Mr. Ivory on a Perpendicular Degrez at Beachy Head. 7 



Mag. for June last, and have found for the length of a de- 

 gree, 



At Greenwich 60826 fathoms ; 

 AtDunnose 60815; 

 and the mean of these, or 60820*5, is the proper rate of con- 

 version In the present instance. The difference of latitude 

 between Greenwich and Beachy Head will now be 44' 18''; 

 and if the latitude of Greenwich be taken at 51° 28' 39", that 

 of Beachy Head will be 50° 44' 21". 



The distance between the parallels of latitude passing 

 through Beachy Head and Dunnose, as found in the Survey, 

 is 7376*5 fathoms; which being converted into degrees, at 

 the rate of 60815 fath. to one degree, gives 7' 16"*7 for the 

 difference of latitude of the two stations. The latitude of 

 Dunnose is therefore 50° 37' 4"*3. 



But as the azimuths at the extremities of the geodetical line 

 drawn between the stations are given, we may deduce the 

 latitude of Dunnose from that of Beachy Head by another 

 method. Let B and D denote the azimuths, and A and A' the 

 latitudes, of Beachy Head and Dunnose; then, a and a(\— e) 

 being the axes of the terrestrial spheroid, the general pro- 

 perty belonging to every geodetical line, will give this equa- 

 tion in which the square of s is neglected, 



cos X' sin D cos X sin B 



V 1— 2 « sin (i >.' a/ I — 2gsin*A 



from which we easily derive this formula, log. cos A' = log. 



( C ° S s inD B ) + Ms ( sin9 K - sin3 *')> where M = * 43429 & c -> 

 the modulus of the common logarithms. Now, computing by 

 this rule, we shall find A' = 50° 37' 5"'65. This result is as 

 little different from the former one as can reasonably be ex- 

 pected, considering that the methods of calculation are very 

 different, and likewise proceed upon experimental data quite 

 independent of one another. Both results are confirmed by 

 actual observation, Capt. Kater having found 50° 37' 5"*27 for 

 the latitude of Dunnose*. We may therefore definitively fix 

 the latitudes of the two stations as below : 



Beachy Head 50°44' 21" 



Dunnose 50 37 5 



and it is very improbable that either of these results errs so 

 much as 1" from the truth. 



The two latitudes we have found are so little different from 

 those in the Survey, as to produce no sensible change in the 

 ulterior calculations of the difference of longitude and the 



* Phil. Trans. 1819, p. 413. 



length 



