IHn'KKMINATKJN OK Uli: IIMK UK A SINCI.r: VlllKATION. 



Tlic method of tlctcmiiniiig tliu iH'ii««! of ii |h-ii<1ii1uiii which liiw been 

 most generally used is known as tlie "nieth(Ml of coinciilencca. " A (htIous oh- 

 jcction lo this nielhixl is ihnt iw tlic cxjut nionicnl of coimiihincc «mnot 1« 

 ;\ccnnitoly iiscertuincil the total time of swiri';ing innst Ihj long in onU-r t«) «x-nre 

 a high (legale of acctinu-y in the reuniting |Hirio<I of a «ingle viliration. If a 

 clironograjth and brcak-tiroiit clock or chronometer be matle »ise of, there seeiiu 

 to Ik; no <li>nl)t that U-ttcr results than by the method of coincidence« may lie 

 obtiiined in several ways. Assititant C. S. I'eirce of the U. S. Coast Surv<?y in 

 liis recent elaborate series of iK>ndnlura experiments at initial stations in Europe 

 and America, has made use of a Chronograph by telegm|)hing the transit« of a 

 l>oint on the pendulum over the wires of a telescojHj. Abxking a ]ien(hdum 

 record or count its own vibrations electrically has also Ixjen acconiplishe«! by 

 various devices. Many of these are objectionable on account of the friction exerte<i 

 against the motion of the jxjndnlum. 



In the plan svlopted in these experiments it is Ix'lieved that this objection 

 to an automatic record was entirely removed. It in%'olve8 the use of a chrono- 

 graph, a break-circuit clock or chronometer, and an arrangement by means of 

 which the exjicrimental pendulum could \hi made to break the circuit at any 

 desired vibration. In the Ix'giiming the whole numlier of seconds refpiire«! for 

 a given number of vibrations may be determine«! by letting it break the circuit 

 at every vibration, or, better, at every sixtieth or Inmdredth vibration, which 

 can easily \)c accomplished by counting and raising the break-circuit apparatus 

 to its proper jwsition undernejith the |iendultun at the right moment. In our 

 arrangement this a|)paratU8 consisted of a very small and light "tri|>-hammer" 

 made of fine wire, which \mw so adjuste«! that by pressing u|X)n a button it wan 

 brought up to such a ])oiiit that it would be just "tlirown" by the pendulum in 

 its pas.s;ige through the lowest |H>iiit of its arc. Although th.e resistance offered 

 to the pendulum can be made extremely small, yet it is so great as to interfere 

 quite jierceptibly with its motion if the pendulum is obliged to ojierate the 

 brcak-circuit at each Vieat, as exjieriment has proved. But it may be rejected 

 after the first two or thrt-e trials, not only on account of the resistance which it 

 introduces but also because it is not necessary to continue it« use. The whole 

 numK'r of seconds ro<iuired for a given number of vibrations lieing known, it 

 only renmins to detennine the fractional part of a second as accurately a« jiossible. 

 It is therefore only necessary to cause the penduliun to break the circuit twice, 

 once at the l)eginniiig of the perio<I and once again at the end. By this nunns 

 all objection to the jtrocoss on accoimt of resistance is rcmovi^d. Iiidc<'<l it is 

 in the |>ossibility of detenuining these fractional parts of a «i'xx>nd at the N-gin- 

 ning and at the end, that the merit of this method consists. The clironograph 



