4() Messrs. Ayrton and Perry on the Determination 



since the reading of our paper, to take up the complete 

 mathematical investigation of the influence of the " kick " we 

 referred to on the time of vibration of a long wire pendulum. 

 First, for Arc. — We said that the result of this correction 

 was unimportant, and we did so for this reason. The length 

 of the pendulum was 939*09 centims.; the amplitude or the 

 length of a complete swing backwards and forwards varied on 

 different days from 50 to 20 centims., but was always less than 

 30 centims. for the observations given in our paper ; so that we 

 have to consider an elongation of 7 J centims. on each side of 

 the vertical line. The correcting factor to reduce to infinitely 

 small arcs is, of course, 



X 16V939-09/ J ' 



which leads to an addition of only j2 5*000 of the whole value 

 for g, considerably less in fact than the tenth of a millimetre 

 per second per second. 



Secondly, for Buoyancy. — On page 300 of our paper we said 

 this correction adds 0*16 centim. per second per second to the 

 value of g, which calculation may easily be verified from the 

 given size of the brass ball, namely 8*20 centims. in diameter. 



Thirdly, for Resistance. — We stated that this was negligible ; 

 and we still do not see how it can be otherwise when the re- 

 sistances due to air-friction, to the tip of the platinum wire at 

 the bottom of the bob passing at each swing through the two 

 or three millimetres of mercury, &c. were so small that the 

 well-known formula for n swings, 



*-£&.($> 



failed to give, even for a considerable value of n, a value of 

 this logarithmic decrement differing sensibly from nought. In 

 fact it is well known that, for a metal ball of 8 or more centi- 

 metres diameter, the resistance arising from viscous friction of 

 the air is insignificant. 



The number then for g, as given in our paper, was corrected 

 for arc, for buoyancy, and for resistance. 



There is, however, a fourth correction, which, although some- 

 times included under " resistance," is not a correction for a 

 resistance or retarding force at all, but for the increased mass 

 moved due to the inertia of the air — a correction which, by the 

 by, can only be applied in the roughest way possible to a 

 Kater's pendulum, or to any pendulum other than a sphere 

 suspended by an infinitely thin wire. This air-inertia correction, 

 which is perfectly definite for a simple pendulum such as we 



