183’ 
HAL 
alterate proportion ; when, after fome meditation, he 
concluded from it, that the centripetal force muft de- 
creafe in proportion to the fquares of the diltances reci¬ 
procally. Finding himfelf, however, unable to make 
this out in any geometrical way, he applied for affift- 
ance, firft, to Mr. Hooke and fir Chriftopher Wren ; and, 
after failing of fuccefs in this application, he went to 
Cambridge, to confult Mr. Newton, who fnpplied him 
fully with the calculations which he wanted. In the 
courfe of his converfations with that great man, he 
found that he poffeffed an immenfe treafure of aftrono- 
■mical learning, and would not reft till he had prevailed 
upon him to enrich the public with it. To this inter¬ 
view, therefore, the world is in fome meafure indebted 
for the Prindpia Mathematica Pkilofophia Naturalis. That 
invaluable work was publiftied in 1686 ; and Mr. Hal¬ 
ley, who had the whole care of the impre.ftion, prefixed 
to it a difcourfe of his own, containing a general ac¬ 
count of the aftronomical part of the book, and alfo an 
elegant copy of verfes in Latin. Before the appearance 
of this work, in 1685, Mr. Halley was appointed aftift- 
ant fecretar.y to the Royal Society; foon after which he 
delivered in two valuable-papers, the former of which 
contained an improvement in the fcience of gunnery, 
and the other a difcovery of the eafy method, fince fo 
well known, of meafuring heights by the barometer. 
Thefe were followed, in 1686, by the publication of, 
The Hiftory and phyfical Caufe of the Trade-winds and 
Monfoons ; together with a Chart, reprefentiffg their 
Direftion, wherever they are found to blow, through 
all Parts of .the Globe known to the Englifti Mariners. 
In 16S.7 he,undertook to explain the caufe of a natural 
phenomenon, which had till then baffled the refearches 
of the able.ft geographers. It has .been obferved that 
the Mediterranean never fwells in the leaft, although- 
there is no vifible difcharge of the prodigious quantity 
of water that runs into it from nine large rivers, befides 
feveral fmall ones, and the conftant fetting in of the cur¬ 
rent at the mouth of the Streight. This difficulty he 
folved fo much to the fatisfadtion.of the Royal -Society, 
;that.he was requefted to profecute his enquiries on the 
(iibjedf. With this requeft he complied ; and having 
iftievvn, by tjie moft accurate experiments, how that vaft 
acceffion of .water was actually carried off in .vapours 
raifed by the adtion of the fun and wind upon its fur- 
face, he .proceeded with the like fuccefs, to point out 
the method .ufed by nature to return the Laid vapours 
, into the fea. This circulation he 'fu.ppofes to be car¬ 
ried on by the winds driving.thefe vapours to the moun¬ 
tains, where, being collected, they form fprings, the 
ftreams from which, uniting, become rivulets, or brooks ; 
and many of thefe again, meeting in the valleys, grow 
into large rivers, which at length empty theriifelves into 
the fea. In this beautiful manner did he (how tl;e way 
in which the equilibrium between the receipt and ex¬ 
penditure is continually preferve’d in the pniverfal ocean. 
Mr. Halley next entered the field of fpeculative georne-, 
.try, where, obferving.fome imperfections,in the methods 
before laid down for, 1 co,nftructing foiid problem?, or 
■ equations of the third and fourth,powers, he furniflied 
new rules which were both more eafy. and more elegant 
i than any of the former ; together with a new method of 
.finding the number of roots in fuch equations, and the 
limits of the fame, 
Mr. Halley’s, next undertaking was to publifh a more 
. Correct ephemeris;for the year 1688, there being; then 
great want of proper ephemerides of any tolerable ex- 
aCtnefs, the common ones being juftly complained of by 
Mr. Fiamfteed. 'In *691 he publiftied tables of the con¬ 
junctions of Venus and Mercury with the fun ; and. he 
afterwards fhewed one valuable ufe to be made.of thofe 
tables, viz. for difcovering the fun’s parallax, and thence 
the true diltance of the earth from the fun. In 1692 he 
produced his tables for fhowing the value of annuities 
on lives, calculated from bills of mortality ;• and his 
L Y. 
univerfal theorem for finding the fod of optic glaffes. 
But it W'ould 1 be endlefs to particularife all his valuable 
difcoveries communicated from time to time to the 
Royal Society, and publiftied in the Philofophicai 
TranfaCtions, of which his pieces were for many years 
the chief ornament and fitpport. Their various merit 
is thrown into one view by M. Mai raft, the writer of 
hie Eloge in the Paris Memoirs, who, hawing mentioned, 
his Hiftory of the Trade-winds and Moi'ifoons, proceeds 
in thefe terms: “This was immediately followed by 
his eftimation of the quantity of vapours which ,the fun 
raifes from the fea ;.the circulation of vapours ; theori- . 
gin of fountains ; queftions on the nature of light, and- 
tranfparent bodies; a determination of the degrees of 
mortality, in order to adjuft the valuation of annuities 
on lives; and many other works, in almoft all fciences ; 
aftronomy, geometry, and algebra ; optics and dioptrics; 
balliftics, and artillery ; fpeculative and experimental 
pliilofophy-; natural hiftory, antiquities, philology, and 
criticifm ; being about twenty-five or thirty differta- • 
tions, which he produced during the ten years of his 
refidence at London ; and alii^bounding with ideas new, 
lingular, and ufeful.” 
In 1692, Mr. Halley refigned his appointment of af- 
fiftant fecretary to tlie Royal Society ; and in '1696, upon 
the ^ftablifhment of five different mints, for the re-coin¬ 
age of the friver fpecie, he was conftituted comptroller 
of the office at C.hefter. This employment occafioned 
his refidence in that city for two years; during which , 
time he diligently purified his philofophicai inveftiga-, 
tion§, accounts of which were regularly tranfmitted to 
the Royal Society, and publiftied in their Tranfafflions. 
In 1698, king William appointed him commander of the - 
Paramour pink, with orders to fearch out by obferva- 
tions, and lay down, the longitudes and latitudes of the 
Englifti fettlem&nts in America, &c. On this attempt 
he let fail in November 1698 ; but after lie had crofted 
the Line, his .men growing fickly and untrafflable, and 
his firft lieutenant mutinying, he returned home in June, 
1699. Having got the lieutenant tried and calhiered, 
in the month of September following, he Let fail a fe- 
cond time, in the lame Ihip, accompanied with another 
of a fmaller fize, which was alfo placed under his com¬ 
mand. With thefe ftiips lie tiaverfed the Atlantic 
ocean, from one hemifphere to the other, till the ice in 
the cold regions of the fouth opftructed Itis navigation; 
and on.his voyage home he touched at St. Helena, the 
coaft of Brazil, Ba.rbadoes, Cape Verd, Madeira, the 
Canaries, tlie coaft of Barbary, and many ether la-ti— 
tudes. He arrived in England in September 1700, fur- 
nilhed with a competent number of obfervations; and 
in the following year publiftied, A general Chart, Ihew- 
ing-atone View the Variation of the Compafs in all thofe 
Seas where the Englifti Navigators were acquainted. By 
this invaluable work he firft laid a. foundation for the 
difcovery of . the law by which the variation changes in 
all.parts of the world. Captain Halley, as he was now 
. called, had. been at home little more than half a year, 
when he received a commifiion from the king to obferve 
the courfe of the tides, with the longitude and latitude, 
.of the principal head-lands in the Britilii Channel; 
which he executed with his ufual accuracy, and foon 
after his return publiftied a large chart of the Britilh 
: Channel, ' 
In 1702, .the emperor of Germany refolving to make a 
fafe and convenient harbour for flapping in the Auftrian 
r territories on tlie Adriatic, captain Halley was lent by 
.queen Anne to take a furvey of the ports in Dalmatia, 
After, palling through Holland and Germany to Vienna, . 
he proceeded thence to I ftp a, with the intention of car¬ 
rying the emperor’s defign into execution ; but, owing 
to fome oppofition from the.Dutch, is was for fome time 
laid afide, and he returned to Vienna. Being intro¬ 
duced to the emperor, he gave him an account of two har¬ 
bours on the Iftrian coaft, and was prel'ented by his ma- 
