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direction of an absciss or an ordinate. The stronger the curvature of 

 a curve and the more rapid the changes of curvature take place, 

 the more uncertain the determination of the direction of the tangent 

 at any point becomes. 



The point s at which the curve under examination has no curva- 

 ture, is easily found under the microscope. 



A number of points in which the curve is cut by the abscissae 

 or ordinates, are successively brought to the crossing point of the 

 wires in the eye-piece and in all these points the angles of inclination 

 are measured in the above described manner. It is noticed that with 

 increase of the abscissae the angles of inclination first increase and 

 then decrease. At the point of transition must be situated the required 

 point at which the curvature of the curve is or q = oo. 



In this Avay the angle of inclination in the point sought, is directly 

 known, while the distance of this point from the second position of 

 equilibrium of the quartz thread can at once be read off on the 

 reticular scale. Millimetres are directly indicated, tenths must be 

 estimated. 



A curve wi-itten by the quartz thread has in many cases a fairly 

 considerable breadth. We can then consider it as a double curve, and 

 carry out the measurement of the angles of inclination as well at 

 the upper as at the lower side of the image of the quartz thread, 

 in this way applying a control by which the accuracy of the final 

 result is enhanced. 



Before mentioning the amounts found by direct measurement, we 

 must dwell a moment on the velocity of motion of the sliding frame. 

 Most photograms were taken with a speed F of 500 mm. per second. 

 In order to render values of v that are expressed in the millimetre- 

 micrampere system, but were measured with different values of V, 

 mutually comparable, they are all calculated for V^ 500. For this 

 purpose we use the formula: 



in which ?« means the virtual resistance of the quartz thread with 

 a speed of the frame of Fa mm. per second, ?'^ being the corre- 

 sponding value with a speed F^s. 



We must further take into account the circumstance that the reticle 

 on the photogram does not always consist of accurate squares. As 

 was already mentioned in the preceding chapter, the rotational velocity 



