PAPER BY PROF. HAGEN. 11 



arms uuder various loads, this could be subtracted each time from the 

 resistance observed with the disc iu place and thereby the resistance 

 of the various discs lor various velocities be determiued. 



The ivory spiudle arouud which the threads wind was, like the axis, 

 very carefully turned cylindrical, and is 1.1 inches high and l.G inches in 

 diameter. The i)ortion of the axis extending above the spindle is also 

 turned cylindrical so that for any i)ositiou of the ui)per perforated brass 

 I^late it is securely held with very little play. Under its slightly coni- 

 cal flat head are louud, as the figure shows, two openings perpendicular 

 to each other, one square and the other circular. The first serves for 

 the introduction of a small crank handle by means of which the axis is 

 turned backwards when the weights are being raised. Before taking 

 off the arms a wire is put through the circular opening which pre- 

 vents the axis from turning forward while the observer is taking off 

 tne crank and putting on the arms and discs. Moreover, at a distance 

 of 12 inches from the axis there is placed a bent lever, one arm of which 

 stands upright and hinders the turning of the arms that carry the discs 

 when the weight fastened to the other arm of the bent lever hangs 

 freely. While the arm carrying the discs is thus held by the bent lever 

 the stout wire is withdrawn and the air is allowed to come to rest. It 

 the weight be placed on the neighboring table then the bent-lever arm 

 falls and the apparatus starts in motion. 



The pitch of the screw of the axis below the spindle is O.Oo inch, and 

 this distance corresponds to the width of both threads so that the latter 

 lie regularly close to each other on the surface of the spindle. This 

 always occurred very regularly even when the axis was turned very 

 rapidly by means of the crank handle. The threads, the so-called " iron 

 twine," were so strong that each with safety carried 4 pounds, which 

 weight, however, was never even distantly approached in practice. The 

 threads were so light that 40 feet weighed only 0.1 loth, so that the fall 

 of the index by G feet increased the driving power by only 0.03 loth. 

 Nevertheless, for very feeble loads iu the scale-pans a slight increase iu 

 the velocity was apparent during the descent, and in order to prevent 

 this the small increase iu the weight was annulled by means of two equal 

 threads suspended from the scale-pans to the floor. 



Since the two former or driving threads were fastened to the rod they 

 •were thereby prevented from turning and unwinding, which I had been 

 able to avoid iu my earlier work only by guiding the scale-pans by 

 means of taut wires. Even if, however, the threads by this method of 

 fastening did not materially change, still it remained to be proved 

 whether perhaps they lengthened sensibly with greater tension, in 

 which case the relation between the path of the index and the rotation 

 of the arms could not remain constant. Such an extension could not 

 be mistaken when I laid a weight of 1 pound on the empty scale-pans 

 when they were at their lowest position. The index then sank at once 

 0.2 of an inch. A further extension, however, did not follow ; at least 



