650 TRANSACTIONS OF SECTION G. 



the length of the cylinder and divided by twice the area of one of its ends. 

 Three examples are considered in the paper ; 



(i) A bridge having parallel chords and panels of equal length. 



(ii) A thin-walled rectangular box. 



The results in these cases are shown to be in agreement with those given by 

 other and longer methods. 



(iii) The torsion stresses in the suspended span of a bridge similar in design 

 to the New Quebec bridge. 



In this example it is shown how the stresses in the lateral system may be 

 calculated immediately by use of the above theorem, and how the stresses in the 

 main trusses may be found by means of a short graphical process. 



5. An Inquiry into the Possible Existence of Mutual Induction between 

 Masses. By Professor Miles Walker. 



The closeness of the analogy in the behaviour of matter in motion and 

 electricity flowing in a circuit leads us to inquire, ' Is there any action Letwee-i 

 masses analogous to the mutual induction between electric circuits ? ' If we 

 accelerate a fly-wheel does it produce any force upon an adjacent co-axial disc? 

 It is quite possible that a small force of the kind might pass iinnoticed if not 

 specially looked for, just as the gravitational attraction between two movable 

 bodies would ordinarily escape observation. 



The author described and exhibited apparatus constructed at the Manchester 

 School of Technology in 1912 for the purpose of finding out whether any force 

 of the kind is observable. 



A steel fly-wheel, A, 56 cm.s. in diameter and 11 cms. thick, is mounted on 

 a vertical shaft and driven by an electric motor. Above the fly-wheel is sus- 

 pended a disc, B, 51 cms. in diameter, made of very pure porcelain, weighing 

 about 10 kilograms. The suspension is made of two round steel wires each 

 "025 cm. in diameter. The length of the suspension is 21 metres. The distance 

 between the bifilars is about 015 cm. The torsional control on B is extremely 

 small, amounting to only 28 dyne-cms. for a deflection of 1 radiam. The 

 angular swing of B upon its principal axis has a natural period of 2,460 seconds. 

 A mirror is attached to B, which enables the movement to be accurately observed 

 on a scale at 6 metres distance. A movement of '01 cm. on the scale corre- 

 sponding to a deflection of 1/12,000 of a radiam can be estimated, so that one 

 can observe the effect of acting on the edge of the disc with a force amounting 

 to only 10"^^ of the weic^lit of the disc. The paper described some of the 

 precautions taken to avoid the effect of accidental disturbances. 



The procedure in making the experiment is as follows : The disc B is 

 brought as nearly as possible to rest. The fly-wheel A is then rapidly accele- 

 rated (say, anti-clock-wise) and run up to a speed of 2,700 r.p.m., so as to 

 give an impulse to B if that were possible. The speed is then maintained 

 constant for one-half the natural period of the swing of B. The fly-wheel is 

 then rapidly slowed down and the direction of rotation reversed and the speed 

 increased to 2,700 r.p.m. (clock-wise). This is repeated several times, so as to 

 set up resonance in B. 



In the early experiments made in 1913 it was found that if there were any 

 effects of the kind looked for they were of an exceedingly small order, and that 

 the observed movements of B were mainly due to accidental disturbing forces. 



At this time it was possible to assert that the ratio t — , the change in 



the angular momentum of B to that of A, was certainly less than 23 x 10 '^. 



In the later experiments the chief aim was to diminish the disturbing forces 

 as far as possible, so that the negative result might be stated with tlie smallest 

 possible limit of error. 



The introduction of a suspended screen and other refinements so improved 

 the steadiness of B while A was running that we can now state that the ratio 

 for this apparatus is less than 5 X 10"'". 



