322 Mr Sang on Captain Eater's Experiment 



other errors more vitally affecting the progress of mechanical 

 science. 



When a rod is slightly bent, one side of it is distended, and 

 the other side is compressed, so that between the two there 

 must exist a locus of no compression and of no distension : it 

 had hitherto been believed that this locus is in the middle of 

 the bar, but Captain Kater has in this paper announced a new 

 doctrine, viz., that the neutral plane is nearer to the convex 

 surface of the bar, its distance from that surface being scarcely 

 one-third part of the whole thickness. 



If this inference be correct, it must follow that solid bodies 

 resist distension with an energy eight times greater than that 

 with which they resist compression. Yet all the experiments 

 which have been made on this subject go to shew that, to mo- 

 derate compressions and distensions, the resistances are alike, 

 but that, on being pushed nearly to the destruction of the sub- 

 stance, the resistance to compression seems to be rather the 

 greater of the two. 



The discrepancy between these results and that of Captain 

 Kater is so great as to leave no doubt on the mind that, in 

 one set of observations or in the other, some important over- 

 sight has been committed ; and I now proceed to shew that 

 the oversight has been entirely on the side of the Captain. 



When a thin bar is slightly bent, a shortening must take 

 place in the distance between the two extremities of the neu- 

 tral plane, since the straight line is shorter than the curved 

 one ; but the distance between two points on the upper sur- 

 ace will be augmented or diminished according to circum- 

 stances. Thus, if the upper surface be" distended, and if its 

 distension be greater than the shortening due to the curvature 

 merely, an increase in the distance will be observed ; while, 

 when the upper surface is compressed, a shortening will ap- 

 pear equal to the sum of the shortening due to curvature, and 

 of the shortening due to compression. So that, in order to ob- 

 tain the effects due to compression or distension alone, the 

 shortening arising from curvature, or, as it is called, the re- 

 duction of the arc to its chord, must be allowed for. This al- 

 lowance has been made by Captain Kater, and although in 

 this he has committed a treason against the laws of geometry, 



