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Sandablagerung von ihr in keiner Weise modificirt wurde, also eine normale Curve entstand, während bei den folgenden Versuchsreihen je mehr und mehr Stauungen entstanden, durch welche die Curve modificirt wurde,

zuerst allerdings noch so schwach, dass diese Modificationen in den, durch den ziemlich primitiven Apparat veranlassten Beobachtungsfehlern aufgingen, später aber so kräftig, dass ihr Verlauf den Beobachtungsreihen mit aller Sicherheit entnommen werden kann. Fassen wir zunächst die normalen Curven in's Auge, so verlaufen sie von dem höchsten, unter dem Trichter stehenden

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Punkte aus, so nahe nach beiden Seiten symmetrisch, dass die kleinen Abweichungen in den Fehlern der Beobachtung und des Apparates, namentlich in dem mangelhaften Parallelismus der beiden Glastafeln, hinlängliche Erklärung finden. Für die kleinern Sandmengen (10, 20, 30 ) zeigen sie, wie der beistehenden, der Normalcurve für 30 entsprechenden Figur zu entnehmen ist, entschiedene Hut- oder Glockenform, für grössere Sandmengen (60, 90) verliert sich dagegen diese charakteristische Form immer mehr, und geht am Ende, wenn der Gipfel des Sandberges die Trichteröffnung erreicht, in zwei an

gr

derselben zusammenlaufende Gerade über, welche der sog. natürlichen Böschung entsprechen. Bleiben wir behufs näherer Prüfung bei der abgebildeten Curve stehen, so finden wir zwischen derselben und der durch

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gegebenen Fehlercurve eine so grosse Aehnlichkeit, dass eine genauere Vergleichung zu lohnen scheint. Setzen wir zu diesem Zwecke

v = α. X und ❤ (v) = ß.y und führen überdiess diese Hülfsgrössen

2

1

u = a2 t = Lg ẞ m = x2. Lge n= Lg y +

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2

ein, wo

Lg n= 0,4971499

Lge= 0,4342945

ist, so erhalten wir nach 1 zur Bestimmung der a und ß, respective der t und u, die Bedingungsgleichung

t+m.u+n= = 0

welche wir so oft aufschreiben können, als wir correpondirende Werthe von x und y, respective von m und n, besitzen. Nun haben wir in unserm Falle, wenn die x (entsprechend der Figur) von der Mitte aus gezählt, und für die y die Mittel aus den sich entsprechenden Ordinaten vor und nach der Mitte genommen werden, nach Tab. XXVII die 5 correspondirenden Werthe *)

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*) Die spätern Werthe von x und y wurden als relativ etwas unsicherer, vorläufig weggelassen.

XXVII. 3 u. 4.

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G

t + 0,0000. u+1,8073 = 0
t + 0,4343. u + 1,7537 = 0

t + 1,7372 . u + 1,6342 = 0

t+3,9087. u 1,4472 = 0

t+6,9487. u + 1,1517 = 0

aus welchen die Normalgleichungen

5. t + 13,0289. u+ 7,7941=0 13,0289 . t + 66,7688 . u + 17,2599 = 0

und somit successive die Werthe

- 1,8012 (8,1988) u = 0,0930 a = 0,3049 f = 0,0158 folgen. Berechnet man nun mit Hülfe dieses & nach 2 die v, schlägt sodann zu letztern in der auf meinen Wunsch, zu Gunsten dieser und anderer Untersuchungen, von Herrn Wolfer in etwas grösserer Ausdehnung als gewöhnlich berechneten Tab. XXVIII die entsprechenden Werthe von (v) auf, und bestimmt aus diesen mit Hülfe des ẞ wieder nach 2 die y, welche zur Unterscheidung von den beobachteten mit y' bezeichnet werden mögen, so ergibt sich die folgende Tafel correspondirender Werthe:

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und da sich in den Differenzen yʻ—y kein systematischer

Gang zeigt, auch ihr mittlerer Werth, trotzdem hier auch

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