Musschenbroek, Petrus van, Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae

Table of Notes

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          <head xml:id="echoid-head137" xml:space="preserve">DISSERTATIO</head>
          <p>
            <s xml:id="echoid-s4738" xml:space="preserve">Corol 2. </s>
            <s xml:id="echoid-s4739" xml:space="preserve">Quoniam ſinus 3 ?</s>
            <s xml:id="echoid-s4740" xml:space="preserve">graduum æqualis eſt dimidio radio, adſcen-
              <lb/>
            ſus Acus Inclinatoriæ ſecundum lineam vel planum A D, in diſtan-
              <lb/>
            tia 60 graduum a Meridiano Magnetico A I, erit hic dimidium ma-
              <lb/>
            ximi adſcenſus.</s>
            <s xml:id="echoid-s4741" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4742" xml:space="preserve">Londini, ubi Inclinatio Acus pedis unius eſt 73 {3/4} graduum, & </s>
            <s xml:id="echoid-s4743" xml:space="preserve">
              <lb/>
            adſcenſus ejus â Nadir 16 {1/4} graduum: </s>
            <s xml:id="echoid-s4744" xml:space="preserve">ſed Inclinatio Acus 4 pedum
              <lb/>
            eſt 75 {1/6} graduum, adeoque ejus adſcenſus eſt â Nadir 14 {1/6} graduum:
              <lb/>
            </s>
            <s xml:id="echoid-s4745" xml:space="preserve">Ideo adſcenſus in diſtantia 60 graduum abhinc, erit 8 {1/8} grad. </s>
            <s xml:id="echoid-s4746" xml:space="preserve">per-
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            Acum unius pedis, & </s>
            <s xml:id="echoid-s4747" xml:space="preserve">7 {5/12} graduum per Acum 4 pedum. </s>
            <s xml:id="echoid-s4748" xml:space="preserve">Notat Whi-
              <lb/>
            ſtonus ſe hoc variis temporibus exploraſſe, an experientia compro-
              <lb/>
            baretur, ſeſeque eam reſpondere demonſtrationi non modo in hoc
              <lb/>
            angulo, ſed in aliis deprehendiſſe.</s>
            <s xml:id="echoid-s4749" xml:space="preserve"/>
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            <s xml:id="echoid-s4750" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s4751" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4752" xml:space="preserve">Conſtructio præcedens ſupponatur in plano perpendicu-
              <lb/>
            lari ad horizontem, ſupra eandem A I, tanquam ſemidiametrum
              <lb/>
            ejuſdem circuli: </s>
            <s xml:id="echoid-s4753" xml:space="preserve">tum id ſupponatur locari a centro Acus Inclinato-
              <lb/>
            riæ ſecundum Magneticam directionem, ita ut ſinus A c, A d &</s>
            <s xml:id="echoid-s4754" xml:space="preserve">c,
              <lb/>
            repræſentent vires obliquas, ut antea: </s>
            <s xml:id="echoid-s4755" xml:space="preserve">tum inde ſupputare poſſumus
              <lb/>
            quantitatem iſtarum virium, tam in horizontali, quam in verticali
              <lb/>
            ſitu Acuum; </s>
            <s xml:id="echoid-s4756" xml:space="preserve">uti una enim linea exhibet vires Acus horizontalis, ita
              <lb/>
            altera exhibebit vires Acus Inclinatoriæ, cujus planum eſt in Ma-
              <lb/>
            gnetico æquatore. </s>
            <s xml:id="echoid-s4757" xml:space="preserve">Si quantitatem virium deſideramus in plano verti-
              <lb/>
            cali, prout Londini eſt, in Acubus unum pedem longis, hoc eſt
              <lb/>
            reſpectu totius virtutis ſecundum Magneticum Meridianum, hæc
              <lb/>
            eſt, uti ſinus 73 {3/4} graduum ad ſinum totum, qui eſt uti 96 ad 100.
              <lb/>
            </s>
            <s xml:id="echoid-s4758" xml:space="preserve">adeoque tempora oſcillationum duarum Acuum Londini, vel in
              <lb/>
            Meridiano poſitarum Magnetico ſunt, uti hi numeri, vel proxime, ut
              <lb/>
            98 ad 100, vel 49 ad 50, quod congruit cum experientia. </s>
            <s xml:id="echoid-s4759" xml:space="preserve">Si eo-
              <lb/>
            dem modo deſideramus quantitatem virium in plano horizontali,
              <lb/>
            erit hæc reſpectu virium abſolutarum in Meridiano Magnetico, po-
              <lb/>
            ſita Acu unius pedis, uti ſinus 16 {1/4} graduum ad Sinum totum, ſive
              <lb/>
            ut 28 ad 100, & </s>
            <s xml:id="echoid-s4760" xml:space="preserve">poſita Acu 4 pedum, uti ſinus 14 {5/6} graduum ad
              <lb/>
            Sinum totum, vel ut 2560 ad 10000, ſive proxime uti 1 ad 4. </s>
            <s xml:id="echoid-s4761" xml:space="preserve">ad-
              <lb/>
            eoque tempora vibrationum ab his A cubus peractarum, quæ ſunt in
              <lb/>
            ſubduplicata proportione horum numerorum, ſunt in primo caſu
              <lb/>
            uti 52 {9/19} ad 100, & </s>
            <s xml:id="echoid-s4762" xml:space="preserve">in ſecundo proxime, uti 500 ad 1000, hoc eſt
              <lb/>
            uti 1 ad 2, quod convenit cum Experientia.</s>
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