266 M. L. v. Karolyi on the Products 



a x cos a ! + a 2 cos a 2 + a 3 cos a 3 + a 4 cos a 4 = constant, 

 a 1 sin «j +« 2 sin a 2 — a 3 sin a 3 — « 4 sin « 4 = constant ; 

 .*. « x sin a { 8oi x -f « 2 sin a 2 Sa 2 + # 3 sin u 3 Sa 3 + *z 4 sin cc 4 Sa 4 = 0, 

 «! cos u x Su x + « 2 cos a 2 Sa 2 — « 3 cos a 3 Sa 3 — « 4 cos a 4 Sa 4 = ; 



which, since ot 2 =zu 1} a 3 = a 4 , give 



a 1 Boc 1 + a 2 Ba <2 =O i a 3 $ct 3 + a 4 8ot 4 =0. 

 Also 



(W 1 + W 2 -fW 3 + W 4 )V 



= W 1 Z> 1 sin(a 1 + /9 l )+W 2 (« 1 sina 1 + ^ 2 sin (a 2 + &)) 

 + W 3 (a 4 sin a 4 + Z> 3 sin (<* 3 + #,))+ W 4 6 4 sin (a 4 + £ 4 ) -f constant j 



... (W, + W a + W 8 + W 4 )8V 

 = g« 1 (w i ^ + W 2 H 1 -W 2 /^) + ^(w 3 H 4 -W 3 /^ 4 +W 4 4 



\ « 2 / \ a 3 / 



8ct } and Sa 4 must both be positive. Hence the equilibrium will 

 be stable if 



W, h + w3 be not < w3- and w3 + W 4 ^ not < wA 

 *«i ^j ^tf 2 d « 4 4 « 4 6 a 3 



In the example aready given, the arch would be stable in this 

 position of the load, however great the load is. 



J. H. Pratt. 

 Murree, August 1, 1863. 



XXXVill. On the Products of the Combustion of Gun-cotton and 

 Gunpowder under circumstances analogous to those which occur 

 in practice. By L. v. Karolyi*. 



THE gun-cotton manufactured according to Major-General 

 Freiherr von Lenk's method at Hirtenberg near Wiener 

 Neustadt, has, in consequence of special previous experiments, 

 been used by the GeDie Corps for mining-purposes ; and not- 

 withstanding the fact that there are still numerous difficulties in 

 the way of its use for gun-charges, it is also used by the Royal 

 Imperial Artillery for hollow projectiles. 



The first-mentioned use led the Genie Committee, to which I 

 belong, to cause experiments to be made which are calculated to 

 give greater insight into the chemical deportment of this sub- 

 stance. Among these is the attempt to ascertain the products 

 of combustion of the gun-cotton produced in Hirtenberg ; and in 



* Translated from PoggendorfPs Annalen, April 1863, by Dr. Atkinson, 

 Royal Military College, Sandhurst. 



