174 
SHORT NOTES ON PROFESSIONAL SUBJECTS. 
Suppose, now, that it were necessary to bring the gun up at 15 ft., we should 
have 
y ” -77T- “ ‘0067 X 15 = 3-84; 
oD 
and a would be 10° 4S'. 
In this case it would probably be found expedient to construct the railway so 
that it should curve upwards, and the semicubical parabola would be found to be 
a highly suitable curve for the purpose. Its equation is 
yt = a?x 8 ; 
a? = ^= -00239, 
dy _ 3a x i 
dx 2 
= tan 6. 
Hence the angle of ascent would increase from 0 to 15° 31'. 
Keturning to our heaviest gun, and assuming that, contrary to expectation, the 
recoil has carried it to the summit of the slope, we have next to calculate, on its 
running down again, what velocity it will acquire by the time it reaches the bottom. 
It is evident that gravity will bring it down, and friction will retard it. Hence we 
have 
acceleration = (j (sin a - /x cos a) = t; y. 
ds 
Integrating, 
8 — q . 4* O. 
2 g (sm a — fx cos a) 
When S — o v = o, . *. C == o ; 
v = a/2 gs (sin a - /x cos a) ; 
and putting 8 = 120 (strictly 120 sec 1° l'*5), v = 9*26 at the bottom of the 
slope. 
The gun will then travel over about 100 ft. on the level, and will then rise up 
another inclined plane made to consume the remaining energy; after which, it will 
run down again, and come to rest not far from its first position when fired. 
In the foregoing calculation the resistance of the air is neglected, being small and 
on the right side. 
111. New Iron Siege Carriages. By Captain W. Kemmis, B.A. 
The following iron carriages are proposed for the siege train, and of them the 
first named has recently been approved, namely ;— 
Nature. 
Weight, 
empty. 
40-pr. M.L.R. of 34cwt., gun-carriage . 
64-pr. M.L.R. of 64cwt. (II. & III.), gun-carriage... 
8-in. M.L.R. of 46cwt., howitzer-carriage. 
Siege limber ... 
cwt. qrs. lbs. 
24 2 0 
30 2 O 
40 1 14 
11 0 14 
