and a Method of difcovering the Longitude. 389 
to the other there can be no limits, for it meafures 180 dee 
grees on either fide. Not fatisfied with doing thus much, in 
order to avoid the inconvenience, trouble, and inaccuracy 
arifing from the ufe of large volumes of charts of {pherical 
triangles, and of tables for reducing obferved lunar diftances 
to true, I contrived an infirument, for which, as well as fe- 
veral fuperior furveying and other inftruments, I have alfo 
gota patent. This inftrument, which I have denominated 
a fuit of circles of calculation, performs this operation with 
eafe, accuracy, and expedition. It alfo determines the true 
Jatitude, without knowing the latitude by account, either by 
double altitudes and the time between, by double altitudes 
and the difference of magnetic azimuths, (which my in- 
ftruments will correétly give,) or by fimply having the alti- 
tude of two known fixed ftars, It determines the time of the 
day, &c. &c. In a word, it refolves all manner of {pherical 
triangles or fpherical trapezia, &c. The refolution of the 
few of thefe that conftitute the effentials of nautical aftro- 
nomy and geography, becomes by this means obvious, eafy, 
and pleafant; whereas the under{tanding, or even the appear- 
ance of the previous burthen of requifites, creates, as is well , 
known, a great if not infuperable obftacle to the generality 
of otherwife well-informed feamen. 
Having thus, I truft, explained my regard and efteem for 
the lunar obfervations and chronometers, all I would have 
underftood of the method of difcovering the longitude by the 
dip is, that it is eafily underftood by the moft ordinary capa- 
city; that to others, in every inftance, it becomes an auxi- 
liary or corroborating proof, and, in the time of greateft ne- 
ceffity and peril, a moft eftimable fubflitute; not requiring, 
in this cafe, any calculatiomwhatever. Thus, from the pre- 
ceding theory, the dip in all places remaining the fame, 
the navigator, being perhaps feveral days without feeing fun, 
moon, or ftars, fo as to make any ufe of either towards de- 
termining his longitude, has this benefit left him, that he 
¢an, at any moment of the day, in which the extremity of 
the horizon can be feen, determine his correét dip, and 
therefore his vicinity towards the land he wifhes to make or 
avoid; where otherwife he might ejther be caft away, or, under 
the 
