16 
MINUTES OF PROCEEDINGS OF 
This theory was, however, disproved by Huyghens, who. showed, in a 
treatise published in 1690, that the path of the projectile would be a 
logarithmic curve, if the resistance was proportional to the velocity. Sir 
Isaac Newton appears to have been the first who proposed a theory that 
the resistance was proportional to the square of the velocity. John and David 
Bernoulli, Herman, Brook Tayler, &c. have also written, about this time, on 
the subject of the air's resistance to the motion of projectiles. 
It is, however, to Mr Robins that we owe much of the progress that 
has been made in the science of gunnery. 
Mr Robins published an account of his invention in a treatise on the 
" New Principles of Gunnery," printed in 1743. 
The experiments made by Mr Robins were conducted with musket balls, 
and the largest pendulum employed by him weighed but 97 lbs.; and yet 
the results of subsequent investigation in different countries, assisted by 
every improvement which mathematical or mechanical science could devise, 
have but served to corroborate the fundamental laws laid down by him ; a 
singular proof how much more work depends on the workman than on his 
tools. Robins' work was translated into German by M. Euler, who added 
elaborate notes and remarks. This translation was re-translated into 
English by Mr H. Brown in 1777, and received several valuable additions 
by Mr Landen, a gentleman of high mathematical talents. Mr Robins has 
not investigated the nature of the curve described by a projectile in a 
resisting medium, but this has been done by Euler, Robinson, Legendre, 
and others. 
Shortly before the publication of Mr Brown's translation of Euler’s 
Robins, Dr Charles Hutton was appointed Professor of Mathematics at the 
Royal Military Academy, Woolwich, and in 1775 he commenced a series of 
experiments in gunnery. These experiments were carried on by means of a 
ballistic pendulum, constructed according to the method invented by Mr 
Robins, but much larger than the instrument used by the latter. The 
smallest pendulum used by Dr Hutton weighed about 600 lbs., and in the 
prosecution of his experiments new pendulums were made successively larger 
and larger, till he at length reached a weight of about 2600 lbs. In 
these investigations, Dr Hutton was led to make many improvements in 
the construction of the ballistic pendulum, especially in the manner of 
suspension and method of measuring the angle of recoil. Dr Hutton's 
experiments were carried on at Woolwich, and were most extensive and 
valuable; they extended from the year 1775 to 1791. 
In 1778 he published a report of his first series of experiments; this 
report being presented to the Royal Society, was honoured by them with 
the gift of the annual gold medal, and printed in the Philosophical 
Transactions for 1778. 
The results of Dr Hutton's valuable experiments are fully discussed in 
his work on the subject. 
In addition to the experiments with the ballistic pendulum, a series of 
observations on the resistance of the air to bodies moving with low velocities 
were made by Dr Hutton, by means of the whirling machine invented by 
Mr Robins. As this machine has been described by so many authors, it is 
not my intention to refer again to it. It is fully explained in Colonel 
