PAPER BY PROF. HAGEN. 19 



The resistance of the air against the dislis is therefore proportional 

 to the square of the velocity, and a single observation would suflSce to 

 give the coefficient r if the value of s were known, but since this is so 

 very variable, therefore at least two observations at two different veloci- 

 ties are necessary. The further extension of the measures is unneces- 

 sary, as already before mentioned, because the greater accuracy at- 

 tained surpasses the other inevitable errors j but for greater security 

 and especially to avoid possible mistakes I have always repeated these 

 two measures, and in such a way that beginning with the less velocity 

 I then execute the two measures with the greater velocity and finally re- 

 turn again to the less. 



From the values of r found in this manner the pressure that the disk 

 experiences for various velocities is directly given. Let a be the known 

 distance of the axis of rotation from the center of the threads wound 

 round the spindle and R the distance of the same axis from the center 

 of pressure of the air against the disk, then this pressure becomes 





But - is the velocity of the thread, hence the A^elocifcy of the center of 



pressure of the disk is 



0=:? 



at 



and D= — r c^. 



R^ 



if we introduce the pressure on a unit of surface, since F is the whole 

 surface of the disk, we have 



D_a^ r , 



f-r^f''-"'' 



In order to reduce the constant r to the barometric pressure of 28 

 inches or 336 Paris lines, and to reduce the temperature to 15° C, we 

 have for an observed pressure. A, in Paris lines, and an observed tem- 

 perature r in centigrade degrees during the observations the reduced r 



=^ (0.9480 + 0.00347T) r. 

 A. 



The distances R, on account of the great lengths of the arms in com- 

 parison with the width of the disks, agree quite nearly with the dis- 

 tances of their centers of gravity from the axis of rotation, but they are 

 always somewhat larger and there is no reason to omit this correction, 

 which is easily executed. 



We consider first a rectangular disk whose height is h and width h. 

 As the origin of abscissas we may take its center of gravity whose dis- 

 tance from the axis of rotation is A, and consider the disk divided into 



