438 
AUTO-SIGHTS. 
NOTE BY PROFESSOR A. G. GREENHILL, M.A., F.R.S. 
Professor of Applied Mathematics at the Ordnance College. 
The mathematical treatment of this subject is quite correct, but a 
little more laborious than is necessary. I think TO may be re¬ 
placed by TE, in the author’s figure I, with sufficient accuracy for 
practical purposes, provided the suitable value of p is chosen. 
Firf. 3. 
If the pivot leans forward zj/, and the sight is directed on the target 
T, the automatic sight will give the elevation requisite for the range 
GC, so that the trajectory will be GED, where GD — GC. 
Drawing DE, making the angle TDE equal to P L the range table 
angle of descent at the range GC or GD to cut the sea level SL is E, 
then E may be taken with sufficient accuracy as the point where the 
shot strikes the water, and the error in range is 
TE = AiR ( + ) suppose. 
Then 
A,R = TE = TD . /3 ' [and TD = TO] 
1 sin (P 1 + M) '• J 
_ Tfl sw Pi 
sin (p x + M) 
_ T t sin Pi 
sin (M— 4 ) sin (P x + M) 
rrp sin 4 ' sin & 
„ sin (M— 4 ) sin {/ 3 1 + M) 
and GT = R,. while the sines may be replaced by the angles, all ex¬ 
pressed in minutes, so that 
A x R __ 4 x fa* 
R ~ (M'-T) (&' + M') 
and the percentage error is 
100 ^ Pi _ 
R (M— 4 ) (ft + M) 
400 p 
~ (M— 4 ) (p + M) 
Re¬ 
takingand p ! as practically undistinguishable. 
