34 PROCEEDINGS OP SECTION A. 



In each of these rods two holes equidistant from the beam are drilled, 



through which the upper ends of the thread forming the V suspension 



pass. Ordinary binding screws on the upper surface of the rods serve 



to make fast the strings and render quick adjustment of length easy. 



The distance between the holes in each rod should, of course, be 



sufficient to enable the V of string supporting either bob to clear the 



bed, the bobs of the pendulums being vertically under the beam and 



bed and able to move only in a vertical plane parallel to the axis of the 



beam. 



To the upper side of the beam, opposite the runners, at either 



end are attached two platforms on which the masses used to vary the 



coupling can be placed. It was shown in § 3 that the square of the 



coupling or 



. 9 , mi »i2 



sm w = 



{M + mi) {M + m^) 



where M is the total mass of the beam, so by increasing the load on the 

 beam, M in the above will be increased and the couphng diminished. 



8. In order to exemplify the use of the model for the purpose of 

 illustrating the properties of coupled circuits, I will describe some 

 experiments on the relation of the resultant periods to the natural 

 periods and the coupling. 



Adjust the pendulums to be of about the same length, put different 

 masses for the bobs, say make one twice as hea^y as the other, and make 

 the coupling loose by arranging that the mass of the beam shall be at 

 least ten times the mean of the masses of the bobs. 



Determine by observation the natural period of each pendulum. 

 As has already been explained, this is done for the first by placing the 

 bob of the second on its platform and counting the number of swings 

 made by the first in a given time in the usual way ; similarly determine 

 the natural period of the second pendulum. 



The natural periods can now be computed by means of the formula 

 in § 3 if the masses and lengths have been measured. 



To the actual mass of the beam and its loads must be added a 

 correction for the wheels to obtain the value of M in the formula 

 referred to. It is easy to show that if the wheels are constructed as I 

 have described, this correction is equal to 



o i^^R' + i 



{R + rf 

 where )u is the mass and 1 the moment of inertia of each complete 

 roller. It the radius of a wheel and r the radius of a spindle. 



The agreement between the observed and calculated natural 

 periods will enable one to judge of the perfection of the model. 



Now impart motion to the system, the initial conditions being 

 those already specified in §§ 4, 5. 



