in Theory and Practice. 



415 



Double Periodic Error. 



Supposing as before that there is no overlapping of the 

 lines, we have the following : — > 



fl 3 = fl± 



Places. 



2ttN 

 ba® ' 



Intensities, 



[Joihafi) J Q (ba 2 fi)y 



Primary order. 



ba Q ' 

 ba 



L. 2 ^ 



^ 5 = ^±K 



A*6 = /*± 



^7 = /*± 



2*2 



ba ' 

 e x ± 2e 2 



ba$ 

 2e 1 ±e 2 



ba 



Se r 



&C. 



Pi(K/*i) Jo(^i)] 2 . ] Ghosts of 1st 



r order. 

 [Joiba&z) J^ba^)] 2 . J 



r T /7 N T ,1 x-i-2 I Ghosts of 2nd 





^9 



[J 3 (^/a 9 ) J (6a 2 /^ 9 )] 2 . J 

 &c. 



Ghosts of 3rd 

 order. 



Each term in this table of ghosts simply expresses the fact 

 that each periodic error produces the same ghosts in the 

 same place as if it were the only error, while others are added 

 which are the ghosts of ghosts. The intensities, however, 

 are modified in the presence of these others. 



Writing Ci = ba l /n and c 2 = bajm 2 . 



The total light is 



2J 2 *(*,) Jo 2 fe) 





which we can prove to be equal to 1. 



2 F 2 



