Length of a Degree of a Parallel of Latitude. 235 



Length of a Degree of a Parallel of Latitude. 



1. Knowing the reduction of latitude (formula (6)) and the ter- 

 restrial radius (formula (7)) corresponding to any place, the length 

 of a degree of the parallel of latitude at the same place, may be 

 readily found as follows : The parallel being the circle generated b}'' 

 the point m, during the revolution of the generatrix, will have its 

 radius equal to x : now we have already shown, that a; = pcos.(4' — ^) 5 

 and if we designate by I, the length of the degree sought, we shall 



have ?=7q7;pcos.(4^ — (5) ; if in this we place the value of p given 



by formula (7), we shall find 



cos. (4^ — 5) 



/=3963 miles X 



Xi 



(8.) 



180'^[l + .006678sin.2(^|>-5)]i 

 2. Having first found ^, by formula (6), and then substituting the 

 value of 8 thus found, in formula (8) we shall at once reduce the 

 corresponding value of Z; and it is in this manner that we have con- 

 structed the following table, in which columns A exhibit the latitudes 

 differing by 1°, and columns B the corresponding length of a degree 

 of the parallel of latitude. 



Lengths of Degrees of Parallels of Latitude. 



B 



Miles 

 69.167412 

 69.1669 

 69.1256 

 69.0733 

 69.0100 

 68.9060 

 68.7910 

 68.65:54 

 68.4987 

 68.3214 

 68.1234 



B 



Miles. 

 68.1234 

 67.9189 

 67.6656 

 67.4060 

 67.1258 

 66.8254 

 66.5048 

 66.1639 

 65.8029 

 65.4220 

 65.0213 



A! B 

 „ Miles 



20 65.0213 



21;64.6 



22,64.1608 



23,63.7012 



24 6.3.2237 



25 62.7242 



62.2069 

 61.5290 

 61.11.58 

 60.5424 

 59.9504 



B 



Miles 



59.9.504 



.59.3402 



58.7137 



58.0658 



57.4020 



56.7205 



56.0218 



55.3059 



54.5732 



53.8239 



53.0580 



A[ B 

 Miles 

 53.0580 

 52.2759 

 51.4778 

 50.6640 

 49.8347 

 48.9900 

 48.1304 

 47.2560 

 46.3671 

 45.4639 

 44.5466 



Af .B 



„ Miles, 

 50 44.5466 



43.6160 

 42.6715 

 41.7142 

 40.7440 

 ■39.7615 

 38.7663 

 37.6726 

 36.7416 

 35.6535 



60134.6700 



B 



Miles 



.34.6700 



33.6184 



32.5564 



31.4842 



30.4026 



29 3114 



28.2110 



27.1022 



25.9848 



24.8.592 



23.7261 



B 



Miles 

 23.7261 

 22.5859 

 21.4385 

 20.2842 

 19.1239 

 17.9574 

 16.7855 

 15.6086 

 14.4266 

 13.2402 

 12.0776 



B 



Miles. 

 12.0776 

 10.8554 

 9.6578 

 8.4572 

 7.2541 

 6.0484 

 4.8409 

 3.6320 

 2.4219 

 1.21U 

 0.000000 



Should the parallel pass through a place whose latitude falls be- 

 tween two consecutive ones given in the table, the length of the 

 degree may be approximated to, with a sufficient degree of accuracy, 

 by a method entirely similar to that explained in the subject of the 

 length of a degree of the meridian ; but if the utmost accuracy be 

 required, then we must deduce the length of the degree from the 

 formula. 



