28 



siu. R, for developing the equation 



sin. t = e. sin. {R-\-z) 



by Lagrange's well known theorem, 



2 = e. sin. R + ^e". sin. 2fl -f ^e^. sin. 3R, &c. 



and the entire expression comes within the application of Par. (a) 



2. The excentricity of an instrument also produces an error 

 of a different description, when the graduation is placed on the 

 edge, as in the Greenwich circles, instead of the plane as is 

 usual ; for it alters the run of the microscopes. In fig. 3. let 



OC be the distance of the 

 limb from the object glass of 



a microscope when correctly ^l^^-^-^v^c tm) 



adjusted : let the image be then 

 formed at ED, where the micrometer is placed whose screw mea- 

 sures ED the image of five minutes by five revolutions. If OC 

 be' increased by a quantity zz h, the image is formed at E'D', and 

 when projected on the plane of the micrometer covers the space ID, 

 for it is viewed by an eye-piece equivalent to a lens of the focal 

 length FD placed at F. The difference between ID and ED is 

 the error of the micrometer in 5' which decreases from that to zero. 

 Let DE = I, D'E' = I', DI = I", OC = D, FD = /, and the 

 focal length of the object glass = F, we have 



O 

 B 



/' = 



/" = 



CD—CD'=k=- 



I(D-F) 

 D—F+h 



[D — F).(D—F+h) 



I.{D-F)\f 



f^k f.{D-Ff + h.(f.[D-F)+F') 



