351 



Art. Xlll. ASTRONOMICAL AND NAUTICAL 

 COLLECTIONS. 

 No. XIV. 

 i. The Resistance of the Air, determined from Captain Kater's 

 Experiments on the Pendulum. 



The effect of resistances of various kinds on the vibrations of 

 the pendulum is become a subject of increased importance, 

 from its influence on the determination of a standard measure : 

 for although the effect of these resistances on the time may be 

 wholly inconsiderable, it is by no means superfluous to prove, 

 by demonstrative evidence, that they are actually insensible. 



A constant resistance, and a resistance proportional to 

 the square of the velocity, produce either no change at 

 all of the time of vibration, or an infinitely small change 

 when the arc is infinitely small : but a resistance simply pro- 

 portional to the velocity, if it be at all considerable, may pro- 

 duce a sensible retardation, even in an evanescent arc. It 

 becomes, therefore, of some importance to inquire, what is the 

 law of the resistance to very slow motions ; and the elaborate 

 experiments of the indefatigable Captain Kater will afford us 

 the information that is required for establishing, in this respect, 

 the suflSciency of the superstructure that has been built on them. 

 It is, however, necessary, to take the mean of a large numbet' 

 of separate registers of observations, in order to investigate the 

 laws of the retardation ; for the question is so delicate, that the 

 results of any small number of experiments might lead to very 

 erroneous conclusions: but when properly analysed, the expe- 

 riments, related in the third part of the Philosophical Transac- 

 tions for 1819, are amply sufficient to show that a certain por- 

 tion of the resistance to the motion varies simply as the velo- 

 city ; and that it cannot be correctly expressed, as Mr, 

 Gilbert has supposed, by a constant term and a term 

 proportional to the square of the velocity only. Sir Isaac 

 Newton, indeed, has hinted in the Principia, that a constant 

 term, expressing the resistance derived from the thread suspend- 

 ing his pendulum, with another term proportional to the square 



Vol. XV. 2 A 



