13 Art. 3-K. Sotoine: 



When the radius of curvature is small, and the bubble length 

 fairly long, the case (i) occurs, exhibiting a periodic motion. But 

 in the sensitive level, the radius of curvature is necessarily long, 

 but the bubble length cannot be proportionately long. This class 

 of instrument corresponds to the cases (ii) or (iii), which represent 

 an aperiodic motion. In these two cases the bubble comes to 

 rest asymptotically, that is, after the lapse of an infinite time. In 

 other words, the bubble of our sensitive level does not come to its 

 destination theoretically in a finite time. In practice, however, to 

 wait even a pretty long time is useless, as some other disturbing 

 cause may interfere with it in the meanwhile. 



Let tx be the time interval, during which we wait for the rest- 

 ing of the bubble (practically, a minute or two), and d^ the corres- 

 ponding value of 6. Thus, — 



Then we are referring to d^ instead of as the resting point of the 

 bubble. As this discrepancy can be looked upon as caused by 

 internal friction or viscosity of the liquid, the sense of d^ will be 

 naturally opposed, when the direction of motion is opposite, giving 

 -6^. Therefore,, when the bubble has moved from opposite direc- 

 tions the resting points would difïer by the quantity 26^. This 

 property would afïord a method of determining the magnitude of 

 ^i, which we may call the resistance of the level. 



The occasional lack of parallelism in the two level bubbles of 

 the zenith telescope, commonly experienced by latitude observers, 

 can partly be explained by the above phenomenon, as the parallelism 

 would change by the sum of the resistances of the two levels, when 

 the two bubbles come to rest from opposite directions. 



Having thus examined the existence of a defect of the level 

 from the theoretical standpoint, I proceed now to ascertain the 

 order of magnitude of the resistance d^ from the experimental side, 

 depending on the principle cited above. 



The instrument I made use of in my experiments was a level 

 trier made by Hilldebrand in Freiburg, and the levels subjected to 

 the examination were the following nine pieces : — 



