,a                                      
,,discourse                             
,,on ,,the                              
,theory of ,gunnery4                    
,a                                      
,,discourse                             
,,on ,,the                              
,theory of ,gunnery4                    
,,delivered ,,at ,,the                  
,anniversary ,meeting of the ,,royal    
,,society1                              
,november #cj1 #aggh4                   
,by ,sir ,,john ,,pringle ,baronet4     
,,published ,,by ,,their ,,order4       
,illustration                           
,,london3                               
,,printed ,,for ,,the ,,royal ,,society4
                                        
,,mdcclxxviii4          ,illustration   
,,gentlemen1    ,among the several      
experiments communicated to the society1
 during the  course of the preceding    
year1 none seeming so much to engage    
your  attention1 as those contained in  
the ,paper1 intituled1 ,the force of    

fired gun-powder1 and the initial       
velocity of cannon-balls1 determined  by
 experiments3 with much pleasure        
therefore ,i acquaint you1 that1 on     
account of the pre-eminence of that     
communication1 your ,council have       
judged the author1 ,mr4 ,,charles       
,,hutton1 worthy of the honour of the   
annual  medal1 instituted on the bequest
 of ,sir ,,godfrey ,,copley ,baronet1   
for  raising a laudable emulation among 
men of genius1 in making experimental   
inquiries4 ,but1 as on former occasions1
 so now1 your ,council1 waving  their   
privilege of determining the choice1    
have acted only as a select  number     
deputed by you1 to prepare matters for  
your final decision4 ,i  come then1 on  
their part1 briefly to lay before you   
the state of the  ,theory of ,gunnery1  
from its rise to the time when its true 
foundation  was laid1 in order to evince
 how conducive those experiments may be 
to the improvement of an art of public  
concern1 as well as to the  advancement 

of natural knowledge1 the great object  
of your institution4  ,and if1 upon a   
review of the subject1 you shall        
entertain no less  favourable an opinion
 of ,mr4 ,,hutton's performance1 than   
what your ,council  have done1 it is    
their earnest request that you would    
enhance the value  of this prize1 by    
authorizing your ,president to present  
it to our  ingenious brother in your    
name4    ,artillery 7in the large       
acceptation of the term7 took place long
 before  the invention of gun-powder4   
,we trace the art to the remotest       
antiquity1  since the ,sacred ,records  
acquaint us1 that one of the kings of   
,judah1  eight hundred years before the 
,christian ra1 erected on the towers and
  bulwarks of ,jerusalem engines of war1
 the contrivance of ingenious men1  for 
shooting arrows and great stones for the
 defence of that city#a4  ,such machines
 were afterwards known to the ,greeks   
and ,romans by the  names of balista1   
catapulta and others1 which had amazing 

powers1  and were not less terrible in  
their effects than the cannon and       
mortars  of the moderns4 ,it appears    
that the balista was contrived to shower
  volleys of darts and arrows of a very 
large size upon the enemy1 whilst  the  
catapulta or onagra 7as it was otherwise
 called7 was fitted  not only for that  
purpose1 but for discharging stones of  
an enormous  weight2 ,i might say rocks1
 since some of them are reported to have
  weighed several hundred pounds4       
,batteries composed of numerous pieces  
of  that kind of artillery1 nothing     
could withstand4 ,yet1 if we are rightly
  informed1 their sole principle of     
motion consisted in the spring of a     
strongly-twisted cordage1 made of animal
 substances singularly tough and        
elastic4 ,these warlike instruments     
continued1 not only during the time  of 
the ,roman empire1 but to the #abth and 
#acth centuries1 as we find from        
history2 nor indeed is it probable that 
they were totally laid aside1  till     

gun-powder and the modern ordnance1     
attaining a good degree of  perfection1 
superseded their use4 ,the very         
intelligent commentator of  ,,polybius#b
 is of opinion1 that the military art   
rather lost than gained  by the exchange
 of the catapulta for the mortar3 but   
however that  point may be determined in
 speculation1 it is not likely that the 
ancient  tormenta militaria will ever be
 revived2 but that all nations will keep
  to the art of gunnery and study how to
 improve it2 that is1 they will  adhere 
to a system of artillery1 wherein the   
moving power depends on the  expansive  
force of gun-powder1 or of some other   
substance of a similar  nature4    ,upon
 the first application of this principle
 to the purposes of war1  nothing       
perhaps was less thought of than to     
assist so empirical a  practice by      
scientific rules2 for1 however aiding in
 these matters the  ancient mechanicians
 might have been1 who1 like             
,,archimedes1 had invented  or perfected

 some of the balistic machines1 no      
praise seemed now due  to the           
mathematicians for either the discovery 
or improvement of the new  artillery4   
,in fact1 we find the practice of the   
art had subsisted about  #bjj years1    
before any geometer considered it as one
 that admitted a  theory1 or at least   
such a theory as was grounded on        
geometry4    ,it seems but just to trace
 and commemorate the inventors of the   
ingenious  arts which furnish matter for
 discourses on these occasions2 and not 
only the main inventors1 but even those 
who first turned their thoughts  upon   
the subject3 for1 though such men may   
not have produced any thing  perfect1   
yet they may have suggested ideas to    
others of a less inventive1  but of a   
more executive genius1 and who1         
unprovided with those hints1  would     
never have made any notable discovery4  
,i must therefore observe1  that the    
,italians were the first who emerged out
 of those thick clouds  of ignorance and

 barbarism which had so long overspread 
this quarter of  the world4 ,they       
profited by the unhappy fate of         
,constantinople2 for by  liberally      
receiving the learned emigrants on that 
distressful occasion1  they were largely
 repaid by their arts and sciences1 and 
still more  abundantly by their         
language1 whereby they were enabled to  
read and to  translate those ancient    
manuscripts1 which the ,greeks had saved
 out of  the wreck of their country4    
,the art of printing1 which was         
established  soon after1 was the means  
of quickly disseminating those treasures
 of  knowledge1 and concurred with the  
fall of the eastern empire to form an   
epoch for the advancement of learning1  
unparalleled in the annals of  letters4 
,the end of the #aeth century1 and the  
whole of the #afth1 were chiefly        
employed by the ,italians in the study  
and in the translation of the  old      
,greek authors4 ,the geometry of the    
ancient ,greeks1 as well as the         

arithmetic in numbers and species of the
 ,arabians1 were cultivated2  but both  
remained1 as it were1 sciences by       
themselves1 unassisting to1  or at best 
but weak and reluctant auxiliaries to   
the philosophy of the  schools3 and     
indeed how could the abstracted         
doctrines of numbers and  quantities be 
strained to co-operate with a system1 in
 which neither  the laws of motion1 nor 
any but the superficial1 and often      
delusive  properties of matter1 were to 
be met with8 ,the genius of the ,greeks1
 all  acute and brilliant as it was1 had
 never been properly directed to the    
interpretation of nature1 and was indeed
 unfit 7as ,lord ,bacon pronounced7  for
 a study that made so slow and painful a
 progress1 by re-iterated and  varied   
experiments and observations4 ,it was no
 wonder then1 if the mixed  mathematics1
 as they are called1 descended to the   
moderns in a state  no-wise             
corresponding to the elegance and       
certainty of those parts of the  science

 which were elementary and pure2 and    
that those mixed parts should  have been
 found defective and erroneous1 in      
proportion 7if ,i may so  express       
myself7 to the physical considerations  
that were to be taken into  the inquiry4
 ,the imperfection of the ancients1 with
 regard to natural  philosophy1 was not 
perceived at that time2 nay1 at the     
period we are  treating of1 the learned 
were firmly persuaded of the contrary1  
and that  all that was wanting to be    
known concerning the laws of nature1 and
 the  properties of matter1 was to be   
taken either directly1 or by deduction1 
from the physics of ,,aristotle4 ,it was
 not till the #agth century was         
somewhat advanced1 that men of science  
began to listen to ,lord ,,bacon and    
,,galileo1 the great founders of the    
experimental and the true philosophy4   
,mean while1 in the beginning of the    
#afth century1 unqualified as the       
,italians then were for entering upon   
physico-mathematical inquiries#c1  they 

nevertheless made the attempt1 and in   
particular took the theory  of          
projectiles into consideration4 ,some   
imagined that a body impelled  with     
violence1 such as a ball discharged from
 a cannon1 moved in a right  line till  
the force was spent1 and that then it   
fell in another right  line             
perpendicularly to the earth4 ,upon this
 principle1 absurd as it  was1 we find  
one of the earliest authors grounding   
his whole theory  of gunnery#d2 whilst  
others1 dissenting from his hypothesis1 
admitted  only the straight line1 in    
which the ball moved for some time after
  coming out of the piece1 and that     
other straight line in which it fell  to
 the ground2 but asserted that these two
 were connected by a curve  line1 and   
that this curve was the segment of a    
circle4 ,,nicolas ,,tartaglia  of       
,brescia1 a mathematician of the first  
rank in those days1 and still           
celebrated for his improvements in      
algebra1 hath been supposed to be the   

author of this doctrine1 no less        
erroneous than the former1 and for which
  two of his books have been quoted#e4  
,those ,i have never seen2 but from     
another of his works1 professedly       
written on this subject1 and translated 
into ,english under the title of        
,colloquies concerning the art of       
shooting in great and small pieces of   
artillery#f1 him ,i find1 contrary  to  
the opinion of his contemporaries1      
maintaining that no part of the  track  
of a cannon-ball is in a right line1    
though the curvature in the  first part 
of its flight be so small1 that it      
needeth not to be attended  to4 ,but    
,,tartaglia is far from supposing1 that 
the line in question hath  any relation 
to a parabola1 or to any regular curve4 
,it would seem  then1 that if this      
mathematician had at first been so far  
mistaken1 as  to fancy that some part of
 the course of a projectile was in a    
straight  line1 he had afterwards       
changed his opinion1 and was perhaps    

singular in  what he finally embraced4  
,from numerous instances one would      
imagine1 that in those days1 so far     
were men of science from making         
experiments themselves1 that they even  
shut their eyes against what chance     
would have presented to their sight4    
,for1 whoever had minded the roving shot
 of an arrow1 the flight of a  stone    
from a sling1 or had attended to a      
stream of water issuing from the  spout 
of a cistern1 might have been convinced1
 that the path of every  projectile was 
in a continued curve1 whatever little he
 otherwise knew  concerning the         
properties of that one4    ,but had the 
observation of the philosophers gone so 
far1 they had  still been at a distance 
from the truth4 ,they might have        
perceived a  likeness between the track 
of those bodies in motion and a         
parabola1  and concluded1 from analogy1 
that all projectiles delineated that    
curve  in the air2 but they could never 
have realized their conjectures by      

mathematical demonstration1 without     
previously knowing the law of           
acceleration in falling bodies3 a       
discovery reserved for the next         
century1 and for ,,galileo#g1 one of the
 greatest ornaments of it4    ,it was he
 who first investigated the effects of  
gravity on falling  bodies1 and upon    
that foundation demonstrated1 that all  
projectiles  would move in a parabola in
 a non-resisting medium4 ,and as he made
  little account of the resistance of   
the air1 whose properties were then     
imperfectly known1 he proved that a ball
 shot horizontally would1 in its        
flight1 describe half a parabola2 and   
when the piece had an elevation  above  
the horizon1 the ball would describe a  
whole parabola1 supposing it  to fall on
 the plane of the battery4 ,by the same 
method of reasoning he  shewed1 that    
whatever the ranges of the projected    
body1 or the elevations  of the piece   
were1 the ball would still trace that   
curve line1 of a  greater or lesser     

amplitude1 by the time it descended to  
the level of the  place from whence it  
came4    ,thus far went ,,galileo1      
confining his projections to the        
horizontal plane  of the battery2 but   
,,torricelli his disciple soon after    
carried the  theory farther1 by tracing 
the shot to its fall1 whether that place
 was  above or below the plane2 and     
still found1 by geometrical deductions1 
that it flew in a parabola of a larger  
or a smaller amplitude1 according  to   
the angle of elevation of the piece1 and
 the strength of the powder4    ,various
 and numerous had been the disputes in  
,italy about the laws of  motion in     
general1 and especially about those of  
projectiles1 from the  time the         
mathematicians had begun the inquiry1   
till the publication of  the dialogues  
of ,,galileo on that subject 7a space of
 upwards of a hundred  years7 but from  
that period1 so evident did his         
demonstrations appear1  that all contest
 ceased1 and every man of science was   

convinced1 that  all projectiles moved  
in the track which he had discovered4   
,for1 as to  the resistance of the air1 
which he had not passed unnoticed 7as   
,,galileo  himself had been the first1  
at least of the moderns1 who started the
  notion of the weight of the air and   
the pressure of the atmosphere7 yet  so 
thin and so yielding did they esteem    
that fluid to be1 that they were        
assured it could occasion no sensible1  
at least no material1 deviation  from   
that curve4 ,as they had the principle  
from ,,galileo1 so they believed        
themselves warranted by that respectable
 author1 not to fear from that  cause   
any objection1 which he himself had     
suggested1 but had removed4  ,among     
these projectiles 7says he7 which we    
make use of1 if they are of  a heavy    
matter and a round form2 nay if they are
 of a lighter matter1 and  have a       
cylindrical form1 such as arrows shot   
from bows1 their track or  path will not
 sensibly decline from the curve of a   

parabola#h4    ,here then was the theory
 of gunnery laid1 in appearance1 on the 
most  solid foundation4 ,and thus far   
the ,italians having proceeded1 they    
seemed  to have taken leave1 and to     
commit the subject to other nations1    
whose  greater power1 or greater        
ambition1 was more likely to make them  
avail  themselves of the perfection of a
 military art1 than their instructors4  
,we had reason therefore to expect1 that
 a neighbouring state1 intent upon  the 
advancement of the arts and sciences in 
general1 would not fail to  give        
particular attention to those that      
should appear most subservient  to its  
grandeur4 ,accordingly we find1 that our
 sister-society of that  kingdom had not
 been many years established1 when an   
ingenious member of  that illustrious   
,body1 not questioning the soundness of 
the ,galilean  principle in regard to   
projectiles1 in the year #afgg1 proposed
 to the  academy1 as a problem for the  
improvement of artillery1 how to direct 

a piece 7suppose a mortar7 so as to make
 the shot fall where one had a  mind2 or
 in the common expression1 to hit a     
mark1 the strength of the  powder being 
given#i4 ,this thought met with general 
approbation1 and so  far were the       
academy from raising any difficulty     
about the obstruction  which the air    
might occasion to a body moving with so 
much velocity  in it1 that we do not    
find the making experiments on that head
 was  considered by them as an essential
 step to the solution2 but that their   
principal geometers straightway set     
about solving the problem as it had     
been announced to them1 some following  
one method1 some another1 and all  upon 
the supposition of a projectile moving  
in the line of a parabola4  ,but ,m4    
,,blondel1 who had been the proposer1   
and who more particularly had  studied  
the question1 composed a large volume on
 the subject1 which he  published a few 
years after#aj1 under the title of      
,l',art de jetter les  ,bombes2 a       

performance much celebrated at the time1
 and that continued in  no small request
 long after1 as containing1 besides his 
own1 the labours  of several other      
members of that society of the most     
distinguished  merit4 ,so many1 and such
 hands concurring in framing this work1 
it was  no wonder that the learned      
throughout ,europe were confirmed by it 
in  the ,galilean theory2 and the more  
as ,m4 ,,blondel had obviated the only  
objection they supposed could be made to
 it1 the resistance of the air1  which  
he had taken care expressly to mention1 
and so to combat as to  persuade the    
reader1 that the retardation arising    
from that cause was so  inconsiderable  
as to be of no account in the practice4 
,this illusion about the small or       
non-resistance of the air to bodies     
rapidly moving in it1 was so prevalent  
at the end of the last century1  and in 
the beginning of the present1 that in   
the history of the ,royal  ,academy for 
the year #agjg1 we find their worthy and

 most accomplished  secretary1 after    
taking notice of the joint labours of so
 many able  mathematicians concerned in 
,,blondel's publication1 venturing to   
say1 it  did not appear that any thing  
was then wanting for the practice of the
  art of ,gunnery except perhaps        
perfecting the instruments for pointing 
a cannon or mortar 444 but that geometry
 had done its part1 so to speak1  with  
regard to practice4 c4#aa    ,but far be
 it from our intention to relate the    
imperfections of others1  in order to   
raise ourselves by the comparison4      
,candour requires of us not  only to    
acknowledge1 that in this country1 as to
 the point in question1  we did not     
surpass our neighbours2 but ingenuously 
to own that1 on the  contrary1 we were  
perhaps more liable to exception4 ,for1 
some years  before ,,blondel's work     
appeared#ab1 a treatise was published by
 one of  our own artillerists1          
,,anderson 7a person of eminence in his 
profession7  intituled ,the genuine use 

and effects of the gun1 in which the    
author  strenuously supports the        
,galilean theory2 nor do we learn he was
 ever  contradicted among us1 although  
he undertook to answer all those who    
should make objections to it4 ,nay1 when
 he had an opportunity afterwards  of   
making experiments on the ranges of     
bombs1 and by those trials was  assured 
that their flight was not in a parabola2
 yet so far was he from  ascribing the  
deviation from that figure to the       
resistance of the air1  that he had     
recourse to an hypothesis1 repugnant to 
all the laws of  motion1 to salve       
appearances1 and to reconcile those     
experiments with his  former            
doctrine#ac4    ,and did not ,dr4       
,,halley1 so long the ornament of this  
society1 communicate  in the year #afhf 
a ,paper1 which he calls ,a discourse   
concerning  gravity1 in which1 treating 
of the motion of projectiles1 he says1  
that  being aware of the deflexion from 
the parabolic curve that might be       

occasioned by the resistance of the air1
 he had made some experiments1  even    
with cannon-balls1 to estimate the force
 of that resistance2 yet  conclude1     
,that in large shot of metal1 whose     
weight many thousand times  surpassed   
that of air1 and whose force is very    
great1 in proportion to  the surface    
wherewith they press thereupon1 this    
opposition was not  discernible4 ,and   
again1 ,though in small and light shot1 
the opposition  of the air ought and    
must be accounted for2 yet in shooting  
great and  weighty bombs1 there need be 
very tittle allowance made2 and so these
  rules those1 to wit1 grounded on the  
principle of ,,galileo may be put  in   
practice to all intents and purposes1 as
 if this impediment the  resistance of  
the air were absolutely removed#ad4     
,such conclusions1  which we now find to
 be erroneous1 were the less to be      
expected from so  eminent a person1 as  
they argued too much haste to finish a  
theory1 that  was to be made subservient

 to present use4    ,it might indeed    
have been expected1 that men of science 
applying  themselves to this study1     
would have been sooner awakened to the  
consideration of the great opposition of
 the air1 by the ,principia of          
,,newton1 published a little after this 
,paper of ,,halley's#ae4 ,for in that   
excellent work the illustrious author   
had demonstrated1 that the curve        
described by a projectile1 in a strongly
 resisting medium1 differed much  from a
 parabola1 and that the resistance of   
the air was great enough to  make the   
difference between the curve of         
projection of heavy bodies and a        
parabola far from being insensible1 and 
therefore too considerable to be        
neglected4    ,have we not then less to 
plead for not attending to the          
,principia of  ,,newton in this         
article#af1 than the mathematicians of  
other nations1  who1 as ,m4 de          
,,fontenelle observes#ag1 partly from   
the difficulty  of understanding that   

concise and profound work1 and partly   
from a  misapprehension of its tendency 
7which they fancied was to revive the   
exploded doctrine of occult qualities7  
were late in becoming acquainted  with  
it8 ,but it is not so easy to account   
for their inattention to  ,,huygens1 a  
known and even then a much esteemed     
author1 and who indeed  was second to   
,,newton alone in science and in genius4
 ,for he in the year  #afij had         
published a treatise on ,gravity1       
written in a popular manner1  wherein he
 gave an account of some experiments he 
had made at ,paris1 and  in the academy1
 by which1 as well as by mathematical   
investigations1  he was convinced of the
 truth of ,,newton's conclusions1 in    
regard to  the great opposition of the  
air to bodies moving swiftly in it2 and1
  by consequence1 believed that the     
track of all projectiles was very       
different from the line of a            
parabola#ah4    ,but excepting ,,newton 
and ,,huygens1 the learned seemed       

universally to  acquiesce in the        
justness and sufficiency of the         
principles of gunnery  invented by      
,,galileo1 enlarged by ,,torricelli1    
confirmed and reduced to  system by     
,,anderson1 ,,blondel1 ,,halley and     
others2 and so far were the  theorists1 
in that branch of science1 from         
suspecting any defect or  fallacy in    
these principles1 that they seemed      
rather to reproach the  practical       
artillerists1 for not profiting more by 
the instructions which  they had so     
liberally imparted to them4 ,nor do we  
find that an apology  was made for the  
empirical exercise of the art1 by any   
author of note  in that line1 earlier   
than the sixteenth year of this century1
 when ,m4  de ,,ressons1 a ,french      
officer of artillery1 distinguished by  
the number  of sieges at which he had   
served1 by his high military rank1 and  
by his  abilities in his profession2    
when he1 ,i say1 thus qualified to bear 
testimony1 presented a memoire to the   

,royal ,academy 7of which he was  a     
member7 importing1 that although it was 
agreed that theory joined to  practice  
did constitute the perfection of every  
art1 yet experience had  taught him1    
that theory was of very little service  
in the use of mortars4  ,that the work  
of ,m4 ,,blondel had justly enough      
described the several  parabolic lines1 
according to the different degrees of   
the elevation of  the piece2 but that   
practice had convinced him there was no 
theory in the  effects of gun-powder3   
for that having endeavoured1 with the   
greatest  precision1 to point a mortar  
agreeably to those calculations1 he had 
never been able to establish any solid  
foundation upon them#ai4    ,thus1 after
 the theory of gunnery had exercised the
 genius of the  learned for nearly two  
hundred years1 and for almost fourscore 
of that  time had rested on fundamentals
 which had never been contested1 it was 
pronounced at once to be almost intirely
 useless1 and that by one of  the most  

competent judges4 ,now1 whether it were 
owing to the deference  due to the      
authority of that experienced           
artillerist1 or to some other  cause1 ,i
 shall not determine1 but observe1 that 
it appears not from the  history of the 
academy1 that the sentiments of ,m4 de  
,,ressons were at this  time            
controverted1 or any reason offered     
afterwards for the failure of  the      
theory of projectiles when applied to   
use4 ,nor can ,i pass unnoticed  the    
pause that ensued before any further    
attempts were made to improve  the      
theory of the art1 either upon the old  
principles or upon new ones1  except by 
such authors as seemed ignorant of this 
transaction1 and who of  course were not
 sufficiently apprized of the inefficacy
 of the properties  of the parabola for 
directing practice4 ,or by those who    
were employed in  speculatively         
investigating the nature of the curve   
traced by a ball in  the air2 a curve   
which began at last to be considered as 

one deviating  much from the line of a  
parabola4 ,or1 finally1 by such as1     
having taken  notice that ,,newton's    
ideas had not been duly attended to1    
endeavoured  to avail themselves of     
them1 and of some experiments that had  
been made  by others1 for proving the   
great opposition of the air to bodies of
  swift motion2 but without ascertaining
 the degree of that resistance1 or      
enriching the art by any practical      
rules#bj4    ,such was the unhinged     
state of this part of the mixed         
mathematics1  when within our memory    
,mr4 ,,benjamin ,,robins took cognizance
 of it3 nor  could the subject have     
fallen into abler hands1 endowed as he  
was by  nature with a superior genius   
and unwearied application4 ,mr4 ,,robins
 was  deeply versed in geometry and the 
doctrine of numbers2 but he knew the    
limits as well as the powers of both1   
and how insufficient they were for      
establishing any theory where matter was
 concerned1 without preparing  the way1 

by finding out the physical properties  
of that matter1 by  many and varied     
experiments and attentive observation4  
,those who had  hitherto treated of the 
foundation of gunnery1 by being too     
forward in  the application of their    
mathematics1 had in a manner hurt the   
credit  of that admirable science4 ,they
 ought to have seen the necessity of    
minutely examining every circumstance   
which could affect the course of  a     
projectile1 besides that of gravity4    
,mr4 ,,robins perceived the error  of   
his predecessors in that inquiry1 and   
corrected it4 ,persuaded as he  was from
 sir ,,isaac ,,newton's ,principia of   
the great resistance of the  air to     
bodies moving in it1 and also of the    
uncertainty of the force  of gun-powder1
 and of the variations in the flight of 
shot1 occasioned  by the unavoidable    
varieties in the make of it1 and in the 
make of the  pieces of artillery which  
discharged it2 apprized1 ,i say1 of so  
many  causes of aberration1 he justly   

concluded1 that the foundation here was 
at least as much an affair of physics as
 of geometry1 and that if the art  of   
throwing bombs had not been advanced by 
theory1 it was not because  the art     
admitted of none1 but because the theory
 which had hitherto been  devised had   
been both defective and erroneous4 ,he  
suspected that most of  the writers on  
gunnery had been deceived1 in supposing 
the resistance  of the air to be        
inconsiderable1 and thence asserting the
 track of all  shot to be nearly in the 
curve of a parabola1 by which means it  
came to  pass that all their            
determinations1 about the flight of     
projectiles of  violent motion1 had     
declined considerably from the truth4   
,but in order  to clear this point from 
every doubt1 he found it necessary to   
ascertain  the force of gun-powder1 and 
by that step to estimate the velocity of
  the shot impelled by its explosion4   
,that being done1 he proceeded to       
measure the quickness of a              

musket-bullet1 shot out of a given      
barrel1  with a given quantity of       
powder2 and to confirm the truth of his 
conclusions1 he contrived a machine1 by 
which the velocity of a bullet  might be
 diminished in any given ratio1 by being
 made to strike on a  large body of a   
weight justly proportioned to it2       
whereby the swiftest  motions1 which    
otherwise would escape our examination1 
were to be exactly  determined by these 
slower motions that had a given relation
 to them4 ,the  machine was a large     
wooden pendulum1 which swung freely1 but
 in so slow  a manner1 that its         
vibrations could easily be counted1     
whatever was the  celerity of the bullet
 discharged against it4 ,the thought was
 simple1  ingenious1 and incontestably  
his own4    ,he next inquired into the  
resistance made by the air to           
projectiles of  rapid motion1 and which 
he discovered to be much greater than   
had been  supposed by any writer on the 
subject2 and indeed so great1 that it   

was manifest the curve described by any 
shot was very different from a          
parabola1 and consequently that all the 
applications of the properties  of that 
conic section to gunnery were so        
erroneous as to be totally  useless4    
,for by means of this pendulum1 placed  
at different distances  from the mouth  
of the piece1 he clearly demonstrated   
how much a bullet1  flying with a given 
velocity1 would gradually lose of that  
motion by the  opposition of the air3   
therein furnishing to the learned a     
signal and  instructive instance of the 
fallacy of the most specious theories1  
that  do not proceed hand in hand with  
experiments4    ,i should too much      
exceed the just bounds of a discourse of
 this kind1  were ,i to enter more      
minutely into the system founded by ,mr4
 ,,robins1  confirmed and improved1 as  
,i find1 by the labours of several of   
the  learned in foreign parts of great  
celebrity#ba4 ,i shall only add1  that  
his performance well deserves the title 

he gives it of ,the new  principles of  
gunnery1 since the author may more      
properly be said to  have invented a new
 science than to have added to an old   
one4 ,and ,i  believe ,i may venture to 
say1 that no physico-mathematical       
disquisition  hath done more honour to  
this country1 or to the age1 than the   
writings  of ,mr4 ,,robins on this      
subject1 which have been published1     
partly by this  ,society1 partly by     
himself1 and partly since his death 7in 
the collection  of his whole            
mathematical tracts7 by his learned     
friend4    ,but though our worthy       
brother will ever be celebrated for     
being the  inventor of the true         
principles of gunnery1 yet it would be  
too  flattering to his memory1 to say he
 had carried the theory of this art  to 
perfection4 ,he himself was far from    
entertaining so high an opinion  of his 
labours2 nay he expressly declared1 that
 he left some material  points to be    
inquired into at more leisure 7which    

other occupations  and his immature     
death deprived him of7 and he much      
regretted that he  wanted conveniency   
and opportunities for making experiments
 on balls of  a greater weight1 than    
what he had used for ascertaining the   
initial  velocity of them4    ,much     
therefore are we indebted to ,mr4       
,,hutton1 who1 treading in the          
footsteps of the deceased1 hath resumed 
and prosecuted this last  desideratum1  
and hath shewn himself not unequal to so
 difficult an  enterprize4    ,mr4      
,,robins1 for determining the initial   
velocity of shot1 arising from          
different quantities of powder1 made use
 of balls of about an ounce  weight2    
whereas ,mr4 ,,hutton1 for the same     
purpose1 hath employed those of         
different weights1 from one pound to    
nearly three2 or1 in other words1  ,mr4 
,,robins made trial with musket-shot    
only1 ,mr4 ,,hutton with cannon-balls   
from #bj to about #ej times heavier4    
,this was a considerable step gained  in

 a disquisition of that part of the     
science1 in which the resistance  of the
 air and other circumstances were not   
concerned2 and where neither  analogy   
alone1 nor mathematical deductions      
alone1 nor the two combined1  were      
sufficient for establishing principles  
applicable to the motion of             
cannon-balls1 without making a new      
series of experiments3 and with what    
labour and judgment these have been     
performed1 you understood by the        
account which ,mr4 ,,hutton gave of them
 in his ,paper4    ,but should it now be
 inquired1 what advantages may be       
derived from ,mr4  ,,hutton's           
experiments1 for the advancement of the 
art of gunnery1 and of  philosophy in   
general8 ,i would reply1 that as to the 
former it may be  sufficient to observe1
 that though the improvements be only   
such as can  be deduced from the force  
of fired gun-powder2 yet they are in a  
higher1  more certain1 and in a more    
general manner1 than what resulted from 

the  labours of ,mr4 ,,robins2 who      
indeed led the way1 but who made1 as it 
were  in miniature1 those experiments   
which ,mr4 ,,hutton hath executed at    
large1  and which ,,robins himself      
wished to have made1 as well as others  
who have  considered the subject since  
his time4 ,now these experiments1 though
 made  by ,mr4 ,,hutton with            
cannon-balls of a small size1 may       
nevertheless form  just conclusions when
 applied to cannon-shot of the largest  
size4 ,and  such conclusions inform us  
of the real force of powder when fired1 
either  in a cannon or a mortar1        
impelling a ball or bomb of a given     
weight2  that is1 they discover with    
what velocity a given quantity of powder
  drives those projectiles in a second1 
or in any other assigned portion  of    
time4 ,they also shew the law of        
variation in the velocity arising  from 
different quantities of powder1 with the
 same weight of metal1  and likewise    
that law which takes place upon using   

balls of different  weights4 ,further1  
they point out the advantage obtained by
 diminishing  the windage in cannon1 and
 teach us how we may increase the weight
 of  the shot in the same piece1 by     
making it of a cylindrical form1 instead
  of a spherical3 by this device1 a     
smaller ship may be enabled to do the   
execution of a larger one4 ,and         
experiments of the same kind will also  
determine the just length of cannon for 
shooting farthest with the same  charge 
of powder4    ,lastly1 it is from these 
experiments1 or from others that may be 
made  after the like manner1 we are     
instructed how to answer every question 
relative to military projectiles1 except
 such as depend on the resistance  of   
the air to bodies moving swiftly in it4 
,this indeed is a consideration  which  
leaves room for greater improvement in  
the art1 and for conferring  fresh      
honours on those1 who1 like ,mr4        
,,hutton1 shall have opportunities  and 
abilities for continuing and perfecting 

this very curious and useful  inquiry4  
,as to the advantages accruing to       
philosophy from the labours both of     
,mr4 ,,robins and ,mr4 ,,hutton1 speak  
they not for themselves8 ,the sciences  
of motion and pneumatics are promoted by
 them2 and of what avail their          
perfection would be for the farther     
interpretation of nature1 you need  not 
be informed4 ,in fine1 we have here     
before us1 in these experiments1  the   
surest test of our advancement in true  
knowledge1 which is1 the  improvement of
 a liberal art1 and the enlargement of  
the powers of man  over the works of    
creation4    ,some however may think1   
that the objects of this society are the
 arts of  peace alone1 not those of war1
 and that considering how numerous and  
how  keen the instruments of death      
already are1 it would better become us  
to  discourage than to countenance their
 farther improvement4 ,these naturally  
will be the first thoughts of the best  
disposed minds4 ,but when upon  a closer

 examination we find1 that since the    
invention of arms of the  quickest      
execution1 neither battles nor sieges   
have been more frequent  nor more       
destructive1 indeed apparently          
otherwise2 may we not thence  infer1    
that such means as have been employed to
 sharpen the sword1 have  tended more to
 diminish than to increase the number of
 its victims1 by  shortening contests   
and making them more decisive4 ,i shall 
not however  insist on maintaining so   
great a paradox2 but only surmise1 that 
whatever ,state would adopt the ,utopian
 maxims1 and proscribe the study of     
arms1 would soon1 ,i fear1 become a prey
 to those who best knew how to use      
them4 ,for yet1 alas6 far seem we to be 
removed from those promised times1  when
 nation shall not lift up sword against 
nation1 neither shall they  learn war   
any more6           99       99       99
       99       99    ,here ended the   
,president's ,discourse3 after which he 
turned to ,mr4  ,,hutton1 and said1     

,you have heard1 ,sir1 the account ,i   
have given of the rise and progress  of 
the theory of gunnery1 and of your      
improvement of it2 a recital1  which by 
no means would have done either you or  
the subject justice1 had  it been       
addressed to any other audience than to 
the present4 ,but as my  intention was  
only briefly to recall to the memory of 
these gentlemen  what they knew of this 
subject1 antecedently to your ,paper1   
and to remind  them of the result of    
your experiments1 ,i flatter myself ,i  
have said  what was sufficient on the   
occasion2 being now authorized by them  
to  deliver into your hand this medal1  
as the perpetual memorial of their      
approbation4 ,and let me add1 ,sir1 that
 they make you this present with  the   
more cordial affection1 as by your other
 ingenious and valuable  communications 
they are assured1 not only of your      
talents1 but of your  zeal1 for         
promoting the interests and honour of   
their ,institution4    ,illustration    

,,footnotes      #a #b ,chron4 xxvi4    
#ae4    #b ,m4 ,,folard4    #c ,the     
chief exception that occurs to this     
general remark1 is the rapid  progress  
which in that age ,,copernicus made in  
astronomy2 who was not  indeed an       
,italian1 but was supposed to have      
profited by his early travels  into     
,italy1 which he enlightened afterwards 
by his admirable discoveries4    #d ,see
 ,,montucla1 ,hist4 des ,mathem4 vol4   
,i4 p4 #fbc4    #e ,those were ,la      
,nuova ,scientia1 and ,quesiti ed       
,inventioni diverse4    #f ,published at
 ,london1 ,a4 #aehh4    #g ,he was born 
in the year #aefd2 but few if any of his
 works were  published till after the   
year #afjj1 and his dialogues on motion 
not  before #afch4    #h ,see his #dth  
,dialogue on ,motion4    #i ,see ,hist4 
de l',academ4 ,roy4 des ,sciences1 ,a4  
#agjg4    #aj ,in the year #afhc1 see   
,hist4 de l',acad4 ,r4 des ,sci4 ,a4    
#agjg4    #aa ,hist4 de l',acad4 ,r4 des
 ,sc4 ,a4 #agjg1 under the article      

,mechanique4    #ab ,viz4 in #afgd4     
#ac ,see his treatise ,to hit a ,mark1  
published in #afij4    #ad ,philos4     
,trans4 ,no4 #agi1 p4 #bj4    #ae ,in   
the year #afhg4    #af ,,newton1        
,princip4 ,mathem4 lib4 ii4 sect4 #g4   
#ag ,eloge de ,,newton4    #ah ,discours
 de la ,cause de la ,pesanteur4 ,leide1 
#afij4    #ai ,mem4 de l',acad4 ,r4 des 
,sc4 ,a4 #agaf4    #bj ,,dan4           
,,bernoulli1 ,comment4 ,acad4 ,petropol4
 ,t4 #b4  #c4    #ba ,it is also much to
 the honour of ,mr4 ,,robins1 that his  
writings on  this subject have been     
translated into foreign languages by men
 that were  the best judges of their    
merit4 ,i need only name ,,mm4 ,,euler1 
and ,,le ,,roy4          ,,errata4      
,page #d4 l4 #e4 for this read the      
#af4    #i4 for combate read combat     
#bj4   #ag4 for tract read track        
#bf4   last line of the note1 for ,m4   
,m4 read ,,mm4    ,transcriber's ,note3 
,the errata have been corrected4