PAPER BY PROF. HAGEN. 13 



which the weight acts is equal to 0.81705 inch. This figure is adopted 

 in the following computations, where it is represented by the letter a. 



It remains still to investigate whether the steel wire that carries the 

 axis may perhaps depart so far from the vertical direction by the move 

 ment of the lever on which it rests that it occasionally may exert an 

 appreciable side pressure and thereby in an injurious way increase the 

 friction in the screw threads. The lever is, as was mentioned, not only 

 perfectly balanced, but the point that carries the counterpoise is also 

 situated in the prolongation of the straight line drawn through the 

 supporting point of the wire and the rotation axisof the lever. Therefore 

 for every position of the lever the foot of the wire is pressed upwards 

 vertically with equal force, but it rises only 0.8 of an inch, while the 

 weight that drives the disks around in the extreme case sinks 80 inches. 

 Therefore the deviation of the foot of the steel wire from a mean position 

 amounts only to 0.4 of an inch, or in angle 2° 24' 48", for a length of the 

 lever arm of 9 5 inches. Therefore the deviation from the initial vertical- 

 ly is limited to 0.0086 iuch,aud consequently the wire 12 inches long 

 is inclined 0° 2' 38" to the vertical. Even this small inclination can be 

 reduced by one half if we place the axis of the wire or its upper point 

 in the vertical line that bisects the deviation of its lower end, but such 

 accuracy in the establishment of the apparatus must not be anticipated. 

 It is evident from this that there can be no sensible increase of the fric- 

 tion in consequence of the movement of the lever. 



As regards the execution of the observations the remark must be pref- 

 aced that the Rhenish inch, or the twelfth part of the Prussian foot 

 according to the earlier determination of the standard, and the old Prus- 

 sian loth, of which 32 make 1 Prussian pfuud, have been adopted as 

 units of length and weight.* The divided scale over which the index 

 glides is divided into tenths of inches, but this subdivision is only used 

 for determining the length of one winding of the thread, as previously 

 described. In all other cases only the transit of the index over the 

 heavier division marks for each 10 inches was observed by the beatiug 

 of the seconds clock and the corresponding whole or half seconds noted. 



Since at the beginning of an observation the armsdo not immediately 

 assume that velocity for which the resistance in connection with the 

 friction balances the acceleration, therefore the significant observations 

 began only when the weight had fallen 20 inches or the index had 

 passed over the twentieth inch mark. At the seventieth inch the weight- 

 scale pan had approached the floor, and therefore here the measures 

 must be stopped. When, however, the rotation of the arms was ob- 

 served without disks and the weights employed were very slight, then 

 the speed continued increasing somewhat longer and the time of transit 

 over the twentieth inch could not be used in the calculations. 



[* One Rhenish inch = 1.0297217 English inch = 26.15446 millimetres. One Prus- 

 sian loth = 0.032226 pounds avoirdupois = 14.616 grammes. (See Barnard's Weights 

 and Measures, C. A.] 



