AND THIN ELASTIC RODS. 373 



I will conclude this paper with a short resume of some of the more interesting results of 

 experiment as to the range &c. of the bolts, and the general power of the steel cross-bow. 



First, the " bolts" I used were of two kinds, either capped with iron cones, or with blunt 

 leaden heads ; the iron cones were about 2^ inches long, and three-fourths of an inch broad 

 at the base, the shaft was c)flindrical, about 6 inches long, made of deal, and scooped out in 

 such a manner as to leave three edges between the two ends. The iron-coned bolts pene- 

 trated from about an inch and a third to an inch and a half into sound deal planking. The 

 weight of the bolts varied from about an ounce to an ounce and three quarters, and their 

 flight was remarkably true. The greatest range of the blunt-headed bolts was about 240 yards 

 at 45°, the iron-pointed ones would probably go 20 or 30 yards further ; but as the only 

 available ground I could find for my experiments as to range, was a portion of a public road 

 I had measured, I thought it imprudent to launch pointed missiles upon it, at a distance 

 such that persona might be passing, and yet not be visible to me. 



With a weaker bow the difference was 15 yards in the range between the two kinds of 

 bolts; the iron-headed bolt had a range of 150 yards, and the blunt-headed bolt only 135; 

 the experiment in this case was attended with no danger, as the road was bounded by open 

 fields on both sides up to that distance*. As far as I could judge by mere inspection, I 

 should think the strongest cross-bow with which I experimented was at ieast as efficient a 

 weapon as any I have seen among the numerous collection of ancient arbaletes preserved in 

 the Musee d''Artillerie at Paris, and yet the velocity of a rifle-ball is more than 8 times the 

 velocity of a bolt discharged from so powerful a bow as the one I possess. 



The value of & the coefficient of resistance was obtained from the equation 



CJ?" w'cos-a 



where for a I wrote 



15 



f 1 + — !— ) O! 

 \ cos a J 



X — . 



as 



When a =» 45*, this empirical approximation for s gives results of considerable accuracy ; the 

 approximation being much closer than can be obtained by taking several terms of the series 

 for y, developed as in the books by Maclaurin's Theorem — at least it does so for the particular 



1 

 800 



values of a and k which I had to deal with. For bolts of from l to 1^ oz., k varied from 



to and , when the bolts were not conical-headed. To determine the value of the 



1100 1200 



other coefficients of higher powers of v in the expression for the resistance, no velocity less 



than that imparted by gunpowder is sufficient. In all cases k was found to be much greater 



than its theoretical value. * 



J. H. ROHRS. 



• The ranges of tliese two bows were afterwards increased to 260 yards and 180 yards respectively, for blunt-headed 

 bolts, by using cords lighter than in the first set of experiments. 



