APPENDIX A 
MODE OF DETERMINING POINTS ON THE PARAI^EIi. 
The following is the agreement as to method of determining points 
on the parallel by measures from the tangent. This agreement and 
the accompanying table are copied from the original in the State 
Department. 
TO DETERMINE POINTS OK THE FORTY-NINTH PARALLEL BY MEANS OF THE TANGENT. 
Wherever points of the parallel between the astronomical stations are to be deter- 
mined it is hereby agreed to adopt the method of offsets from the tangent to the 
parallel. 
For computing the length of these offsets the following formula is adopted, being 
that used in computing the difference of latitude of points in secondary triangles or 
those whose sides do not exceed 12 miles in length: 
where 
■dL=kB cos Z + PC sin 2 Z + h 2 D 
rfL=difference of latitude of the two points; 
&=length of side connecting them; 
1 
B = 
R arc 1"' 
tan L 
C_ 2IS 
(1-e 2 sin 2 L)< 
h=kB cos Z; 
R _ a(l-e 2 ) 
(l-e 2 sin 2 L)^' 
a 
N= 
(l-e 2 sin 2 L)* 
a=equatorial radius of the earth=6 974 127.31 yards; 
e=eccentricity=0.081 696 830; 
Z=azimuth of tangent counting from south around by west; whence 
west=90°, east=270°. 
This formula becomes in the present case 
-dL=k 2 C; 
or, taking offset in yards =8, distance in yards on the tangent =D 
log<5=2 log D + 2.915491. 
Jno. G. Parke, 
Lieutenant, Corps Topographical Engineers U. S., Chief Astronomer and Surveyor. 
R W. Haig, 
Captain, R. A., Astronomer British Commission. 
(Camp Simiahmo^, Forty-ninth Parallel, April 23, 1859. 
