PAPER BY PROF. HAGEN. 17 



This then gave, 



z=- 0.724 

 p= + 1.034 

 s = +15.518 



According to this last we obtain for G the values given in the column 

 headed B, whose errors B — G are shown in toe last column. We 

 remark that these latter do not occur regularly, owiug to the change 

 of the signs for the heavier weights, and therefore can be looked upon 

 as accidental errors of observation. The sum of the squares of the 

 errors amounts in the last case to 0.004252, whereas in the first case it 

 was 0.011055, therefore more than twice as great. 



There is still another reason that favors the introduction of the first 

 power of the velocity. So long as I neglected this term there occurred 

 without exception the inexplicable phenomenon that for observations 

 with disks the numerical value of the constant rafter the negative sign 

 was always greater, therefore the friction was always smaller, the larger 

 and heavier the disks were. This anomaly disappeared upon the in- 

 troduction of such a second term. 



There is, moreover, as the observations show, a peculiar condition in 

 connection with the second term. The coefficient p assumes a very 

 small value or entirely disappears when the screw on the axis is freshly 

 oiled. From this we may conclude something as to its significance, i. e., 

 it indicates the resistance that arises from the viscosity of the oil and 

 which is proportional to the velocity. 



When disks are attached, the resistance peculiar to them is found 

 when we subtract from the observed resistance that which the arms 

 experience for equal velocities. This latter, however, is so variable 

 that we must measure it anew every time, and since it assumes various 

 values within even short intervals, therefore there remains only one 

 method to determine the value of the three constants *, p, and s, namely, 

 to allow the arms to revolve alone with three different velocities both 

 before and after each observation. When, however, as usually hap- 

 pened, a second measure again gave somewhat different values, then 

 the appropriate mean value corresponding to the intervening time 

 should be used in the computation. 



In the resistances of the disks found in this manner the second term 

 proportional to the velocity is no longer contained, because the influ- 

 ence of the viscosity of the oil has already been allowed for in the 

 resistances of the arms. The constant z is, on the other hand, so 

 variable that it must be specially deduced from each series of observa- 

 tions. 



80 -a 2 



