74 



H. J. Grayson : 



for measurement. The set of readings here given was obtained 

 before any further work was done on the screw by way of correction. 



The method employed in plotting these observations was as fol- 

 lows : — 



In the figure (1, PI. XIII.), the abscissae along the line O X repre- 

 sents the distance of the centre of the nut from its position at the- 

 first observation where the abscissa =0; measuring the first read- 

 ing or its reduced value from and the last reading (that at 7^ in.) 

 from X both downwards we obtain the points A and B respectively. 

 Then using the straight line A B as base line, all the intermediate- 

 readings were plotted by measuring them upwards from A B. Thus 

 we obtain the curve M X which represents graphically the shape of 

 the screw between the points where the nut was situated at the first 

 and last readings. Thus at the point on the screw represented by M, 

 the interval N M represents the sum of the errors of bend and eccen-^ 

 tricity, M P representing the ordinate at M of the curve formed by 

 the screw, and P N the amount by which the screw is " drunk " at 

 M due to bearing eccentricity; the actual amount of error in each 

 case being given by the scale on the diagram. 



With respect to the value of the microscope readings mentioned 

 above. One division of the microscope scale was actually .00009 cm. 

 but for convenience the observed readings, which obviously were 

 twice the actual error, were plott-ed in each case. The inch values 

 given as a scale to the diagrams are approximate only and repre- 

 sent the errors, not twice the errors. 



Ref/rindinri the Screii'. 



Progress and results at intervals of from 3 to 5 hours. — The 

 series of curves shown in Fig. 2. PI. XIII., have been prepared in 

 order to illustrate the improving shapes of the screw as re-grinding 



