Harmonic Tidal Constants for Certain Chinese and New Zealand PortsAuthor(s): Thomas WrightSource: Proceedings of the Royal Society of London. Series A, Containing Papers of aMathematical and Physical Character, Vol. 83, No. 560 (Dec. 10, 1909), pp. 127-130Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/92872 .

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Harm0onic 'itdal Constants, etc. 127

In the table it is 48&65 R.S. + 5 14 G.S. This iildicates that the resulting equations obtained from these researches are trustworthy, and also opens out a method by which the sensatioin curves can be obtained with great facility. The part of the spectrum froin S.S.N. 64 (X 7220) to S.S.N. 48 (X 4720) is -readily obtained by ordinary methods, as is the portion froni S.S.N. 36 (X 5085) to the extreme violet. The most difficult portion is fromi S.S.N. 48 (X 4720) to- S.S.N. 36 (X 5085), and this can be checked by the method incdicated above.

Ihiarmontc Tidcl Constants for certain Chtnese and New Zealand Ports.

By THOMAS WRIGHT, formnerly of the Nautical Almanac Ofice.

(Communicated by Sir George H. Darwin, K.C.B., F.R.S. Received October 19, 1 909.)

Wei-hai-wei (China), FWoosnng (China), Port Chalmers (New Zealand), Port Lyttelton (NAew Zealand), fTellinyton (New Zealand), and Auckland (New Zealand).

The following results have been obtained by the aid of sums placed at mly service by the Governmlent Grant Comimittee of the Royal Society. Constants for ten other ports, obtained by similar grants, are given in vol. 71, pp. 91-96 of the 'Roy. Soc. Proc.' The observations were redoced by the mlethods described by Sir George H. Darwin in vol. 48, pp. 277-340, and vol. 52, pp. 345-389.

The observations made at Woosung, Wellington, and Aucklanid were the times and heights of high and low water: those for the first port referred to the year 1902; those for the second to the year 1901 ; and those for the third to a period of twelve mnonths, beginning on May 1, 1900. The observations at Port Clhalimiers, Port Lyttelton, and Wei-hai-wei were hourly heights read off fronm automatic records. Those for Port Chalmers referred to the year 1901 ; those for Port Lyttelton to a period of nine months, beginining on October 1, 1901; and those for Wei-hai-wei to a period of seven months, beginning on July 8, 1898.

In dealing with observations of high and low water, the year's observations were divided into four groups of about three months each. Four separate determinations of each tide were made, and a final evaluation obtainied from the means of the four values of H sini K and H cos K. In the case of Woosung

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128 MNr. T. Wright. Harmnonc 'T'dal CJonstants fo?- [Oct. 19,

Port i Port Chalmers Lyttelton iWei-hai-wei Woosung Welgtn Acad

(Nqew (New (Chinia), (China), (e (e Zealand), Zealand), ~~~~~~~~Zealand), Zealand), 1901. 1901-2. 1898-9. 1902. 1901. 1900-1.

Latitude ...... 45 558S. 43 358S. 37 29N. 31 21 N. 41 -178S. 36 508S. Longitude..... 170 82KE 172 49KE 122 13KE 121 30 E. 174 46KE 174 49 E.

ft. ft. ft. ft, ft. ft. A0,...........~ ' 248 2 '945 5'5 6 '553 37 '4 5 '871

811 .... 0'074 0 023 0 '067 I 90 272 259

.... 0'239 0 '137 0,588 0,922 0 108 0.633 .. 107 145 5 75 308 266

8 ..[.. 0 007 0'011 0 002-- ....1335 239 311

1f1{0'003 0 '015 0 '001 . ...344 337 302

ixfH . 0 009 0 .005 0'021 --

..jc .... 165 321 289 ....11 .. 2 '358 2'-777 1,998 2 299 1 702 3'826

ii:2 ....I 104 121 297 34I 123 205 ..f1 . 0'018 0 009 0,028

113 .... 142 247 191- M H ... 0.036 0'036 0 063

-k1 K.....316 182 173 H .. 0,047 0'014 0'019 _-- M ...... 340 47 261

fH .. 0 087 0 '129 0,443 0 212 0 -121 .. 54 46 262 145 194l ~~ ff1 ~~~0 089 0'-144 01706 0,358 0 '071 0 '265

L ... 79 74 36 211 2,75 169 ...... *0'448 0'251 0 029 1 0 '172 ....... ~~~0 75 308 266

* * ~~~~~~ ~~0 197 0 '118 0 '023 18 ...... ~~~313 211 275 169

sf11,..... ~0'005 0 '051 0 '048- > ...... 163 126 11i

.. 034 0067 0'068 .... 69 16 252-

..1... 0'116 0,067 0.114 0 '164 .... 67 104 344 ~ .196

..... 0 '535 0 615 0'033 0 288 0' 449 0 -78 .... 84 89 249 15 83 175

[11 ... 0,175 0'182 0 '136 v ~~50 87 267

[H .... 0-047 0'121 018 IA ..... 64 42 66 T- ... 0,024 K .... 63 . .0016 -

302

.9 92 129 271--

28M{~~~' "1 ~ 0'060 0 '060 0'.029- IC 169 25 226 Ti 0'100_

I. 32 -

0 142 IC .. 2281 .... 0'081I _ K 31- I

SarHj.. 0'-123 0.135 040 0'801 0 '073 0 '354 8a4IC ...... 341 312 149 143 295 139

Sa ...... 0 157 -- 0 096 0 '204 0'224 seK ...... 117 68 212 1242

NOrEm-A - indicates that the -valuLe of the tide was, not determnined. Ani * indicates that there is rea-son to believe that the determinationi of the tide is so i.Mperfect that it is better to neglect it.

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1909.] certain Chinese and New Zealand Ports. 129

and Wellington the values of the L tide, and in the case of Auckland the values of the 0 tide, as determined from the four quarters' observations, differed widely, both in phlase and in height. Inasmuch, however, as the heights of these tides were snmall, it has beenl thought best to reject them. In the case of Port Chalmuers and Port Lyttelton the difference of phase between the S2 and K2 and the K, and P tides suggested imrlperfect evaluationi, probably due to the small height of the K2 and P tides at these ports. The values determined for these two tides have therefore been rejected also.

The constants have been tested by computinig from them heights of water at certain times covered by the periods of the observations, and comparing the computed with the observed heights. Except in the case of Port Lyttelton this test has proved satisfactory. For Port Lyttelton the result is not so good as could be wished, for although the curve derived from the constants agrees in general form with the observed curve, the difference both in phase and in height is far greater than in the case of the other five ports. With the view of investigating this point, the height of water has been comnputed at intervals of two hours oni four days and the results plotted side by side with the observed heights. In the curve for February 3, 1902, the coumputed curve agreed well in form with actuality, biit was systematically too low by 5 or 6 inches. On March 16, 1902, the agreemnent was close, except at high water, when there was a deficien'cy of height of about 5 inches. On April 27, 1902, the agreement was good, save that the computed tides occurred later in some parts to the extent of nearly half anl hour. The worst of these comparisons is that for November 11, 1901, which is exhibited in the form of a diagrami hebewith, the firm line indicating actuality and tlhie dotted

F ? E T

6 / .1. ,.M, ."_

4- - 9

-1 _ __ r -

> __ 4

3

0

I ______ ' X X--

0 2 4 6 8 10 12 14 16. ' s 20 22 HOURS

VTOL. LXXXIII.-A.

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130 P0rof. Hill and Dr. Sirkar. Elect,ric C(Admctivitty [Juine 4,

line tlhe computation. The comparisoni, thlerefore, sugg"ests that whlile predictiolls based on the constants for Port Lytteltoni may be relie(l uiponi to shiow the general formn of thie tide, soimei' sm(all allowance imiust be Ilade as regnar-ds the predicted timi-e and height of high or low water.

h'lie observatioins at W"lei-lhai-wei were a record kept by the officer in charge of H.M.S. " Waterwitclh "; these observations, as well as those for the four New Zealand ports, were kindly supplied to me by the late hydrographer, Admiral Sir W. J. L. Wlarton. The Woosunig observatioins were kindly furnislhed by H. Edgar Hobson, Esq.., of the Custom Hiiouse, Slhanglhai. I am also indebtecl to Sir Georg,e Hr. Darwin for the loan of hiis apparatuis for reducing observationis of hourlly heighlts. Tlhe calculations were inade by Mr. F. Finch.

The Electric Conductivity and Density of Solutions of Ihydrogen Flulor ide.

By Prof. E. G. HTILL, 1).SC., Muil Colleg,e, Allalhabad, an(d Dr. A. P'. SIRKAR,

Mluir College, Allahabad.

(Commuinicated by Prof. H. A. Mliers, F.R.S. Rcec'ived Junie 4,-Read November 25, 1909.)

The only mileasuremiients of the electric condtuctivity of lhydrogen fluoride which lhave been recorded appear to be those of Ostwald.* These were mrnade at low concentrations, of wlhiel the] higchest was 0 5 per cenit. The T)resent work was unidertakeii witlh a view to obtainhig figutires for the electric conductivity of all concentrationis up to the anhydrouis acid, anid (l1so for checking Ostwald's figures.

1in the courseG of the work it also b)ec(aine necess(ary to (leterilimn(e the denisity of hydrogen flutoride for all concentrltions.

PrY epa1rat<ion of Anhydrous iR do(gqe 1Yiutoride. 1Yhe mcietlho(1 a(lopte(1 was that of heatinig potassiumli hydrogen fluoride, whlichl (l h )een heated at 1000 for 1-4 lours arl(l was tlheni drie(l inl VUCiO over stroncg rsulphuric aci(d for five or six (lays. The apparatus emiployed diffeired sli(glitly fromn that used by Gore. It consisted of a )latillulm bottle of 25)0 cc.. capacity, in the neck of wlhich was ground a benit platiniumIi condenising tube 500 mmn. lolng, arid 10 mm. diameter. This condeniser consisted of two palrts, wlichli were ground

* T ab1iysika1isch-(1ieruisc1ie 1'abellen,' Lail(dolt-BWollstein, ed. 1905.

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