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130 



MATHEMATICAL and 



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the beginning of the graduations. No-^ It is to be proved, 

 that the angle SFFI, is equal to twice the angle QAD, 

 which is the diltinguifhing peculiarity of this inftrument, 



DEMONSTRATION. 



Since NGM, is parallel to CBA, the angle NGC, is 

 equal to GCB, and the angle MOB, is equal to GBC, being 

 alternate; but the angles NGC, and MGB, are equal from 

 the laws of reflexion, which make the angle of incidence 

 equal to that of reflexion. Therefore GBC is an ifofcclcs 

 triangle, having the angles at B, and C, equal. 



Again, fince HFS+SFD=:=(HFD^QAD+FEA=QAD+ 



+DEA=.QAD+FBC^QAD+QAD+BFA^2QAD+BFA 

 iQAD+GFA=) 2QAD+SFD. Therefore, HFS=2 



QAD. 



That the infl:rument may be held with greater eafe, an 

 handle may be affixed to the back of it, or another fextant 

 might be added diredly oppofite to the middle of the other 

 two, and the index continued to the oppofite arches, mov 

 ing on the center; which would have its advantages cfpe- 

 cially on land. And as the errors of adjuftment and ob- 

 fcrvation may be correded without the fecond central fpe- 

 culum, it may be negleded. 



This improvement of an inflrument, which was firft in- 

 vented and conftru£led by Mr. Godfrey of this city, and 



which, I do not hefitate, to call the moft ufeful of all 

 aftronomical inftruments that the world ever knew, I hope 

 will make it ftill more ferviceable to mankind. But how- 

 ever this may be, it is fubmitted with all due refpeft to the 

 fociety, by 





Their very humble Servant, 



JOHN EWING 



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