Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii

Page concordance

< >
Scan Original
41 27
42 28
43 29
44 30
45 31
46 32
47 33
48 34
49 35
50 36
51 37
52 38
53 39
54 40
55 41
56 42
57 43
58 44
59 45
60 46
61 47
62 48
63 49
64 50
65 51
66 52
67 53
68 54
69 55
70 56
< >
page |< < (87) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div90" type="section" level="1" n="65">
          <p>
            <s xml:id="echoid-s2428" xml:space="preserve">
              <pb o="87" file="0101" n="101" rhead="SECTIO QUARTA."/>
            cularum mutua adhæſione præveniri potuiſſent. </s>
            <s xml:id="echoid-s2429" xml:space="preserve">Experimenta autem ſunmſi
              <lb/>
            tum de tubo divergente, tum de cylindrico: </s>
            <s xml:id="echoid-s2430" xml:space="preserve">ſingula nunc exponam:</s>
            <s xml:id="echoid-s2431" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div91" type="section" level="1" n="66">
          <head xml:id="echoid-head89" xml:space="preserve">Experimentum 11.</head>
          <p>
            <s xml:id="echoid-s2432" xml:space="preserve">In Figuræ 19. </s>
            <s xml:id="echoid-s2433" xml:space="preserve">tubus formâ coni truncati horizontaliter vaſi erat in ſer-
              <lb/>
            tus, vas ipſum aqua implevi usque in C D, ita, ut altitudo ejus ſupra axem
              <lb/>
            tubi eſſet æqualis 433. </s>
            <s xml:id="echoid-s2434" xml:space="preserve">particulis æqualibus, quibus in toto experimento
              <lb/>
            uſus ſum. </s>
            <s xml:id="echoid-s2435" xml:space="preserve">Pro illa altitudine experimento inquiſivi in punctum Q maximo
              <lb/>
            jactui reſpondens, & </s>
            <s xml:id="echoid-s2436" xml:space="preserve">fuit P Q = 287. </s>
            <s xml:id="echoid-s2437" xml:space="preserve">part. </s>
            <s xml:id="echoid-s2438" xml:space="preserve">dum altitudo o P erat = 146.
              <lb/>
            </s>
            <s xml:id="echoid-s2439" xml:space="preserve">part. </s>
            <s xml:id="echoid-s2440" xml:space="preserve">Sic vidi motum aquæ tum propter aquæ adhæſionem, tum propter Fi-
              <lb/>
            guram tubi fuiſſe valde retardatum, quod in his caſibus fieri debere aliquo-
              <lb/>
            ties monui. </s>
            <s xml:id="echoid-s2441" xml:space="preserve">Debuiſſet autem, ſi nihil obſtitiſſet motui, eſſe P Q = 503. </s>
            <s xml:id="echoid-s2442" xml:space="preserve">part.</s>
            <s xml:id="echoid-s2443" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2444" xml:space="preserve">Deinde Patinam poſui in tabulam horizontalem, cujus ora erant in S
              <lb/>
            & </s>
            <s xml:id="echoid-s2445" xml:space="preserve">R: </s>
            <s xml:id="echoid-s2446" xml:space="preserve">Patinam autem prius madefeci, omnemque aquam ex illa depluere rur-
              <lb/>
            ſus ſivi: </s>
            <s xml:id="echoid-s2447" xml:space="preserve">ſumtaque menſura P R, illam inveni 206 part.</s>
            <s xml:id="echoid-s2448" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2449" xml:space="preserve">Denique diameter G F erat = 13. </s>
            <s xml:id="echoid-s2450" xml:space="preserve">part & </s>
            <s xml:id="echoid-s2451" xml:space="preserve">M N = 17 part. </s>
            <s xml:id="echoid-s2452" xml:space="preserve">longitudo
              <lb/>
            tubi autem erat = 125 part.</s>
            <s xml:id="echoid-s2453" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2454" xml:space="preserve">His omnibus ita præparatis, dum orificium M N dignito obturarem,
              <lb/>
            remoto confeſtim digito aquæ ejiciebantur, earumque pars aliqua in patinam
              <lb/>
            decidebat: </s>
            <s xml:id="echoid-s2455" xml:space="preserve">hanc ſollicite in tubum vitreum collegi cylindricum, cujus diame-
              <lb/>
            ter erat = 8 {1/2} part. </s>
            <s xml:id="echoid-s2456" xml:space="preserve">tubus iſte impletus fuit ad altitudinem 210 part. </s>
            <s xml:id="echoid-s2457" xml:space="preserve">fuit igitur
              <lb/>
            quantitas aquæ in patinam delapſæ = 11922 particulis cubicis.</s>
            <s xml:id="echoid-s2458" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2459" xml:space="preserve">Jam vero deberet iſta quantitas per §. </s>
            <s xml:id="echoid-s2460" xml:space="preserve">20. </s>
            <s xml:id="echoid-s2461" xml:space="preserve">eſſe = nb√{n/g} X log. </s>
            <s xml:id="echoid-s2462" xml:space="preserve">{a/a - e},
              <lb/>
            ubi per n intelligitur amplitudo orificii N M ſeu 227. </s>
            <s xml:id="echoid-s2463" xml:space="preserve">part. </s>
            <s xml:id="echoid-s2464" xml:space="preserve">quadratæ per g am-
              <lb/>
            plitudo orificii G F = 133. </s>
            <s xml:id="echoid-s2465" xml:space="preserve">part. </s>
            <s xml:id="echoid-s2466" xml:space="preserve">quadr. </s>
            <s xml:id="echoid-s2467" xml:space="preserve">denotat porro b longitudinem tubi,
              <lb/>
            quæ fuit = 125 part. </s>
            <s xml:id="echoid-s2468" xml:space="preserve">per a proprie intelligitur altitudo ſuperficiei C D, ſupra
              <lb/>
            axem tubi, hic vero intelligenda potius eſt altitudo conveniens velocitati
              <lb/>
            aquæ in punctum Q incidentis, ſeu 141. </s>
            <s xml:id="echoid-s2469" xml:space="preserve">part. </s>
            <s xml:id="echoid-s2470" xml:space="preserve">ſimiliterque pro e ſumenda eſt
              <lb/>
            altitudo conveniens velocitati particulæ in punctum R incidentis, nempe 73 part.
              <lb/>
            </s>
            <s xml:id="echoid-s2471" xml:space="preserve">Denique vox abbreviata log. </s>
            <s xml:id="echoid-s2472" xml:space="preserve">ſignificat logarithmum Hyperbolicum. </s>
            <s xml:id="echoid-s2473" xml:space="preserve">Factis
              <lb/>
            iſtis ſubſtitutionibus numericis, fit
              <lb/>
            nb√{n/g} X log. </s>
            <s xml:id="echoid-s2474" xml:space="preserve">{a/a - e} = 227 X 125 X {17/13} X log. </s>
            <s xml:id="echoid-s2475" xml:space="preserve">{141/68} = 26830.</s>
            <s xml:id="echoid-s2476" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum