Bošković, Ruđer Josip, Abhandlung von den verbesserten dioptrischen Fernröhren aus den Sammlungen des Instituts zu Bologna sammt einem Anhange des Uebersetzers

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            <s xml:id="echoid-s268" xml:space="preserve">
              <pb o="27" file="0031" n="31" rhead="Von verbeß. Fernröhren."/>
            {m a/m - 1}, q
              <emph style="super">2</emph>
            φ = {m
              <emph style="super">2</emph>
            a
              <emph style="super">2</emph>
            /(m - 1}
              <emph style="super">2</emph>
            X {m - 1/m
              <emph style="super">3</emph>
            } X
              <lb/>
            {1/a
              <emph style="super">3</emph>
            } X {1/2}e
              <emph style="super">2</emph>
            = {e
              <emph style="super">3</emph>
            /2(m - 1)ma}.</s>
            <s xml:id="echoid-s269" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s270" xml:space="preserve">34. </s>
            <s xml:id="echoid-s271" xml:space="preserve">Nun aber wollen wir aus dem vorigen
              <lb/>
            Werthe des {1/q} noch einen Zuſatz ziehen, der
              <lb/>
            uns für jenen Fall dienen wird, da die Licht-
              <lb/>
            ſtraalen durch zwey Flächen, oder durch eine
              <lb/>
            Linſe durchfahren müſſen.</s>
            <s xml:id="echoid-s272" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s273" xml:space="preserve">35. </s>
            <s xml:id="echoid-s274" xml:space="preserve">IV Zuſatz. </s>
            <s xml:id="echoid-s275" xml:space="preserve">Wenn in der Länge A G
              <lb/>
            eine ſehr kleine Veränderung geſchieht, ſo wird
              <lb/>
            die Veränderung, die daraus in A H erfolget,
              <lb/>
            ſich zu jener verhalten, wie A H
              <emph style="super">2</emph>
            zu m X
              <lb/>
            A G.</s>
            <s xml:id="echoid-s276" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s277" xml:space="preserve">36. </s>
            <s xml:id="echoid-s278" xml:space="preserve">Weil {1/q} = {m - 1/m a} + {1/m p}, und
              <lb/>
            {m - 1/m a} eine beſtändige Größe iſt, mithin auch
              <lb/>
            alſo verbleibt, da A G = p wächſt, oder ab-
              <lb/>
            nimmt; </s>
            <s xml:id="echoid-s279" xml:space="preserve">iſt nothwendig die Aenderung des {1/q}
              <lb/>
            mit der Veränderung der andern unbeſtändigen
              <lb/>
            Größe {1/m p} gleich, das iſt {d q/q
              <emph style="super">2</emph>
            } = {d p/m p
              <emph style="super">2</emph>
            }, mit
              <lb/>
            hin haben wir d q : </s>
            <s xml:id="echoid-s280" xml:space="preserve">d p = q
              <emph style="super">2</emph>
            : </s>
            <s xml:id="echoid-s281" xml:space="preserve">m p
              <emph style="super">2</emph>
            = A H
              <emph style="super">2</emph>
            :
              <lb/>
            </s>
            <s xml:id="echoid-s282" xml:space="preserve">m X A G
              <emph style="super">2</emph>
            .</s>
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