OF ARTS AND SCIENCES. 



399 



rection of 7]^ is absolutely insensible, or, in other words, the effect of 

 resistance (supposed proportional to the velocity) vanishes. That this 

 is nearly, in fact, the case for my instrument is shown by the circum- 

 stance that the times of oscillation upon stands of different rigidities 

 agree with the values calculated in leaving the internal friction out of 

 account. 



U. S. Coast Survey. Pendulum. Decrement of Arc due to internal friction of brass 

 of tripod. Pendulum was swumj on brass tripod in Paris, Geneva, and Kew. 

 On a stand ten limes as stiff in Hoboken. The times of decrement given are the SUM 

 of the times with the heavy end up and heavy end down. 



Tlie last interval is probably affected by an error in the graduation of the 

 scale used on one of the stands. 



M. Plantamour proposes to determine the effect of the internal fric- 

 tion of the pendulum-stand upon the correction for flexure, by means 

 of the difference between the statical and dynamical flexure. He has 

 made numerous observations, which, according to his own interpreta- 

 tion of them, would show that, if a pendulum be supported in a certain 

 inclined position until the stand has had time to take its position of 

 equilibrium under this force, and then be let go, the ratio of the ampli- 

 tude of oscillation of the stand to that of the pendulum is not the 

 initial one, but is very different from that. If this were the case, the 

 motion of the stand and pendulum could not be represented, even 

 approximately, in the form (1), for by those equations the logarithmic 

 decrement of the oscillation of the stand is the same as that of the 

 pendulum. It is true that the two parts of the oscillation (nearly in 

 the natural periods of the pendulum and of the stand) have different 

 logarithmic decrements ; and, as the ratio of their amplitudes is not the 



