PAPER BY PROF. HAGEN. 29 



As the first term of the above value of Jc comes out 2.264 or larger 

 than this by nearly 14 per cent., the stronger resistance deduced from 

 the observations is explained by the rarefaction of the air occurring at 

 the rear of the disk, which rarefaction in the case of an assumed out- 

 flow into empty space does not take place. 



Although the present investigation is confined only to those posi- 

 tions in which the disks are turned normal to the direction of their 

 motion, still it was important to be convinced that slight and unavoid- 

 able deviations from this normal position had no important influence. 

 The pins by means of which the disks were fastened to the arms 

 were directed radial' y towards the axis of rotation. Thus the disks 

 could be given any desired inclination to the direction of their motion. 

 One such experience however showed this arrangement to be en- 

 tirely unallowable in the observations, in that the simple relation 

 between the resistance and the velocity of the disk completely disap- 

 peared. The reason for this irregularity is apparent. According as 

 the two disks were inclined downwards or upwards they were pressed 

 up or down by the impinging air, and by so much the more the greater 

 their velocity was. The arms with the inclined disks and with the axis 

 of rotation therefore pressed variably upon the steel point on which the 

 axis rested, and accordingly the screw threads on the axis were varia- 

 bly pressed up or down, whereby the friction each time experienced an 

 important change. When however I inclined one disk upwards and 

 the opposite disk downwards, the axis was pressed to one side, and by 

 so much the more, the greater the velocity was. 



In order not to change the simple arrangements for fastening the 

 disks, I provided the two 5-inch square disks with roof shaped piece, in 

 addition, so that in front of the lower half of the disk the inclined plane 

 was turned upwards, and in front of the lower half an equal plane with 

 the same inclination was turned downwards. Each of the two disks 

 thus changed was thus both raised and depressed by equal forces for 

 all velocities, so that the injurious effect upon the axis of rotation dis- 

 appeared. • 



A complete series of observations (wherein both at the beginning and 

 at the end the arms were set in motion without disks in order to deter- 

 mine the resistance) gave — 



(a) When the roof surface was inclined 40° to the vertical or to the 

 plane disk, 



r = 83.92. 



(b) For an inclination of 20° to the vertical, 



r = 101.16. 



(c) And for the plane disk itself, therefore, after removing the addi- 

 tions 



r = 110.93. 



