition of this substance, and its isomerism with hydrobenzamide, are shown by the following analyses : — Substance Carbonic acid produced . Water produced . . . Ill 100 parts, — Carbon . . Hydrogen . . 6-11 6-01 6*12 The nitrogen was determined by the process of MM. Will and Varrentrapp, as below : — (1.) (2.) Substance . 3-88 grs. 5*036 grs. Platinum salt produced . . . 5-57 grs. 7"28 grs. Per-centage of nitrogen . . . 9*0/ 9*12 (1.) 4-018 grs. (2.) 4-03 grs. (3.) 4-57 grs 12-37 grs. 12-46 grs. 14-14 grs 2-21 grs. 2-18 grs. 2-52 grs 83-96 (•2.) 84-32 1 (3.) 84-38 SALT-BASE FROM BITTER ALMOND OIL. 265 Hydrobenzamide contains by calculation in 100 parts, — Carbon 8456 Hydrogen .... 6*04 Nitrogen .... 9*40 • 100-00 Hydruchlorate. — The hydrochlorate of benzoline is a sparingly-soluble salt even in boiling water. It crystallizes from a hot solution in small but exceedingly brilliant colourless needles, which effloresce in the dry vacuum. It has, in common with the other salts, an intensely bitter taste. The salt, deprived of its water of crystal- lization, gave the following analytical results : — (1.) (2.) Substance 4-25 grs. 4*458 grs. Carbonic acid produced 1171 grs. 12*30 grs. Water produced ... 2*21 grs. 2*32 grs. In 100 parts, — (1.) (2.) Carbon 75-14 75*25 Hydrogen 5-77 5*78 Estimation of nitrogen and chlorine : — Substance 4*16 grs. Platinum salt produced . . . 5*17, grs. Per-centage of nitrogen . . . 7*83 (1.) (2.) Substance 5*838 grs. 4*218 grs. Chloride of silver produced 2*32 grs. 1'76 grs. Per-centage of chlorine . 9*64 10*12 The formula C42H18N2, HCl gives in 100 parts,— Carbon 75*33 Hydrogen 5*68 Nitrogen 8*41 Chlorine . 10*58 100*00 The crystallized salt was found to lose by efflorescence 2*4 per cent, of water, corresponding very nearly to one equivalent. The hydrochlorate of benzoline forms with bichloride of platinum an insoluble double salt of a pale yellow colour, not further examined. Nitrdie.—ThQ nitrate is even less soluble than the preceding salt ; the crystals are 266 MR. G. FOWNES ON BENZOLINE, A NEW ORGANIC small and have but little brilliancy ; they are permanent in the dry vacuum, portion subjected to analysis gave the following results : — Substance Carbonic acid produced Water produced . . . In 100 parts, — 4' 112 grs. 10*51 grs. 1*97 grs. (1.) 6971 5-32 (2.) 4*27 grs. 10-91 grs. 2-03 grs. (2.) 69-68 Carbon . . . • . Hydrogen ..... 5*32 5*28 The formula C42H18N2, NO5+HO, gives in 100 parts,— Carbon 6977 Hydrogen .... 5*26 The acetate is a very soluble salt ; it dries up, on evaporation, to a gummy adhesive mass, and probably crystallizes with difficulty, if at all. Pyrohenzoline. — This, as before observed, is the solid product of the dry distilla- tion of benzoline. It is pressed between folds of bibulous paper to free it as much as possible from oily matter, and then crystallized from boiling alcohol, in which it dissolves pretty freely. It is but sparingly soluble in alcohol in the cold, and appa- rently quite insoluble in water, dilute acids and alkalies. It is tasteless, and the alcoholic solution has little or no alkaline reaction. At a high temperature this substance fuses, and with still further increase of heat distils ; it sublimes at a tem- perature below its boiling-point, the vapour condensing in feathery crystals like those of benzoic acid. Melted pyrohenzoline on cooling forms a mass of radiated crystals, presenting a great contrast to the glassy or resinous appearance of benzoline under similar circumstances. This substance was at first imagined to be a hydrocarbon ; it contains nitrogen, however, and gave on analysis the results stated below. a.) Substance 4*295 grs. Carbonic acid produced 13*42 grs. Water produced . . 2-08 grs. Hence in 100 parts,- (1.) 85*21 5*38 (2.) 3*46 grs. 10*74 grs. 1*71 grs. (2.) 84*66 Carbon ..... Hydrogen . . . . > 5*38 5*49 Estimation of nitrogen : — Substance .4*15 grs. Platinum salt produced ... 6*00 grs. Per-centage of nitrogen . . .9*11 SALT-BASE FROM BITTER ALMOND OIL. 267 These numbers lead to the formula C21 HgN, which gives in 100 parts, — Carbon 85* 1 Hydrogen 5*4 Nitrogen 9'5 10000 This, which appears to be a neutral body, together with its accompanying liquid product, deserves a more extended examination. The hope which I ventured to express in a former paper of the formation of new organic bases from the volatile oils which unite with ammonia, by subjecting their amides to the influence of agents, as caustic potash, capable of bringing about meta- morphosis of the compound into a more stable form or forms of combination, has thus been partially fulfilled. M. Laurent has recently announced the discovery of a new substance obtained from bitter almond oil, isomeric with hydrobenzamide, possessing basic properties, and corresponding in some other respects with benzoline ; it is stated however to be volatile without decomposition, which is certainly not the case with that body. The name amarhie was conferred upon it*. The publication of the experiments in detail will probably determine the identity or separate nature of the two substances. * Comptes Rendus, xix. p. 353. Middlesex Hospital, May 8, 1845. MDCCCXLV. 2 N [ 269 ] X. On the Elliptic Polarization of Light by Reflexion from Metallic Surfaces. By the Rev. Baden Powell, M.A,, F.R.S., F.G.S., F.R.A.S., Savilian Professor of Geometry in the University of Oxford. Received April 24,— Read June 19, 1845. In a former paper, inserted in the Philosophical Transactions, 1843, Part I., I detailed observations on some phenomena of elliptic polarization by reflexion from certain metallic surfaces ; but with reference only to one class of comparative results. From these I have been led to pursue the subject into other relations besides those at first contemplated ; but, from various causes, have only been able at this interval to submit the results to the Royal Society as a sequel to my former observations. The changes in the degree of ellipticity, investigated in my former paper, corre- spond to certain changes in the thickness of metaWic Jilms, If we now consider the case of reflexion from a simple polished metallic surface, and admit that in this case it may be supposed to take place by the penetration of the ray to a certain minute depth, or to some action of a thin transparent lamina of the metal, then, in like manner, — dependent on the law of metallic retardation, — the effect would vary with a difference in the effective thickness of the lamina, produced by changing the incli- nation of the incident ray ; and that this is the case in general is well known, viz. that as the incidence is increased, the ellipticity increases up to a maximum, which occurs for most metals at an incidence between 70° and 80°, beyond which it decreases up to 90°. The original researches of Sir D. Brewster*, to which we are indebted for the first investigation of these phenomena, afford a striking instance of the legitimate process of inductive inquiry in its first stage, in their total exemption from all refer- ence to any physical theory. In these researches, besides the change in ellipticity with the incidence, there is also included the change in the virtual plane of polariza- tion by metallic reflexion, which, though conjectured to be the same as that inves- tigated by Fresnel for transparent substances -f-, was only examined in detail at incidences at or near that for the maximum ellipticity, to which the author's object immediately restricted him. But for a series of metals constant arcs were accurately determined^, which are the azimuths of polarization of the ray, restored to plane polarization after two reflexions from metal plates at the incidence for the maximum ; while the ellipse, from which the appellation of " elliptic polarization" was derived, is a purely empirical representation of the varying arcs of incidence, considered as * Philosophical Transactions, 1830, Part 11. f Ibid. p. 292. % Ibid. p. 294. 2 N 2 ^70 PROFESSOR POWELL ON THE ELLIPTIC POLARIZATION OF LIGHT radii, for the second reflexion to restore plane polarization, at all azimuths of the plane of second reflexion to the first. Though the subject of metallic reflexion is still in a condition of great obscurity, as to the mechanical causes to which its peculiar character is referrible, yet the applica- tion of the undulatory theory at least enables us to trace and connect some of its laws, and in the attempt to pursue such an application to some further relations, the nature of my researches may be briefly explained as follows : — 1. So far as the objects of my former inquiry were concerned, it sufficed to take the formula there employed for the polarized rings in the simplified form resulting from supposing a common coefficient to the two component vibrations ; the plane of original polarization inclined 45° to that of reflexion, and 90° to that of analyzation. With reference however to some of the facts connected with observations at different incidences and azimuths of the polarizer, as well as on other grounds, it seemed desirable to generalize that formula by removing the above-mentioned restrictions ; and I have accordingly here given an expression for the rings in elliptic light of all degrees with general coefficients, and for all positions of the polarizer and analyzer ; which, though without difficulty deducible, has not, as far as I am aware, been stated by any writer. 2. With respect to the general character of the rings, the slightest observation shows that the distinction between the dark and bright centred systems in plane polarized light, though modified, is not lost, in the lower degrees of ellipticity ; it dis- appears only when the light becomes perfectly circular ; when the distinction is only seen in the changed direction of dislocation. When the plane of analyzation is inclined 45° between the rectangular directions, and generally in intermediate positions, the whole appearance is, as it were, distorted ; the dark arcs nearest the centre are situated towards one end of the quadrants, instead of being in the middle ; and in the succeeding rings, though less strongly marked, there is an apparent increase of intensity towards the same end of the qua- drant, owing to a general shade of darkness in the ground towards that side*. Of this appearance, though it must have been constantly seen, as far as I know, no ex- planation has been published. In circular polarization it does not occur. In plane polarized rings the analogous case is that of the well-known system of eight dislocated sectors ; which in ellipticity of lower degrees is combined with, and passes into, that just described. All this is expressed by my formula. 3. The restoration of elliptic to plane polarized light by means of Fresnel's rhomb, and the determination of the ellipticity by the azimuth of the rhomb, though an obvious process, yet has not, as far as I know, been pursued for any series of metals. Such a set of observations I have accordingly made at the incidence for the maximum ellipticity, for a considerable range of metals, some metallic ores, and other reflecting substances. Also in a few principal cases I have made similar observations at other incidences from 80° up to 30°, at which the ellipticity disappears. * See Plate II. fig. 3. BY REFLEXION FROM METALLIC SURFACES. 271 4. In these cases the metallic reflexion performs the part of the first rhomb in Fresnel's experiment with two. If I rightly interpret Sir D. Brewster's process for a similar restoration, before referred to, and if the two metal plates are analogous to the two rhombs, in the change of plane , which he so accurately determined, after the second reflexion, at the maximum incidence, we may infer a correspondence with that produced in the rhomb ; and that it is equal to twice the azimuth of the rhomb. And in fact I find the results from two such different methods agree very closely for all the pure metals ; though for certain ores, very low in the scale, there are some discrepancies. There is also a close agreement between these results and the azimuths of the plane of the ray restored to plane polarization by the action of a crystallized plate, as given by the same author for some of the principal metals*, which confirms the same inference. 5. The changes of plane for successive incidences are in general of a nature analo- gous to tliose in the reflexion from transparent bodies, but not the same. At the incidence for the maximum, if the plane of the polarizer be first adjusted to give, e.g. the dark system, then on changing its plane to 45°, the analyzer, in order to restore what is analogous to the same, that is, the darkest system, must coincide with the plane of incidence, or its azimuth is 0°, in exact agreement with what obtains both by theory and observation in the reflexion from transparent bodies. At greater incidences, to restore the same system, the analyzer must be moved through increasing arcs on rnie side of the plane of incidence, and at lesser incidences on the other, as for transparent bodies. Following up these latter, as the incidence is successively diminished, the azimuth of the analyzer changes in a manner obviously different from that which obtains for transparent bodies, though of the same general character : and the increase is slightly different for different metals ; but in all cases it approaches 45° as the inci- dence approaches the perpendicular. In these cases the azimuth of the polarizer remains at 45°. If it be changed, that of the analyzer preserves a constant relation. Though these observations are of an obvious nature, yet, as far as I know, none of the kind have been published for any series of metals. I have accordingly given such a set for various reflecting substances. But though apparently simple in principle, the process is troublesome in practice, and affected by various causes of uncertainty and difficulty. Some apparent anoma- lies, especially, which caused the arcs at small incidences to appear to increase beyond 45°, for a long time caused me much perplexity. The results however here offered, having been obtained with the use of every pre- caution, and being the means of a great number of repetitions, I trust, on the whole, may not be useless as a first attempt to determine these changes by direct observation. 6. The ellipticity at different incidences cannot be deduced (except at the max- • Philosophical Transactions, 1830, Part II. p. 311. «272 PROFESSOR POWELL ON THE ELLIPTIC POLARIZATION OF LIGHT imum) from the rhomb observations without a knowledge of the change of plane: employing these latter data in combination with the former (3.), I have further estimated the ellipticity at different incidences for four principal metals. 7. For the application of the undulatory theory to these phenomena, we ought to be able to assign the law of metallic retardation, but this has not yet been done. The theory as here given indicates the conditions of the maximum, and shows in general a change, but not its amount. Professor MacCullagh has however proposed, in accordance with a remarkable mathematical analogy, certain modifications of Fresnel's formula, which he has reduced to calculation in the case of steel. My theoretical formula gives rise to an expression for the change of plane, but in- volving undetermined functions of the retardation. 07i deducing the corresponding terms from Professor MacCullagh's data, and introducing them into my formula, I find it gives a very close representation of the observed results for steel. Thus Professor MacCullagh's empirical expression receives an additional confirmation in accordance with a direct deduction from the undulatory theory. The rest of this paper is devoted to the details of the observations, and of the ana- lytical investigation. Theoretical Investigation. (I.) The original vibration in a plane P being a^ivi — {vt—x), in general on reflexion in a plane R inclined to P by an angle i (R' being the plane perpendicular to R) it is resolved into a cos I sin — (vt—x) ... in R, a sin I sin — (vt — x) . . . in R'. (2.) But in the case of metallic reflexion, one of these components is accelerated in phase by a quantity §, and at the same time for the greater generality, supposing the coeflScients unequal, or changing a in the 2nd formula to b, and writing for brevity a=acos^, |3 = ^sin|; after metallic reflexion the component vibrations will be us'm (— (vt—x)) =R, /3sin(^(t;^~aO+f) = R'. (3.) Here we may remark that these formulas give directly the equation to the elliptic vibrations, the ratio of whose axes is that of a to j3, which vary at different incidences BY REFLEXION FROM METALLIC SURFACES. 273 as well as with changes given to | ; or a and h are also functions of the incidence, or of f. When f=2 if a=|3 the light is circular ; this is never the case in any metal at the maximum, though in some the ratio approaches it. For some other value off we may have a=|3, but this does not give circular polarization. When f =0 the same formulas give the inclination of the plane of the rectilinear vibrations*. (4.) On interposing a plate of crystal cut perpendicular to its axis, for any plane Q in the crystal passing through the axis, inclined to R by an angle cos & — /3 sin (p sin -^ cos |> sin 6 — a cos 9 sin >!/ sin ^ j Then, since the intensity I at any part of the image is expressed by I=H2+K2, (9.) Squaring these quantities H and K, and taking the sum, after reduction, we ultimately find for any value of %, or position of the analyzer, (/32 cos^ (p+a^ sin2(p) cos^-vl/ + (|32 sin^ (p+a^ cos^^) sin^-vf^ I=< —a|3 sin 2^ cos 2-^^008^ — a|3 cos 2(p sin 2'v^ cos f cos ^ — a|3 sin 2-^ sin f sin &. (10.) Or, in order to see the consequences of changing the position of the analyzer, or the arc x» we must introduce it by substituting for p its value ^=%— i^, f (a2sin2 (%~'4.)+/32cos2(;^-'4/))cos2'a/ + (a2 C0S2 (;^_^|.)+/32 sin2 {y^- ^))^\n^ y^ !=■{ — aj3cos2'\^sin 2(%— -v^) cosf — aj3 sin 2-4/ cos 2(x— -v//) cos f COS ^ ^ — a/3 sin 2\J/ sin ^ sin ^. (11.) On expanding and reducing this becomes — (a2sin2;^-f (32 C0S2 ;)(;;) COS"* -v// ....]. 4-(a^sin2;;^-j'-j32cos2;i,^) sin^-^/ .... 2. + 2(a2cos2p(^^-/32sin2 5(i)sin2 2^|.. ... 3* I=S — -(a2— j32) sin2%sin2\//cos2'4/ ... 4. ~aj3sin2%cos2 2'4/cosg' 5. +a/3cos2%sin2\//cos2'v}/cosf .... 6. — a/3 cos 2% sin 2-4/ cos 24/ cos f cos ^ . . 7* — a/3 sin 2% sin2 2%!/ cos g» cos & . . - . . 8. — a/3 sin 2-4/ sing" sin ^ 9, BY REFLEXION FROM METALLIC SURFACES. 275 (12.) This formula is general for all positions of the polarizer and analyzer, and for light of all degrees of ellipticity. If we had taken (as in my former paper) ^^=(45—^), and at the same time supposed a=|3=l (which is equivalent to the as- sumption then made for simplification), the formula (9.) would become at once the same as in that paper. The first terms independent of 6 express the intensity of the ground on which, as it were, the rings are formed : those involving ^ vary with the incidence or degree of ellipticity: those involving 6 give the rings; the last only being retained when the ellipticity is a maximum, and disappearing for plane polarization at the incidence 0. From these formulas we at once trace all the well-known phenomena of the rings in plane and elliptic light, by following the changes in formula (9.) on advancing into the adjacent quadrants, or supposing -v// to become •4/+90, and by consequence changing also 9 into (p+90; which gives a change of sign in the terms involving sin 2-^, cos 2-4/, sin 2 disappear without change of sign. 8, for the rings ^ ^^ & & At i|/=45, 4, 6, for the ground *) ,. . , , 7, 9, for the rings j '^'^''PP'''^ '^'"^ '=''''"«" "^ "S"' 5, for the ground, disappears without change of sign. 4, 6, for the ground ■) ^ r. .t ' r disappear with change or sign. 7, for the rings j ^^ o o In general then there are dislocations of the rings, with more or less complete com- plementary changes in the ground both at the quadrants and half-quadrants. At the maximum ellipticity, since terms 5, 6, 7, 8 disappear, there are disloca- tions only at -^=0, with a change in the ground at •4/=45, or a gradual decrease of brightness from one end of the quadrant to the other, which is exactly the appearance observed. In plane polarized light we have the system of eight dislocated sectors, MDCCCXLV. 2 o 276 PROFESSOR POWELL ON THE ELLIPTIC POLARIZATION OF LIGHT intermediate between the dark and bright systems. In the lower degrees of ellipti- city this is modified by, and passes into, that just described. ' (14.) We may illustrate the application of the formula by one or two particular cases : — 1st. If we suppose at some incidence a=/3 while e<2, then )^=45° will give branches with dislocation at •v^=0°, but none at -4^=45°; that is the nearest approach to the dark system. This agrees with formula (15.), where in this case I is a minimum when y^=i4b°, also with (18.). 2ndly. On the same supposition %=0 will give complementary changes both in the ground and in the rings at%^ = 0, and similar changes, though less conspicuous, at '4/ = 45 ; that is the intermediate system. Srdly. For the general values of a and /3 at the maximum cos ^=0 ; and %=0 gives branches with dislocation at -^=0, but no change at 'vf/=45°; or the darkest system. But %=45° will give (since a>j3) a complementary change in the ground at -4/ =45°, and branches with dislocation at 1^=0; or the distorted system. But if in this case a=/3, or the polarization be circular, the term (4.) disappears, and there is no distorted system in any position of p(^. Observation shows this to be the case in perfectly circular light, and very nearly so in the higher degrees of ellipticity. (15.) For the branches, when "4^=0, for x in general we have I=a2 gin2 ^-j-j32 cos^ )^ — a/3 sin 2>^ cos ^. Hence, on making successively cos f=l, cos ^=0, cos ^= — 1, &c., it is obvious that the intensity of the branches for the maximum ellipticity would be a mean be- tween that in the dark and bright systems of plane polarized light if a and /3 were the same in the respective cases, which we shall see is the case; at all events, this relation of the intensities agrees with observation as far as the eye can judge. (16.) Again, for the maximum ellipticity, I=/32+(a2-/32)sin2%, which can never be =0 ; or the branches are never absolutely dark ; but it is evidently a minimum when %=0, and a maximum when p(^=90°, in which cases respectively I=/32, or I=a2. If the polarization were circular these values would be equal, or the brightness the same in all positions of the analyzer. (17.) For incidence 0°, the expression (15.) being made =0, or, I = a2 sin2 %+/32 cos^ p^^ — 2aj3 sin % cos %=0, we have for the position of the analyzer for absolutely dark branches, as in (3.), asin;i(i~j3cosx=0, or tan %= - tan t BY REFLEXION FROM METALLIC SURFACES. 277 But observation shows in this case that tan %=45° when |=45° in all instances, hence for incidence 0° a=&. (18.) More generally, differentiating (15.) in respect of %, we find for any given value of ^, that is of a and /3, the value of % for the minimum, or darkest branches, ^ 2«/3 cos p tan2x=- ^2_^/^ or we might deduce directly lan % - - 2«/3 cos g =5= V V "*" 4«^/3^ cos^g^ " Hence we may make the same inferences as before. And if when cos f =0 we have also a=j3, or circular vibrations, it is worth while to observe that there results 0 tan 2x= Q- But in general for the change of plane, or of x, this formula does not assign any precise values, since the form of the function of § involved in a and /3 is unknown. (19.) In the absence of any thecyretical law 1 have had recourse to the empirical modification of Fresnel's formula proposed by Professor MacCullagh*'. And avail- ing myself of the computed values which he has given, in the case of steel, for the coefficients of the component vibrations a a' (assuming a'=/3 in my -notation) and the retardations ^ I' (where §— ^'=^ in my notation), I have deduced the values of the product a «', of a^ — a'2, and of cos f, and introducing these in formula (18.), I find the resulting values of x ^^ close agreement with those given by observation. The elements of this computation and its results are exhibited in Table IV. Apparatus. The general principle of my apparatus will be apparent from the nature of the ex- periments, but it may not be superfluous (especially for those who may wish to pursue similar observations) to annex an outline of the construction, which, after trial of various forms, I have found best to unite the requisite conditions for the purpose in view ; while it is readily convertible into an ordinary polariscope ; besides admitting of the addition or substitution of other parts, when required, for different objects. The accompanying Plate II. fig. 1 gives a general view of the arrangement and will suflSciently explain itself: the polarizing part (P) contains a Nicol prism which can be turned in azimuth, measured by a graduated circle ; a condensing lens (L) is also attached to it. The analyzing part (A) contains in the eye-piece (E) a lens, a calc-spar, and a tour- maline ; and bears a graduated circle, on which the azimuth of analyzation is read off. The metal under examination is placed on the support (R), which can be raised or * Reports, Royal Irish Academy, October 1836. 2o2 •278 PROFESSOR POWELL ON THE ELLIPTIC POLARIZATION OF LIGHT lowered as required ; and should be capable of a slight inclination for better adjust- ment. The middle part or hinge (M) is surrounded by a graduated vertical circle, by which the parts (P) and (A) can be set at any angle to each other: they are attached to it by projecting arms : the whole is moved by the joint (K) till the reflected light from (R) comes distinctly to the eye through (E), when (it is easily seen) the angle of incidence will be half that measured on (M). The zero of (M) is found by adjusting (P) and (A) with their axes in one line (or reducing the instrument to an ordinary polariscope). The hinge should be capable of being firmly clamped. In observations at very great incidences it will be easily seen to be necessary to have the arms carrying (P) and (A) so fixed, that when the axes of the tubes are brought into one line there shall be a considerable space between their inner ends : there should be also a slight motion about the axis of the arm for adjustment in (P). In observations at very small incidences, it is most convenient to throw the light on to (P) by means of a small mirror placed in a proper position. Fig. 2 represents the mode of applying the Fresnel rhomb (F) to the analyzing part, the rest of the arrangement remaining the same. The eye-piece (E) is removed to a cap on the top of the rhomb ; while the bottom of the rhomb is attached to a short tube, which fits into the aperture before occupied by the eye-piece. Fig. 3 represents the appearance of the rings in elliptic light when the analyzer is at 45° between the dark and light systems. Observations. The determination of the precise position of the analyzer at which the maximum or minimum brightness is attainedj is from the nature of the case open to consider- able uncertainty. But the intervention of the rings, instead of using the simple ana- lyzer, affords some aid in this respect, since the change in the nature and form of the rings offers a more ready guide to the eye ; especially in elliptic light, where there is never a total evanescence. Still the undefined nature of the object observed pre- cludes minute numerical accuracy, and the results in the following tables must be regarded as no more than approximations, though derived from the means of a great number of repetitions. In taking these means, I have omitted fractions of a degree as bearing an appearance of accuracy quite illusory. The greatest care is necessary in the adjustments, especially of the polarizer. They were remade for each set of observations. That for the polarizer to obtain the zero or coincidence with the plane of reflexion, was found by varying the azimuth till the light was perfectly restored to plane polarization ; the analyzer being in the position for dark branches, the zero of its circle was determined at the same time. In the observations at different incidences, in order to secure the constancy of its inclination to the plane of incidence, the polarizer was adjusted to zero before obser- BY REFLEXION FROM METALLIC SURFACES. 279 vation at each incidence. For some of the ores, &c. which reflect but little light, the arcs must be taken as mere estimations. I have found some peculiar discord- ances between different sets of observations, especially in silver and copper : those given are the means. The observations here annexed in a tabular form consist of, — 1. Those with Fresnel's rhomb for ascertaining from the azimuth (y) for the re- storation of plane polarization, the ellipticity at the incidence for the maximum ; or These results for the principal metals and other substances are seen in Table I., columns 3 and 4. Again, in the observations with the rhomb at azimuth y, the plane of the emergent ray is inclined by 2 y to the original plane. In Sir D. Brewster's experiments with two metal plates it is inclined 45+'p. The results are here compared in columns 1 and 2, and sufficiently show that we have 45 +

5 p.m. After a mountain excursion on foot for several hours, and riding ten miles March 20, 3 p.m. After a ride of ten miles ; feet and hands warm March 31, 1 p.m. After two hours' fishing ; pleasantly warm April 2, 1 P.M. After riding ten miles ; moderately warm April 11,4 P.M. After five hours' fishing ; not heated April 17, 2 P.M. After four hours' fishing ; slightly perspiring Tongue. 99-4 99-0 99-3 98-7 99-5 99-1 99-3 99-2 99-3 98-9 99-1 99-1 99-2 98-9 98-9 98-9 99-0 99-2 Pulse. 80 70 80 58 84 60 64 64 78 62 74 98 90 56 62 62 70 84 Respira- tions. 18 16 20 16 18 16 18 18 16 18 16 22 17 16 16 16 16 18 Air. 63 56 62 64 64 65 70 72 49 55 34 32 33 37 54 54 40 55 These observations, selected from a large number of similar bearing, show in a decided manner, that active exercise, not carried to the extent of exhausting fatigue, raises the temperature of the body ; and that the increase is, at least within a certain limit, proportional to the degree of muscular exertion made. DR. DAVY ON THE TEMPERATURE OF MAN. 323 4. Of the Effect of Carriage Exercise on the Temperature. The observations which follow, were made immediately after getting out of the carriage, which was a close one, and its windows commonly closed ; and the dress worn, at the time of being out, was warm. Tongue. Pulse. Respiration. Air. Nov. 17. 1 P.M. After a drive of 8 miles. 97-7 62 18 0 53 19. 3 P.M. After a drive of 1 0 miles. 97-7 48 16 48 25. 2 P.M. After a drive of 10 miles. 97-0 56 16 44 27. 12 m. After a drive of 8 miles. 97-3 56 18 42 30. 12 m. After a drive of 8 miles. 97-4 56 16 44 Jan. 5. 5 p.m. After a drive of 7 miles. 97-7 50 17 32 Feet and hands cool, almost cold, as was experienced in all the preceding instances. These results are strongly contrasted with those given in the preceding section, showing the exalting effect of active exercise on the temperature. I have other results, equally proving how gentle exercise, in a cold atmosphere, has a depressing effect, whether taken in a carriage, on horseback, or on foot, walking slowly. 5. Of the Effect of Exposure to Cold Air without exercise. The few observations I have collected on this point, have been made the instant after returning from an adjoining church, the temperature of which in the cold weather of winter is little above the freezing-point, no attempt being made to warm it, and the congregation which assembles in it at that season being small. Tongue. Pulse. Respirations. Air. Nov. 24. 1 P.M. 9°7-0 52 16 0 42 Jan. 12. 1 P.M. 97-1 50 15 40 Feb. 9. 1 P.M. 96-7 48 15 33 March 16. 1 P.M. 95-9 44 16 32 In each of the above instances, in spite of warm clothing, the sensation experienced by the observer was that of disagreeable chilliness, and in the feet and hands, of cold- ness ; a feeling of drowsiness was also perceived, as if the condition induced were an approach to the state of temperature of a hybernating animal, or to that which is probably the prelude to the sleep in the human being resulting from long exposure to severe cold without exercise. 6. Of the Effect of Excited and Sustained Attention on the Temperature, The state of mind referred to is that accompanied with exertion, such as i.s expe- rienced in composition, or in reading a work of exciting interest. The observations which follow have been made entirely at night, after from two to five hours of sustained attention. Many more were made by day ; but these are not given, as they are not so well fitted for comparison. 324 OR. DAVY ON THE TEMPERATURE OF MAN. Tongue. Pulse. Respirations. Air. Aug. 19- 12 p.m. 98-45 58 15 ^8 29. 11 P.M. 98-5 62 16 62 Sept. 23. 1 A.M. 98-5 54 16 65 Nov. 26. 12 p.m. 98-4 56 15 60 28. 12 p.m. 98-7 60 16 62 Dec. 14. 1 A.M. 98-5 56 15 64 20. 1 A.M. 98-7 58 16 60 30. 1 A.M. 98-0 56 16 55 Jan. 23. 12 P.M. 98-35 60 14 61 Feb. 3. 1 A.M. 98-4 60 17 60 12. 12 p.m. 98-2 68 16 60 21. 1 A.M. 98-4 54 15 60 24. 2 A.M. 98-4 58 14 60 26. 2 A.M. 98-0 56 15 60 Mar.' 4. 1 A.M. 98-5 56 15 60 11. 12 P.M. 98-5 52 14 60 14. 1 A.M. 98-2 54 15 61 April 3. 12 P.M. 98-4 98-4 58 16 68 These observations show an increase of lemperatui-e after sustained exertion of mind. Though the increase is slight, yet I think it must be admitted to be decided, comparing the mean (98"4) with the average result of the observations (97*92) made at the same period of the twenty-four hours, when the attention was not roused, when it was rather in a passive indolent state, as in reading merely for amusement, or in the mechanical process of copying writing, both which seem to have, as is indeed generally believed, rather a sedative influence than an exciting one ; and are to the former very like what passive bodily exercise is to active muscular exertion. 7. Of the Effect of taking Food on the Temperature. The following observations were made after rising from the dinner-table, at which the observer commonly sat down at 5 o'clock, and partook pretty fully, using a mixed diet, — never taking anything between the breakfast and dinner-hour, — and using wine commonly at the latter meal, to the extent of three or four glasses, to the exclusion of malt liquor. Tongue. Pulse. Respirations. Air. Aug. 15. 7 P.M. 98-2 0 22. 6^ P.M. 97-9 60 16 60 25. 6i P.M. 98-1 62 15 59 27. 63- P.M. 98-4 58 16 62 28. 7 P.M. 98-6 76 16 68 29. 7 P.M. 98-3 82 16 63 Sept 2. 6 P.M. 98-5 68 18 17 3. 6 P.M. 98-3 60 15 70 8. 8 P.M. 97-8 60 15 65 22. 6^ P.M. 98-4 70 15 55 29. 6 P.M. 98-5 68 16 62 Nov. 16. 7 P.M. 97-9 62 15 60 23. 1\ P.M. 98-1 70 18 54 Dec. 21. 7 P.M. 97-9 70 14 63 28. 7 P.M. 97-7 64 15 58 29. 8 P.M. 98-0 70 15 55 Jan. 2. ^\ P.M. 97-9 68 15 55 Mar. 24. 6^ P.M. 98-5 98-1 66 15 62 DR. DAVY ON THE TEMPERATURE OF MAN. 336 The majority of these results (the mean temperature of the whole being 98*1) seem to prove, that the amount of heat is reduced by a full meal. In the observer's case, as in most others, drowsiness followed this meal, thus approximating the condition of the animal system to that which precedes sleep. On particular occasions, when a larger quantity of wine than usual was taken, the reduction of temperature was commonly most strongly marked. A light meal, such as that of breakfast, consisting of tea, with a portion of toasted bread with butter, and often an egg, has had little effect in depressing or altering materially the temperature. It may be noticed, as regards the habits of the observer, in connexion with the observations on temperature made at a late hour, that after dinner he never took solid food, only two or three cups of tea, and this about 8 p.m. The preceding observations, generally considered, appear to indicate clearly that the temperature of man, as determined in the manner described, is like the animal functions and secretions, constantly fluctuating within certain limits ; and like them, observing in its fluctuation a certain order, constituting as it were two series ; one regular, as the diurnal, connected with rest and refreshment from rest ; the other, casual or accidental, depending on varying circumstances of irregular occurrence, as exercise, mental exertion, exposure to heat, and the contrary. As the observations brought forward have been made on one individual, the infe- rences from them as regards extended application, can be held to be only probable, but probable, I cannot but think, in a high degree, the average temperature of the observer being nowise peculiar ; and the results moreover being what might be ex- pected reasoning on the subject, taking for data the proportions of oxygen which have been ascertained to be consumed, and of carbonic acid evolved in respiration, at different periods of the twenty-four hours, and under different circumstances. Should observations similarly made on others present the like results (and I cannot but be confident that they will), more particular inferences may be drawn from them, especially in conjunction with respiration and the heart's action, not without interest to physiology; and they may admit of important practical ap- plication to the regulation of clothing, the taking of exercise, the warming of dwelling-rooms, in brief, to various measures conducive to comfort, the prevention of disease, and its cure. A step in advance is made, if it is only determined, as I believe it to be, that in the healthiest condition of the system, there is danger attend- ing either extreme, either of low uniform temperature, or of a high uniform tempera- ture, and that the circumstances which are proper to regulate variability within certain limits, not prevent it, are those which conduce most to health, as well as to agreeable sensation, enjoyment and length of life. The Oaks, Ambleside, May 1, 1845. 326 DR. DAVY ON THE TEMPERATURE OF MAN. * ^^'^ ^ * ■ Appendix, The Tables which follow, containing the monthly observations, require little additional explanation. It may be rigfht to state, that they do not include the obser- vations made under the influence of accidental disturbing circumstances, as active exercise, &c., the most distinct of which have been given apart in a section appro- priated to them. The observations in these Tables, made under ordinary circum- stances, or nearly such, will, I believe, be useful for comparison with the former, and I would hope, for reference, in progress of inquiry. In most instances, it will be found on comparison, that an unusual elevation of temperature has been followed by unwonted depression, and vice versd. Date. Temperature under the tongue. Pulse. Respirations. Temperature 3f air. 7-8 A.M 3-4 p.M 12 p.m. 7-8 A.M. 3-4 P.M. 12 p.m. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. Aug. 6. 98-3 0 9°7-9 o o • 7. 98-8 98-2 56 .... 54 13 .... 15 63 .... 68 8. 98-6 98-5 97-8 56 52 52 13 14 16 63 60 66 9. 98-8 .... 98-2 60 .... 62 14 .... 16 63 .... 70 10. 98-8 .... 97-8 .... .... 70 .... .... 14 . • . . .... 70 11. 98-5 98-6 98-0 56 50 58 14 15 16 62 59 67 12. 98-6 .... 98-0 .... .... 58 .... .... 14 .... .... 68 13. 98-7 98-5 97-7 52 52 58 14 15 16 61 62 68 14. 98-8 98-7 98-1 56 60 52 15 16 15 62 64 61 15. 98-7 .... 58 .... .... 16 .... • • • • 64 16. 98-5 98-5 97-6 56 50 50 16 14 15 63 63 63 17. 98-8 98-5 98-1 54 50 50 15 15 14 62 62 68 18. 98-7 98-4 98-2 62 54 56 16 15 16 60 68 68 19. 98-8 98-4 98-4 m 50 58 18 14 15 60 63 68 20. 98-7 97-9 54 .... 58 16 .... 15 62 « • . . 68 21. 98-6 98-0 58 . . . 56 16 # • • • 15 62 • • • • 66 22. 99-0 98-0 56 58 16 • • • . 15 60 .... 68 23. 98-6 97-7 52 .... 52 16 • . . . 16 60 68 24. 98-5 98-5 97-8 62 50 48 16 16 14 60 61 68 25. 98-7 98-8 98-4 5^ 54 60 15 15 16 60 54 ^S 26. 99-0 98-1 58 50 15 .... 15 60 65 27. 98-7 98-2 54 .... 52 15 • • • • 15 60 62 28. 98-7 98-8 98-1 60 54 54 15 17 17 62 72 68 29. 98-8 98-5 54 .... 62 16 .... 16 61 .... 62 30. 98-9 98-8 97-7 62 54 50 16 15 16 60 63 63 31. 98-7 97-8 Q2 58 16 .... 16 65 .... 68 98-7 98-6 98-0 56-9 52-5 53-1 15-3 15-1 15 61 63 67 DR. DAVY ON THE TEMPERATURE OF MAN. 327 Date. Temperature under the tongue. Pulse. Respirations. Temperaturs of air. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M 3-4 P.M. 12 P.M. 7-8 A.M 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 p.M 12 p.m. Sept. 1. 98-7 98-7 97-8 62 56 56 17 16 15 ^7 ^7 67 2. 98-8 98-7 98-1 54 54 54 16 16 16 68 71 68 3. 98-9 98-7 98-3 58 54 54 16 15 16 70 1 71 68 4. 99-0 98-1 60 .... 48 16 14 72 .... 70 5. 98-8 98-6 98-1 62 54 60 16 16 15 70 68 68 6. 98-8 .... .... 60 .... .... 15 .... 69 .... /• 98-7 98-7 98-2 60 60 56 15 16 16 68 68 68 8. 98-8 98-9 97-8 54 60 52 15 15 16 62 65 64 9. 99-0 99-0 98-1 58 50 15 .... 15 64 64 10. 99-0 .... .... 60 15 .... .... 64 11. .... .... 97-6 .... 50 .... .... .... 67 12. 98-7 .... 98-2 56 50 15 .... 15 62 64 13. 98-8 98-8 98-1 66 52 54 16 17 16 62 60 68 14. 99-0 98-7 98-0 62 52 50 16 16 15 61 60 60 15. 99-0 99-0 98-2 66 58 54 16 18 .17 63 60 69 16. 98-8 ■ ■ * • 97-9 66 52 16 16 62 68 17. 98-6" 97-7 64 64 15 .... 16 62 68 18. 99-0 .... 98-4 62 50 17 .... 14 62 61 19. 99-0 99-0 97-9 64 60 54 15 16 16 60 62 63 20. 99-0 .... 98-3 58 52 15 16 60 .... 58 21. 99-0 98-1 60 54 16 .... 15 58 58 22. 99-0 990 98-5 54 48 54 15 16 16 58 55 65 23. 99-0 .... 97-7 56 52 16 .... 14 65 68 24. 98-7 .... 98-3 54 56 14 15 58 63 25. 99-2 97-2 58 48 16 .... 16 63 .... 66 26. 98-3 99-0 98-3 58 56 54 16 16 l& 58 58 67 27. 98-9 98-0 58 50 16 15 60 68 28. 98-6 .... 97-7 60 62 16 .... 14 62 69 29. 98-6 98-9 98-3 54 56 52 15 16 16 59 63 68 30. 99-0 .... .... 56 16 .... 68 98-8 98-9 98-0 59-3 55-2 55-8 15-5 16 15-4 66 1 63 65 MDCCCXLV. 328 DR. DAVY ON THE TEMPERATURE OF MAN. Date. Temperature under the tongue. Pulse. Respirations. Temperature of air. 7-8 A.M. 3- 4p.m. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 p.m. Nov. 1. 98°'75 98-8 97-6 54 58 16 17 16 0 o 53 54 ^2 2. 98-8 98-5 97-7 60 58 64 17 18 16 52 44 60 3. 98-6 98-5 97-9 52 48 48 16 17 17 50 55 65 4. 98-7 .... 97-9 60 70 16 16 51 .... 66 5. 98-9 .... 97-6 64 .... 52 16 16 62 68 6. 99-2 98-0 66 .... 58 17 .. 16 60 .... 63 7. 98-7 98-7 98-3 58 58 58 16 16 16 51 46 62 8. 99-5 97-8 63 .... 54 17 17 52 .... 68 9. 98-8 .... 62 .... 16 51 11. 99-3 98-3 97-8 62 61 50 17 17 15 52 54 68 12. 98-6 98-7 98-2 60 56 52 17 17 15 47 40 65 13. 98-8 98-7 98-1 56 62 54 16 17 16 52 50 62 14. 98-5 98-0 58 .... 58 16 16 51 .... 64 15. 98-8 98-7 97-9 56 56 60 16 17 17 54 66 63 16. 98-9 98-9 97-7 56 62 58 15 18 15 65 55 68 17. 98-7 .... 97-5 52 52 18 16 63 65 18. 98-6 .... 54 15 . • . . 66 19. 99-1 98-2 60 56 17 . 16 56 66 20. 99-1 .... 98-1 56 56 17 . 16 55 65 21. 98-9 .... 98-0 60 58 17 15 55 62 22. 99-0 98-0 60 56 16 14 65 66 23. 99-0 98-2 60 62 16 . 16 63 . , 66 24. 990 • • • • 98-2 58 62 16 16 52 64 25. 99-2 98-1 56 56 17 16 48 60 26. 98-8 98-4 54 56 15 15 44 60 27. 98-7 97-4 60 50 16 16 43 62 28. 98-6 54 17 48 29. 99-2 98-2 54 60 16 17 49 64 30. 99-0 97-4 54 56 17 16 46 62 98-9 98-6 97-9 57-8 57-6 54-3 16-7 17' 1 15-8 51 48 64 "*■" DR. DAVY 0\ THE TEMPERATURE OF MAN. 329 Date, Temperatuie under the tongue. Pulse. Respirations. Temperature of air. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M.J3-4P.M. 12 P.M. 7-8 A.M 3-4 P.M. 12 P.M. Dec. 1. 9°8-7 9°8-6 98-3 62 58 50 17 16 16 50 64 64 2. 98-8 . . , . .... 54 .... 16 .... 48 .... 3. .... .... 97-0 .... 56 .... .... 15 .... .... 62 4. 98-7 98-7 97-7 56 60 50 16 19 15 44 32 58 5. 98-7 98-2 58 58 16 .... 15 40 .... 62 6. 98-9 97-8 98-3 56 56 60 16 17 16 38 43 60 • 7. 98-6 98-0 98-2 56 54 60 15 16 14 36 47 62 8. 98-5 98-4 98-1 56 50 54 16 16 16 38 43 60 10. 98-4 98-2 97-9 56 54 52 16 16 16 40 44 62 11. 98-5 .... .... 58 16 40 .... 13. 98-6 98-5 58 56 17 .... 15 38 64 14. 98-4 .... 97-9 60 58 16 .... 16 40 58 15. 99-0 98-6 98-3 63 54 56 15 15 16 42 48 62 16. 98-4 97-9 98-1 56 56 66 16 15 16 42 58 60 17. 99-0 97-7 98-0 60 50 58 15 17 14 45 50 64 18. 98-7 98-2 60 .... 58 15 16 45 .... 62 19. 98-8 .... 58 .... 15 .... 45 .... .... 20. 98-8 98-0 97-5 64 56 54 15 16 15 43 43 65 21. 98-6 .... 98-2 58 .... 50 15 15 43 .... 58 22. 98-8 98*4 97-8 52 52 62 16 15 14 43 50 66 23. 98-9 .... 97-9 60 .... 54 15 16 43 .... 62 24. 98-6 98-2 60 .... 54 15 .... 15 .... 65 25. 99-2 .... . . , . 60 .... .... 15 .... .... 43 .... 26. 98-8 98-4 98-3 58 64 52 16 17 15 41 34 50 27. 98-5 97-7 58 66 16 .... 16 43 .... 28. 99-3 98-7 97-5 66 58 62 16 16 15 41 53 55 29. 98-2 98-6 98-0 50 52 56 16 15 16 45 58 55 30. 98-8 98-9 97-3 60 62 66 16 15 16 43 58 58 31. 98-5 98-0 58 .... 16 43 55 98-7 98-2 97-9 58-9 55-2 56-5 15-7 16 15-4 42 47 60 2x2 330 DR. DAVY ON THE TEMPERATURE OF MAN. Date. Temperature under the tongue. Pulse. Respirations. Temperature of air. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. Jan. 1. 9°8-5 o 97-5 58 58 16 15 40 . ° » 2. 98-4 .... .... 54 ... 16 .... 42 3. 99-0 97-9 64 §8 16 17 42 55 4. 98-8 .... 66 .... 17 16 48 5. 99-1 98-7 64 60 18 16 46 66 6. 99-7 98-1 70 66 18 .... 48 66 7. 100-0 98-9 98-1 72 60 52 18 17 16 60 68 65 8. 99-1 98-1 62 56 16 16 49 1 68 9. 99-0 98-3 60 60 16 16 46 61 10. 99-1 98-6 98-3 60 58 64 16 15 16 46 53 60 11. 98-7 97-4 56 58 14 14 47 60 12. 987 98-0 54 60 14 .... 16 47 64 13. 98-9 98-7 98-1 62 60 62 16 14 16 46 53 61 14. 99-2 97-9 56 60 14 15 46 66 15. 98-8 97-7 58 56 14 16 47 64 16. 98-7 97-7 66 60 16 16 47 : 62 17. 98-9 98-1 64 60 15 14 47 62 18. 98-9 98-2 60 58 15 14 47 ' 65 19. 98-8 97-8 60 56 14 " 16 47 60 20. 98-8 .... 98-0 56 54 15 14 44 60 21. 98-7 97-9 58 62 16 16 44 ' 63 22. 9-88 .... 97-9 60 50 16 14 47 .... 63 23. 98-8 .... 56 ■ 16 .... 47 ' .... 24. 98-9 97-3 58 54 15 15 49 68 25. 98-6 .... .... 54 .... IS .... .... 47 .... 26. 98-6 98-1 58 62 15 16 48 66 27. 98-7 97-9 58 54 15 14 46 62 28. 99-0 .... 97-6 62 58 16 15 43 62 29. 98-5 97-9 66 66 15 15 42 60 30. 98-5 98-2 56 68 14 15 41 60 31. 98-8 97-9 60 62 16 16 38 62 98-8 98-07 97-9 68-7 59-3 57-9 15-5 15-3 15-1 46 56 60 DR. DAVY ON THE TEMPERATURE OF MAN. 331 Date, Temperature under the tongue. Pulse. Respirations. Temperature of air. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. Feb. 1. 98-8 o 97-5 60 62 16 16 39 o 62 2. 98-5 98-7 .... 60 52 .... 16 14 .... 38 48 3. 98-7 .... .... 60 . . • . 16 .... 41 6. 98-6 .... 64 .... 18 .... 44 6. 98-8 97-9 56 54 15 15 43 .... 60 7. 98-6 .... 98-1 56 62 14 16 39 .... 60 8. 98-9 98-0 52 64 16 16 40 .... 60 9. 98-1 98-5 97-9 52 56 54 14 16 15 38 60 61 10. 98-7 98-9 97-7 54 68 52 16 15 15 40 48 60 11. 98-7 97-7 56 .... 64 16 15 40 .... 60 12. 98-7 .... 98-2 50 68 14 16 40 60 13. 98-4 98-2 50 .... 54 15 16 40 .... 60 14. 98-2 98-4 97-8 50 54 54 17 15 17 41 48 63 16. 98-8 97-6 64 .... 54 17 16 43 60 16. 98-6 98-7 98-1 54 52 52 15 16 43 48 62 17. 98-5 98-2 64 50 16 16 15 . 44 60 18. 99-0 98-2 68 56 16 16 45 .... 60 19. 98-7 .... 97-7 56 48 15 16 44 60 20. 98-7 .... .... 52 .... 15 45 21. 98-8 98-1 52 .... 58 14 15 45 .... 60 22. 99-0 97-4 60 60 15 15 44 .... 62 23. 98-6 98-3 58 .... 52 15 15 43 .... 62 24. 98-3 .... 97-8 58 .... 54 16 16 42 62 25. 99-0 .... 97-9 56 50 15 15 43 .... 62 26. 98-3 .... 98-0 56 60 16 14 46 62 27. 99-0 97-8 58 .... 52 16 14 47 .... 62 28. 98-7 98-5 64 60 15 15 47 60 98-6 98-6 97-9 66-5 54-4 52-3 15-5 15 16-1 42 48 61 • 332 DR. DAVY ON THE TEMPERATURE OF MAN. Date. Temperature under the tongue. Pulse. Respirations. Temperature of air. 7-8 A.M 1 . 3-4 p.M 12 P.M. 7-8 A.M . 3-4 p.M 12 p.M 7-8 A.M 3-4 p.M 12 P.M. 7-8 A.M . 3-4 P.M 12 P.M. March 1 99-0 98-6 97-6 58 56 58 16 16 16 45 52 60 2 99-1 98-7 97-9 58 52 46 16 15 16 44 55 60 3. 98-5 .... 98-5 52 .... 56 15 .... 15 47 .... 60 4. 99-0 98-3 98-0 60 54 54 15 16 15 45 52 60 5. 98-6 .... 98-0 58 66 17 15 43 .... 60 6. 99-0 .... 98-2 60 54 16 15 43 .... 60 7. 99-0 .... 98-0 60 64 14 .... 15 44 62 8. 99-2 98-1 60 60 16 15 46 .... 60 9. 99-1 98-7 98-0 60 48 54 15 15 15 48 54 58 10. 99-0 97-5 60 54 16 15 48 .... 60 11 J 98-8 .... 97-9 56 .... 48 15 14 47 .... 58 ]2.' 98-4 97-7 54 56 16 14 47 .... 61 13. 98-8 98-2 60 54 15 15 43 .... 61 14.' 98-6 1 .... 97-9 54 46 14 . . ■ ■ 14 44 58 15.' 98-3 .... 97-5 54 60 14 14 42 62 16. 98-7 98-1 58 .... 62 15 .... 14 43 58 17. 98-6 98-0 60 .... 52 15 .... 15 40 .... 58 18. 98-5 98-7 98-0 62 58 48 15 15 15 43 53 60 19. 98-5 .... 98-4 56 .... 54 14 15 43 58 20. 98-6 .... 97-5 54 54 15 .... 15 42 .... 60 21. 98-8 98-6 98-1 54 50 50 14 14 14 44 53 60 22. 99-0 98-5 97-8 56 54 54 15 15 13 48 58 60 23. 99-0 .... 97-8 58 52 15 .... 14 50 61 24. 98-7 98-0 58 48 15 .... 13 53 .... 58 25. 98-4 98-0 54 .... 48 14 .... 14 52 .... 60 26. 98-4 98-2 54 60 15 .... 15 51 62 27. 98-8 97-8 60 52 15 16 52 64 28. 98-7 98-3 54 .... 54 16 .... 15 50 64 29. 98-7 .... 97-3 56 .... 54 14 .... 14 50 65 30. 98-6 98-6 \ 97-8 55 52 48 15 15 15 51 54 62 31. 98-6 .... 97-5 54 54 15 .... 15 51 .... 63 98-74 98-59 97-93 57 53 54 15-1 15-1 ! 1 15 46 54 60 DR. DAVY ON THE TEMPERATURE OF MAN. 333 Date. Temperature under the tongue. Pulse. Respirations. Temperature of air. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. 7-8 A.M. 3-4 P.M. 12 P.M. April 1. 98-3 o 98-0 58 .... 58 16 15 o 53 0 62 2. 98-7 98-8 97-7 58 58 52 15 16 15 63 62 64 3. 98-8 .... 97-7 56 .... 48 15 .... 14 56 .... 62 4. 98-8 .... 97-8 54 60 15 14 68 .... 64 5. 98-9 .... 98-1 60 .... 64 15 16 58 64 6. 99-3 98-8 97-9 62 60 50 15 15 16 56 61 62 7. 98-8 98-8 98-2 54 56 56 14 15 16 68 61 63 8. 98-5 .... 97-9 56 .... 56 15 15 68 .... 61 9. 98-6 .... 98-1 60 .... 58 14 .... 15 64 .... 62 10. 98-5 98-3 98-0 62 52 62 14 14 15 62 52 63 11. 98-7 .... 97-6 60 54 14 15 61 63 12. 98-4 97-9 56 50 15 .... 15 49 .... 59 13. 98-5 98-7 97-6 54 54 54 15 15 15 49 55 60 14. 98-7 .... 98-0 56 .... 54 15 14 52 ... 60 15. 98-6 98-8 .... 56 60 .... 15 14 49 58 16. 98-4 97-7 58 52 15 15 62 .... 62 17. 98-8 97-8 56 .... 50 15 .... 14 56 58 18. 98-4 98-8 98-1 60 54 54 15 15 15 60 60 66 19. 98-7 98-6 97-6 60 52 50 15 16 15 58 60 62 20. 98-7 .... 98-3 58 .... 54 15 15 60 .... 64 21. 98-7 .... 97-3 58 .... 56 16 .... 13 60 .... 62 22. 98-4 98-1 98-0 60 56 50 16 15 15 62 66 64 23. 98-5 97-7 56 .... 54 15 15 62 62 24. 98-7 98-2 97-7 58 52 52 16 16 16 64 64 65 25. 98-6 98-4 97-9 64 52 52 16 15 16 65 63 62 26. 99-0 98-0 58 50 15 .... 14 62 .... 62 27. 98-8 98-8 97-9 54 52 50 15 14 15 60 57 63 28. 98-6 .... 58 .... 16 .... .... 68 29. .... 98-3 98-2 .... 54 52 15 15 60 64 30. 98-9 98-7 98-2 58 56 48 14 15 14 58 58 65 98-66 98-57 97-88 56-5 54-8 53-6 15-4 15 14-8 64-6 59-8 62-4 [ 335 ] XV. Contributions to the Chemistry of the Urine. On the Variations in the Alkaline and Earthy Phosphates in the Healthy State, and on the Alkalescence of the Urine from Fixed Alkalies. By Henry Bence Jones, M.A., Cantab., Fellow of the College of Physicians. Communicated by S. Hunter Christie, Esq., Sec. R.S. Received January 23, — Read June 19, 1845. On the Variations of the Earthy and Alkaline Phosphates in a healthy state of Urine. JllAVING observed the occurrence of a great excess of earthy phosphates in the urine in some cases of disease, and having made frequent examinations as to the quantity present on successive days, I found so great a discrepancy, that it became necessary before any further progress could be made to ascertain the variations in the amount of earthy phosphates in the urine of a healthy man, and, if possible, to trace the causes which determined the presence of an excess or deficiency of these salts in the urine. At the same time it was thought desirable to note the variations which the alkaline phosphates presented in the same water, and to see if they were influ- enced by the same, or by different causes. A healthy man taking food twice daily, with moderate exercise for three hours, was the subject of the following experiments. The method followed was to take the specific gravity of the urine, if ever it was not strongly acid adding a drop or two of hydrochloric acid. Then from a weighed quantity, usually about 1000 grains, to precipitate the earthy phosphates by means of pure ammonia, to filter, wash with ammoniacal water, and heat them to redness, adding at last a drop or two of nitric acid. Thus the earthy phosphates were determined. The alkaline phosphates were estimated by taking usually about 500 grains of urine, adding an excess of chloride of calcium and then pure ammonia ; by this means all phosphoric acid was precipitated as phosphate of lime ; this was filtered, well- washed, and heated to redness with nitric acid ; by deducting the previously determined earthy phosphates, the difference was considered as alkaline phosphate*. Though neither the calculation nor the method were perfectly accurate, yet they answered well for the purposes of comparison ; and in disease the short delay before a result was arrived at which might determine the diagnosis, and sometimes the treat- * The formation of a small quantity of carbonate of ammonia and the precipitation of some sulphate of lime, which even long washing cannot entirely remove, make the result too high. The equivalent of lime being less than that of soda tends to reduce the error. It must be remembered that the phosphoric acid is pre- cipitated in combination with three equivalents of lime. MDCCCXLV. 2 Y 336 DR. BENCE JONES ON THE VARIATIONS IN ment, was a matter of considerable importance ; a few hours being usually all that were required to tell in what excess or deficiency the phosphates might be present. I. (1.) Breakfast on bread and meat with coffee at 9J o'clock. Dinner at 6 : meat, potatoes, and little bread. Earthy phosphates. Water passed 6 o'clock, evening 32 per 1000 urine 10 o'clock, evening '97 Spec. gr. 1022-8 Alkaline phosphates. 6-50 per 1000 urine. 5-45 1027*3 6 o'clock, morning -81 1017'4 4*01 (2.) Food as before. More exercise. Dinner at 7- 7 o'clock, evening '37 1027-2 7*26 1 1 o'clock, evening 1-22 1029-9 6*06 5 o'clock, morning 1*41 1025-5 3-64 (3.) Food as before. Still more exercise. 7 o'clock, evening '75 1028-0 8*10 12 at night 1-29 1025-5 6-67 (4.) Food as before. Exercise very great excess. 7 o'clock, evening -21 1028*2 8-22 1 at night 1*85 1034*3 5-94 (5.) Food as before. Exercise much less. 7 o'clock, evening -35 1029*3 7*75 1 at night 1*91 1033-2 4-72 Average mean of five days. Long after food, and soon after exercise. Spec. gr. Earthy phosphates "40 per 1000 urine 1027*9 Alkaline phosphates 7*56 1027*9 From this five days' experiment, it appears that the earthy phosphates are greatly increased in the water secreted soon after food ; the quantity varying after dinner from 1*91 per 1000 urine, specific gravity 1033-2, to '97 per 1000 urine, specific gravity 1027*3; the mean of all the experiments being 1*45 per 1000 urine, specific gravity 10300. The earthy phosphates are far less in the water secreted a long time after food ; the quantity varying from -21 per 1000 urine, specific gravity 1028-2, to '75 per 1000 urine, specific gravity 1028*0; the mean of all the experiments being '40 per 1000 urine, specific gravity 1027*9. The alkaline phosphates are in excess in the water secreted a long time after food and soon after exercise ; the quantity varying from 8-10 per 1000 urine, specific gravity 1028-0, to 6-50 per 1000 urine, specific gravity 1022-8; the mean of all the experi- ments being 7*56 per 1000 urine, specific gravity 1027'9. The alkaline phosphates are far less in the water secreted soon after food ; the quantity varying from 6'67 per 1000 urine, specific gravity 1025-5, to 4*72 per 1000 urine, specific gravity 1033*2 ; the mean of all the experiments being 5*77 per 1000 urine, specific gravity 1030*0. Soon after food with perfect rest. Spec. gr. 1*45 per 1000 urine 1030*0 5-77 1030-0 THE EARTHY AND ALKALINE PHOSPHATES. 337 (6.) A child twenty months old, fed on bread with some meat and milk, gave in the water passed during the day, — Earthy phosphates. Spec, gr. Alkaline phosphates. •32 per 1000 urine. 1012*2 4*00 per 1000 urine. (7.) On the same food. Earthy phosphates. Spec. gr. Alkaline phosphates. •33 per 100 urine. 1017*4 4*60 per 1000 urine. II. I next endeavoured to ascertain on what the variations depended, and first with I'egard to food. For three consecutive days bread alone was taken with water, tea and wine, at the same hours as in the previous experiments. (8.) The first day brown bread only. Earthy phosphates. Spec, gr. Alkaline phosphates. 5J o'clock, evening '27 per 1000 urine 1025'7 7*89 per 1000 urine 11 at night. 1*37 1030*0 6*39 (9.) The second day no analysis was made. The third day white bread only. Earthy phosphates. Spec. gr. Alkaline phosphates. 6 o'clock, evening ^37 per 1000 urine 1024*7 8*19 per 1000 urine 11 o'clock, evening 1*86 1032*1 5*56 (10.) Meat only was taken for three days with water, wine, and tea. First day exercise very little. Earthy phosphates. Spec, gr. Alkaline phosphates. 6 o'clock, evening *42 per 1000 urine 1024*3 4*04 per 1000 urine 11 o'clock, evening 1*11 1021*9 4*21 (11.) The second day no analysis was made. The third day exercise rather more. Earthy phosphates. Spec. gr. Alkaline phosphates. 6 o'clock, evening '48 per 1000 urine 1024*7 5*06 per 1000 urine 11 o'clock, evening *8l 1024*8 4*31 (12.) Meat only for dinner with distilled water, and tea with distilled water. Earthy phosphates. Spec, gr. 5J o'clock, evening *33 per 1000 urine 1025*7 9J o'clock, evening *67 1026*5 From the comparison of these numbers with the previously given average, it ap- pears that the earthy phosphates are not materially influenced by a diet of meat or diet of bread ; that they are in excess after either is taken ; and that even when animal food and distilled water alone were taken there was after food a decided increase, though the quantity was considerably below the average. That the alkaline phosphates were in excess when bread alone was taken for food ; and when meat alone was taken there was a considerable falling off in the amount excreted. 2 y 2 338 DR. BENCE JONES ON THE VARIATIONS IN The next point was the effect of exercise. (13.) Nothing was taken from dinner on the previous day to dinner this day; both meals consisted of mixed diet of meat, bread, and potatoes. The exercise was mo- derate, between three and six o'clock. 12J o'clock Earthy phosphates. •45 per 1000 urine Spec. gr. Alkaline phosphates. 1 025-1 2-95 per 1000 urine 3 o'clock •48 1026-0 2-92 6 o'clock 1027-1 total phos. per 1000 urine 4-77 lOj at night ro2 10'27-6 3-99 (14.) Nothing was taken since dinner on the previous day until dinner at six; mixed diet with more bread. Exercise also greater between 3 and 5J o'clock. Earthy phosphates. Spec. gr. Alkaline phosphates. 3 o'clock -36 per 1000 urine 1025-4 5-69 6 o'clock 1 027-1 total phos. per 1 000 urine 778 lOj at night 1-37 1032*5 5-50 (15.) Nothing was taken since dinner on the previous day, which consisted of meat only, with distilled water and wine. Very strong exercise was taken between 3 and 5 J, the pulse always above 100. Earthy phosphates. Spec. gr. Alkaline phosphates. 11 J o'clock -52 per 1000 urine 10229 3-04 3 o'clock -36 1026-9 4*36 5 J o'clock 1028-9totalphos. per 1000 urine 6-81 In these experiments, the water, which was secreted longest after food, was not in sufficient quantity to admit of the determination of the earthy as well as alkaline phosphates. In all the experiments which were previously made, the exercise was always most between 3 and 6 o'clock, and yet at this time the earthy phosphates were always present in smallest quantity ; so that the quantity of earthy phosphates does not appear to be quickly influenced by exercise. The total quantity of phosphates which was found in the water secreted longest after food, and during strong exercise, was about one-third more than the total quantity previously present. This considerable increase so long after food, leads to the conclusion that the amount of alkaline phosphates is influenced by exercise, though, as appears from the previous experiments, not to the same extent as by the kind of food which is taken. III. I pass now to the influence of different medicinal substances on the amount of earthy phosphates excreted. (16) Breakfast as before, at 9 o'clock. 15 grains of chloride of calcium taken in about an ounce of distilled water at 3 o'clock. Earthy phosphates. Spec. gr. 3 o'clock ^30 per 1000 urine 1024-6 5J o'clock -22 1016-4 THE EARTHY AND ALKALINE PHOSPHATES. 339 (17.) Experiment repeated. Earthy phosphates. Spec. gr. 3 o'clock -67 per 1000 urine 1024-4 5i o'clock -32 1020*8 (18.) Breakfast, bread only. 22 grains of chloride of calcium taken at ^ to 1 o'clock. Earthy phosphates. Spec. gr. I to 1 o'clock 1-18 per 1000 urine 1028-6 3 o'clock 1-08 1025-2 (19.) Breakfast, bread and meat. 35grs. of chloride of calcium in Ij ounce of water at 5 to 1 . Earthy phosphates. Spec. gr. i to 1 o'clock 1-23 per 1000 urine 1026-8 3 o'clock 1-26 1023-8 51 o'clock 1-08 1022-3 lOi at night 1-82 1030-1 (20.) Breakfast, bread and meat. Nochlorideof calcium taken. Dinner as before at 6, chiefly meat. Earthy phosphates. Spec. gr. 3 o'clock -60 per 1000 urine 1027*4 6 o'clock -36 1027-0 11 at night '97 1032*7 From these experiments 15 grs. of chloride of calcium in an ounce of water pro- duced no, or very little, effect in two hours and a half; 22 grs. in rather more water produced an increase in two hours and a quarter ; 30 grains produced a still more marked increase in the same time, and the effect continued to be perceptible for at least ten hours. (21.) Breakfast as before, with rather more meat. 30 grains of dry sulphate of magnesia were taken at 1 o'clock in about an ounce and a half of distilled water. Earthy phosphates. Spec. gr. 1 o'clock water -82 per 1000 urine . 10266 3 o'clock water '27 10260 5 J o'clock water '36 1025*8 (22.) Breakfast at 9 as formerly. 40 grains of dry sulphate of magnesia taken in about two ounces and a half of water at a :J to 1 o'clock. Earthy phosphates. Spec. gr. 1 to 1 o'clock water *88 per 1000 urine 1029-3 3 o'clock water 74 1031*0 5i o'clock water -90 1029*3 9i o'clock water 1*64 1032-3 (23.) A patient of Dr. Seymour's in St. George's Hospital had taken senna with 340 DR. BENCE JONES ON THE VARIATIONS IN about two drachms of sulphate of magnesia in the morning, which did not act on the bowels; at 12 beef-tea and bread. Earthy phosphates. Spec. gr. 3 o'clock 2-99 per 1000 urine 1027'6 A second experiment with the same urine, at the same time, gave nearly the same result ; the alkaline phosphates were only 1*45 per 1000 urine, specific gravity 1027*6. (24.) Another patient of Dr. Seymour's in St. George's Hospital, who had taken senna and salts in the morning, with beef-tea and arrow-root for dinner, gave Earthy phosphates. Spec. gr. 2-93 per 1000 urine 1026'2 The quantity of sulphuric acid present in this urine =3*21 per 1000 urine, specific gravity 1026*2 The amount given by Becquerel is = '95 1018'9 The quantity stated by Becquerel is however below the average. From these experiments, 30 grains of dry sulphate of magnesia in an ounce and a half of water produced no, or very little, effect in two hours. In four hours and a quarter the effect was distinctly visible. 40 grains in two ounces and a half of water produced a visible effect in two hours and a quarter, and a still more marked effect in four hours and three quarters. The effect continued to be perceptible for 9f hours after the medicine was taken. As compared with the previous experiments, though the quantity taken appears to have been more, the effects seem not to have been so strongly marked ; but in fact less of the base was taken in the last than in the previous set of experiments, for 30 grains of chloride of calcium are equivalent to 15*1 grains of lime, 40 grains of sulphate of magnesia are equivalent to 13*6 grains of magnesia. As sulphate of magnesia is one cause of increase in the amount of earthy phosphates precipitated by ammonia, and as this salt also interferes in analyses regarding the quantity of sulphuric acid which is thrown out of the system, any means of knowing when it has been given as a medicine may be valuable. Most frequently it is pre- scribed with infusion of senna, which communicates a greenish yellow colour to the urine. This colouring matter, whether it has passed through the system or not, I find has the property of becoming of a deep red on the addition of an excess of any alkali, though it is most bright with ammonia. The red colour disappears again on neutralizing the alkali by an acid. It has a strong affinity for phosphate of lime. If rhubarb is taken, a less bright colour is given by the same reagents. I have lately found that Sir E. Home in some of his experiments on absorption used the reaction of potash on tincture of rhubarb because it is so remarkable*. (25.) Breakfast as before. 45 grains of dry magnesia taken at 10 o'clock. It had no action at all on the bowels. * Philosophical Transactions, 1808, p. 45. According to the researches of Schlossbeegek, this reaction is caused by chrysophanic acid which exists in the rhubarb.— Annalen der Chemie, vol. 1. p. 214. THE EARTHY AND ALKALINE PHOSPHATES. 341 Earthy phosphates. •90 per 1000 urine Spec. gr. 10267 •69 1027*8 1-19 1029-6 1-48 1028-0 2-69 1032-8 f magnesia taken at J to 1. It did not act Earthy phosphates. 1*79 per 1000 urine Spec. gr. 1030-4 1-19 1032-2 11:^ o'clock, water acid 1^ to 1 o'clock, water alkaline 3 o'clock, water alkaline 5J o'clock, water very acid 1 0 o'clock, water very acid (26.) Breakfast as before. 30-8 grair on the bowels. :j to 1 o'clock, water acid 3 o'clock, water acid ^jo'clock, both acid 1-69 1032*3 9 J o'clock, water very acid 2-44 1034*5 (27.) Breakfast as before. No magnesia taken. Earthy phosphates. Spec. gr. 3 o'clock 1*00 per 1000 urine 1030-3 6 o'clock -59 1031-4 9i o'clock 1*39 1031-6 Hence 45 grains of magnesia produced no increase in the phosphates in two hours and three quarters ; in five hours there was a marked increase ; in seven and a half hours there was a still further increase, which was very marked at the end of twelve hours, and from the large quantity of earthy phosphates present the following morning, perhaps the magnesia had not ceased to act in twenty-four hours. 30-8 grains of magnesia produced no evident increase in two hours and a quarter ; in four hours and three quarters the increase was marked, and after eight hours and three quarters it was quite perceptible. From the analysis of the urine after twenty- six hours, it seems probable that the magnesia had not then ceased to influence the amount of earthy phosphates. (28.) Water of the same child as (6.) and (7.) 15-4 grains of magnesia taken about 7 2 o'clock. Did not operate until after last water was passed. Food as before. Earthy phosphates. Spec. gr. 11 to 1 o'clock, water alkaline '62 per 1000 urine 10253 3 to 5 o'clock, water acid 1*57 per 1000 urine 1027*7 (29.) Same child. Food as before. No magnesia. Earthy phosphates. Spec. gr. 2 to 5 o'clock, water acid -36 per 1000 urine 1018-5 (30.) Same child. 19*3 grains of magnesia at 8 o'clock. Medicine acted about three o'clock. Earthy phosphates. Spec. gr. 11 to 1 o'clock, water neutral '45 per 1000 urine 1014-4 3 to 5 o'clock, water acid •SO 1017*1 342 DR. BENCE JONES ON THE VARIATIONS IN The conclusions from these experiments are — I. As regards variation in the phosphates. The earthy phosphates soon after food were found to vary from 1-91 per 1000 urine, specific gravity 1033-2, to '97 per 1000 urine, specific gravity 1027*3. Long after food they vary from *21 per 1000 urine, specific gravity 1028-2 to '75 per 1000 urine, specific gravity 1028*0. The alkaline phosphates long after food, and soon after exercise, vary from 8*10 per 1000 urine, specific gravity 1028-0, to 6*50 per 1000 urine, specific gravity 1022-8. Long after food the quantity varies from 6-67 per 1000 urine, specific gravity 1025*5, to 4*72 per 1000 urine, specific gravity 1033-2. n. As to the causes of the variation. (a.) As regards food. The earthy phosphates were not materially influenced by a diet of meat or of bread. They were in excess after either was taken ; but on distilled water and meat alone, the excess was considerably below the average. A long time after food the earthy phosphates were greatly diminished. The alkaline phosphates were present in greatest quantity when bread alone was taken for food ; when meat alone was taken, the deficiency was more marked than the excess with bread alone was. There was the most marked difference when the bread diet was compared with the meat diet. (b.) As regards exercise. Exercise produced no marked effect on the earthy phosphates. On the alkaline phosphates exercise caused an increase of nearly one-third the amount previously excreted. This difference is not so great as that between bread and meat diets ; so that probably though exercise has some influence, the kind of diet has a greater influence. in. As to the effect of medical substances on the earthy phosphates. (a.) As regards chloride of calcium. 15 grains of chloride of calcium produced no, or very little, effect in two hours and a half. 22 grains in rather more water produced a very decided increase in two hours and a quarter. 30 grains produced a still more marked increase in the same time, and the effect continued to be perceptible for ten hours. (b.) As regards sulphate of magnesia. 30 grains of sulphate of magnesia in IJg water produced no, or very little, effect in two hours ; in four hours and a quarter an increase was distinctly visible. 40 grains in 2jg of water produced a very slight effect in two hours and a quarter ; in 4| hours an increase was very distinct, and continued to be perceptible for nine hours. (c.) As regards calcined magnesia. THE EARTHY AND ALKALINE PHOSPHATES. 343 45 grains of magnesia produced no effect in two hours and three quarters ; in five hours there was a marked increase ; in seven hours and a half a still greater increase, which was very marked at the end of twelve hours, and possibly continued for twenty-seven hours to influence the amount of earthy phosphates. 30-8 grains of magnesia produced no increase in two hours and a quarter ; in four hours and three quarters the increase was very evident ; and after eight hours and three-quarters it was still very marked ; and after even twenty-six hours it still in- creased the amount of earthy phosphates in the urine. These last experiments give the explanation of the rapid increase of phosphatic calculi, and of the enormous quantities of earthy matter discharged, when magnesia or lime-water have been taken in calculous affections. They show that these sub- stances, having probably combined with different acids, pass off by the urine, and when this latter is alkaline react on the phosphate of soda, and thus increase con- siderably the amount of earthy phosphates in the deposit. The result of these experiments is, that the amount of earthy phosphates precipitable by ammonia, depends chiefly on the amount of earthy matter taken into the body ; and that the amount of alkaline phosphates is also most chiefly influenced by diet; yet that there is an additional cause constantly acting in the state of health, namely the production of phosphoric acid by the changes in the tissues of the body. And as in disease some of these tissues may be more particularly engaged, so then may the amount of alkaline phosphates point out the character, and declare the nature of the structure which is the seat of the affection. On Alkalescence of the Urine from Jixed Alkali. The cases in which the urine is alkaline may be divided into two classes. In the one the alkalescence arises from volatile alkali, and in the other from fixed alkali. In the first it is caused by carbonate of ammonia, and in the second by carbonate of soda, or potash, or alkaline phosphate of soda. Decomposition of urea is the origin of the one, and disordered secretion of the other. Whenever alkalescence arises, the earthy phosphates, whatever their quantity, are generally precipitated ; and hence the expression phosphatic diathesis, a term which makes no distinction between the different kinds of alkalescence, nor between cases in which the earthy phosphates, sometimes far below their average quantity, simply appear in consequence of their insolubility in alkaline fluids, and cases in which a vast excess of earthy or alkaline phosphates is being excreted. The object of the present paper is to point out the fact and the value of the distinc- tion between the different kinds of alkalescence. M. Pelouze has shown how rapidly decomposing mucus effects the conversion of urea into carbonate of ammonia. Irritation of the mucous membrane may give rise to mucus which produces this change, and in consequence the blue colour will be restored to reddened litmus paper if dipped into urine containing such mucus ; or if MDCCCXLV. 2 z 344 DR. BENCE JONES ON THE VARIATIONS IN blue paper be used, this, whilst wet, will retain its colour ; but if the test-paper be left to dry in either case it will be found that a change takes place. From the red- dened litmus paper first used the blue colour will disappear, whilst the blue paper, when quite dry, will become red in consequence of a slight decomposition of the am- moniacal salt. This decomposition I have elsewhere shown to be the result of the evaporation of all ammoniacal solutions, and thus a ready and easy way is afforded of determining in any case of the alkalescence of the urine, whether it is caused by some ammoniacal salt, or whether it results from the presence of some fixed alkali*. It not unfrequently happens that alkalescence is caused by fixed alkaline salts in those who, though not ill, yet suflfer from indigestion whilst leading sedentary lives. I have more especially observed it where the octahedral crystals, usually supposed to be oxalate of lime, have been present. After a breakfast consisting chiefly of bread, in an hour and a half the water passed may be found healthily acid to test-paper, but that which is next passed, that is, from two to four hours after breakfast, will have an alkaline reaction. Frequently blue test-paper will be found, when dry, to undergo no change from the action of such urine. It will remain of nearly as deep a blue as before when the fluid has perfectly evaporated. This urine when passed will, though alkaline, often be perfectly clear, and if it be heated a granular precipitate will fall, the fluid becoming turbid from the deposit of earthy phosphates, which dissolve in dilute hydrochloric acid, usually without any effervescence. Such a precipitation by heat takes place when the urine is not even neutral. It may be slightly acid. When boiled a precipitate falls, and if the fluid is then tested it is found to be more acid than before. If such a deposit from acid urine is left to become cold, the earthy phosphates are found to be partially, and sometimes even entirely redissolved, being again precipitable by boiling, and again partially or en- tirely dissolving on cooling. If such urine as I have mentioned is passed alkaline and thick from deposit, it will be found, if immediately examined by the microscope, to be entirely granular (Plate V. fig. 2), the supposed form of phosphate of lime. Dilute hydrochloric acid, if added occasionally causes an effervescence, which in some cases arises from some alkaline carbonate in solution. If the alkalescent or neutral urine is left for some hours, the surface becomes covered with an iridescent pellicle (fig. 1). This examined with the microscope contained here and there a long prismatic crystal, but the pellicle itself consisted of plates covered with spots of amorphous deposit. Some of these were triangular, some quadrilateral, some with regular and others with a ragged margin. The iri- descence depended on these plates, which probably consist of phosphate of lime, as in some cases not a single prismatic crystal has been visible. In some who suffer from indigestion the deposit of amorphous phosphate is con- * This method, however, I have found to fail when, much urate of ammonia and only a small quantity of fixed alkali chanced to he present. THE EARTHY AND ALKALINE PHOSPHATES. 345 stantly seen about three hours after breakfast, and very rarely at other times. In others the alkalescence of the urine is frequently observed, but the deposit is rare ; whilst in others the deposit by heat from acid urine is very frequently to be found ; and alkalescence is seldom to be detected by test-paper in the water secreted from two to four hours after food, and these three states often alternately occur in the same case. Dr. Andrews of Belfast stated to me, that having observed a case otherwise in perfect health, in which the urine was almost invariably alkaline about two hours after breakfast, so much so as frequently to be loaded with a deposition of phosphates whilst still in the bladder, he was led to observe the urine of about fifteen students in good health immediately after it was voided about noon. He found it to be alka- line in about two-thirds of the cases. Whether this tendency to alkalescent urine may, as Dr. Andrews thinks, be connected with the immunity enjoyed by the inha- bitants of his district from calculous affections, or whether alkalescence at this period of the day is far more general everywhere than has been supposed, future observations must determine. At the present time I know five physicians in whom the above phenomena at this period of the day are more or less frequently visible in a greater or lesser degree ; and in London this alkalescence will be found in those who are considered generally healthy much oftener than is imagined. Supposing that acid phosphate of soda was the cause of the acid reaction of healthy urine, it was thought that some explanation of the deposit on boiling might be gained by observing the behaviour of phosphate of lime and phosphate of magnesia with phosphate and biphosphate of soda. Pure solutions of these salts and of chloride of calcium, and sulphate of magnesia were used, and the following results obtained. The deposits were examined with a magnifying power of 320 times. Chloride of calcium gave no immediate precipitate with a strong solution of acid phosphate of soda. If left to stand many hours, a crystalline precipitate formed (fig. 3). When boiled no cloudiness was observed, if the quantity of phosphate of lime present was small ; but if much was in solution, a crystalline precipitate fell on boiling; and when cold, if filtered and again boiled, a very small crystalline precipi- tate was occasioned, which did not entirely redissolve on cooling. When a solution of biphosphate of soda is mixed with chloride of calcium, an immediate precipitate is caused by a drop or two of any alkali, and this is crystalline (fig. 3), or granular (fig. 2), or these mixed according to the quantity of alkali added, that is, according as much or little of the acidity of the solution is removed. If this precipitate was separated by filtration and the clear liquid boiled, a deposit fell which was at first gelatinous (fig. 2), the fluid becoming more acid to test-paper. The precipitate, if the solution was very acid, changed into the crystalline form (fig. 3), and partly dissolved on cooling. If chloride of calcium was added to common phosphate of soda, a plentiful granular 2 z 2 346 DR. BENCE JONES ON THE VARIATIONS IN precipitate fell (fig. 2). This remained granular or changed into the crystalline form (fig. 3), according as the phosphate of soda was or was not in excess. If the chloride of calcium was added in excess, the fluid became acid to test-paper ; the precipitate was at first gelatinous, but changed after some hours into crystalline, the fluid be- coming less acid after some time. If phosphate of soda was in excess, the precipitate remained of a mixed granular and crystalline appearance, containing some crystals but more granular phosphate of lime (fig. 4). If common phosphate of soda was poured drop by drop into chloride of calcium, a precipitate fell, which was at first gelatinous (fig. 2), the fluid becoming strongly acid to test-paper ; if left to stand, the precipitate became crystalline (fig. 3), and at length lost some or all its acid reaction, which it reacquired again on boiling. If common phosphate of soda was dropped into solution of nitrate of lime in excess, the result was the same gelatinous granular precipitate first forming, the same acid reaction, and the same change into the crystalline form on standing. If any of these precipitates were separated by filtration, and the clear liquid boiled, a further slight precipitation occurred, which was granular (fig. 2). If the phos- phate of soda was not in excess, the boiling caused an increase in the acid reaction of the liquid. The precipitate which falls when chloride of calcium is added to phosphate of soda, completely dissolves in solution of biphosphate of soda. Such a solution, if heated, gave a plentiful precipitate when boiled ; this was granular, and partly dissolved on cooling ; but if a great excess of biphosphate of soda was added, the precipitate was much less, and crystalline ; and if filtered, but little precipitate again fell on boiling. If sulphate of magnesia was added to a solution of biphosphate of soda, no preci- pitate fell ; nor on boiling did any change occur. If but little alkali was added, no precipitation occurred on boiling ; if rather more, a small, highly crystalline preci- pitate fell (fig. 5) ; if still more, heat threw down a plentiful gelatinous granular mass (fig. 2), which most rapidly dissolved on cooling. If sulphate of magnesia was added to common phosphate of soda, little or no pre- cipitate occurred, but if boiled a gelatinous precipitate fell; this dissolved as the fluid cooled. Under the microscope it was seen to be amorphous (fig. 2). If it was. in such excess as not entirely to redissolve on cooling, a few drops of biphosphate immediately made the liquid clear. This, if boiled, gave a plentiful precipitate, and more quickly dissolved on cooling than before. If the liquid was very acid from biphosphate of soda, a slight crystalline precipitate fell, consisting of minute rhombic crystals, similar to those which were seen in the experiment with biphosphate of soda (fig. 5). If a solution of phosphate of soda was dropped into an excess of sulphate of mag- nesia, after long standing a crystallization of small needles took place (fig. 6), but the fluid did not become acid to test-paper : nor if dropped into an excess of solution of chloride of magnesium was an acid reaction perceptible. THE EARTHY AND ALKALINE PHOSPHATES. 347 If to perfectly healthy and strongly acid urine a drop or two of a solution of chlo- ride of calcium is added, no precipitate falls. If the acidity is lessened by any alkali, on boiling a granular precipitate is occasioned. This, when the urine is still acid, is partly or entirely redissolved on cooling ; or if alkaline, immediately dissolves in dilute hydrochloric acid without any trace of effervescence. Between three and five hours after food, at which time the earthy phosphates are always in excess, if healthy acid urine which gives no deposit on boiliilg has some of its acidity removed by fixed alkalies, or alkaline phosphate, a deposit takes place on boiling, and this is always granular, the fluid becoming more acid than before. If to such alkaline urine as is passed thick from earthy phosphate a little biphos- phate of soda is added, the phosphate redissolves ; and if the biphosphate is not added in excess the earthy phosphates can be precipitated by heat, the reaction be- coming more acid ; but if an excess be added, the fluid remains perfectly clear on boiling. There is then the closest coincidence between the deposits of earthy phosphates in some states of the urine, and their deposit from solutions of the phosphates of soda ; and the same method which is followed for obtaining a precipitate of earthy phos- phates dissolved in biphosphate of soda, will give a precipitate from healthy acid urine, and that which hinders precipitation in the one has the same effect on the other. The deposit of phosphate of magnesia by boiling was supposed by M. Riffault to depend on the formation of a more basic phosphate of magnesia. The same expla- nation is still more probably the truth regarding the precipitation of the phosphate of lime by boiling, whether from solutions of phosphates of soda or from the urine. llie formation of crystalline earthy phosphates when great excess of earthy phos- phate was present while at the same time the biphosphate of soda made the liquid very acid, gives the explanation why crystalline phosphate of lime is so seldom seen in the urine. Still it may occasionally be met with. Crystalline phosphate of mag- nesia, from its greater solubility, can scarcely appear. The amorphous deposit of phosphate of magnesia when urine is boiled may perhaps be recognised by its far greater solubility than the phosphate of lime as the fluid cools. In the state of health acid phosphate of soda, mixed probably with common phos- phate of soda, holds the earthy phosphates in solution. No precipitate is occasioned by chloride of calcium. If, after the water is passed or before from medicines, or particular food, or state of body, some of the acid phosphate is converted into com- mon phosphate, a precipitate takes place on boiling the acid urine. If this very rapidly dissolves before the fluid is cold, the precipitate contains most probably phosphate of magnesia ; if very slowly, it is more likely to be phosphate of lime. If the urine be neutral to test-paper, that is, contains still less biphosphate of soda (the common phosphate being decidedly alkaline to test-paper), then the precipitation 348 DR. BENCE JONES ON THE VARIATIONS IN is more marked and the re-solution on cooling very much less. If the urine be alkaline, containing only common phosphate, this may be passed clear, and still may contain some phosphate of magnesia and a little phosphate of lime, these being somewhat soluble in common phosphate of soda, and these will be precipitated on boiling. If the phosphate of lime is from any cause in great excess, it may be deposited as a granular deposit, and never in the crystalline form, unless it be in so great an excess that it is deposited from urine containing very much biphosphate of soda. The occurrence of the alkaline condition at the particular period of the day which has been observed is well worthy of attention. The whole truth cannot be arrived at without a very lengthened inquiry into the variations in the amount of acids excreted by the kidneys, but partly at least it must depend on the food which has been taken in the morning, that is on the passage of alkaline phosphates, or carbo- nates, or salts of the vegetable acids through the system. Recent analyses of the ashes of seeds, flesh and blood, do not show any trace of alkaline carbonates, but as these cannot be heated to a red heat with common alkaline phosphates without the loss of carbonic acid, it will be seen how difficult it is to arrive at certainty on this point. The conclusions from these observations are — 1. That there exist two kinds of alkalescence of the urine; the one long known as ammoniacal, the other not distinctly recognised, arising from fixed alkali. This last appears most frequently in water secreted from two to four hours after breakfast in persons suffering only from indigestion. 2. Water made at this period may be thick when passed from amorphous sedi- ment, or it may be alkaline to test-paper, and still clear ; or it may be free from deposit and slightly acid. If either of these last be heated, an amorphous precipitate may fall, which is soluble in dilute hydrochloric acid, or in solution of biphosphate of soda. 3. Healthy urine may at any time be made to give a precipitate of earthy phos- phates by heat, even though it be acid, by having a little of its acid reaction removed by any alkali, or by common phosphate of soda, the fluid becoming more acid when boiled. 4. The solution of earthy phosphates in biphosphate of soda, gives also a precipi- tate on boiling if some of its acid reaction is removed by any alkali. The fluid when boiled becomes more acid to test-paper, indicating the formation of a more basic earthy phosphate. 5. A precisely similar result is obtained when common phosphate of soda, phos- phate of lime, and a little biphosphate of soda exist in solution together ; and by varying the quantities of each of these substances, the various phenomena which the urine occasionally presents may be produced at will. THE EARTHY AND ALKALINE PHOSPHATES. 349 6. The time at which the alkalescence of the urine from fixed alkali generally occurs, indicates the existence of some alkaline phosphate or of some carbonated alkali in the food*. 7. The result as regards diagnosis may be thus arranged : — Alkalescence of the urine from local causes. 1 Alkalescence from general causes. Blue paper made markedly red on drying. Alkalescence constantly present. Always contains mucus in excess. Prismatic crystals always to be found by microscope. Blue litmus paper not made red on drying. Alkalescence variable, usually soon after food. Rarely contains mucus in excess. When first passed generally contains only granular deposit. PLATE V. Fig. 1. Iridescent pellicles on some alkaline urine. Fig. 2. Amorphous deposit in alkaline urine. Deposit on boiling phosphate of soda with chloride of calcium, or with sul- phate of magnesia. Fig. 3. Chloride of calcium with acid phosphate of soda, or with common phos- phate of soda ; after long standing. Fig. 4. Phosphate of soda with little chloride of calcium. Bone-earth phosphate. Fig. 5. On boiling phosphate of soda with sulphate of magnesia and little biphos- phate of soda. Fig. 6. Phosphate of soda with sulphate of magnesia ; after long standing. Appendix. Later experiments have shown that the alkalescence from fixed alkali does not depend on the nature of the food. For example, with a diet of animal food and di- stilled water, the urine in four hours has been observed to be alkaline. Rather longer after dinner it has also been found to be alkaline. Usually however, after a late dinner, even if the water is secreted alkaline, it becomes mixed in the bladder during sleep with acid water which is afterwards secreted and thus the alkalescence escapes notice. It seems highly probable that the quantity of acid poured out into the stomach sets free alkali sufficient in some cases to make the urine alkaline ; and from facts which have been stated to me, it seems even possible that the same effect on the water may sometimes be produced by the separation of acid by the skin. * See Appendix. [ 351 ] XVI. On the Gas f^oltaic Battery. — Voltaic Action of Phosphorus, Sulphur and Hydrocarbons. By W. R. Grove, Esq., M.A., F.R.S., F.P.H.I., Prof. Exp. Phil, London Institution. Received June 5, — Read June 19, 1845. IN a paper which was honoured by publication in the Philosophical Transactions for 1843, I described certain forms of the gas voltaic battery, together with a series of experiments in which different gases were employed as voltaic combinations, and the consequent application of voltaism to eudiometry. To ensure confidence in the accuracy of the eudiometric experiments, it was essen- tial that the position which I laid down as to the absence of all voltaic action in a combination of oxygen and nitrogen should be rigidly true. I may state with cer- tainty that it is so, but an apparent exception noticed (Exp. 21.) in my last paper obtains during the first few minutes after the circuit is closed, and sometimes for a much longer time. The examination of this temporary action in the first instance, with the view of ascertaining whether it was a specific action of the nitrogen or attributable to adventitious circumstances, led me to the results which I have the honour of laying before the Royal Society in this paper. Before detailing these results, I will for convenience sake premise that they were all obtained by the form of battery represented in fig. 8 of my last paper (which, with a slight addition to be referred to presently, is again represented at fig. 2, Plate VI.), charged with distilled water slightly acidulated with pure sulphuric acid. I will also, when alluding to my last paper, to avoid the needless repetition of the word experiment, refer to the number of the experiments as though they were para- graphs, and continue those numbers in the paragraphs of this paper. As the form of battery (fig. 2) by which the interfering action of the atmosphere is entirely prevented was not devised until the greater part of the experiments in my last paper had been completed, I repeated some of them which seemed to require such verification with this battery ; to one of these only is it essential that I should now refer. I should likewise mention, that in the experiments to be described the proper reductions for temperature and pressure have been made when necessary ; where it was practicable the experiments were examined on days when the tempera- ture and pressure were, as nearly as may be, the same as when they were set by. (31.) Oxygen and deutoxide of nitrogen, which in the open form of battery gave only a temporary action (9.), when employed in the closed form (fig. 2) gave a con- tinuous current. The following three sets of experiments were continued each for a MDcccxLv. 3 a 352 MR. GROVE ON THE GAS VOLTAIC BATTERY. month in closed circuit, during which time they were constantly tested by the galva- nometer and evidenced a continuous voltaic action ; at the expiration of the month the results were as follows : — Experiment 1. — Rise of liquid in tubes of Oxygen =0*32 cubic inch. Deutoxide of nitrogen. . . =1*26 cubic inch. Experiment 2. — In oxygen tubes =0-5 cubic inch. Deutoxide of nitrogen. . . =2-5 cubic inches. Experiment 3. — In oxygen tubes =0*2 cubic inch. Deutoxide of nitrogen . . =0*75 cubic inch. In oxygen tubes, rise . . . =0*34 cubic inch. Lin deutoxide tubes, rise . . =1*5 cubic inch. The slight excess being undoubtedly due to the greater solubility of the deutoxide, it appears that four volumes of deutoxide of nitrogen are absorbed in the gas battery for one of the associated oxygen, and the result would be a compound of 1 equiv. nitrogen + 3 oxygen, or hyponitrous acid, which is exactly that formed by the slow combination of these two gases in the ordinary chemical way. The difference of amount of action in the three experiments depended on the temperature, the second experiment being made towards the close of last summer, the last experiment during the continuous cold weather of the present spring. These experiments, coupled with the converse ones with hydrogen and deutoxide of nitrogen (30.), afford very satisfactory instances of the illustration of the law of definite combining volumes by the gas battery, exhibiting in one result, and itself registering that result, the action of equivalent chemical combination, catalysis and voltaism. (32.) I now pass to the experiments which will form the more immediate subject of this paper. The temporary action to which I have alluded (21.) being greater when nitrogen and oxygen were the gases used, if the nitrogen were obtained by burning phosphorus in atmospheric air, than if procured from other sources, it natu- rally occurred to me that this action was due either to some phosphorous acid re- maining in a state of vapour in the nitrogen, or to a slight portion of the phosphorus itself being held in solution in the nitrogen, as believed by Vauquelin and the older experimentalists. If this last supposition were the correct one, it seemed to offer a means of rendering phosphorus, though a non-conductor and insoluble in aqueous liquids, yet a permanent voltaic excitant analogous to the oxidable metals. (33.) A small piece of phosphorus having been carefully dried, and weighing when dry 9'6 grains, was passed up through the liquid into the large tube of a gas battery by means of a small loop of mica, which kept it separated both from the glass and the platinum ; the tube was now charged with pure nitrogen, and the associated tube with pure oxygen, the level of the gases or water-mark being noted by a little slip of paper pasted on the tube ; a check experiment of oxygen and nitrogen without phos- VOLTAIC ACTION OF PHOSPHORUS, SULPHUR AND HYDROCARBONS. 353 phorus was charged at the same time ; the whole was carefully closed from the atmo- sphere and set by for twenty-four hours in closed circuit, to get rid of any current from adventitious circumstances ; the next day, when tested by the galvanometer and iodide of potassium, a very decided action was apparent in the phosphorus battery, the iodide being decomposed and the galvanometer needle swinging round to 30°, the nitrogen with the phosphorus representing the zinc of an ordinary voltaic combi- nation ; the check experiment gave not the least deflection or decomposition. The experiments were suffered to remain in closed circuit for four months, from August 10th to December 14th, 1844, having been frequently tested in the interim, and the galvanometer always evidencing a continuous voltaic action in the phosphorus battery. On the 14th of December, the water in the oxygen tube having by its rise denoted the absorption of a cubic inch of oxygen plus the slight quantity 0*05 cubic inch of oxygen due to solution, as proved by comparison with the second battery, the expe- riment was examined ; the result was as follows : — Rise of liquid in oxygen tube 1 cubic inch. In nitrogen tube 0. Original weight of phosphorus 9*6 grains. Present weight of phosphorus 9'2 grains. The battery was again charged in a similar manner, and put by on the 19th De- cember 1844 ; the phosphorus weighed 2*8 grains. This, in consequence of the ex- tremely cold weather which has prevailed almost without intermission from that time to the present period, proceeded much more slowly, and was not examined until May 17th, 1845, when the results were as follows : — Permanent deflection of galvanometer 8°. Rise of liquid in oxygen tube 0'35 cubic inch. In nitrogen tube 0. Weight of phosphorus =2*65. Taking a mean of these two experiments, which in their relative results approximate more closely than I could have anticipated under the circumstances, we get 0*415 as the proportional weight of phosphorus lost for a cubic inch of oxygen. Now as 24 : 31*4 : : 0*34 : 0*444. The result of these experiments therefore leaves no doubt that phosphorous acid is the product of the voltaic action, as it is of the slow com- bustion of phosphorus in air. The experiment was repeated with distilled water ; the action was at first very trifling, but increased every day, and the water gradually acquired an acid reaction. No light was apparent in any part of the apparatus when examined in the dark, indeed the action was much too slow to render such an eff"ect probable ; though if subsequently by heat or other means I should succeed, as I hope, in producing light, it will be curious to observe in what part of the circuit the luminous effect in the voltaic combustion is perceptible. A series of ten cells of phosphorus and nitrogen associated with oxygen were charged, and perceptibly decomposed water with platinum electrodes. 3 a2 354 MR. GROVE ON THE GAS VOLTAIC BATTERY. The result of the above experiments gives, I believe, the first instance of the em- ployment of a solid, insoluble non-conductor as the excitant of a continuous voltaic current ; it proves that the existence of diffused phosphorus in nitrogen, as noticed by the old experimentalists, is not a consequence, as was once believed, of a partial combustion, but of an effusion continuing as long as the previously diffused phos- phorus is abstracted, and it gives the very curious result of a true combustion, the combustible and the ' comhurant' being at a distance ; phosphorus burned by oxygen which is separated from it by strata both of water and gas, of an indefinite length. This result, arrived at by a progressive series of inductions, scarcely now appears ex- traordinary, but would have been in all probability listened to with incredulity if simply stated as a fact a few years ago. By the galvanometer we may also ascertain the rate of this very slow and minute chemical action ; thus if by an apparatus, as above described, my galvanometer gives a deflection of 8 degrees, I know that the phos- phorus is being consumed at the rate of the seven millionth part of a grain per minute. (34.) The next step was to ascertain whether this action was peculiar to nitrogen or common to other gases ; for this purpose, a day or two after the first experiment was set aside, the following were also made, and the dates and results were as fol- lows : — No. 1. Phosphorus suspended in protoxide of nitrogen associated with oxygen: weight of phosphorus 5*3 grains. Charged August 11th, 1844. No. 2. Similar experiment, but without phosphorus. Tested occasionally by galvanometer, the first battery gave invariably a small de- flection, but less than in experiment (33.) ; the second gave no deflection. Examined the 22nd April, 1845. No. 1. Water risen in tube of oxygen 075 cubic inch. In protoxide tube 1*7 cubic inch. No. 2. Water risen in oxygen tube 0*1 cubic inch. In protoxide tube 1*6 cubic inch. Phosphorus weighed 5 grains, therefore loss =0*3 grain. In this experiment the rise of liquid in the tubes containing protoxide was evidently due to the solubility of that gas, as it was very nearly equal in both the batteries, and the second gave not the slightest galvanometric deflection ; the result gives 0-65 cubic inch of oxygen consumed by 0*3 grain of phosphorus, bearing nearly the same relative proportions as experiment (33.) ; the only difference between the action of phosphorus in nitrogen and in protoxide of nitrogen is, that in the former it is more rapid, as proved both by the galvanometric deflection and by the quantity of oxygen absorbed in a given time. (35.) Charged August 11th, 1844. No. 1. Phosphorus in carbonic acid gas associated with oxygen; weight of phos- phorus 5 9 grains. VOLTAIC ACTION OF PHOSPHORUS, SULPHUR AND HYDROCARBONS. 355 No. 2. Same without phosphorus. Tested by galvanometer, No. 1. always gave a deflection. No. 2. none. On the 3rd of December the carbonic acid gas in both batteries had been absorbed, and the liquid had reached the extremities of both tubes. In the oxygen tube of No. 1, rise of liquid =075 cubic inch. In No. 2, 005 cubic inch. Phosphorus weighed 5*6 grains, the proportional weight was therefore 0*3 grain phosphorus to 07 cubic inch oxygen. Here again the proportions came out just as in (33.) and (34.), the intensity of ac- tion being intermediate, less than the former and greater than the latter. (36.) Charged 18th December, 1844. No. 1. Phosphorus in pure oxygen associated with oxygen, great care being taken to exclude atmospheric air: this arrangement having been kept in closed circuit for twenty-four hours, gave a very feeble deflection of the galvanometer. Examined 15th February, 1845. The rise of liquid in the tube containing phos- phorus was equal to 0*3 cubic inch, in that containing the associated oxygen = 0*05. I find no note of the phosphorus being re-weighed ; probably I considered it useless, as the consumption of oxygen in the associated tube was so very trifling, scarcely sufficient to be distinguished from the effect of its solubility. (37.) Charged 23rd April, 1845. No. 1 . Phosphorus suspended in deutoxide of nitrogen associated with oxygen ; weight of phosphorus = 4*3 grains. No. 2. Same without phosphorus. Examined May 27th, 1845. Galvanometer gave 25° permanent deflection in No. 1, and 10° in No. 2. No. 1. Rise of liquid in deutoxide tube =07 cubic inch. Rise of liquid in oxygen tube =0*6 cubic inch. No. 2. Rise of liquid in deutoxide tube =07 cubic inch. In oxygen tube = 0*2 cubic inch. Weight of phosphorus 4*17 grains. Consequently had lost 0^13 grain for 0*4 cubic inch of oxygen. In this and all the preceding experiments the residual gases were unchanged in quality, and in this experiment it appears that the action of the deutoxide of nitrogen and the oxygen was perfectly unafflected by the phosphorus, the consumption of deut- oxide of nitrogen being exactly the same in both batteries. In another experiment, which I did not record on account of a minute bubble of air having entered the tubes Containing the deutoxide, the phosphorus appeared to have exercised a retard- ing influence on the voltaic combination of deutoxide of nitrogen and oxygen ; this I attributed to a slight deposit of phosphorous acid upon the platinum, by which its catalytic power was deteriorated. (38.) It thus appears that the effect we have been examining, of the diff'usion of 356 MR. GROVE ON THE GAS VOLTAIC BATTERY. phosphorus in gas, is not due to any peculiarity of nitrogen, and is not peculiar to any particular gas, as once believed ; but being in all probability common to all gases which do not exercise a specific action on the phosphorus, it may be more properly called a volatilization of phosphorus at ordinary temperatures than a solubility in gas ; the ordinary slow combustion of phosphorus in air is, in fact, a combustion of its vapour. I incline to think that the inferiority of its vaporization in pure oxygen is due to a protecting film being formed, and that the phenomenon is in some respects analogous to the inactivity of iron in nitric acid. (39.) Phosphorus in nitrogen was associated with hydrogen in the gas battery to ascertain their voltaic relation ; the hydrogen was positive to the phosphorus, i. e, represented the zinc of an ordinary voltaic combination. (40.) To realize the curious novelty of two non-conducting solids forming the elements of a voltaic battery, and producing a continuous current, phosphorus sus- pended in nitrogen in one tube of a gas battery was associated with iodine in nitrogen in the other ; a very decided current was the result, which continued for months, the nitrogen remaining unaltered in volume, but the liquid becoming gradually tinged by the excess of iodine vapour. The following is the result of the experiment : — Charged January 1, 1845. Examined May 17, 1845. Weight of iodine . . =5 "9 grains. Weight of iodine . . =4*6 grains. Weight of phosphorus . =6*4 grains. Weight of phosphorus . =6*28 grains. The phosphorus has consequently lost 0*12 grain, the iodine I'S. Assuming that the phosphorus consumed 3 equivalents of oxygen, as in experiments (33.), (34.), (35.), (37.), we should have 3 equivalents of hydrogen eliminated, and consequently 3 of iodine consumed, or 31-4 : 126-6 : : 0-12 : 0*48 0'48X3 = l-44. The result is tolerably near, but from the iodine vapour in solution an excess and not a deficit in the consumption of this was to have been expected. (41.) It was necessary for my own satisfaction to make a great number of other experiments for the purpose of checking and eliminating any adventitious results which might possibly interfere with the actual voltaic action of the gas battery, such as placing phosphorus in single tubes containing the different gases, but with platinum foil and without associated tubes, others without the platinum foil or associated tubes ; but as these had no influence on the results, and were merely used as tests for my bwn satisfaction, it would be useless and tedious to detail them. (42.) Having examined the action of phosphorus in the gas battery under these various circumstances, my next step was to ascertain if any other substance produced a similar effect. Sulphur, the nearest analogue of phosphorus, was the body which naturally presented itself, but from its different characteristics required a different mode of manipulation. The following was adopted. Into a little capsule of glass. VOLTAIC ACTION OF PHOSPHORUS, SULPHUR AND HYDROCARBONS. 357 having a long solid leg (see fig. 1), was placed a small piece of solid sulpimr ; this was held in the large aperture of a gas batteiy cell, while the tube was passed care- fully over it ; the platinum in this tube was connected with the zinc of a single cell of the nitric acid battery, while an anode of platinum was placed in the liquid through the central aperture; by this means all the oxygen of the atmospheric air was exhausted, and the surplus hydrogen was in turn taken away by connection with the associated tube charged with oxygen ; the same effect might have been more slowly produced by the process described (29.). The sulphur was now in an atmo- sphere of pure nitrogen, and this could have been effected in no other way that I am aware of without wetting or forming some deposit on the sulphur. Having connected it in closed circuit with the oxygen tube for twenty-four hours, the galvanometer gave no deflection. A small hoop of iron with a handle was now heated and passed over the tube containing sulphur and nitrogen, the wires being connected with the galva- nometer (see fig. 2). The result was very striking : I had directed my assistant to watch the galvanometer while I attended to the manipulation. At the same instant he exclaimed that the galvanometer was deflected, and I that the sulphur was melt- ing; the galvanometer continued deflected during the whole time that the sulphur re- mained fused, and indeed some time afterwards, until all the sulphur vapour diffused in the nitrogen had become exhausted. The sulphur represented the zinc of an ordinary voltaic combination. It was of course impracticable in this case to ascertain the equivalent consumption. This experiment very strikingly exhibits the analogy of sulphur with phosphorus, and proves that the instant sulphur is fused it becomes a volatile body, as phosphorus is when solid ; the suddenness of its action, coupled with the insoluble character of sulphur, leads to the conclusion that solution in the electrolyte is not a necessary antecedent to voltaic action in the gas battery. Indeed this might have been deduced from the experiments with phosphorus, as its vapour must have been nearly, if not absolutely insoluble in the electrolyte, or the equivalent results would not have come out so accurately ; possibly solution and electrolysis are in these cases synchronous. (43.) I was now led to try in the gas battery other substances differing from phos- phorus and sulphur, but possessing characters which had hitherto prevented their being used as voltaic excitants; as, if my view of the volatility of phosphorus and sulphur were correct, other volatile bodies ought to act similarly. Camphor was the first substance I experimented on. A piece of camphor weighing 12-9 grains, was placed in a similar manner to the phosphorus (33.) in nitrogen, and associated with oxygen ; tested by the galvanometer it gave a feeble deflection, which, however, was continuous ; it was allowed to remain four months in closed circuit; at the expiration of that time the liquid had risen in the oxygen tube 0*3 cubic inch ; the nitrogen in which the camphor was suspended had increased in volume 015 of a cubic inch. The camphor weighed 11*4 grains, but some minute crystals of it were observed at the top of the tube, so that the loss of weight was greater than that due to voltaic action. 358 MR. GROVE ON THE GAS VOLTAIC BATTERY. (44.) The smallness of the quantity of the gas which had been added to the nitrogen, precluded an accurate analysis of it ; enough was ascertained, however, to lead me to believe that it was hydrocarbonous, and it then became my aim to produce it in greater quantities. I attached a piece of camphor to a platinum wire, and to the same wire I also attached a piece of sponge platinum ; I passed these up into a tube of nitrogen over distilled water, and at the expiration of three months the gas had increased O'l cubic inch ; this proved that the camphor vapour was decomposable by the catalytic action of platinum at ordinary temperatures, and that the effect in the nitrogen cell of the battery was not due to its voltaic association ; but the experiment did not give me a sufficient quantity of the gas for analysis. (45.) I therefore had recourse to the apparatus, fig. 3. a is an inverted cylindrical test-glass ; h a platinum capsule with a pin-hole in the bottom for drainage, standing on an ivory pedestal ; c, c two very stout platinum wires ; d a coil of fine platinum wire. Into the capsule h was placed the camphor, the glass a filled with distilled water was inverted over it and charged with pure nitrogen, to a level marked some- where below the capsule ; the wires w w' are now connected with a voltaic battery of sufficient power fully to ignite the wire d. (46.) After the wire was ignited the volume of the gas gradually increased ; when the original volume was doubled, the gas was examined. It had a strong disagree- able odour, very similar to that of coal-gas ; it burned with a blue flame, slightly tinged with yellow: placed in an eudiometer, such as I formerly described*, and mixed with hydrogen, it underwent no alteration. Two volumes of it, mixed with one volume of oxygen, contracted one-sixth of the whole volume, and subsequently agitated with lime-water, contracted two-sixths more, lining the tube with a crust of carbonate of lime. The residual gas was nitrogen. It was thus clear that the vapour of camphor was decomposed by the ignited wire into carburetted hydrogen and carbonic oxide, and the analogy is too direct to leave any doubt that these gases were also formed in experiments (43.) and (44.) by the influence of the platinum foil and spongy platinum. The apparatus (fig. 4) offers a most convenient means of decomposing volatile hydrocarbons, and possibly other substances. (47.) Portions of oil of Turpentine and of Cassia were now placed in capsules (fig. I), weighed and exposed each to an atmosphere of nitrogen in the large tube of a gas battery, by the same means as described (42.) ; they gave a very decided deflection (the nitrogen representing zinc). This deflection continues, and the liquid is slowly rising in the oxygen tubes, but the rise is too slight at the time of my writing this paper to derive any useful result from examining the present weight-J-. * Philosophical Magazine, August 1841, p. 99, and Philosophical Transactions, 1843, p. 105. t Dec. 1845.— The rise of liquid has been slow but continuous, and the galvanometer feebly deflected. In the Turpentine experiment the rise is =0-7 cubic inch, in the Cassia 0-5 ; the weights, however, from the irregu- larity of absorption and evaporation, give no data as to the equivalent consumption ; thus the Turpentine has lost 0-7 grain, the Cassia gained 005 grain. VOLTAIC ACTION OF PHOSPHORUS, SULPHUR AND HYDROCARBONS. 359 (48.) Alcohol and ether were tried in a similar manner, and produced notable voltaic effects ; alcohol the most powerful probably, on account of its greater solu- bility in water. (49.) The rationale of the action in experiments (43.) and (47.) is curious. It seems that the platinum in the nitrogen tube first decomposes the vapour of the hydro- carbons*, and then the same platinum, with its associated plate, recombines the separated constituents with oxygen. In experiment (43.) the decomposition takes place more quickly than the recomposition, as indeed would be expected from the absence of the resistance of the electrolyte in the former case, and hence the increase of gas in the nitrogen tube. (50.) The analogy of the action of the above volatile substances strengthens the position advanced (38.), that solid phosphorus should be regarded as volatile at ordinary temperatures, and sulphur when fused ; the whole of these experiments also serve to introduce the galvanometer as a new and delicate test, and in some cases a measurer of volatilization. (51.) As the gas battery was shown in the former paper, which I had the honour to communicate to the Society, to give us the power of introducing gases which had been previously untried as voltaic excitants, and to ascertain their electro-chemical relations, it has, by the means detailed in this paper, opened a field for ascertaining the voltaic relations and quantitative electro-chemical combinations of solid and liquid substances, which from their physical characteristics had not hitherto been recognised in lists of the voltaic relations of diff'erent substances, and consequently formed to a certain extent a blank in the chemical theory (may we not now call it law ?) of the voltaic pile. These results, coupled with the previously-arranged tables of electro-chemical relations, and with the great improvements in apparatus for measuring these relations recently made by Mr. Wheatstone and others, offer every promise of the ultimate establishment of accurate measures of affinity. I give the following tables as an approximative list, without attempting to give the degrees of intensity, which can only be filled up by a careful series of reseaiches exclusively devoted to this object. (52.) Chlorine. Bromine. Iodine. Peroxides, Oxygen. Deutoxide of nitrogen. Carbonic acid. Nitrogen. Metals which do not decompose water under ordinary circumstances. ♦ I use this word here and in the title to avoid periphrasis ; it is not quite correct as applied to some of thjese bodies. MDCCCXLV. 3 B Camphor. Essential oils. defiant gas. Ether. Alcohol. Sulphur. Phosphorus. Carbonic oxide. Hydrogen. Metals which decompose water. 360 MR. GROVE ON THE GAS VOLTAIC BATTERY. Though carbonic acid and nitrogen appear to be neutral, and consequently might be bracketed with the metals which do not decompose water, as forming the nodal point or zero of the table, yet, in consequence of the peculiar action exercised by them, and detailed (29.) and (30.), 1 have placed them above the metals*. (53.) The results embodied in my present and my former paper, I think sufficiently indicate the field of research opened by the gas battery, a field which may of course be indefinitely extended. I have never thought of the gas battery as a practical means of generating voltaic power, though in consequence of my earlier researches, which terminated in the nitric acid battery, having had this object in view, I have been deemed by some to have proposed the gas battery for the same purpose ; there is, however, a form of gas battery which I may here describe, which, where continuous intensity or electromotive force is required, but the quantity of electricity is altogether unimportant, appears to me to offer some advantages over any form of battery hitherto constructed, and which, independently of any practical result, is, from circumstances peculiar to the gas battery, not without interest. It is shown at figs. 4 and 5. A A' is a long glass tube, with a series of legs or glass tubes attached to and opening into it ; the lower extremities of these are open, and the main tube or channel A A' terminates at the extremity A in a glass stopper, and at A' opens out into a funnel, as shown in the figure. Into a series of glasses B B' are cemented platinum wires having attached to them strips of platinized platinum foil, two to each glass, the one being four inches long and half an inch wide, the other Ij incli long by one inch wide; the former set are placed lower than the latter, so that when the glasses are filled with liquid the former set shall be just covered, and the latter bisected by the water-rnark ; the last glass B has no platinum. These platinum strips are connected metallically by ex- ternal wires, the narrow platinum of one cell with the wide one of the next, and so on in series. The glasses having been filled to the top of the narrow platinum with acidulated water, let a piece of zinc be placed on a pedestal in the vessel B, and the stopper being out of the extremity A, the apparatus A A' lowered into the glasses, the tubular legs covering each one of the narrow platinum plates. The tubes will of course be full of water, and the main channel full of atmospheric air; this will gradually be displaced by the hydrogen ascending from the zinc, which hydrogen, in consequence of the curve at A, will retain its position. When it is judged that the greater portion of air has been expelled, the stopper at A, covered with a little grease, is to be in- serted ; the hydrogen now will rapidly descend in all the tubes until the zinc is laid bare, and then remain stationary. We have now a gas battery, the terminal wires of which will give the usual vol- taic effects, the atmospheric air supplying an inexhaustible source of oxygen, and the hydrogen being renewed as required by the liquid rising to touch the zinc; by supplying a fresh piece of zinc when necessary, it thus becomes a self-charging battery, * I have been lately much struck with the difficulty of reconciling the theory of Grotthus with many of the combinations in the gas battery, and have stated this difficulty in the Philosophical Magazine for Nov. 1845. VOLTAIC ACTION OF PHOSPHORUS, SULPHUR AND HYDROCARBONS. S61 which will give a continuous current ; no new plates are ever needed, the electrolyte is never saturated, and requires no renewal except the trifling loss from evaporation, which indeed is lessened, if the battery be in action, by the newly composed water. There is an aperture in the pedestal with a moveable slide, through which the vessel B' can be removed, when necessary, to replace the zinc, and the remaining part of the apparatus is never disturbed. This battery would form an elegant substitute for the water battery ; it would much exceed in intensity a similar number of series of that apparatus ; it would be applicable to experiments of slow crystallization and possibly to the telegraph. Its construction is difficult and makes its prime cost expensive, but after that it is the most durable, the most easily charged, and the most free from local action of any known form. I have had one of ten cells constructed, shown at fig. 5, which succeeds perfectly, giving sparks, decomposing water, &c., and is ever ready for use. Any number of such sets might be united by adapter-tubes ; or indeed it would be much more economical, and reduce to a minimum the damage from breakage, to. have the main channels A A' made of varnished wood or porcelain, with apertures into which separate glass tubes might be cemented. London Institution, May 30, 1845. 3 B 2 [ 363 ] XVII. On the Compounds of Tin and Iodine. By Thomas H. Henry, Esq. Communicated hy R. Phillips, Esq.^ F.R.S. Received March 31, — Read June 19, 1845. In a paper by Sii- H. Davy, published in the Philosophical Transactions, 1814, he describes the compound of tin and iodine procured by heating these bodies together, out of the contact of air, as of a deep orange colour, fusible at a moderate heat, and volatile at a higher temperature. The compound obtained by Gay-Lussac, by gently heating tin with twice its weight of iodine, and more recently by Rammelsberg, by the same method*, is described by them as a reddish-brown, transparent substance, yielding a powder of a dirty orange-yellow colour, and easily fusible. A compound of tin and iodine was procured by BouLLAY-f-, by precipitating a solution of protochloride of tin with iodide of potassium, in slight excess. The combinations procured by these methods have been considered to be identical in composition, although the compound procured both by Gay-Lussac and by Ram- melsberg is stated by them to be decomposed by water, while the salt of Boullay is described by him as soluble in water without decomposition. It will be seen, I think, from the following experiments, that the substance procured by heating tin with twice its weight of iodine, is a mixture of two salts, differing in composition, one of which is soluble in water to a slight extent, without suffering decomposition, while the other is immediately decomposed on bringing it in contact with water, the former being the real protiodide described by Boullay, and the latter a biniodide, a salt which has not yet, to my knowledge at least, been described, but which must have been the compound mentioned by Sir H. Davy, as it is of a brilliant orange colour, and sublimes at a temperature of 356° Fahr., while the protiodide, I find, may be heated to redness, out of the contact of air, without subliming. lOOgrs. of tin, in a state of minute division, were mixed with 220 grs. of iodine, the mixture placed in a porcelain crucible well-covered, and sufficient heat being applied to fuse the iodine, violent action immediately took place, accompanied by the evolution of much heat and the sublimation of a portion of the iodine ; when the action had ceased and the crucible had become cool, a brown transparent crystalline mass, weighing 310 grs., was removed from it ; 10 grs. of iodine had been sublimed, therefore, by the heat evolved during the combination ; upon breaking this mass, however, a button of metallic tin, weighing 45 grs., was found inclosed in it. This * Gmelin, Handbuch, vol. iii. f Annales de Chimie, xxxiv. 372, 364 MR. HENRY ON THE COMPOUNDS OF TIN AND IODINE. substance could not be the neutral compound, for the 210 grs. of iodine would require 98 grs. of tin to form the protiodide instead of only 55 grs. The mass was therefore heated again in a Florence flask well-corked, with 45 grs. of tin in very fine powder, to rephice the button removed from it, in order to ascertain whether the neutral compound could be procured by digesting this substance with the metal in a state more favourable to combination. The mass readily fused without any further action on the tin ; but an orange-red sublimate was formed, condensing on the sides of the flask in brilliant acicular crystals. As the mass in the flask dimi- nished in quantity, it became less fusible, until at length it required a degree of heat little short of dull redness to produce that effect, and then it ceased to giv^e off" vapour. The flask was now allowed to cool ; when cold, it was cut, and the fused residue removed, which was found to weigh 86*5 grs. after the separation of 37*5 grs. of tin still uncombined. This substance was of a deep red colour and crystalline texture, affbrding a powder of a bright red colour similar to that of minium ; 50 parts of it were treated with strong nitric acid, which acted violently upon it, expelling iodine and leaving peroxide of tin, which weighed after ignition 22*1 patts = 17-38 metallic tin =34-76 per cent. ; a compound of one equivalent of tin = 59, and one of iodine = 126, would give 31-89 per cent. This excess in the quantity of tin arose from the heat employed in sepa- rating the two compounds, producing a portion of oxide by the decomposition of the protosalt, as will be seen further on. To ascertain the composition of the sublimate, 50 parts of it were decomposed by nitric acid, and gave 122 parts of peroxide = 9597 metal = 19-19 per cent. 100 parts, treated with a solution of pure carbonate of potash in slight excess, were decomposed, carbonic acid being evolved and peroxide of tin precipitated ; the iodide of potassium produced was separated by alcohol, and after dilution with water, was treated with nitrate of silver; the precipitate dried and fused weighed 148-5=79-99 iodine. This gives Theory. Experiment. 2 Iodine =252 81 79-99 1 Tin . = 59 19 19-19 311 100 99-18 It was therefore a biniodidc. In the next experiment, I took one atoni of each substance, viz. 59 grs. of tin and 126 grs. of iodine. The action was violent as before ; there were 16 grs. of tin un- combined, and after the sublimation of the biniodide, the fused protosalt weighed 66 grs. ; this was exposed to the air as little as possible during the process of subli- mation, which being performed in a retort, less oxide was formed in consequence. 50 parts gave 21*1 peroxide of tin =33*2 per cent, metal. In order to ascertain the action of heat upon the protiodide of tin, I prepared some by precipitating a warm concentrated solution of recently prepared protochloride of tin, by a strong solution of iodide of potassium, in slight excess ; the salt formed on cooling in beau- iMR. HENRY ON THE COMPOUNDS OF TIN AND IODINE. 365 tiful acicular crystals, which, after being washed with a little water, lost their lustre by drying at a very gentle heat. 50 parts gave 20*7 parts peroxide =32"36 per cent, tin ; 10 grs. of tliis were heated in a small tube, tightly corked, at first gently, and afterwards to complete fusion ; a little water condensed on the upper part of the tube with a minute portion of binio- dide. When cold the tube was cut, the fused mass removed, and found to have lost \'o gr. ; it was slightly oxidized on the surface, and perfectly resembled the protiodide procured in the former experiments. 25 '3 grs. of the same salt were heated to from 380° to 400° in an open porcelain crucible, a sublimate was produced, which was received in a paper cone, so placed on the crucible as not to prevent the access of air ; when no more vapour was given off, the crucible was cooled and weighed ; the residue was found to weigh 6 04 grs. ; it was ignited, and then weighed 5*91 grs., and was peroxide of tin. The sublimate, which was in small brilliant orange-red crystals, was biniodide of tin ; for 460 grs., decomposed with nitric acid and ignited, gave 1*115 peroxide = 1 906 per cent, of metal. Now, supposing that two atoms of protiodide of tin had been decomposed, giving rise to one atom of periodide, and cme atom of peroxide of tin, 25*3 grs. of protiodide should have left 5*13 grs. of peroxide, which is sufficiently near the quantity obtained to determine the nature of the decomposition. Berzelius states that the proto- fluoride of tin is converted, by the action of the atmosphere, into SnF^, SnO^ ; a decomposition exactly analogous to that above described. I have not succeeded in obtaining a combination of tin and iodine corresponding to the sesquioxide, although Boullay conjectured that some yellow crystals, which he obtained on adding to a solution of protochloride of tin a solution of iodide of potassium, in which an additional half-atom was dissolved, were sesqui-iodide ; the crystals I obtained by this method were found to be pure protiodide. On adding iodine to a solution of protochloride of tin, this salt suffers a remarkable decomposition ; if its solution be concentrated, an iodide of tin is precipitated, and a combination of chloride and iodide of the metal, in definite proportions, remains dis- solved in the solution. If the iodine be added in excess, so that the solution acquires a brown colour, it yields crystals of biniodide on evaporation ; if, on the other hand, the protochloride be in excess, a portion of the protiodide is precipitated, and the re- mainder unites with protochloride of tin, in the proportion of one equivalent of each substance, and it remains dissolved in the solution of protochloride, but may be sepa- rated by evaporation in the form of delicate acicular crystals of a silky lustre, and straw-yellow colour. On adding iodine to an equal weight of protochloride of tin, dissolved in a small quantity of water, I obtained some minute red crystals, which yielded on analysis Per cent. Iodine 79*30 Tin ...... 19-98 99-28 366 MR. HENRY ON THE COMPOUNDS OF TIN AND IODINE. it was the biniodide therefore; with 380 grs. of the protochloride of tin and 150 grs. of iodine, a precipitate was obtained, which was found to yield — Per cent. Iodine 67/8 Tin 31-67 99-45 it was therefore protiodide of tin. The solution remaining after the precipitation of the protiodide was evaporated at a gentle heat, until sufficiently concentrated, and allowed to cool; some crystals were thus obtained which were freed as much as possible from the mother-liquor, by pressure in bibulous paper, but on attempting to purify them for analysis by redis- solving them in water, they were immediately decomposed, giving a scarlet crystal- line precipitate of protiodide of tin, while chloride of tin remained in solution ; they were therefore pressed as dry as possible in bibulous paper, and afterwards retained in vacuo over sulphuric acid for some hours. 10 grs. were then treated with a solution of pure carbonate of potash, evaporated to dryness, redissolved in cold water and separated from the protoxide of tin by fil- tration ; the solution acidulated with nitric acid, and the iodine precipitated by nitrate of palladium while hot, the precipitate washed, dried, and ignited, left 1*94 gr. of metallic palladium =4*586 grs. iodine. The chlorine was afterwards precipitated by nitrate of silver; the precipitate, washed, dried, and fused, weighed 5*22 grs. ; upon dissolving the chloride of silver in ammonia O'l gr. of metallic palladium was sepa- rated, which had subsided with the chloride of silver as a subsalt ; this leaves 5-12 for the true weight of the chloride of silver =1*263 chlorine ; 5 grs. decomposed with nitric acid in excess, evaporated to dryness and ignited, gave 2-68 grs. peroxide of tin =2-108 of metallic tin. This gives in 100 parts — Theory. Per cent. Experiment. One atom chlorine = 35-4 or 1267 12*63 One atom iodine =126 or 45*10 45*86 Two atoms tin. .=118 or 42*23 42*16 279*4 100-00 100-65 It is therefore a compound of one atom of protochloride of tin, and one atom of prot- iodide of tin. The excess in the quantity of iodine in the above analysis, is probably owing to the tendency of the protonitrate of palladium to subside as a basic salt in company with precipitates, which is a great objection to its employment in analysis. As the protochloride of tin is stated by Gmelin*, on the authority of Berzelius, to contain one atom of water of crystallization, while the late Dr. Turner, in the last edition of his Elements, published during his life-f-, states that it contains three atoms * Handbuch, vol. iii. 4^ Edit. y. p. 550. MR. HENRY ON THE COMPOUNDS OF TIN AND IODINE. 367 of water of crystallization, and several works of character do not give the composi- tion of the crystallized salt at all, it became necessary to analyse the salt used in the above experiments ; it was obtained by digesting strong hydrochloric acid with tin in excess at a moderate heat, and when a tolerably concentrated solution was ob- tained, decanting it and setting it aside to crystallize ; the strongly acid mother-liquor was again digested with the tin and took up a fresh portion (it appears impossible to saturate hydrochloric acid with tin at once). The salt was in small prismatic crystals and dissolved in water, after drying on blotting-paper, forming a perfectly clear solu- tion, and producing a great degree of cold ; 700 grs. dissolved in 3oz. of water re- duced the temperature from 58° to 27° Fahr. The crystals were coarsely powdered and pressed as dry as possible in bibulous paper; 25 grs. were dissolved in water acidulated by sulphuric acid, and the tin pre- cipitated by sulphuretted hydrogen, the protosulphuret washed and dried, weighed 17*23 grs. ; 16*2 of these were ignited in a porcelain crucible, and the ignition, repeated with a little carbonate of ammonia, gave 15-6 grs. of peroxide ; this corresponds to 16-59 on the total quantity of sulphuret, which is equivalent to 1309 of metal. The excess of sulphuretted hydrogen was removed by a little sulphate of copper, and the chlorine, precipitated by nitrate of silver, gave 30-94 grs. of fused chloride of silver =7'72 chlorine. To determine the water, 23*58 grains were retained in vacuo over sulphuric acid for twenty-four hours, and were found to have lost 3-87 grains = 16-41 per cent. ; we have therefore — Chlorine . Experiment. . . 30-88 Theory. 31-50 Atom. 1 35-4 Tin . . . . 52-36 52-49 1 59 Water. . . . 16-41 16-01 2 18 99-65 100-00 112-4 The following table contains the principal analytical results of this communica- tion : — Protiodide of tin . . . SnI, solid and fixed, sparingly soluble. Periodide of tin ... Snig, solid, volatile, decomposed by water. Chloriodide of tin . . . SnCl, SnI, solid, fixed, decomposed by water. March 28, 1845. MDCCCXLV. 3 C INDEX TO THE PHILOSOPHICAL TRANSACTIONS FOR THE YEAR 1845. A. Airy (George B., Esq.). On the Laws of the Tides on the Coasts of Ireland, as inferred from an extensive series of observations made in connection with the Ordnance Survey of Ireland, 1. Alkali {vegeto-), an account of the artificial formation of a, 25S. Ammonia, solidification of, 169. ^Afi6p-fl7w.MDCCCXLV^. Flat»IV:p. zffg. ^ofh.I^u^'-u.ccc, del . JiBaszTC'. so. Fig-.S Fig-. 5 o LJ Pfal Tra.rL5m)CrXjyXN~.FljOite Y.p. 3^ fig. 2 iim^ 7ia. 4. Jig-. 6. ,]XBi3.i-!re, \iih.. fl^ . 2 Fuf Phil Tranj MJ) OCCXLVpiat^^n p . 's^i . t'iq 4 Fiff ,i ( Rf^iT hi [fl f\tW\ fi^^^il f: ^^ifTN .1 Ba.<(r^ Li^h I l-J-. ;• '""■'' Q Royal Society of London 4.1 Philosophical LB transactions V.135 Appiied S4. PLEASE DO NOT REMOVE CARDS OR SLIPS FROM THIS POCKET UNIVERSITY OF TORONTO LIBRARY -