THE ROYAL ARTILLERY INSTITUTION. 
159 
EXPLANATORY NOTES 
ON 
BASHFORTM’S “MOTION OE PROJECTILES.” 
BX 
CAPTAIN E. 'KENSINGTON, R.A., 
INSTRUCTOR IN MATHEMATICS, R.M. ACADEMY. 
1. Professor Bashforth* s excellent treatise has been written for the 
purpose of throwing light upon the very complex problem of calculating 
tha path of a projectile in air. It is not possible to over-estimate the 
value of this work to the artillery officer, accompanied as it is by 
tables for practical use. Though it possesses these advantages— 
and is, moreover, the only toxt-book upon the subject written in modern 
times and published in our language—yet there is reason to fear lest 
its great value should not be recognised by many artillery officers who 
may find it difficult to follow Mr. Bashforth in some of the subtle 
reasonings and difficult calculations necessary. 
Officers fairly acquainted with the calculus do not always find it an 
easy task to go through these calculations—which are the record of 
many difficult obstacles overcome, of original experiments carefully 
worked out under difficulties, and of theory reduced to practice, by the 
Professor to whom we British gunners owe a deep debt of gratitude. 
The following paper is published in order that Mr. Bashforth* s work 
may be utilised by every artillery officer, even though unacquainted 
with the differential and integral calculus. That' this may be the case 
the writer has endeavoured— 
lstly. To supply steps which Mr. Bashforth has thought it unneces¬ 
sary always to insert; and also to aid those who are fair mathematicians 
by stating and explaining difficulties which have occurred to himself 
while reading the treatise, or which have been pointed out to him by 
others. 
