4^2 TIIIRD REPORT 1833. 



made by means of a cast-iron ball, 44 lbs. weight, suspended 

 by a cord from the top of a room with a radius of 16 feet. The 

 ball, when hanging freely, just touched laterally an uniform 

 bar of cast-iron, sustained at its ends in a horizontal position 

 by supports under it and behind it, four feet asunder. The 

 intention was to strike the bar, sometimes in the middle and 

 sometimes half-way between the middle and one end, with im- 

 pacts obtained by drawing the ball and letting it fall through 

 given arcs, shifting the bar when the place of impact was to 

 be changed, and obtaining the deflections of the bar at that 

 place by measuring the depth which a long peg, touching the 

 back of the bar, had been driven by the blow into a mass of 

 clay placed there. The results were : 



1. The deflections were nearly as the chords of the arcs 

 through which the weight was drawn, that is, as the velocities 

 of impact. 



2. The same impact was required to break the beam, whe- 

 ther it was struck in the middle, or half-way between the middle 

 and one end. 



3. When the impacts in the middle and half-way between 

 that and the end were the same, the deflection at the latter 

 place was to that at the former nearly as three to four, which 

 would be the case if the locus of ultimate curvature, from suc- 

 cessive impacts in every part, was a parabola. 



The preceding deductions the author had found to agree 

 with theoretical conclusions, depending on the suppositions, 

 (1.) that the form of a beam bent by small impacts was the 

 same as if it had been bent by pressure through equal spaces ; 

 and (2.) that the ball and beam, where struck, proceeded to- 

 gether after impact as one mass. These suppositions likewise 

 gave as below : 



4. The power of a heavy beam to resist impact is to the 

 power of a very light one, as the sum of the inertias of the 

 striking body and of the beam is to the inertia of the striking 

 body. 



5. The time required to produce a deflection, and conse- 

 quently the time of an impact, between the same bodies, is 

 always the same, whether the impact be great or small. The 

 time, moreover, is inversely as the square root of the stiffness 

 of the beam. 



6. The results of calculations, comparing pressure with im- 

 pact, gave deflections agreeing with the observed ones, within 

 an error of about one eighth or one ninth of the results. 



