II. LENGTH. 



73 



As to the two positions I. and II. of the rollers, it needs be shown that a 

 motion d<j> of the disc M causes the same effect. 



In the position I. the motion of the roller is : 



pq = a8<f>. 

 In the position II. the motion of the roller is not equal nm. 



But: 



mo = nm cosj 

 consequently : 



cos j = -- and nm=a l 



therefore : 



Fig. 5. 



The motion of the rollers, therefore, in the two positions is equal. 



To connect the distance of the points from which the mean height is 

 measured by the instrument to a point given by levelling, the height of a 

 point P of the buoy over the water is carefully measured. 



This may be very exactly done by putting the buoy into a vessel filled with 

 water. The buoy afterwards is lifted a little by the weight D (Figure 1). 

 This is easy to calculate from the area of the buoy, the weight D, and 



