xlvi GEODESY. 



Radius of curvature of meridian section p,„ in feet, 

 logp,,. = + 7.3199482 



— [4-34482] COS 2(f) 

 + [1-274] COS 4</> 



Radius of curvature of normal section p„ in feet. 

 logp„ = -\- 7.3214243 



— [3.86770] COS 2<^ 



+ [0-797] COS 4<^ 



The numbers in brackets in these formulas are logarithms to be added to the 

 logarithms of cos 2(f> and cos 4<l). The numbers corresponding to the sums of 

 these logarithms will be in units of the seventh decimal place of the first constant. 

 Thus, for (fi = o, 



logp„= 7.3214243 



- 7373-9 

 _+ 6^ 



= 7.3206875 = log a. 



7. Length of Arcs of Meridians and Parallels of Latitude. 



a. Arcs of Meridian. 



For the computation of short meridional arcs lying between given parallels of 

 latitude the following simple formulas suffice : 



<f> = ^(<^2 + «/>:), (i) 



AJ/=p„. A</,. 



In these, ^1 and ^o are the latitudes of the ends of the arc, A J/ is the required 

 length, and p„, is the meridian radius of curvature for the latitude ^ of the middle 

 point of the arc. The formula for AJ/ implies that A(/) is expressed in parts of 

 the radius. If A(f> is expressed in seconds, minutes, or degrees of arc, the for- 

 mula becomes — 



Meridional distance AM in feet. 



p„, Ac^ (in seconds) 

 206264.8 



Pm ^(f> (in minutes) 



~ 3437-747 ' 



p,„ A(f) (in degrees) . 



~ 57-29578 ' (2) 



log (1/206264.8) = 4.6855749 - ID, 

 log (1/3437.747) = 6.4637261 — ID, 

 log (1/57-29578) = 8.2418774- ID. 



(p,, <p„ = end latitudes of arc, A^ = ^2 — ^,, 

 Pm =^ meridian radius of curvature for (p = 4^(02 + ^1) ; for log p„ see Table 10. 



