Captain Owen on Circummeridian Altitudes. 171 
To convert a small Arc of Time to its equivalent Azimuth. 
Mr. Raper’s rule is applicable to small arcs only, and is founded 
on the differential triangle here adopted ; his demonstration is labored 
and circuitous. 
Owen’s is as follows : — 
t.D\—a? =z. Av D\ = cosine declination. 
A\ = cosine altitude. 
But the sum multiplied by difference 
= difference of their squares, therefore 
t.D‘+a log. cpio. BySyo t = time in are. 
t.D\—a log. Aap Oo des d z= azimuth in same. 
pe a= diff. altitude. 
ZEA log. oho os Giller 
rag del log. op ooo otis 
— A\ log. — .,.... subt.orlog. sect. add. 
Azimuth z log.— .,.... difference. Q. E. D. 
The converse of this is similar. 
To convert an Arc of Azimuth into equivalent Time. 
Given z log. aigaeae Te 
A‘ middle altitude log. cosine .,...- 
Zz * A\ log. bis. kets SUM. 
Ze log. og a oon GRE 
+a : wae ° log. of a*. 
Sum =7. D” Catjuchicnich ou) Erie 
t. D\ log. pie) srarenea als. 
—D log. cosine —. ,.. . . or add log. sect. 
Acct.log, = -,+.- « difference. 
For turning Azimuth into corresponding Time. 
Rute.—To the log. of azimuthal difference z, add the log. 
cosine middle altitude, the sum is z. A‘; double this sum will be 
