XIV 
The INTRODUCTION. 
the Deficiencies con fe fifed by the Moderns, they are really fo many Points of Knowledge, as to which 
the Ancients had not the leaft Conception ; and though we have not hitherto attained them, which 
is a Misfortune ; yet we know what they are, and, in fame meafure, how 7 ' they may be attained^ 
which is a great Felicity. 
As for Infta’nce, we know the great Importance of difeovering an eafy and certain Method of find- 
ing the Longitude j and this in our own, and other Nations, has induced the Publication of great 
Rewards for the making of fiich Difcovery. And if this Method were carried farther into Practice, 
and final ler Sums were offered for intermediate Difcoveries, I do not at all doubt that much greater 
Things might, in a few Years, be attained, than were formerly reached in whole Ages. 
There are, indeed, feveral Methods by which the Longitude may be dilcovered, befides this j and 
becaufe it is impoffible that the Reader fhould enter into the true Merit of fuch a Difcovery as this 
would be of the Theory of magnetical Variations, without having a competent Notion of thofe Me- 
thods, I fhall venture to difcourleof them here, as I have done of other Things in an eafy and fa- 
miliar Way. The only Method the Romans had of fettling the Diftances of Places, and thereby 
framing Defcriptions or Maps of Countries was, by actually meafuring them ; and by this Means 
that Map or Ddcription of the World, which was depided from Agrippds Tables in the Reign of 
the Emperor Augufius , in a Portico erebled for that Purpofe, was made. It is generally believed, 
that the celebrated Itinerary afcribed to the Emperor Antoninus , was extrabled from thence. A. 
Work wonderfully exaft and worthy of the greateft Commendation, confidering the Time in which 
it was made But Ptolemy , the Geographer, as we have before obferved, was the firft who intro- 
duced the Method of fixing the Diftances by Longitudes and Latitudes, which has been fince fol- 
lowed,, as being both eafier and more exabt than the former. It is, however true, that there are 
many, and thofe very grofs Miftakes in the Geography of Ptolemy ; as, for Inftance, he places the 
Fortunate IJlands under the fame Meridian, and yet gives them feveral Degrees of Longitude ; and in point 
of Latitude, he is at leaf! ten Degrees out in his Computation. Lie fpeaks of a City in China t lying 
in the Latitude of three Degrees South, whereas we now certainly know that the moft Southern 
Part of China lies in twenty Degrees North-Latitude. He has fo defcribed the great Ifland of Pa- 
prohand , that it is in a manner impoffible to determine, at leaf! with Certainty, whether it be Ceilon „ 
Sumatra , or Borneo. Hence fome very judicious Perfons have doubted whether the introducing Aft* 
tronomy has been of any Ufe to Geography, or whether on the contrary, it has not contributed to 
embarrafs and perplex that Science, by which it is rendered much more uncertain than if the old plain 
geometrical Method had been ftill followed. But, in Anfwer to this, it may be very truly affirmed 
that the Errors of Ptolemy do not arife from his Ufe of aftronomical Principles, but from his fol- 
lowing bad Memoirs, and the great Inaccuracy of the Obfervations made in thofe Times for want 
of good Inftruments. 
The Moderns, who, without Queftion, have difcovered much better Methods of making Ob- 
fervations, have, confequently, been able to correbt thefe Errors, and eftablifh a new Way of difeo- 
vering the Longitude with Certainty, which is that of Eclipfes. To fet this Matter in a clear 
Light and in as few Wcrds as poffible, I fhall have Recourfe to an Example. As foon as it was cer- 
tainly known that an Eclipfe of the Sun or Moon was obferved earlier at Stockholm than at Paris 9 
it followed that Stockholm muft lie Eaft from Paris. When farther Obfervations had determined that 
an Eclipfe was obferved an Flour fooner at Stockholm than at Paris , it followed, from the fame Prin- 
ciples, that Stockholm lay 15 Deg Eaft of Paris ; fo that, agreeable to the Edibt of Lewis XIII. 
which fixed the firft Meridian in the Ifland of Ferro , and confequently the City of Paris in the 
Longitude of 20 Deg. 30 Min. the true Longitude of the City of Stockholm was found by this 
Obfervation to be 35 Deg. 30 Min. To make this ftill plainer, let us take another Example. It 
has been found, that an Eclipfe has been obferved in the Illand of Caienne three Hours and an half 
later than at Paris ; from whence it is evident, that Ifland muft lie 52 Deg. 30 Min. Weft from Paris, 
and that for this Reafon : The Equinobtial being divided into 360 Deg. and making one Revolution 
in twenty-four Hours, there muft confequently be fifteen Degrees allowed to an Hour, upon which 
this Calculation is grounded. 
As this Method of afeertaining the Longitude of Places, by the Obfervation of the Eclipfes of the 
Sun and Moon, contributed greatly to the Improvement of Geography 5 fo this very Method has ac- 
quired much greater Feffebtion fince we have fallen into a Way of Obferving the Eclipfes of the Sa- 
tellites of Jupiter , which the moft learned Perfons have pronounced to be, of all others, the fhort- 
eft, eafieft, and moft certain Method of fixing the Longitude. In order to this, there is nothing 
more requifite than to have Tables very exabtly adjufted for thefe Eclipfes to any given Place, and by 
obferving feveral of thefe Eclipfes carefully at any other Place, the Difference in point of Time, will 
fhew exabtly, when reduced to Degrees and Minutes, the Difference of Longitude between the two 
Places, or, in other Words, how far one is Eaft or Weft from the other. I muft not, however, dif- 
femble, there having been fome Objebtions made to this Method, notwithftanding the Sentiments of fo 
many great Mathematicians in its Favour, particularly by the celebrated Ricci oil, in his reformed Geo- 
graphy, who declares, that he will never confent to this Method of fixing the Longitude by Eclipfes, 
unlefs it fhall appear, that it agrees exabtly with the Differences found by geometrical Methods, that 
is, by plain Meafuring, which, tho’ in fmall Diftances, it may do, yet in greater, it has been known 
to fail. The Inferences made from hence, appear at firft Sight, fo clear, and fo ftrong, that they 
fee m to be conclufive, and to throw us back into that Degree of Uncertainty, from whence this Me- 
thod promifed to deliver us. 
But, upon mature Confideration, we may, perhaps, fuggeft a Solution of this Difficulty, which 
may prove fausfabtory, and thereby bring Things once more to Rights. In order to this, I muft take 
c ' ~ No- 
1 
