18 



THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



The following observations were made with two square disks of 6 

 inches on each side.* G' indicates the weight placed in each scale pan, 

 and this changes to G when we subtract the weight required to over- 

 come the resistance of the arms for equal velocities. The second col- 

 umn contains as before the times during which the index sinks by 1 

 inch, as found from the two measurements respective'^-. 



Adopting the expression, 



^ = ^ + 1 r 

 P 

 I find as most probable values 



- = - 0.335 

 r = -f 124.L'4 



From this the values of G given in the column marked A are deduced 

 for the respective times. The errors of these, as contained in the fol- 

 lowing column, vary so much in sign that we can consider them as 

 accidental and there is no reason to introduce still another term in the 

 above exijression. In this connection it must still be mentioned that 

 when in the computation of the earlier observations I have assumed the 

 coeificient^ equal to zero, a satisfactory agreement of the resistances 

 appears for larger disks as soon as I set the resistance proportional to 

 the square of the velocity. This is explained by the fact that the value 

 of the term ^ is very small in comparison with the stronger resistances 



which the disks experience. 



[*In all that follows it is to be understood that before and after each series for the 

 determination of the resistance of the disks a special series has been made with 

 the arms without disks for the determination of the combined correction for arms 

 plus friction, and that thence the correction for the resistance due to the arms has been 

 computed. G' is the weight required to overcome the friction plus the resistance of 

 the disks and arms ; G is the weight required to overcome the friction plus resistance 

 of the air to the motion of the disks ; :: is the weight required to overcome the 



friction ; — is the weight required to overcome the resistance to the disks. — C. A.] 



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