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brdnnoo-sprlng,dopendlngontlroly upon tho rntfo 6f tho spring's tension, followlffg tlio proportion ol tlio nrosof lnfloctlon; u bnlnnco spring, therefore, "of nny foroo whatovor, hnvlng tho progression roqulrod by tlio law of lsoohjonlsm, will preserve this property, whothoj It.bo nppllod ton bnlnnco making quick, or slow vlhrntloiis; for wlilch rouson, . in tho picsont inquiry ovoiy circumstance Is purposely Omitted, which gives to the bulnitco its -poolflo character, as weight, dlnmetor, oto,, und It is trentod simply us tlie balance. Wrlglitorson Isochronlsm npponi"s to hnvo considered.the vibrations of tho balance In ll» totality, and to hnvo reasoned lor tlio most part on the times of vibrations In their entirety; but a bottor plan, it Is submitted, would bej to oonsldor tlio tlnie of encli semi- vibration of tlio balance, to consist of scttne number of every minute equal portions of time, and then by applying tho known Invvs of forces to thp motion of tlio" balance, to detorniiiio-wliat nre tlio specific conditions uudor which tho vibrations themselves shall, In tho totality, ho Isochionoiis. Tho clastic force of balance springs be¬ longs to thnt class of forces culled con¬ tinuous, because the action is not by a single impulse, which then ceases, but by a number of consecutive impulses, following each ot her In such rapid succession as to constitute an uninterrupted nnd continuous force; but which force Is uniformly lncrpas>n« during the bending oi the spring nbjd unhonnly decreasing whilst It is unbonaUtg. Tho first step towards tlio/coinprelioiislon •of. Isochronlsm Is tho j-ceognftlon of tlic accelerated and retarded motion of the balance; for which /purpose it must be followed step by stop, through the entire vibration, upon the supposition that the Hinoofeneb soml-vlbnitlon is divided into, or oomposod of, nny convenient number of equal parts, as foi Instance, ten. If then the balance be supposed to bo movod by the finger from the position where It will stand, when ut test, ovor an arc of any number of degrees, and bo thero hold, It will be pet- 'eelvod that the spring Is wound into tension, mid bus acquired an amou,nt of elastic foice- proporflonnto to tho angle over wlilch It Is Inducted, which force is then rencttng against - the finger, by which the'balance Itself is iidd in a state of rest. i'ho instant, however, that the linger Is withdrawn, the olustlo forco of tho spring vv ill bo exerted In overcoming tlio absolute ineiila of tho balance, and nt the expiration of tlio first short poilodof time (or one-tenth ol fho time of UBOini-vlbintlon,) the spring will havVeoramunlcated n slight motion to the balance. During tho second tenth, tho spi fug's forces is exerted against the bnlunee In motion, Instead or bolng nt rest as It w as ut the commencement of tlio lirst tenth, and the spring will necossurlly acceloiato the motion thnt tho balance hud previously acquired; and bo on during tlio thlid( fouith, und every other succeeding tenth, the elastic loree of tho Bprlng, though continually decreasing, will be urging the balance lorwnrd, and will therelore continue tp at celerate It until tlio apilng arrives nt tho position ol quiescence, wlioro It censes I uither to Hi go tho balnu'O. I'ho balance having thus returned to tho position of rest, from w lieneo it was moved b) tho finger, tho Hist half of tho vibration is lully complokod, and n change of circum¬ stances taken place, the spring, w bleb con¬ tinued to communicate motion to the balance uiilll now that the whole nl Its loreo has bull tiansfeired thereto, has resumed Tor an Instant a statu ol quiescence.^ The b dance has nlbo assumed u view churiieter, having acquired a sulllcioiit velocitykof motion and momentum to carry It thiough ihci 6thet liult ol the vihiallmi, nnd In so doing to lulled the spring through an angle equal to thnt which wns orlginully moved thiough by the linger, and to give "tho s'pt lug the requisite tension for performing tho next succeeding vibration. During tlio Hi st few tenths of the,second half ol the viluatlon, the spring has so little tension Hi it Its loi ce roturds but sllghtl) the motion ol tlio balance, dm lug the succeeding tenths tho tension gruduully luci eases, until at length the spring iicqulles sullielont loreo, to ontiiely iu rest the motion ot the balance at tho same extent of tiro on tho otliur side ol tho plate of qiileseenco us that to which it was oilglnally moved b£ the linger. Diagram, Fig. 1, shows tlio magnltudo of of the sevornl nrcs Unversed bv nn Index nftlxod to the rim of tho balance, during each of tho successive tenth portions of the time Into, which a somUvlbratlon of 176 degrees. Is conceived to bo dlvldod. An inspection of tlio figure, and a com¬ parison of tho splices described, during tho Hist and last tenth of each aeuil-vlbratlon, will" sti dice lo show that each vibration of the balance .Is composed- ol nn alternately uccoluratfil and retarded inrftlon, ibid how Tapldlv tho ratio botvvcen them proceeds, although it Ib not probable that the oye .could deteet to ho tho case, even In a liiibine of the slow est motion. , The specific conditions under which fho vibrations themselves, eotislilcvejj In their totality, whether long or short, shoidd bu Isoehionoiis, aie these; . 1st. It the time of each seml-viUiatlpji. be eoinpo-ed ol the same number ot^veiy small equal Instants of time, mid wbothei be the extent nt ihe arc tiaversed, that the Hist and las[ ot tlio these minute instants of time preolsly concspond with the com¬ mencement and conclusion of each eciul- vibratton, the vibrations, whethci long or short, of such a balance, will be Isoehionoiis. or be performed In equal times. 2nd. Tlie elastic force of a balance- spriug lucicu'es In direct propoiilou to the angle of inflection by vv hleh it is wound Into tension'; mid hence It Is obvious that the in¬ creasing and diminishing tension, which causes the biilaiK e to follow a definite law ol aceeleiatlon and rctaidatlon, must Itself also lallutt some definite ialio of Increase lUid dtcrease, hi ordei that the Hist and lust*' of the very small equal instants ol tllne shall coirespond with the commencement mid conclusion ofI'ui'lL.tumi-vibration, ,'iid. it is IlkUwWe- evident ill it the ratio of changes In the torsion may be eltliei ono which pi.oceeits too uipldly, anil con¬ sequently produies'uii opeiutluu In defect, on which account there me two vmlellis ol spilng which do dot pioducc Isoibioiions vibrations. lib. In the lornici variety, piodiu lug mi opolatlon in c\ccsh, the spilbg icquliesa greater amount ot elastic foice than tint which Is due lo the angle ol lutli'clion lu an Isochronal spiiug, wluueelt tollows ihul the greufei the mc ol vibiullou, I In. guatci will be the angle ol Inflexion, ami con¬ sequent!), the gicati'i the excess oi undue tension. Ihuellcetol this undue tuiislon will be to lull ry thcbalainc loi waul, din lug the 111 st half ol the vlbi.itlou with loo greut eelcill), mid thus cause It to mrlvi nl the eonduslon hcloii' the complete ituiuhci of minute Instants due lo the Isocliionous vibration bus ixpired, A similar ellutls piodiued during the second hull ol the vibration bv the undue excess ol tension ill letting the balance beloie the full nuiiibei ol Instants has entirely expired. Duilug each seinl-vlbiallon, Hick fore, ibioiighout the dit), some ol these minute Instants will bo lelt unemployed, and their accumulation will bo the amount gained In the long ares of vlbintlou lu comparison with the pel- formulae of the same watch in tlie short arcs, ___ _ - Bth. In the lnttei vnilety, the elastic forco due to tile angle ol Inllectioii will not be siilllcleiilly gieat, and Ibo Hpriuj; will not huvo tlio icqiilsiio tension to cany—rtur bulauco ovei the Hist somi-vlbiiitloii ol a long mo, in the iiumbel of instants allotted to It, nor to arrest it no soon ns tlio Isocbto- noiis term of tho second scml-vlbrntloii re-1 quires. ^!noh soml-vlbratlon, therefore, will occupy too Inrgo a number of Instants In Its performance, and tho accumulated amount of them throughout the day will Indicate tlio Iosb during tlie long aros of vibration In comparison with the porformnnco of tlie same wntoh In tho short arcs. To U iqitinittd MARINE LAW. VESSEL— CHAIlTKn l>ARTY-"-L"RN TOR MIIV runs of coAf. Hi8l. Court., S. D. Xew Yorfc~ JVoo.."., 1882. By the terms ofiichartor party the charterer wns to pro^ldo nnipay for all the coal required. Tho'master and crow were to be appointed and paid by tho owners, but tho master wnB to be "under_tho orders and dlreej'fluir" of the charterers "ns rpgnrlls om- -ptoymontg, agency, nnd other arrange; monts." Benedict, D. J. This Is an notion to enforce a Hen upon the Gentian steamship India, for the price of a quantity of cold dellvei ed on hoard that vcbbcI ut Philadelphia iu Juno-lusL Tlio undisputed facts nre us follows: ^ __/ The steamer India Is a foreign vessel owned In Hamburg. > In .Tune, 1382, being then in.the port of Now York, she wns ohuitered by the dim of Hnsei, Watson 4 Company of Now York, for "nil luwlul service nndoHiployinent between the United Stntes und Briirll, one roiiqd voyiigo, with libelty to call n't intermediate poit* for cargo." By the terms of thoehnrter Huser, Wiilsnn it. Company weio to provide and pay loi all coals required. The master and crew were to be-uppolntcd and paid by ,the owncis^buLUif master was to be "under tlio oj'ders and directions of Huser, Watson & Company" "as tegards employment, agency, and other arrangements," and HusBrr-Wutson it Company agreed to in- demunify the ow ners foi all consequences or liabilities that might arise fiom tlie captain signing bills of lading or complying with their ordeis. All derelicts, towago, ami salvage were to be loi tlio ovvnois' mid chnitcrcrs' equal benefit. By virtue of this charter the possession und control ot the steamer passed to llusor, Watson & Com¬ pany of New York, und as the answer ex¬ pressly states, the steamer was in tlie posses¬ sion of Hnsei, Watson & Company ut the time of the pin chase ol the coals In question. At Philadelphia the consignees of thostetim- ei weie b. Morris Wain & Company. This, I liudeiatuud b. Mollis Wain to menu when !'c told the llbellmit that the. sleamei wns oomlng lo his linn. The coals in question were ordered for the use ol tho steamer on her then intended voyage by S. Morris Wuln ifc Company Tlicy were delivered on bimid Ihe vessel by the libellunts, mid were llieic received by the muster of the steamer Aller theii deliver) a hill maid out against the sleainer and owners was pu sen ted by Ihe libellunts to:?. Moiris Wuln & Company but was not paid because of the llbellaut's ictusal to make a deduction claimed bv h Munis Wiilin i\, Companv b) icason ol a deli'iition of (be steamer alleged lo have been caused by the Ituclhini's taihne lo deliver tho coals in piopei time. On the return ol ih<* steamer to New Yoik she was libelled In this action, und ihe question now to he determined is whether 'the llhdlniits acquired a'lien upon the steamer foi the couls so dollvered by them Upon the testimony there Is no dilllciilty In finding that the coals wore supplied upon the credit ol ihe sleainer, and not upon tne peisoiuil credit ol S. Morris Wuln it Com¬ pany. There is testlnlony from Jncob i. Wuln tending to show that the credit of his linn was relied on, but this Kstimuli) Is lbitl) contradicted by Berwind the other party theioio, and utouover Is not incon alsleiit with u tellnnie upon the vessel's credit A material innu may, and general!) does rely lipou ii personal credit ns well us the credit ol the vessel. Tho question here Is whether tho coals weio furnished upon personal (redll alone. The testimony forbids siKh a i(inclusion. It Is, however ctuluied th it the coals weio notoidered b) the master of the steamer, noi b) theowuei of the steamer, mil b\ any authorized agent of the owner, mid Iheiiloic It Is Insisted that miTTeii nllachtd to the vessel. But the inastei ol the vissel ,is- sumod cluirgo ot the icielpt of the coals. 1 • i .;- > -riL abd ha Imstenod Ihe delivery and nnnumed to direct the same, while tlio order for tho coal was'given by tho conslgneo of tho steamer, 'tho consignment of the Bteamor to S. Mmils" Wuln & Company In the absence of nlftlce to the contrary, con¬ ferred upon S. Morris Walri <Ss Company ap¬ parent authority to net lor tho owner of tho . steamer In such a matter ns ordering neces¬ sary coals, r say |u the absence of notice, • because, while the testimony of Jacob 9. Warn Js tfi the eil'eot that he Inloimed the libelhmtB that he was acting for a ebnrnoter, and not foi (ho general owner of the steam¬ er, this testimony is nlsiTcoiytrndloted by the witness Berwind, und Berwind is to some extent corrobniteil by the undisputed fact lliatu bill fWtJie ecru) wns, at the time, nyrtilo out against tlie steamer nnd owners, and tho """ Ninie loeelved by S Morris Wain ills Com- . - puny without objection made to its form. In this state orVevlilence, theielore, it cannot' be held that notice of the existence of tho chin lor wns given to tlie llbellnnts, and they \ "chargeable with knowledge that S. Morris Wain it Company were not acting in behalf of the general owners of the steamer, The ease lu tills respect Is the ordinary one of supplies lor a lorelgn vessel ordered by tho agents ol the geueiid nw nor and delivered to the inasti'i upon the credit of the vesael and hei owneis, and b) the maritime law a lien Is eieated upon the vessel for supplies so furnished But ihe liabillt) ol tho vessH Is also clear, 11 the testimony of Mr. Wuln bo lonsldered us tlie true account of_lht> \transaetloii be¬ tween Ills Hi In and the ICbelliints respecting this coal, mid the llbellnnu held chuigeiibie, withTTiiow ledge of the terms of the charter -*~, and that Morris Wuln it Company were acting ns agents of Huser, Watson & Com- pun) und pot us airetits of the general , ■owner of the steamer. For Huser, Wuison it Company of New York, vvherej_bv the ehnrtei, constituted owners ol the Bhip pro hue vice. The steamer was iu their posses¬ sion, and not In the possession of the general owner. Au tho answer states. Tho master wns subject to their direction of Iho general owner. In uny aspect of the testimony, theiefnie, the libellunts were dealing with n vessel foreign to the port ot Philadelphia, mid the vessel became bound tor the coals furnished upon her credit In such lorelgn port upon the oi dci of the agent ot tho special owueis r It is not i.s-uitlal lo the creation of a lien for supplies liirnislicd a foreign ship that the supplies be oideied by the general owniM ot his agent. When the general ownei dfu ship Intrusts her entire posses¬ sion iindlcontrol lo unothei us her '■peelul owni'i, hf theitjbv assi nts to the creation of liens upon the ship ioi necessaries supplied by onhi Mil the special owner, and when such iictcssmlcs aie so supplied upon the nidltol the ship, the ship js bound, al¬ ibi ugh no [a ison il liability lit inclined by tin gi iiciid owui i M) t(inclusion, tlietuloic, Is that Iho llbellants luqulnd a Ihn upon this slcmnor loi the vnlue ol Ihe kiiiIs in the libel menti¬ oned Ibis (onclii'dnn Is not lu conflict wllb the dnl'loiis In tin cisisillcd lu bo' hall ol tin 11 dm ml Li l n dune he emend 111 favor of the llbdlauts loi the sum ol if 1,1118.111, with lu¬ ll resls | ioiii Jinn l'l 1H!U, ii nl the lostsol this action \ NEW Ml I lion I tilt I'HOl'l.I I.lNG ( \S vl IIOAl-s. lie luvililni ol i hi w sj-lcinol pinpell- ing, or i din i low in.!, ho n- upon llic i male cxliibilid his Invdillon lo tin Nivv \oik ■si lie Liiglneii and Miivivui a lew dnys igi>. lu this s^u iu llu tin its nte iiiovcd b) nn eiitlli » wlie tiibli siintlii lo thui used to piopi I Mm t ( ii-, m p iiaied b) rilatlonaiy cllglnt ■> loi ili 'I al dltb u ul points along Ibe lanal 1 hi-( dili is ahovi tin bai'iks mi! mIUiIii i (M k nil win n tin boal> an sleeied noal llic side of Ihe c und, the boatman bj a simple doviee, utl idling mi sell-ieeoveilng luwllne to the iiible. This line is eontioiled by u lib llou brake which beats oil the line until tin boat plains the s inn spidlasthe ...i.i. ••--.- ■■ ' ■ iiilili, thus pieveutiug jerks and snains be- luii Hie bill „o Is mull i imj t nn lul cstl- lualis bj pi u lb al I ugliM't'in show ll|o sjs- n iu i in he u|i|iliiil and opcialiil in towing hints tot Isssihan tin thitt|icsi itit'thod no'* In use. It-Ullkilv that a suli(i"ol a iiillu in uioie will Ii Ui>d dining tin coming st imiii upon some pin lion ol the Idle eanill.