12 



THE MECHANICS OF THE EARTHS ATMOSPHERE. 



it was not to be observed iu the short interval occupied by each sepa- 

 rate observation. In consequence of this extension of the threads it was 

 incumbent to lay those weights that were to be used to set the axis iu 

 motion during the next observation upon the scale-pan while the latter 

 was at its lowest position. The threads were therefore always wound 

 up under the same tension with which they were to do the work. 



The question now arose whether with stronger tensions the spiral 

 windings of the threads perhaps lay flatter on the spindle than with 

 weaker tensions, and whether therefore the length of a winding or the 

 path that the index described for one turn of the arms became shorter. 

 This point was decided in that with various loads in the scale-pan 1 

 measured the path that the index described during a certain number 

 of revolutions. The above-mentioned bent lever offered the opportu- 

 nity of always stopping the arms at the same point, but it was necessary 

 to bring them to rest by gentle pressure, because with a strong blow 

 against the upright standing arm the horizontal arms carrying the discs 

 could easily turn somewhat on the conical head of the axis. After the 

 position of the index was read off I allowed the arms to make five com- 

 plete turns and again read off the position of the index on the scale, 

 estimating only to the hundredth part of an inch. 



The lengths of the paths for the corresponding weights in each scale- 

 pan are as follows : 



* Prussian loths. t Rhenish inches. 



A very slight shortening of the path appears from this to occur for 

 the heavier loads, but if it actually exists it is so small that it is far less 

 than the accuracy of the measurement of the path of the index on the 

 divided scale. It may therefore be assumed that the velocity of the 

 index stands in a constant ratio to that of the arms or disks. 



The lengths of the individual windings of the thread around the 

 spindle as resulting from the above measures do not correspond in all 

 accuracy to the circumference of a circle that is normal to the axis of 

 the spindle, and at a distance therefrom equal to that of the central axis 

 of the threads, inasmuch as the threads lie spirally around the spindle. 

 Now the pitch of the screw measures 0.05 inch ; therefore the threads 

 on the surface of the spindle make an angle with the horizon 0° 33' 29". 

 Since the average length of one winding of the thread is 5.134 inches, 

 therefore the equivalent thread encircling the normal is somewhat 

 smaller, namely, 5.1338. Hence the resulting distance of the center of 

 the threads from the axis of rotation or the length of the lever arm by 



