HOROLOGY. 
360 
time ought to be 3 m 5 5 s '91 of folar time, but in 24 h of 
liijereal time, 3'" 56 s "5S, provided the machines performed 
with perfect truth; one or other of thefe two ftandard 
numbers, therefore, muft be ufed as the meafure of the 
daily error, accordingly as the interval is a folar or a 
fidereal day. In making the companions previoufly to 
the calculations being entered upon, it is not neceflary to 
have more than five columns; one for the day of the 
month, a lecond for time per watch, a third for the time 
per dock, a fourth for the barometer, and a fifth for the 
thermometer; which form being lb Ample requires no fac 
limile. But the calculations, grounded on the data in the 
By a mean of 11 days' coinparifons, from May 6th to 
May 17th, the watch being in a horizontal polition with 
the face upwards, gets at the rate of 1^-509 per day upon 
mean time. 
Explanation. The firft column Ihows the days of the 
month ; the fecond, the interval of time, according to the 
watch, between the attefted companions of the watch each 
day with the traniit clock; the third column contains the 
quantity of minutes and feconds which the watch lofes of 
the clock in the laid interval; the fourth column Ihows 
how much the watch Ihould lofe of the clock in 24 hours 
of the watch, according to the proportion expreffed in the 
lecond and third columns ; the fifth column gives the daily 
gaining or lofing of the tranfit clock with rel'pecf to fide¬ 
real time, as deduced from the obferved tranfits of the 
fixed liars over the meridian, the fign being fet down 
If we include here both the 6th and 17th, there will be 
12 days in this calculation, during which the watch gained 
in the whole 3 m 51 s- 8 or 23i s- 8, therefore -— iqs'22 
12 
is the rate on this mode of comparifon, which agrees very 
well with the preceding one calculated on the fame period. 
Explanation. According to the arrangement in this lalt 
Table, the firft column contains the day of the month ; 
the fecond, the obferved tranfit of the fun’s centre over 
the meridian, according to the time of the tranfit clock ; 
the third column lhows the time by the clock, when com¬ 
pared with Mr. Harrifon’s watch ; the fourth, the apparent 
time at the fame companion ; the fifth, the equation, of 
Vol. X. No. 667A 
faid five columns, require many more columns, for which 
we ftiali not give any previous directions, but infert Dr. 
Malkelyne’s two methods of arrangement, extracted from 
“ The Original Obfervations of the Going of Mr. Harn- 
fon’s Watch from Day to Day,” as publilhed by the board 
of longitude; which methods will be better underftood 
from the forms of his tables, and explanations, than from 
any verbal rules of ours, which muft neceffarily be complex. 
Example. Let it be required, from the data contained 
in columns 1, 2, and 3, of the fubjoined Tables, to deter¬ 
mine the rate of Mr. Harril'on’s time-keeper, taken on aft 
average of the 11 days trial contained in the Table. 
in cafe of the clock’s lofing, and — in the cafe of its 
getting. This correction, applied to the numbers of the 
fourth column, produces the fixth column, or the lofing 
of the watch from day to day; with relpeCt to fidereal 
time, in 24 hours of the watch. The leventh column 
gives the daily gaining of the watch upon mean time, and 
is found by taking the difference of the preceding column 
and 3 m 56 s -5 fidereal time, gaining fo much upon mean 
folar time in 24 hours of mean time; or rather more 
exaftly, in 24 hours of the watch, which generally cor- 
refponds to lefs than 24 hours of mean time by near 20 
feconds. The eighth column contains the mean ftate of 
the thermometer for the day; and the ninth and laft co¬ 
lumn ftiows the mean ftate of the barometer. The watch 
was kept in a horizontal pofition, face upwards. 
time, which, applied to the numbers in the precedino- 
column, gives the mean time contained in the fixth co¬ 
lumn ; the feventh column gives the time fhown by Mr. 
Harrifon’s watch, when compared with the clock ; ialtly, 
the eighth column ftiows how much the watch is too 
fall, for mean time each day. Original Oblervations, p. 
xxvii-xxix. 
The general problems for finding the errors and rate of 
a time-keeper, by equal altitudes of the fun, or of a fixed 
ftar, have been given under the article Astronomy, 
vol. ii. p. 454, to which we (hall add only the two following. 
1. To find the Error of a Time-keeper by equal Altitudes of 
the Sun, the lhip being under way.—Let feveral fets of 
5 A equal 
Firfi Method. —Calculations of the Going of Mr. Harrifon’s Watch from Day to Day. 
Interval of 
Compan¬ 
ions. 
Watch lofes 
of Clock. 
Watch lofes of 
Clock in 24 1 ' of 
Watch. 
Clock varies 
from fidereal 
Time per Day. 
Watch lofes of 
fidereal Time of 
24 11 of Watch. 
Watch get 
mean Time 
Day. 
on 
per 
Mean Hate 
of Ther¬ 
mometer. | 
Mean ftate 
of Baro¬ 
meter. 
1766. 
h. in. 
m. s. 
m. 
s. 
s. 
m. 
s. 
s. 
Deg. 
Inch. 
May 6 to 7 
i3 30 
3 33 
3 
37 'S 3 
+ 1- 34 
3 
38-9 
17 
*6 
54 
29-9 
7 8 
24 4 
3 37 
3 
36-4 
ri-1*22 
3 
37-6 
18 
'9 
57 
297 
' 8 9 
23 52 
3 34 
3 
37-2 
— 1 ' 1 7 
3 
36-4 
20 
*1 
55 
29-5 
9 1 o- 
24 4 
3 36 
3 
3 5'4 
4-1-13 
3 
36-5 
20 
*o 
54 
29-3 
10 11 
23 57 
3 36 
3 
36'4 
-j-n6 
3 
37-6 
18 
•9 
49 
29'5 
11 12 
24 I 
3 36 
3 
3 5*9 
+ r 12 
3 
37-0 
19 
*5 
5 ° 
29-6 
12 13 
24 9 
3 37 
3 
35-6 
+ i'°S 
3 
36-6 
J 9 
'9 
5 i 
29-6 
n 14 
2'3 49 
3 33 
3 
34 '76 
1*02 
3 
3 5'8 
20 
7 
52 
2 9'8 
14 15 
24 8 
3 37 
3 
3579 
+ 1-02 
3 
36-8 
19 
7 
52 
30-1 
. 1 5 
24- • 2 
3 36 
3. 
35 70 
+ o-8o 
3 
3 6 '5 
20 
*o 
54 
30-2 
16 17 
24 9 
3 38 
3 
36-64 
+0-58 
3 
37 ' 2 
19 
* 3 
5*5 
30-1 
11)209 
• 5 6 
19-509 
Second Method. —Compsrifons of Mr. Harrifon’s Watch with Mean Time. 
Obferved Tranfit 
of Sun per 
Clock. 
Time per Clock 
at comparifon 
with Watch. 
Apparent Time. 
Equation of 
Time. 
Mean Time. 
Time per Watch 
at comparifon 
with Clock. 
Watch fall for 
mean Time. 
1766. 
h.m. s. 
h. m. s. 
h.m. s. 
m. s. 
h. 
m. s. 
h.m. s. 
m. s. 
(J May 6 
2 S3. 3o-2> 
3 39 1 
0 45 23-60 
3 39'8 
O 
4143-3 
O 42 O 
0 l6'2 
? - 7 
2 57 20-50 
3 12 34 
O 15 11*10 
3 45 '° 
O 
1126-1 
0 12 0 
0 3 3'9 
ji 12 
3 437 i 
3 28 33 
0 11 47-38 
3 59'32 
O 
7 48-0 
OIOO 
2 12*0 
% 1 5 
3 28 28-77 
3 45 20 
0 16 48-47 
4. 1*10 
O 
12 47-4 
0160 
3 12-6 
b 1 7 
3 36 21-83 
4 3 34 
0 27 7-68 
3 59'47 
O 
23 8-2 
O 
N 
O 
3 51 'S 
