by means of Two known Stars. 191 
method may be reduced to the same conciseness ; in which 
case*both methods would be perfectly identical : but the tri- 
gonoinetrical method will always have this advantage,— 
that it gives the formule at sight, while analysis cannot 
attain to them but by going a great round about, whereby 
one is apt to be misled. 
The differential formule remain to be compared’: but 
without these formule, leaving and h’ indeterminate, the 
errors da and dg that will result from dk and dh’ may be 
ascertained while calculating a and ¢. 
Jn the first place it is evident that the errors dh and dh’ 
can have no effect on x, V nor D: they only begin to have 
any influence on W. 
By calculating W, I see that the logarithm of 2 will 
lucrease 20°5 parts for each second of error ind’, and 
will Jessen as much for each second of error in dh. 
Let us then suppose that and h’ are too great, the lo- 
garithm of m will be too great by — 20,5 dh + 20,5 di’, 
n will be too great of itself by —0 00001dh + 0-00001dh’; 
for by any uncommon coincidence, increases 0°00001 
in the same manner as / increases 1’, when the logarithm 
is increased 20°5 parts; 2—1 will, therefore, be too great 
by —0:0000! dk + 0°00001 dh’. 
The logarithm (m—1) will therefore be too great by 
—38,7 dh + 38,7 dh’. 
- The logarithm of tang A will be too great by 42,1 dh. 
The logarithm of cos W will be too great by + 3,4dh + 
38,7 dh’; but W decreased 26-9» part for 1”. W then is 
too small by ee dh + a dh, or by 0°1264 dh 4- 
1°4387 dh; wis then too great by the same quantity, since 
u=V—W. 
_ Thus, by supposing that dh = dh’ = 10”, w will be too 
great by 15”,65 = 1°2964 + 14387. 
Cos wu will be too little by 0°5056dh + 5°7548 dl’. 
Cot h will be too little by 42,1 dh 
‘Tang z too little by ..... . 42°6036 dh 4+ 5°7548 dh’. 
, %toolittle by ..... - 1°0096 dh + 0°1364 dh’. 
é + 2 tov little likewise by the same amount. 
Tang w will be too great by + 14:700dh + 167-320 dh’. 
Sin ztoo long by ...... —22°219dh — 2:864 dh’. 
C cos ($+2) too long by —27:361 dh — 3696 di’. 
Tang A too great by ..... —34'873 dh + 160°760 dh’, 
A too great by ..... —0°3350dh + 1°5444 dh’. 
Thus, supposing dh = dh’ = 10”, da will be + 12094, 
the horary angle too great by 12”. Cds 
