Prof. G. Forbes. Exterior Ballistics. [Dec. 19, 



Thus in (1) X'/C'-X/C, and V is unchanged. Therefore t'i remains- 

 unchanged, or v\ = VL And in (2) t'/t = c'jc = l/m ; or f = */ro. 

 Also VQ is found from the equation 



T (v f } T (V) - M' = T (V) - ^ = 

 \j O 



Therefore v'o = % 



Again, in (3) 



^' = C'{D(V)-D(^ )} = < 





It appears then that if the air-density be increased m-iold and the 

 range diminished m-fold, the elevation and time of flight must be 

 diminished m-fold, but the remaining velocity is the same. 



The above is founded on Niven's formulae, but those of Siacci and 

 Mayevski lead to the same result. 



Another important correction is that of muzzle velocity, which 

 depends upon age of gun and on temperature and nature of explosive. 

 If there were no air-resistance the ordinary formulae tell us that the 

 elevation for any range varies inversely as the square of the muzzle 

 velocity. I find empirically, by comparison of range-tables based 

 on experiments with different muzzle velocities, that the same law 

 holds over a very considerable range of muzzle velocities up to 

 elevations of 10 at least. This has been tested with the Naval guns- 

 of 13 - 5 inch, 12 inch, 9*2 inch, and 6 inch diameters. 



We can now subject these two laws (air-resistance and muzzle 

 velocity) to a very severe test. Take the Naval range-table for 12-inch 

 B.L. Gun, Mark IX, with an 850 Ib. shot and muzzle velocity 

 2433 feet per second and from it calculate (by the two laws above) 

 a range-table for the 6-inch Q.F. gun, Marks III, IV, and VI, with a 

 100 Ib. shot and muzzle velocity 1960 feet per second. 



To do this, note that the ratio of 



Diameter 2 12100 1 



Weight 6 2 850 0'4706 



Hence we must multiply the ranges and elevations of the 12-inch gun 

 by 0-4706. We must further multiply the new elevations by 1-540, 

 the f ratio of the squares of muzzle velocities. The following table 

 shows the results, and a comparison with the data for the 6-inch gun 

 from the Addenda to Naval Kange-Tables, and the differences : 



