s t 
bv such Indulgences. .Dr. Fotherglll ob- 
serves, tnat “ the due regulation of the pas- 
s-ions per! laps contributes more to health and 
longevity than any of the other nonnaturals.” 
\I he cheerful and contented are certainly 
more likely to eniov good health and long 
life than persons of irritable and fretful dis- 
positions ; therefore whatever tends to pro- 
mote good humour and innocent hilarity, 
must have a beneficial influence in this re- 
spect; and persons whose attention is much 
engaged on serious subjects should endea- 
vour Id preserve a relish for cheerful recrea- 
tions. 
LONGITUDE of a slur, in astronomy, 
a.i arch of the ecliptic, intercepted between 
tlie beginning of Aries and the point of t he 
ecliptic cut by the star’s circle of longitude. 
Longitude of a pi ice. SeeGEOGRA- 
THY. 
Longitude, in navigation, the distance 
of a ship or place, east or west, from another, 
reckoned in degrees of the equator. 
As the discovery of a method to find the 
longitude would render voyages safe and ex- 
peditious, and also preserve ships and the 
lives of men, the following rewards have been 
offered as an encouragement to any per- 
son who shall discover a proper method 
for finding it out: — In the year 1714, the 
British parliament offered a reward for the 
discovery of the longitude : the sum of 
10,000/. if the method determined the lon- 
gitude to 1° of a great circle, or to 60 geo- 
graphical miles; of 15,000/. if it determined 
it to 40 miles; and of 20,000 /. if it deter- 
mined it to 30 miles; with this proviso, that 
if any syich method extend no further than 
30 miles adjoining to the coast, the proposer 
should have no more than half the rewards. 
The act also appoints the first lord of the ad- 
miralty, the speaker of the house of com- 
mons, the first commissioner of trade, the 
admirals of the red, white, and blue squad- 
rons, the master of the Trinity-house, the pre- 
sident of the royal society, the royal astrono- 
mer at Greenwich, the two Savilian profess- 
ors at Oxford, and the Lucasian and Plu- 
mian professors at Cambridge, with several 
oilier persons, as commissioners for the lon- 
gitude at sea. The Lowndian professor at 
Cambridge was afterwards added. After this 
act of parliament, several other acts passed 
in the reigns of George II. and III. for the 
encouragement of finding the longitude. At 
last, in 1774, an act passed, repealing all 
other acts, and offering separate rewards to 
any person who should discover the longi- 
tude, either by the watch keeping true time 
within certain limits, or by the lunar method, 
or by any other means. The act proposes as 
a reward for a timekeeper, the sum of 5000/. 
if it determine the longitude to 1° or 60 geo- 
graphical miles; the sum of 7500/. if it de- 
Xermine it to 40 miles ; and the sum of 
1 0,000/. if it determine it to 30 miles, after 
proper trials specified in the act. If the me- 
thod is by improved solar and lunar tables, 
constructed upon sir Isaac Newton’s theory 
of gravitation, the author shall be entitled to 
5000/. if such tables shall show the distance 
of the moon from the sun and stars, within 
fifteen seconds of a degree, answering to 
about seven minutes of longitude, after allow- 
ing half a degree for the errors of observa- 
tion. And for any other method, the same 
LONGITUDE. 
rewards are offered as those for timekeepers, 
provided it gives the longitude true within 
Hie same limits, and is practicable at sea. 
1 he commissioners have also a power of giv- 
ing smaller rewards, as they shall judge pro- 
per, to any one who shall make any disco- 
very for finding the longitude at sea, though 
not within the above limits; provided, how- 
ever, that if such person or persons shall 
afterwards make any further discovery as to 
come within the above-mentioned limits, 
such sum or sums as they may have received 
shall be considered as part of such greater 
reward, and deducted therefrom accord- 
ingly. 
To find the longitude hj a time-keeper. 
Fiie sun appears to move round the earth 
from east to west, or to describe 360°, in 24 
hours, and therefore he appears to move 15° 
in an hour. If therefore the meridians of 
two places make an angle of 15° with each 
other, or if the two places differ 15° in lon- 
gitude, the sun will come to the eastern me- 
ridian one hour before he comes to the west- 
ern meridian, and therefore when it is twelve 
o’clock at the former place, it is only eleven 
at the latter; and in general, the difference 
between the times by the clock at any two 
places, will be the difference of their longi- 
tudes, converted into time at the rate of 15° 
for an hour, the time at the eastern place 
being the forwardest. If, therefore, we can 
tell what o’clock it is at any two places at 
the same instant of time, we can find the dif- 
ference of their longitudes, by allowing 15° 
for every hour that the clocks differ. 
Let, therefore, the timekeeper be well 
regulated and set to the time at Greenwich, 
that being the place from which we reckon 
our longitude ; then if the watch neither gains 
nor loses, it will always show the time at 
Greenwich, wherever you may be. Now to 
find the time by the clock at any other place, 
take the sun’s altitude, and thence find the 
time ; now the time thus found is apparent 
time, or that found by the sun, which differs 
from the time shown by the clock by the 
equation of time. We must, therefore, apply 
the equation of time to the time found by 
the sun, and we shall get the time by the 
clock; and the difference between the time 
by the clock so found, and the time by the 
timekeeper, or the time at Greenwich, con- 
verted into degrees at the rate of 15° for an 
hour, gives the longitude of the place from 
Greenwich. For example : let the time by 
the timekeeper, when the sun’s altitude was 
taken, be 6h. 19', and let the time deduced 
from the sun’s altitude be 9h. 27', and sup- 
pose at that time the equation of time to be 
7', showing how much the sun is. that day 
behind the clock, then the time by the clock 
i ' 9h. 34', the difference between which and 
6h. 19', is 3h. 15'; and this converted into 
degrees, at the rate of 15° for 1 hour, gives 
48° 45', the longitude of the place from 
Greenwich; and as the time is forwarder 
than that at Greenwich, the place lies to the 
east of Greenwich. Thus the longitude 
could be very easily determined, if you 
could depend upon the timekeeper. But as 
a watch will always gain or lose, before the 
timekeeper is sent out, its gaining or losing 
every day for some time, a month for in- 
stance, is observed; this is called the rate of 
going of the watch, and from thence the 
mean rate of going is thus found: 
Suppose I examine the rate of a vatch for 
30 davs ; on some of those days I find it has 
gained, and on seme it has lost; add toge- 
ther all the quantities it lias gained, and sup- 
pose they amount to 17"; arid together all 
the quantit.es it lias lost, and suppose they 
amount to 15"; then upon the whole, it lias 
gained 4" in 30 days ; and this is called the 
mean rate for that time ; and this divided by 
30, gives 0". 133 for the mean, daily rate of 
gaining ; so that if the watch' had gained re- 
gularly 0", 1 33 every day, at the end of the 
30 days it would have gained just as much 
as it really did gain, by sometimes gaining 
and sometimes losing. Or you mat get the 
mean daily rate thus: Take the diilerenee 
between what tiie clock was too fast or too 
slow on tlie first and last days of observation, 
if it be too fast or too slow on each day ; but 
take tlie sum, if it is too fast on one day and 
too slow on the other, and divide by tlie 
number of days between the observations, 
and you get the mean daily rate. Thus, if 
the watch was too fast on the first clay IS", 
and too fast on the last day 32", the* diffe- 
rence 14" divided by 30, gives 0",466, the 
mean daily rate of gaining. But if the watch 
was too fast on the first day 7", and too slow 
on the last clay 10", the sum 1 7" divided by 
30, gives 0",566, the mean daily rate of los- 
ing. After having thus got the mean daily 
rate of gaining or losing, and know ing how 
much the Watch was too fast or too slow at 
first, you can tell, according to that rate of 
going, how much it is too fast or too slow at 
any other time. In the first case, for in- 
stance, let the watch have been B 17" too fast 
at first, and I want to know how much it is 
too fast 50 days after that timh : now it gains 
0", 133 every day; if this is multiplied by 50, 
it gives 6",65 for the whole gain in 50 days; 
therefore, at the end of that time, the watc h 
would be V. 23", 65 too fast. This would be 
the error, if the watch continued to gain at 
the above rate ; and although, from the dif- 
ferent temperatures of the air, and the im- 
perfection of the workmanship, this cannot 
be expected, yet the probable error will by 
this means be' diminished, and it is the best 
method w'e have to depend upon. In watches 
which are under trial at the Royal Observe- - 
lory at Greenwich, as candidates for the re- 
wards, tliis allowance of a mean rate is ad- 
mitted, although it is not mentioned in the 
act of parliament : the commissioners, how- 
ever, are so indulgent as to grant fit, which 
•is undoubtedly favourable to the watches. 
As the rate of going of a watch is subject 
to vary from so many circumstances, tlie ob- 
server, whenever he goes ashore, and has suf- 
ficient time, should compare his watch for 
several days with the true time found by the 
sun, by which he will be able to find its rate 
ot going. And when he comes to a place 
whose longitude' is known, he may then set 
his watch to Greenw ich time ; for w'hen the 
longitude of a place is known, you know the 
difference between the time there and at 
Greenwich. For instance, if he go to a 
place known to be 30° east longitude from 
Greenwich, his watch should be two hours 
slower than the time at that place. Find 
therefore the true time at that place, by the 
sun, and if the watch is two hours slower, it 
is right; if not, correct it by the difference, 
and it again gives Greenwich time. 
In the year 1726, Mr. John Harrison pro- 
