THE ROYAL ARTILLERY INSTITUTION. 
119 
7. Tlie experience which I have had with Major Navez’s instruments 
enables me to say, that if ordinary care be taken in their use, and the 
instructions carefully followed, the instruments are so nearly perfect as 
to leave little to be desired, while the ease with which they can be 
manipulated, and the innumerable important problems which can be 
readily solved by their means render them an invaluable, an almost 
indispensable adjunct to every school of instruction. 
8 . Two instruments, Nos. 24 and 32, were used in these experi¬ 
ments. The times of vibrations of the pendulums were carefully 
determined by means of a stop watch, and the rate of the watch was 
ascertained by comparison with an astronomical clock. The observa¬ 
tions made for this purpose are given in Appendices Nos. I. and II., 
and from them it appears that the time of a small oscillation in instru¬ 
ment No. 24 is 0*3320 seconds, while in No. 32 it is 0*3337 seconds. 
9. In Appendices III. and IY. are given corrected tables showing 
the relations between the arcs passed through and the corresponding 
durations for T = 0 * 3320 sec. and for T = 0 * 3337 sec. 
10 . The experiments referred to in this report have regard chiefly 
to initial velocity alone, and for the small distance concerned the law 
of resistance adopted may be thought of small practical importance, 
especially as before the experiments now being carried on are con¬ 
cluded, the Committee will doubtless be in a position to say whether 
this law is better expressed by a function of the form v 2 + a, v d , as 
proposed by General Piobert, or by one of the form v 2 + /3 v\ as pro¬ 
posed by the Count de St. Robert and Colonel Mayevski. In the 
present instance, both the law of resistance and the values of the coeffi¬ 
cients given by General Didion in his invaluable work have been fol¬ 
lowed, although it may perhaps be inferred from a passage in the recent 
edition of the “ Traite de Balistique,” that late experiments with the 
electro-ballistic apparatus do not give results in quite so close an accord¬ 
ance with theory as might have been expected. 
11. In the first edition of General Didion’s work, published in 1848, 
a term was introduced into the expression of the resistance of the air 
dependent upon the diameter of the projectile, and this form of the 
expression has been generally used upon the continent, but a recalcu¬ 
lation of the data upon which this result was founded, has led General 
Didion to conclude that the coefficient is independent of the calibre, 
and that the resistance is represented with sufficient accuracy by the 
equation 
f — - 027 ir R 2 » 2 ‘ -|j- { 1 + 4 I 3 }.(2) 
where R zz radius, v = velocity, S = density of the air at time of 
observation, and zz standard density of air; the metre and the kilo¬ 
gramme are taken as units. 
In this formula the density of the air is denoted by referring its 
weight to a standard of comparison, which is assumed as the weight of 
a cubic metre of air at a temperature of 15° Centigrade, semi-saturated 
with vapour, and under a barometric pressure of 750 millimetres. 
Now if in equation ( 2 ) the English foot and pound be taken as 
units, the value of the numerical coefficients will be altered, and the 
equation becomes 
' = '0005137. R 2 , 2 .-|-{i +li |__} 
In the ordinary determinations of initial velocity it is hardly neces¬ 
sary to take the variations of the density of the air into account, and 
A 2 
