ON RIFLED GUNS. 31 



(35)— The angle made by the inclined edges of the cutter does not appeal* to be given. 

 For the sake of illustration, this angle will be supposed equal to that given in the figure on 

 the plate fronting page 299; so that 



i <!> — Sl°.45'. 



(36) — Take at random from the table any weight and its corresponding cut; say 



W = S000 lbs., and a = 0,78 in. 



These data in Eq. (21) give 



A = 792S10 lbs. Log 5.8991090. 



(37) — Now, suppose this cut of 0,78 in. to be produced by the action of the expanding gas 

 in the gun; Eq. (24) will give 



P = 5005 lbs. 



(38) — -It may be objected that the function in Eq. (22) gives the maximum pressure P at 

 the middle point of the penetration. The objection is of little worth, for the object being to 

 find the maximum pressure to which the gun is subjected, it matters not where it occurs, so 

 that it be found. That function is employed to find the work of p over the distance 1; 

 and this work being measured by the area included between the curve of which Eq. (22) is the 

 equation, the extreme ordinates, which are nothing, and the path 7, that area will be sensibly 

 the same wherever the maximum ordinate P may be found. 



(39) — The several values of m, as deduced from the table and tested by the method of 

 least squares, give the mean error equal to 0,4411; the probable error in any one determina- 

 tion 0,299G; and the probable error in final result 0,0831. But among these values there 

 are three remarkable for discordance with the others. If these be rejected, as having been 

 influenced by something extraneous to the recognized agencies of the experiments, we find 

 the mean error 0,2G81; probable error in any one determination 0,1816; and probable error 

 pi final result 0,0572 — a sufficient proof that the method proposed for evolving the law of 

 copper resistance will lead to the desired result. 



(40) — As before remarked, the copper should be neither hammered nor rolled, as these 

 processes break up the homogeneousness of the material and develop unequal resistance at 

 different points and in different directions. 



The form of Major Rodman's cutter seems to be objectionable. It would be much better 

 to use a conical point, and rely upon a Filar Micrometer, with great magnifying power in the 

 eye-glass, to measure the surface diameter of the penetration. 



West Point, 1865. 



(343) 



