160 
MINUTES OF PROCEEDINGS OF 
2ndly. To enable those officers who may have forgotten mathematics 
from want of practice, but who are still acquainted with algebra and 
can use logarithm tables, to apply the results of Mr. Bashfortids 
treatise in working out trajectories or in solving other problems in 
gunnery. 
This paper is intended, therefore, for two classes of readers—those 
who are well acquainted with mathematics, and those who are not; 
and the writer hopes that he will be excused by the one class for giving 
detailed explanations of what must be obvious to them, and by the other 
for inserting proofs and using language which in some cases must 
appear unintelligible. 
The writer trusts that the latter may be enabled to understand the 
general scope of Professor Bashfortffis work ; but they must be content 
to take for granted formulae proved by the calculus, or by other pro¬ 
cesses beyond their reach. 
Sentences containing proofs of this description will commence with a 
word in italics , in order to save the time of such readers—who should, 
however, note the results. 
At times, the manner in which such a result is arrived at may be made 
clear by algebraical explanations. 
Throughout this paper reference will constantly be made to Professor 
Bashfortffis work, and the equations will retain the numbers given to 
them there; while, to make it complete, extracts will be occasionally 
inserted which do not require explanation in themselves. 
“ Art. ;; refers to articles in the treatise, and the symbol “ § 99 to sec¬ 
tions of this paper. 
2. Equations of Motion for Determining the Resistance of 
the Air. 
It is carefully explained in Chap. III. how, by means of the Bashforth 
chronograph, the times of a projectile passing through several screens 
in succession can be accurately recorded. Thus sufficient data are 
obtained for determining the resistance of the air, to which the diminu¬ 
tion of velocity is principally due. It is, of course, evident that gravity 
retards during the ascending branch of the curve described by the 
projectile, and accelerates during’ the descending branch. 
There are two distinct methods of measuring a force :— 
(1) Statically, by the weight it will sustain. 
(2) Dynamically, by the increase or diminution of velocity it will 
produce in a given mass cc m" during a given time; or—which 
comes to the same thing—by the momentum it will generate 
in one second. 
These two measures of the same force are connected by the equation 
P = mf- } ....... (a) 
