308 Elastic Stability of Long Beams under Transverse Forces. 



with an error of about 1 part in 2000. The angles of twist 

 in the torsion experiments were determined by setting a small 

 mirror fixed to the vertical circle of a theodolite normal to a 

 line of sight attached to the specimen. The average error in 

 these angles was about 1/600 part. 



The values found for the bending and torsional rigidities 

 were 



/8 2 = 1*382 x 10 7 grammes weight cm. 2 



7 =2'l74xl0 7 „ 



/3i was throughout treated as infinite in comparison with /3 2 , 

 being in fact about 300 times greater. 



The results which it was attempted to verify were (6) and 

 (7) of this paper, as well as Euler's result for a long column. 



The specimen was placed in a vertical plane with its axis 

 horizontal, and supported in such a manner as to very approxi- 

 mately realize the conditions postulated in each case. 



In all the experiments counterpoises were used to apply 

 forces directed vertically upwards at points 10 cms. apart 

 along the axis, each force being equal to the weight of 10 

 cms. of the specimen. By this means the effects of the 

 weight of the specimen were almost eliminated. These forces, 

 as well as the test loads, were applied by means of steel hooks 

 fitting in small double-counter-sunk holes drilled through the 

 specimen. The verticality of the upward directed forces was 

 ensured by the following arrangement. The balance-beam 

 from which each hook and the corresponding counterpoise 

 were suspended, was itself hung from one end of a second 

 balance-beam at right-angles to the first, and both balance- 

 beams were free to turn in azimuth. This arrangement served 

 its purpose very satisfactorily. 



The specimen was adjusted before each experiment so that 

 no lateral deflexion occurred with a moderate load. The test- 

 load was then gradually increased until the point of appli- 

 cation would remain at rest in contact with either of two stops 

 placed about 1 cm. on each side of the initial position. The 

 smallest load which would produce this effect was adopted as 

 the critical load. In every case a marked movement to one 

 side or the other occurred with weights 1 or 2 per cent, less 

 than the least which would maintain a deflexion to either side. 

 It is probable, therefore, that the critical load adopted as the 

 result of experiment was slightly in excess of the true critical 

 load. 



The specimen was tested as a cantilever (formula 6) in four 

 positions, being twice inverted and once reversed end for end. 



