J^g PROBLEMS IN SPHEROIDAt TRIANGLES. 



ing nearly right ones. The obfervalions at Beachy Head and 

 Dunnofe give -j-^'-g-^-j for tlie C'tiiprefiion ; but it muft be re- 

 marked, that the Hate of the data is very unfavourable in this 

 example. 



The rules which our folution gives for computing the iiori- 



jconial angles from the latitudes and difFerence of longitude, 



will be found, I apprehend, much fliorter than Mr. Dalby's, 



befides the advantage they poflefs of affording us the means of 



afcerlaining the figure of the earth by a very iimple procefs, 



from obfervations made with the fame inftruments and by the 



fame obfervers. 



The preceding The theorems we have been detailing, with fome others 



rules applicable v\,[,jc>}, y^^y perhaps form the fubicft of another letter, would 



to anellipf)idj . , , • ^ . ,- , , , r 



butthemana- give US the relative pofition or one place to another on the lur- 



gers of the tii- face of the earth, were its figure an ellipfoid of known dimen- 

 avoid this af- fions ; but as this is ftill confidered as problematical, the me- 

 fumption. thod adopted by the gentlemen who have fo ably condu6led 



the furvey of our ifland, is certainly preferable. They firfl 

 obtain the length of a degree upon the meridian, and its per- 

 pendicular in a given latitude, and employ thefe data for com- 

 puting the geographical fituations of all the places near that 

 parallel, and not far diftant froni a known meridian. In the 

 Imaller triangles the truth may be thus obtained to the fradion 

 of a fecond, and in the larger ones th^y have very fuccelsfully 

 employed the beautiful property of fpheroidal triangles, which 

 we have fo often mentioned. 

 How to apply ^^^ though we give the preference to their method of com~ 



the rules. putation, I conceive the preceding rules will be found equally 



accurate, if we make ufe of the values of c, a, and 3 deduced 

 from their obfervalions ; or if we aifume near values of them, 

 and note the agreement or difagreement of the computations 

 with obfervations made at a place confiderably diftant from the 

 firft fiatlon. We may thus afcertain nearly the error of our 

 iuppofitions, and then correct the intermediate ftations. This- 

 cautious method of proceeding is rendered neceffary by the 

 anomalies which have been dilcovcred in the meafures of de- 

 ^rtfcs in different latitude?;, as well as by the general rule^ 

 which ought to be our guide in all philofophicai inquiries, to- 

 frame as lew hypothefes as poflible, but to make accurate ex- 

 periments, and infer the liulh from them by fair and genuine 

 induction. 



I mean 



