38 



Excess on a Spheroidal Triangle. 



[No. 121. 



SPHEROIDAL EXCESS. 

 Latitudinal Factors for computing Spheroidal Excess. 



Lat. 



T R" 



Log. 



Diff. 



Lat. 



Log. 



Diff. 



Lat. 



t R" 



Log. — - 



2yv 



Diff. 





2yv 







2yv 













0-37505 



1 



30 



0.37360 



8 



60 



0.37071 



8 



1 



504 







31 



352 



9 



61 



063 



9 



2 



504 



1 



32 



343 



9 



62 



054 



8 



3 



503 



1 



33 



334 



10 



63 



046 



8 



4 



502 



2 



34 



324 



9 



64 



038 



8 



5 



0-37500 



2 



35 



0*37315 



10 



65 



0-37030 



8 



6 



498 



2 



36 



305 



9 



66 



022 



7 



7 



496 



3 



37 



296 



10 



67 



015 



7 



8 



493 



3 



38 



286 



10 



68 



008 



7 



9 



490 



3 



39 



276 



10 



69 



001 



7 



10 



0-37487 



3 



40 



0-37266 



10 



70 



0-36994 



6 



11 



484 



4 



41 



256 



10 



71 



988 



6 



12 



480 



5 



42 



246 



10 



72 



982 



6 



13 



475 



4 



43 



236 



10 



73 



976 



5 



14 



471 



5 



44 



226 



10 



74 



971 



6 



15 



0-37466 



5 



45 



0-37216 



10 



75 



036965 



5 



16 



461 



6 



46 



206 



10 



76 



960 



4 



17 



455 



5 



47 



196 



10 



77 



956 



4 



18 



450 



6 



48 



186 



10 



78 



952 



4 



19 



444 



7 



49 



176 



10 



79 



948 



4 



20 



0*37437 



6 



50 



0-37166 



10 



80 



036944 



3 



21 



431 



7 



51 



156 



10 



81 



941 



3 



22 



424 



7 



52 



J46 



10 



82 



938 



3 



23 



417 



8 



53 



136 



9 



83 



935 



2 



24 



409 



7 



54 



127 



10 



84 



933 



2 



25 



0-37402 



8 



55 



0-37117 



9 



85 



0-36931 



2 



26 



394 



8 



56 



108 



10 



86 



929 



1 



27 



386 



8 



57 



098 



9 



87 



928 



1 



28 



378 



9 



58 



089 



9 



88 



927 







29 



369 



9 



59 



080 



9 



89 



927 







30 



037360 





60 



0-37071 





90 



0-36927 





As an example, suppose it were required to find the excess on a triangle having its 

 middle point in latitude 24°, the sides a and b being 40 and 50 miles, and the contain- 

 ed angle C =65°, the logarithms of a and 6 in feet being 5*3246939 and 5-5007852, the 

 calculation would stand thus : — 



Tab Long for 24°, ... ... ... ... 0-37409 



Long. Sin C = 65o, ... ... ... ... 9-55728 



Long, a, ... ... ... ... ... 5-32469 



Long, b, ... ... ... ... ... 5-50079 



Long. E = 5.'/7l28, ... ... ... ... 0.75685 



It is of no great importance to know the latitude of the middle of the triangle much 



within a degree, because the difference of the tabular logarithms for a degree never 



exceeds unit in the 4th place, which will scarcely ever give any sensible difference on 



the resulting excess. 



It will hereafter be shewn, that the error arising from assuming the area as equal to 



that of a plane triangle having the same sides and contained angle, is utterly insensible. 



