344 Mr. Mallet on the Physical Conditions 



In imperfectly elastic solids, such as masonry, brickwork, earth, &c., the resistance to 

 penetration, immediately after impact, may be assumed to vary as something between the 

 diameter and its square ; it will certainly be much less than proportional to the areas of 

 the great circles of the respective spheres.' It will be safe, therefore, to say, that the 

 penetrative power of the 36-inch shell will be at least sixfold that of a 13-inch shell. 



Experimental data are wanting to enable any precise calculation to be made for any 

 given material. We do not know in what way or to what extent the surrounding material 

 is moved or compressed. A 13-inoh shell penetrates solid sand and earth about 2-5 feet; 

 the Antwerp shell penetrated such earth about 7-5 feet, or three times the depth, its weight 

 being about five and a half times as great. 



The 36-inch shell might, therefore, be presumed to penetrate at least 15 feet into com- 

 pact earth; and, upon exploding, to excavate a crater of 40 feet in diameter; and, as a 

 depth of about 6 feet in earth has been found to give the maximum excavation or crater 

 li'om the explosion of a 13-inch shell, so this depth of 15 feet would give about the same 

 result for the 36-inch. 



Thrown at a low velocity, the resistance of the air, to shells in flight, is, perhaps, 

 directly proportionate to the area of their great circles, or to D'^ ; or, in this case, again com- 

 paring the 13-inch and 36-inch shells, to 169 : 1296, or as 1 : 7-66, or nearly as 1 to 8. 



The energy of motion, however, or their respective powers, at equal velocities, to 

 overcome this resistance, is as their respective weights, or as 200:2966, or as 1: 15 

 nearly. 



The retarding to the moving forces, therefore, in the two shells, are as — 



8: 15, 

 or nearly 2 to 1 in favour of the large shell. 



It is certain, therefore, that much smaller proportional charges of projection may be 

 used for equal ranges with these large shells; and that, with equal projectile charges, the 

 velocity of descent from the trajectory will be much greater. 



The projecting charges for 13-inch shells varies from 15 to 20 lbs., the extreme range, 

 at 45°, being 4700 yards, or 2-10 miles. 



Assuming equal horizontal ranges at equal elevations, as due to equal velocities, the 

 charges for projecting different shells with equal velocities must be in proportion to the 

 work done in each case ; or as 



MV'-.M'V 

 or as 



3/: J/- when F= F'. 



This would give a projecting charge at maximum of nearly 140 lbs. for the 36-inch shell ; 

 but, as indicated in the text, the proportional effects of very large masses of powder are 



