CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="390"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'managed',cRay: '91d405764a7bfd00',cH: '6v9lz1jcE0YvDDpA5vZah4nfV9mjgBjRlnA2x.M01ng-1741454616-1.2.1.1-OUWwUlV1ClXZ3DhhX.UygPrLsPXuhVr_gBBcU.M4boO479L9lgopgMeCBPuM8yg3',cUPMDTk: "\/search?q=Telegraphist%27s%20equations&__cf_chl_tk=yk9nMbDVEgBheGivboHNMfBDT7ANdFq15vsGU2fQAxI-1741454616-1.0.1.1-TnGja7nbOCT4YeRnZka_cO2mUTIaUVd7CEXzfFvm7io",cFPWv: 'g',cITimeS: '1741454616',cTTimeMs: '1000',cMTimeMs: '390000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/search?q=Telegraphist%27s%20equations&__cf_chl_f_tk=yk9nMbDVEgBheGivboHNMfBDT7ANdFq15vsGU2fQAxI-1741454616-1.0.1.1-TnGja7nbOCT4YeRnZka_cO2mUTIaUVd7CEXzfFvm7io",md: "tlRxnPZk3Arq_tGR4.DvpV47ax6tg16Q3WMfzUiLKC4-1741454616-1.2.1.1-Dqrr.eSBlmkou9K1YcvBJYFnxMnGH0gaV4wlQ.yBV_55Oig8xCBkHOFdgdPsypaoH7WLpi_tBICqn7tipv8Xt5G0QMfaGGlZFPXaYui6NIPqo0RaktSSBaFz7DGJdbzZlTBtmNQ4OJ4nPSy2lNqYfP8XbyMlSfNXy01nsfx1IINMULsjrHyfCTRtCBKx.tMmO5vQf1zV8cBRbHVQS_u6upLlHGE5y6evPnbsFVFzeH3OgnB7R64O8lYEO6M6srLyD2qAwqdrcLN8CORvwKMOqKsyyGKiGR8awoBKxAA5TSUstdxlOk9lmHOKDRKy5OKWHiT0Juts5PbmLCE7IW1ys8ydCcsCz7ZbvVnuu1EiTO2fR8yK2vnSgfV5jxO_FDv6dalXPTP7fmU2965cbPB3WL0Rjz7It.Ak5BZQeK9Go0NngkRokPJvXsvdyPz0r.wGqCE8RWTdgNyl0K6yBjci7O_1GTm2kDd92Fw8rJj03GFCpzK3LHwQodvBUO52iq6Md8_2UrrQP.ELPHk8VOPq0MqKFMPtXLh7_8WwVQx.O8vN9XPH37nuyWtqNs2MGEIa9k6XVARUtHnts1_MhT6gT.dq2cJoCUu6qK6Ud8d1tL7pZx1lH6MK4_4hMsh0rRD8bm7aeqJPprYmlOj6LObLz9BQgDh6c4CMniBsYLLbUxSNQ8I_yqrLjpmgmj4LQqUzGhwjPzSnItBC3cHI2YJ0TiVbgq_ebqPdA40na8MXAGMn_A3NwMbNWsJPcZO5m0Hs45g.RRN.rjRWDOVGb3yIPSZA_AIFy9hbo3_U73vZ9WBilXlArNjEJxt78WXO7jL7Xsq4cIK2z1rl5keN_p20w6_pnF1IcWX3umscVfLNYUdkvE60dv6090jvA1a5wUeHxe6wQLsJD1I4q_f4yq0BKsxqg8cWMlHSycrSz65HRZqHxp0xkiPGOG_ZpT_1bgckrvdbFsIcm9HeYe4WC5tHVOxdK27uRcZ_PqqcREsC37Ot51f5d3eWIMLE8JgZz_71tz_btZHr2VbtswM4OaKQ8Da0hFUAlL5XW_d.k8_SJVS.3GYD7Zw1NmiUYU2ioI4idqF5ODs4OdqH_mpcbvKc.My8TAB_b.Zv4raM1RkZbfq2rkH48aa6PKjI__sMLxg0TBDuwY.eTdAtET4Lt87_Fcktd.YMeWwa0sepWU9MnXSpY1p7NFbjvG52gRsxkCVNtwVh.0fO6mLCxXf5.IIXmGhMDYBsFQ7DdSheoDx_5wAV7yyiAM.uNA8ipboUQiO4bNVS3TeRIEgp7dtul9teJw",mdrd: "q8uSwaodgjfKLRxPplRN7VH6qVyKPq4Cly7QQOirriE-1741454616-1.2.1.1-XOXZWgK4f_dUw.nq_1uUK_rcR.Ahy6Bw6PkeGGR3Z4M6MLvxcZSTz7rlqE6L00k9s0j95kEYVbqd__VdbO8modhp6yrcxYGfhREiq_e8_qR6ChQI.LKlwc2mqfHpvc2cfsQzUpCMsfQWXaJTZTiyuJBSG3yqllZGpyLqWAA3MDLjjCKLZwG.hHEKuHzDPK5kI7944x6jPkLVXavXPZu6KXI6RaYGpDOfiwdO3S.caCkiP93X5r1dtEQjowWXRMtgTQWNYKU62NTSPQQ9IAcsw4S9KDBwBqLCVIkMWroSEy0Ou1ie1D0ZOIg8Lj0zThE30jeJcheMcC8lfzp3C95a6SNogQTkYMTB1I7IPOR2QlUhJ6yZGCKE4b2oIKuSFnBFFaH1XblIK_TQrhO_EnuPJfQQxpkdbSr_aIrmbec9J8E88QlfdE8H4ibQPvl2b.4rVpNzh9IijUdEr__kxeaMoTjWRlYYP4u1JP48r3jMPHFQYjnsHDDpZ_t7h4ArdQGLThuwpSG8orSTDwsAf7LbC8TgA.Gf4sqNWDtTGCwffjhDi2SuH1dm8v7OL0cOydpDXhCI6eAaI73JZiImRbLahDINZmfvvkdY7WAJgtcxKkTbNOAP3Tr8wKfiB8X8n7RM11EeI7leXSHcNFlf66hb.gwAopQCj59gy59Zrbt.idceLVkiqsomoGH8rS7w_kGPUN20oVDHUn2EgdKsCgFhh5SUfQbfMEnle6G3YrvDvOKHMaF34bbVRKuXduPNYb2dGbgVOtn.Sx6RMtnivmJrEkwN_9GsAbeqhC6qN8GNEXqNtd_0o5euVLqdj7SDW8jkleNAsDc.TZ9QXv4Qqm6mrgDYwQQ9FvYluWmbwxIDp_hu.8l2idOa4JqRImJGAk_J7ZUe.5cosmgkLTc75iilRK9LURStXR743R4d.eAYPOkpbA0V8PUPAkobxrGhy2vE4r8bvxqVbk7934toqYABLtc9RXx9Gt.egACUmQdCO4RaeL96pkx57k0bjgmSWbhL2FqdKG6RQNcg3q2ZZA678tXrT0T3NsvulP_iNK5Y4M0ZCEo8v.luJkndfXvkN8uGbHm0sMNohrfj2LV3k8JHjbgFZjmIWl8qcmtUYtRJXwI0EDYLOW_4AP4eVsZ38LvnXRH2eornfHR2DRamxQ40RBclZ_iVNQxUjEsN9JBPv_fmjpBBT1i7s9RvFGjV9Qe_1aPtG6.ujaoQ5EjQEsIvwVufuafvQ8MjYFp9g4OZp0HD0BJb0i34Al_oJhUunKGm3Jq1YAyzwPeNrp7MD3544LG61520bSYrgZ.KopNHg4DANjoeqXr6PNUu7tQpoq_s8OsKCHK9jJ.yC078wqE522PyOq58mjq7Tg7tCClIXJOxpjnw.p1E9U7j9bH70Ywxx6WrAcWYKprKDVeAxhX7amRAoU_sULxyydnBQPC2VsYDAi3LOtmp4SCMFUOuAO4LzkMqfcD2DvoP0STgzFPwQnmReLnhQutHpe7Db6USg6ShGDOrRi9Q9wqRkeezIZXDv0emBfMHts4JV2VrHkenMGNgrrsx6OqFNn25wky0hzRXsRTVO9Qg89R5FeozuSmUSorpJgXiZcgkz2h.B7Wd8LM3YGe1f3AcnFbtbd5EduTM1N5fWPy7XXUBIpmVKd2WKB4PiiomCkNoP90Ia2sBs_WXPs.EaA62WPAYOdLtr5Cqm_jFcDFKOMJalm_uiUMbsNcCQyaSTr4E4ZDdasj8_IlNVu7Emerav.Tp7VRhqsN4sPG.9_W3r8C3xJ2NpNCnVNO_WGrN6eYoNwVSmw5sNo8vMKq0udTdm53ZbrttQbA6djXNHjck5IX8yxShaRW_7hTZq9IP6WtA52zJKOifR9v0DL9P7l11yGSkUmPqOSYltFkQUxT3MgtCrIdEMgNpC4KDtFknudvdLue_rSu8xVUc02jCT8zmJqk7_5suJ4DddYchpH4C2BVa_M9_6JOp"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/g/orchestrate/chl_page/v1?ray=91d405764a7bfd00';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/search?q=Telegraphist%27s%20equations&__cf_chl_rt_tk=yk9nMbDVEgBheGivboHNMfBDT7ANdFq15vsGU2fQAxI-1741454616-1.0.1.1-TnGja7nbOCT4YeRnZka_cO2mUTIaUVd7CEXzfFvm7io" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>