324 Mr Sang on Captain Katefs Experiment 



while the inclination of the extremity is \ I s multiplied by the 

 same constant. But when the same bar is supported at the 

 ends, the depression of the middle is proportional to ^y 4 , while 

 the inclination at the extremity is as £P. Hence, from what 

 was previously well known, it turns out that the inclination in 

 the one set of experiments is exactly double that in the other, 

 so that, supposing this ratio of one to two to have been found 

 experimentally, we ought to have concluded that the plane of 

 neutrality is equidistant from the two surfaces of the bars, 

 Captain Kater's experiments, therefore, so far as they go, con- 

 firm the truth of the old doctrine, and refute this new one pro- 

 pounded by himself. 



This result has been obtained, by taking, as I have said, a 

 very crude view of the state of a bent rod. Let us conceive 

 the rod, while straight, to have been mai'ked off into a multi- 

 tude of rectangular portions : these rectangles have been sup- 

 posed to change into trapeziums by the flexure. This suppo- 

 sition is, however, but a rough approximation, barely admis- 

 sible in the case of a thin bar, very slightly bent. The true 

 form of the rectangular portions of a solid, after that solid has 

 been subjected to pressure, is yet unknown ; the want of that 

 knowledge being one of the obstacles to the farther advance- 

 ment of this branch of mechanical science. Seeing, then, the 

 nicety of the instruments with which Captain Kater wrought, 

 and the evident care which he had taken, I was in the hope of 

 eliciting some information on this point from his experiments ; 

 and, with this view, commenced a minute discussion of them. 

 But at the very threshold of the inquiry, difficulties, most un- 

 expected in such a quarter, at once arrested my progress. 



In making the reduction of the arc to its chord, I found 

 that Captain Kater had used some processes quite as startling 

 as the proposition, the fallacy of which I have just exposed. 



Some of the bars on which he experimented were longer 

 than others, while the distance between the dots was in all 

 cases nearly the same, viz. 36 inches. The difference be- 

 tween the whole arc and its chord having been computed, the 

 reduction of the observed arc to its chord was thence found 

 by direct proportion. Thus the reduction on an arc of 60 

 inches having beencomputed at .0001000, that of a portion of 



