192 A Method for ascertaining Latitude and Time 
Cos A too great by...... + 1474 dh — 67954 dh’. 
Tang (?+2) too greatby —43-919dh — 5:9399 dh’. 
Tang u @ too great by .... —=42°445 dh. — 12°7976 dh. 
¢ too great by.... —0-9803 dz — 0-29959 dh’. 
And, supposing dh = dh’ = 10”, the latitude will be too 
little by 1278: by recommencing the calculation and using’ 
. the two altitudes as increased 10”, [had found da = + 127 
and de = — 13”. 
This method of Jogarithmic differentials is general; it is 
More concise than the direct calculation with mereased alti-: 
tudes, but it requires a very minute attention. The for- 
mulz are more commodious. | begin with mine. 
Cot D9:7274 «=Vangh.... 0°0113.. CsinD o0544 
Csin W 0::035 Cot W.... 9°8927.. Csin W 01035 
+0°6775 9309 0°8017.... 9:9040.. 01579 
— 0'8017 
— 01242 dh —1°438 dh’ = — du. Let us suppose dh = 
dh’ = 10”, we shall have du +- 0°1949dh J- 1-438 dh’ = 
15°622: the logarithmic variations have given 157,65. 
Cotuw.. 07278 —sin?..—9°1635 —cosé.. — 99053 
Cos A,. 9°9905 siA-. OSIST~ ‘Si Ayn. oe OoUe 
+ 52210 ory7g == 00801 “§-4796 Cos? h.... 03126 © 
— 0'0301 C sinus. s. O-7348 
este. C7... 0°7153 90729 
aR Togs heyy a 93151 eae, 
1242 90941 1438 01579 O14 70gah 
+1:5427dh' 
+1 0718 dh 
+ 12”,05, 
+0°1333dhk0:124541°5427dh' 01883 
dx = +0°133 dh + 1-6718 dh’. 
Suppose di = du = 10”, we shall have da = 
the logarithmic variations have given 19’ ,09. 
cy. RESO OMOGL os, ee OE ioe Fev ecas sas —0°2061 
Cosh. . 9°8437 —sin kh —Q'%552  cosh...... 9845 
Sin 3... 9° 1635 cos & 9°9953 . cosd...... . _ 99953 
cosu'QQ925 sint..... ‘ 0°2652 
4+0°1634,. 92133 —1'1197 OO49I —0'2042 ' —9 3103 
+0:1034 01242 9 0941 
—0°9563dh ' —0°0254 $4044 
—0'0254dh + 
do = $0 9817dh —0°2042 — 93103 
f= 2—0-293Gdh' ( 1-438 | 01579 
—02939 94682 
Supposing dh = dh’ = 10”, dg = — 12”,756. The lo- 
» garithmic diferentials have given — 12778. A more satis- 
factory coincidence cannot be wished for. These formulz 
_appear to require more calculation than the logarithmic 
differences, but they do, not require so minute an attention, 
ne Mr. Gauss’s 
