192 Mathematical Problems, by Mr. Adams. [Marcn, 
Half sum corres-2 _ 40 . > ape 
ating fosin, D =a eat ee ty = 9-8619354 
A dog: C08. Dis | xo’ eae ae lairn Viaipietas Suge <p», ==). DEVEDORE 
COR. Aas UNS SR aioe a savers mane ateleaes seea- = 9°9831840 
cos. true distance..=63 5 15 ...... = 9:6557408 
The same as determined by Mr. Sanderson’s rule. By Borda’s 
theorem, it is 63° 5’ 8”. See Dr. Gregory’s Trigonometry, 
~ page 179. 
Example 3.—Given the apparent altitudes of the moon and sun 
22° 15’, and 21° 35’; the true altitudes 23° 6’ 22”, 21° 32’ 44”, 
and the apparent distance 119° 20’ 34”; to find the true dist- 
ance. 
From the data 
ee 0° 0 177 B= Go? ay d7”,-and 4 = 1" aa ae. 
Then per Rule 2. 
Log.2...... Fie: i Beni baw wren hickwiu ah bs» es ee = 0:3010300 
Re ee ee wa ee StO.8 Dye". 4 eerie = 9°9375513 
UTE. ES he gree aes soo. 20 T7yl Solan = 9°9345950 
cos. sun’s true alt... =21 32 44 ........ = 9°9685417 
cos. moon’s true alt.=23 6 22. ........ = 9:9636838 
cos, sun’s app. alt...=21 35 0 (ar.com.) = 0:0315714 
cos.moon’s app. alt. =22 15 0 (ar.com.) = 0:0336046 
ore a 6 Rae aN ..= 1 33 38 (ar.com.) = 0°0001611 
Sum: of logarithms) .'. 01.1, o/s 0 olste sie dias sls we OT 07389 
Half ar. com. of 
sum comespond. =55 14 23 owe... . == 9:9146305 
ing tosm.D... 
Qlog. cos. D...... so nats a Vinw tetas akis ies sa aa 
PORSO oi's, cate et ote las semnrumt tak we eons = 9-9998389 
sum of logs. -as above. sp sissnes 20. beee = 01707389 
Cos; aap, trac dist.== Glia 122 ants he ee 9-6825472 
true distance. ....=118 46 48 F 
The same as given in Dr. Kelley’s Spherics, p. 184, and as 
determined by Mr. Sanderson’s rule. 
If the logarithmic sines and cosines be taken from Mr. 
Michael Taylor’s very valuable tables, the solution of the problem 
would then be rendered very easy ; but I am apprehensive that 
the necessary high price of those excellent tables prevents their 
being used as often as they otherwise would be. Thisinconvenience 
might, in a great degree, be obviated, by. printing the sines and 
cosines only in one volume ofa convenient size ; which is all that 
is here required. Indeed if Government were to keep such 
