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" • The inyestisation of the time data of the Oharleston oortib- qnake havinc been completed and a final raralt being reached, it is deemea proper, with the consent of the Director of the Oeoloffical Snrvey, to publish a brief abstract of the discossion. The foU disdunon will i^pear in the final report upon the earthqoaike, whidi re|x>rt is now well adTanoed towwd com- pletion. Immediately after the earthquake all practicable measures were taken to collect infwmation, and specul effort was directed to obtaininff the hurgeitt unount of tune data. Throuffh the courtesy of tiie AsMdated Press, notices were publisned in newly all tiie newvpapers of the country requesting those who had made such obeervations to forward ti&em to the Director of the Oeolog^l Surrey. Many per mis did so. The Ohief Sigmd Offico* iiBstmoted the observers ut that bureau who had noted the time of the diook to report it, and he forwarded all suo^ reports to the survey. The Western Union TdeoratA Oo. instructed its operators to forward reports and rimibr in- structions were sent bv the Lightbonse Board to light-keepers. Spedbl effort was made to secure newspapers from as many localities as poestbki Most of th e leaaing papers of the Ax. Jooa. Sot'-TuM* inns, Tok XXX7, Ha SOC— lutn liM '' ^f^t !-M!i^ ^"^''^--''''''ri 'i i i li--iBi.tiwgfe-^\':.w. !^ ^--•5^^^?™- - " ■j^wJTviwV-rH^nvifai* ■>t'^3ri->> Newcomh and Dution — Speed of > country have an agent or reporter at Washington and he usually keeps a file of the paper he serves. The library of Congress keeps files of two or more papers from every State. As many of tnese as practicable were thoroughly examined. Many local papers were requested to fumitu copies of their issues ot Sept. 1st, 2d and 3d, and most of them complied. Many marked copies of papers were sent to the survey from unexpected sources. Altogether more than four hundred time reports were gathered. As might be expected a portion of these were useless. Ini order that it may be apparent which were selected for considera- tion and which rejected, the following account is given. There were about thirty which stated that the shock occurred " about 10 o'clock " or " a few minutes before 10." As a single min- ute is a very important quantity here, all such reports were summarily rejectea as too mdefinite. The reports from light- houses in most cases proved unavailable. These structures being situated most frequently where access to standard time is difficult, their clocks are regulated by the sun and an almanac. The uncertainties of this method of time keeping were evidently too great to justify any attempt to utilize them. But a few lighthouses keep standard time and in all such cases their reports were admitted to consideration. There were a few (nine or ten) which gave times so widely aberrant, difFering by a quarter to half an hour from the great mass of records, that they were rejected. The whole number which received preliminary consideration was 316, many of which it was expected would also be rejected after a more thorough examination, due cause being assigned. These 316 observa- tions were catalogued in alphabetical order, the latitudes and longitudes of the localities being roughly ascertained and also their distance from the centrum. By far the most important time determination is that of the centrum, which was computed to be about six seconds earlier than that of Charleston. The time at Charleston is derived as foUowa Among the numberless clocks stopped in that city by the earthquake, there were four which had compensated seconds pendulums and second hands and were of the pattern generally classed as " jewelers' regulators." All were conipared daily with the time signal of the Western Union Telegraph Co., and the testimony is positive that none of them had errors on August 31st exceeding nine seconds, while the mean probable error of the four was certainly much less than this. The first was the regulator of James Allan & Co., Jewelers, No. 285 King street. It was regulated by means of a " sounder," which was daily put into circuit with tne Western Union time signal wire. The clock was corrected only when its error exceeded ONI or^ la twin e usually Congress As many any local OT Sept. marked expected 5 reports less. In lonsidera- . There d " about [igle min* orts were >m light- tructnres iard time and an ! keeping ;o utilize ad in all I. There aberrant, ,t mass of er which which it thorough i observa- ^udes and and also lat of the ids earlier lerived as that city le jMittem compared ^ph Co., errors on I probable The first 3, No. 286 sr," which ime signal exceeded W^ Propagation of the Vharkston EaHhquake. 3 nine seconds. Mr. Allan is authority for the statement that its reading -next morning was 9:51 exactly. He had received the time signal on August 81st, but as the clock was within the limit of tolerance he did not correct it. Subject to this limit he had no knowledge of the exact error of his clock and his memory on this point did not serve him The second clock was the regulator which controls the time of the North Eastern Railway. This clock was compared with the time signal on August 3 1st, but was not corrected, its error being within the limit of tolerance, which was eight seconds. It had been reset two days previously. Its reading was 9:51:15. It was stopped by the point of the pendulum catching behind the metallic arc in front of which it properly vibrates. The third clock was that which regulates the time of the Charleston & Savannah Railroad. It had been reset two days previously and compared with the time signal on August Slst, and was within the limit of tolerance, eight seconds. Its reading was 9:51:16 and it was stopped in the same manner as the preceding one. The fourth clock was that of the South Carolina Railroad. It had been reset by the daily time signal on the day of the earthquake. Its reading was 9:51:48. Although these records range through an interval of 48 seconds they may be reconciled. The azimuths of the planes of oscillation of their pendulums were as follows : James Allan & Co's N. 85° E. North Eastern Railroad N. 40» E. Charleston & Savannah Railroad N. 66° E. South Carolina Railroad N. 30° W. These azimuths may be put into relation with what is now known concerning the varying phases of the shocks, their respective durations and directions of vibratory motion. The earthquake at Charleston began as a light tremor, steadily in- creasing in power through an interval estimated to be fron^ 10 to 15 seconds' duration ; then suddenly or by swift degrees it swelled into the full power of the first maximum, then sub- sided to a minimum, then swelled suddenly to a second maxi- mum and lastly died away gradually. The interval from the beginning of the first maximum to the close of the second maximum is estimated at from 35 to 65 seconds ; the subsid- ing tremors are estimated at about 6 to 8 seconds : the total duration from 66 to 75 seconds. It may be exptreseed graphi- cally by the following curve in which the abscissas represent time and the ordinates an arbitrary scale of intensity. In the first maximum the waves were mainly normal and came from N. 30° W. In the second maximum the direction of vibration was abtfut at right angles with the foregoing or f\r'J Ji:•^^^ 4 Newcomb and Dutton — Speed of about N. 60° E. It Mrill now be Been that the planes of oscil- lation of the first three clocks made wide angles with the di- rection of motion of the first maximum, while the plane of the fourth clock was almost exactly parallel with that direction and perpendicular to the direction of motion of the second max- imum. The fourth clock, then, may easily have escaped arrest thSlm Mm to* Sim SOi 51m aoi 51m M Bim lOi aim until the second maximum while the other three would have little chance of escaping the first maximum, even if they did not stop during the lighter preliminary tremors. That the sec- ond and third clocks stopped during the first maximum is ren- dered probable by the way in which their pendulums were caught. It would require a considerable acceleration in a di- rection perpendicular to their planes of oscillation and at times when the pendulums were near the extremities of their arcs of vibration in order to throw their bobs far enough backward to catch in the manner they did. These two clocks are relied upon as giving the time of the first maximum. The chances are, however, that the pendulums were not caught in this par- ticular way during the first three or four oscillations, but went staggering along for a very few beats until finally caught. An interval of three or four seconds was probably occupied in the rapid swelling of the quake from the preliminary milder phase into the full power of the maximum. If we assume for the beginning of the first maximum an instant of time about three or four seconds earlier than that indicated by the two railroad clocks, i. e. 9:51:12, our actual error, it is believed will not exceed four seconds. The clock of James Allan & Co. prob- ably stopped at a slightly earlier phase. If it may be assnmed to have oeen six or eight seconds slow, its stopping would have been easily possible at that phase; for many less sensitive clocks throughout the country were arrested by tremors no more forcible than those in Charleston at the particular phase thus indicated. We shall reach the same result, 9:51:12, if we throw out the fourth clock as relating to the second maxi- mum end (giving the weight 2 to both the second and third clocks and tiie weight 1 to the first) take the mean readings of the three. The whole tenor of the evidence from other clocks in Charleston points strongly to a time a few seconds later than 9:51 for the first maximum. It is plainly necessary to select some phase of the earthquake in Charleston or at the centmm as the oeginning, with which the beginning in all other places must be compared. It must % Propagation of the Charleaton Earthquahe. 8 plainly be a phase at which the shocks had very great power, sufficient to make themselves felt hundreds of miles away. This phase should obviously be that which han Ijeen called the beginning of the first maximum. It still remains to find the corresponding time at the centrum. As the speed of propaga- tion is now known to have been in the neighoorhood of three miles a second and as the distance of Charleston from the theoretic centrum is 20 miles, the subtraction for the time at the centrum is taken to be six seconds, making the time of be- ginning at that point 9:51:06 standard time of the 75th meridian. The full catalogue was next examined in order to ascertain what reports should be finally rejected. In the final report this catalogue will be published, together with a list of the rejected observations showing the grounds of rejection. For present purposes a summary view of these reports is given, showing the number of observations correspondmg to specific minutes or falling betweeen consecutive minutes. Table showing the numbers of reports corresponding to specified minutes or falling between consecutive minutes. 9:47 and seconds 1 9:48 -- 3 9:50 82 9:51 6 9:51 and seconds 6 9:62 26 9:52 and seconds 9 9:53 28 9:53 and seconds ^6 >-:54 31 9:64 and seconds 9 9:55 f6 9:65 and seconds 8 9:66 21 9:66 and seconds 2 9:67 9:58 9:58 and seconds • 9:39 10:00 13 10:01 2 10:02 -. 1 Total . 316 There are thus four reports giving times earlier than 9:50 and three later than 10 o'clock. The synopsis illustrates well the tendency of people to give time in terms which are multiples 6 NevBComh and Dntton — Speed of of five minutes. Thus we have 32 giving 9:50, but none giv- ing 9:49, and only six giving 9:51. There are 13 giving 10 o'clock and tliere would have been many more of them if the catalogue had included those which stated the time as being "about" 10 o'clock or "near" 10 o'clock. There are 8fi, or more than one fourth the whole number, which give 9:56. Every one of the 9:50 reports is rejected. It is certain that they all involve errors greater than one minute too early, and the large number of them would introduce a large systematic error into the mean ; and as there is no apparent reason for re- jecting or keeping one observation rather than another, all of them are thrown out. All of the 10 o'clock observations are thrown out. For, upon further examination, all giving 9:58 and seconds, 9:59, 10:01 and 1():02 will be rejected on their merits. This would leave the 10 o'clock reports as an isolated group in an otherwise comparatively orderly series, and its eflfect would be to introduce an error of unknown magnitude and of anoma- lous character. In dealing with those giving 9:55 there is more difficulty. The following course has been adopted. Wherever a report states clearly, or raises a strong presump- tion, that this was really the nearest minute observed, to the exclusion of any other, it is accepted if otherwise unobjection- able. Where this evidence is wanting the report is rejected. It is quite probable that some thus rejected are very good ob- servations ; but it is clearly better to reject many possiblv good observations (provided a sufficient number remain) than to admit a few bad ones with the certainty of introducing an un- known error. The number of 9:65 reports thus rejected is 43, which happens to be just one half. Still otner ol)servations are rejected on their merits. A ma- jority of these are thrown out for what are presumed to be large xmexplained errors. There are 29 of them, of which 15 are rejected for being two minutes or more too early and 14 for being as much, or more than as much, too late, when com- pared with a larger number of much better observations in the same locality or in the immediately surrounding region. The rejection of these 29 observations does not greatly affect the deduced speed, but it does diminish notably the computed probable error. The total number rejected for all causes is 130 and the number accepted is 186. These have been sepa- rated into four groups, each containing data which are consid- ered to be as nearly nomogeneons as possible ; that is to say, in each group the observations are presumed to have the same sources of error, whether accidental or systematic. The first group is required to fulfill the following condi- tions : (1) The report must specify the beginning, or the time when the tremors first became sensible. (2) It must give not Propagation of the Charleston Eart/ujuake. [none jfiv- ving 10 ui it the R8 being |ire 80, or ve 9:65. rtain that early, and iystematic on for re- ler, all of ations are g 9:58 and eir merits. 1 group iu feet would of anotna- )5 there is adopted. presnmp- ired, to the lobjection- s rejected. ygood ob- sBibly good in) than to »ng an nn- ected is 43, ts. A ma- imed to be : which 15 rly and 14 when com- tions in the gion. The affect the I computed II causes is been sepa- are consid- is to say, in ) the same xring condi- or the time it give not only the minutes, 'but also the seconds, with an uncertainty not exceeding 15 seconds. (3) It must have been obtained from a clock kept running with accuracy upon standard time or equally reliable local time, or fronj a clock or watch compared with such time within a few hours of the occurrence. There are five observations besides that of Charleston which meet these re(|uirements. The second group will consist of those which fulfill the same conditions as the first, except that they will be refjuirud to give only the mincte or half minute nearest to the begiiming. There are eleven which answer to these requirements. The third group will include all that reiuaiu after taking out groups I, II, and the 6toppe4 i E. C. Simpson. N. J. 622 54 G. W. Holstein. N. Y. 646 64 30 N. Y. Herald. Mass. 765 66 i J. 0. Jacot. N. Y. 770 £6 1 W. G. Tucker. Propagation of the Charleston Earthquake. uto temiB. I from the ant with a IB tliroe or in with tlie iibly exact. . For tlie B are hero larthquake. ObMiTcr. . Newcorab . McAdie. landolph. ). Whitney. 8 Hughes. f condition From these wo may form the following equations. »DB are: 109 dt Ol! S205 ± 168 ning to the . Leonard. Brookshaw. ,. Goodwin. i. Norton. . Line. [. Tower. '. Simpson. V. Holstein. r. Herald. . Jacot. 3. Tucker. Weight. RcildnMli « -f Of/ = 2 - 1-6 X -j- 438»/ = 144 1 - 9-8 X + 4H8v =: 165 1 — 6-3 X + 49(\v = 144 1 + 6-3 X + fi4Sy = 174 1 — 06 X + 604.y = 174 2 -fll-6 X 4- 620.»/ = 174 i + 16'6 X + tt22y = 174 1 -I-17-2 X -f 646.V = 204 1 - 6-6 X + 76fty = 294 i -68-4 X + 770y = 234 1 + 31 The normal equations are : 12 « + 6898-5 y = 1811. 6898-6a; -f- 3677366-6 y = 1100677. The solution gives x= - 1-6b. db 7'7b. y = 0'31 ± 0-014s. The resulting speed is, 8-226 ± 0147 miles or 6192 ± 236 meters per second. Group III consists, of reports which fail to give either the means of judging of the comparative accuracy of docks and watches or of determining to what phase the observation re- fers. Many and indeed the majority of them are defective in both of these respects. Quite probably some of them are good observations but fail to give the evidence of it. So far as errors of clocks and watches are concerned the errors nky be considered as belonging to the accidental class. But all errors as to the phase must be systematic. That some of them refer to more or less advanced phases Ib certain, and it becomes difficult to determine how many of them do so, and how great is the average tardiness. It is obvious that the effect of all such errors is to make the time too late and the resulting speed too slow. The general indications are, however, that this system- atic error is not a large one. By comparing miscellaneous reports from those cities which have also given better verified repoits belonging to groups I and II there seems to be a ten- dency of the averaf^e value of this error to fall between one- tenth and one-twentieth of the mean value of the time-interval. In discussing this group it seems unnecessary to go to the length of formulating a hundred equations of condition, and an equally good result or even a better one may be obtained by the following moi-e summary process. We may take them in sets, the first of which shall comprise all times within 200 miles of the centrum, the second set all between 200 and 800 miles, the third all between 800 and 400 miles, and so on lutil the last. 10 Newcomh and Dutton — Speed of which shall compriee all beyond 800 miles. In each set we may then take the weighted arithmetic means of the times and dis- tances as if they were single observations. Gboup III. — List o/'126 miscellaneous Time Reports. Locality. state. Dlstnnce. Time. W't. BemarkB. Statesburg, ao. 80 51 "SO* I Coluin1)ia, S.O. 89 52 1 SaTunnnh, Ga. 89 61 63 2 mean of 3 ohs. Augusta, Ga. ill 61 30 2 mean of 2 obs. Laurinburg, N. C. 135 51 I Dnrien, Ga. 138 52 30 1 Brunswick, Ga. 165 62 I Macon, 6a. 203 52 1 Jacksonville, Fla. 211 52 2 mean of 3 obs. Fernandina, Fla. 225 63 ] Olustee, Fla. 355 53 1 Palatka, Fla. 255 53 1 Thtimasjville, Ga. 273 62 20 1 Wytheville, Va. 284 62 27 1 Knoxvillo, Teun. 302 54 J Zellwood, Fla. 80t> 53 1 Chattanooga, Tenn. 329 63 1 Norfolk, Va. 349 54 1 University, Ala. 363 52 1 Ashland, Va. 367 62 1 Shelby Iron Works, Ala. 377 5t 1 Catiettsburg, Ky. 406 52 30 1 mean of 2 obs. Pungoteague, Va. 410 53 1 Decatur, Ala. 412 63 ] Iron ton, 0. 414 56 1 Nashville, Tenn. 438 54 30 ] WHshinjrton, D. C. 452 63 41 'a : mean of 4 obs. Louisville, Ky. 486 64 38 1 mean of 2 obs. Baltimore, Mi 487 53 1 Dayton, Ky. 487 54 11 1 Newport, Ky. 488 53 21 Cincinnati, 0. 491 63 41 ' V mean of 6 obs. Lancaster, 0. 491 54 Wyoming, 0. 601 63 41 ColumbuB, 0. 513 63 41 ! mean of 4 obs. HamUtoo, 0. 513 64 11 Paris, Tenn. 620 66 Pittsburg, Pa. 626 64 30 I mean of 2 obs. Brookville, •Ind 626 63 New Philadelphia, 0. 632 64 Sewickly, Pa. 536 64 Mt. Vernon, 0. 636 66 Wellsville, 0. 538 66 Oxford, MiBB. 548 66 Paducah, Ky. 668 62 16 Philadelphia, Pa. 566 63 Burlingto::, N.J. 634 63 Indianapolis, Ind. 584 65 i mean of 3 obs Cairo, ni. 588 63 Titusville, Fa. 6U8 66 Helena, Ark. 609 65 Toledo, 0. 657 66 Newark, N.J. 640 53 Jamestown, N. T. 642 66 Propagation of the Charleston Earthquake. 11 let we may )8 and dis- forta. rk*. 1 obs. 2 obs. t obs. i oba. 1 obs. i obs. Sobs. 4 obs. 2 obs. 3 obs. Remarks, moan of 4 good obs. mean of 10 obs. mean of 6 oba. mean of 2 obs.- mean of 2 good obs. Locality. State. Distance. Time. W't. Brooklyn. N. Y. 643 54'>'30' 3 New York, N. Y. 646 64 12 6 Haokensack, N.J. 664 54 Warwick, N. Y. 661 56 Oowanda, N. Y. 666 66 Detroit, Mich. 675 56 12 Valparaiso, Ind. 705 53 London, Ont. 706 56 Peoria, 111. 710 55 New Haven, Conn. 711 56 30 Port Huron, Mich. 712 66 Hudson, N. Y. 747 57 Hartford, Conn. 747 54 46 Stuyvesant, N. Y. 760 57 East Saginaw, Mich. 766 68 Albany, N. Y. 770 56 40 Fonda, N. Y. 776 65 Saratoga, N. Y. 797 53 Greenfield, Mass. 799 66 Keokuk, Iowa. 810 56 2 2 obs. Dighton, Mass. 812 56 Davenport, la. 827 55 r^e Placid. N. Y. 827 66 Jamaica Plain, Mass. 828 57 Blue Mt. Lake, N. Y. 830 56 Bellows Falls, Vt. 832 63 Boston, Mass. 832 55 30 12 obs. Dubuque, la. ■ 878 57 Prairie du Chien, Wis. 924 66 30 , Taking these in groaps in the manner just indicated we have: WelBht. Residuals. Centrum « + Oy = 2 + 406 Oto 155 X + 11 '.y = 3» ® 203 to 284 X + 240y =84 8 302 to 377 X + 342y = 122 7 405 to 491 X 4- 462y = 158 16 601 to 588 X -h 642y = 184 18 608 to 675 X + 647y = 217 20 705 to 799 X -f 744y = 255 15 810 to 924 X 4- 8:{7y = 278 11 1-90 — -28 — 4-43 — -60 — -05 + 1-80 — 4-00 + 3-85 The normal equations are : 10635 + 65768y = 18940. 66768a! + 34474772.y = 11668675. The solntion give^ » =+ 4-06 ± IT seconds, y = 0-3319 ± 0-0039. The resulting speed is, 3-013 ± 0-027 miles or 4848 ± 43 metres per second. To this result some correction must be applied for the systematic error, which, as already stated, there is reason to believe probably lies between one-tenth and one-twentieth of the mean time-interval and therefore of the speed. Suppose it be taken at one-lifteenth of the amount, with a probable error of one third of the correction. This -.•«|liM*Mpk 12 Newcomh and DntUm — Speed of : 0-072 miles or 5171 would make the corrected result 3 '2 14 d= 116 metres per second. Stopped Clocks. It is natural to suppose that if a clock were stopped by an earthquake and if its error at the time were known it would give the best possible record of the time of advent of the shock. An examination of the time reports of this earthauake, how- ever, strongly contradicts this conclusion. A clock may stop at almost any phase of the disturbance. A sensitive one may pass tlirough an earthquake of considerable violence and not stop at all. A jeweler's clock in Charleston was found goinff the next morning, and when the telegraph wires were re-opened its error was found to be small, showm^ that its escapement had missed very few beats, if any. Clocks in Columbia, Savannah, Augusta and Wilmington, 'N. C, in many cases kept gomg Inquiry at Wilmington elicited the reply that no iewelers clocks had been stopped. Several reports describe clocks whose rates are satisfactorily vouched for but whose times can be ac- counted for only upon the theory that they were stopped by the second powerful shock, which was felt at Charleston about five minutes after the principal one, e. g.y Branchville, S. C., Augusta, Rome, Ga., Cape Canaveral, Camden, Ala., Memphis, Tenn. There are some cities where the time of beginning is well established by independent observation and which also reh port stopped clocks. In every such case the time of the stopj^d clock is much later. Thus at Nashville the time of beginniM was noted by a clock which continued going for 42 seconds and then stopped. Similar means of comparison come from Cincinnati, Covington, Ky., Pittsburg, Newark, N. J., Brooklyn and New York. And in general wherever stopped clocks can be compared with really good personal observations theymvan- ably show a later time and usually a much later one. The dif- ference is plainly due to the fact that it generally takes a con- sideK3,ble time and an accumulation of the effects of the vibra- tions of the building upon the pendulum to stop a clock. An attempt has been maae to evaluate this difference by taking those cases where a comparison can be made between the read- ings of stopped clocks and independent detenninations of the times of the beginning in the same locality. liOOalttr. Nashville, Covington, Cincinnati, Pittsburg, Brooklyn, New York, State. Tenn. O. P». N. Y. N. Y. Intenrali by penoDftl o^•. Beoondi. 144 ■toi InterrsU bj ipped cIocKR. Becondt. 155 155 174 204 204 Mean ratio, 186 235 106 284 284 249 BatlM. Welghta. 1-29 2 1 1 1 1 1 1 52 '26 34 •15 •22 •28 1 2 1 1 2 es or 6171 ped by an rn it would the shock, nake, how- may stop one may ce and not )und goinj e re-openei pement had , Savannah, kept going, ao jewelers' locKS whose 9 can be ac- stopped by eston about iville, S. a, ., Memphis, )eginning is nich also ra- the stop^d if beginnmg 42 seconds come from r., Brooklyn [ docks can they invari- 8. The dif- lakes a con- if the vibra- clock. An e by taking len the rea£ .tioBs of the Ratio*. 1-29 1-52 1*26 1-34 1'15 1-22 1-28 WeicfaU. 2 1 2 I 1 2 Propagation of the Charleston Earthquake. 13 In the above table the comparison at Cincinnati takes account only of a single clock, whose error happened to be known ex- actly. The time of beginning in that city is also known with exceptional certainty and accuracy. It will not differ more than eight or ten seconds from 9h. 1 6m. (Cincinnati local mean time or 9h. 58m. 41s.). If we consider Cincinnati and suburban towns within fifteen miles of the city which are supplied with local time from the Cincinnati observatory, we have no less than twenty-two time reports, of which nine are stopped clocks. Two personal observations giving 9:15 local have been rejected because they are multiples ot five. One report giving 9:17:45 has been rejected because its author, be- siaes indicating that it refers to an advanced phase, throws doubt on his own observation. Of the remaining ten personal observations one gives 9:15:40, eight give 9:16, and one gives 9:16:80. Of the stopped clocks, three were in the centr^ of- fice of the Western tjnion Telegraph Co. They kept standard time and were read only to the nearest minute. AU three are reported to have stopped at 9:54. The clock in the fire tower is the one whose error was known. Its corrected reading was 9:16:40. The remaining docks gave (9:16). (9:16), (9:17), (9: 17:20), and (9:19). Four of the latter were irom the suburban town of Lockland Reducing to standard time and taking their mean, the ratio of the time-interval by stopped clocks to that by personal observation is 1.26, a result identical with that de- rived from the clock in the fire tower alone and nearly the same as that in the tabla There is reason to believe, however, that this ratio is a little too great for the mean of stopped docks throughout the entire country, and especially so for those of very distant localities ; for if the ratio were uniform, the absolute differences between the two kinds of data would be very wide in remote regions and small near the centrum. This is not the case. The absolute differences at very remote localities are very little, if any, greater than those at the middle distances. This difficulty prevents us from assigning any spedfic value to the correction and from determining its prob- able error. iNeverthelees the comparisons just made inaicate that the systematic error is probably of such magnitude that, if due allowance were made tor it, tne corrected result for the topped docks would not differ much from those of the i>re- cedinf^ groupa While this group furnishes evidence which strongly supports the approximate correctness of the results of the other turee it cannot be a source of greater precision nor can it famish the means of reducing the final probable error. 14 Newcmnh and Dutton — Speed of LOCKlltf. Centrum, Charleston, Columbia, Savannah, Langley, Au}!U8ta, Cochran, Macon, Jacksonville, Atlanta, Catlettsbarg, Nashville, Columbus, Covington, Cincinnati, Cincinnati, Meridian, Locktand, Havre de Grace, Pittsbnrg, Newcastle, Atlantic City, Wooster, Newcastle, Indianapolis, Memphis, Cairo, Meadville, Newark, Brooklyn, New York, Ithaca, Manistee, Gboup IV, SUte. s. c. S. C. s. c. 6a. s. c. Ga. Ga. Ga. Fla. Ga. Kv. Tenn. Miss. o. o. Miss. O. Md. Pa. Del. N. J. O. Pa. Ind. Tenn. III. Pa. N. J. N.Y. N. Y. N.Y. Mich. — Stofiped Clocks. DUtftnce. 20 89 89 103 111 192 203 211 252 405 438 481 488 491 491 600 506 515 526 538 552 558 565 581 687 588 «)08 640 643 645 696 866 Time, 61 '"06' 51 12 51 51 56 53 52 52 51 30 52 62 22 63 54 12 66 55 64 64 21 54 64 26 56 65 54 54 55 46 55 55 54 50 53 55 65 68 66 16 56 67 No. of clocks. 4 2 2 1 1 2 1 1 4 I 1 1 1 3 1 1 4 1 1 1 1 1 1 i 6 1 1 1 1 2 1 1 wt. 3 2 2 1 1 2 1 1 3 1 1 1 1 2 I 1 3 1 1 1 1 1 1 1 4 1 1 1 - I 1 1 1 We may arrange these in groups or sets according to their distances, as was done in the discussion of group III, and ob- tain the following equations of condition. Weight. BmMiuU. to 89 a + 59y = 15 7 + 1229 103 to 192 X + 150y =69 4 - 7-21 203 to 262 a + 234y =110 5 — 16*37 405 to 491 » + 469y =194 7 - 11-29 600 to 688 X + 549y = 209 16 + 4'04 608 to 696 X + 642y = 237 6 + 12*80 866 X -\- 865y = 364 1 - 24*97 The normal equations are : 45a; + 183336 y = 7172. V I8886a5 + 9667896 y = 8717238. » locki. Wt. 8 2 2 1 1 2 1 1 8 1 1 1 1 2 I 1 8 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 ne to their II, and ob- Propagation of the Cka/rle^ton Earthquake. 15 From which a? = + 5'0, y = 0-379. The resulting speed is 2 '638 ± O'lOS miles, or 4246 ± 168 meters per second. If the correction for the systematic error has a value approximately that which has been derived from the comparisons of the stopped clocks with well determined times of particular locali- ties, or not less than one-fifth the amount, the corrected speed would be from 5100 to 5200 meters. We may now proceed to combine the results of the first three groups and obtam from them a single mean. The probable error of the fourth group being uncertain it is necessary to omit it. Taking the weights inversely as the squares of the probable errors we have : Group I, Group II, Group III, Mean result, 5205"' ± 168"» 6192'° ± 236'° 5171°' ± 116'° 6184'»± SO"" wt. 2 I 4 It remains to inquire whether the data indicate any variation of the speed. The answer is in the negative. The data are inconsistent with any variation of a systematic character and thera is no apparent means of detecting an unsystematic one. A smdl irregular variation, such as mi^ht be caused by varying density and elasticity of the propa^ting medium, would not be inconsistent with the data ; but nie evidence of it cannot be separated fiom the errors of observation. MiuU. 12-20 7-21 16-37 11-29 4-04 12-80 24*97 "iHB^K ■^aeB9m»,M»-fa^' tm rrr" ♦•*