118 Prof. K. Honda and Mr. S. Konno on the 



oscillating system below x from the upper end; we have the- 

 relation 





o, 



where Y is the displacement of the centre of the lead sphere. 

 Integrating twice this equation with respect to x, and putting 



#=0 and I in the result, we have, since ~=0 for # = 0, 

 / ^Y ]%Yx Z 3 EJa» £5a» iT _ 



\rw + ~ry 3 + "IT Y + it it - v> 



^cPY /Ma , E4a«\_ f 6a 3 rfY „ 



The solution of this equation is 

 Y=Y ft ^ 8/3M cos 



Hence \ — 



/2tt« \ 

 ?6a 3 T 



16MF 



16M/ 3 X 



6o«T 



Thus, by observing the period and the logarithmic decre- 

 ment of the suspended system, £ can be determined. In this 

 case, both the period and the amplitude of oscillations are 

 fairly large and admit of an accurate determination. 



5. The arrangement of experiment is shown in fig. 2. 

 B is a stout bell- jar made of thick cast iron resting tightly 

 on a plane disk E ; the jar can be evacuated by a Gaede 

 rotary pump through the tube F. The oscillating system is 

 firmly fixed to the head-piece A in the manner as shown in 

 fig. 3. D is'a metal tube with a caoutchouc tube and a 

 stopper ; by puffing air through the pipe at intervals equal 

 to the period of oscillations, the amplitude of oscillation can 

 be increased to a desired magnitude, m is a small mirror 

 attached near the upper end of the band. A narrow beam 

 of light coining from a slit S passes through the glass 

 window o, and is reflected by the mirror m ; after the ray has 

 passed through the lens L of a large focal length, it is again 

 reflected downwards by a large mirror M to the cylinder G 

 of a chronograph. A second beam of light from another 

 slit S' adjacent to S follows nearly a similar way to the first 

 beam, the first reflexion, however, taking place at a fixed 

 mirror (omitted in the figure) adjacent to the vibrating 



