Permanence of the Butherfurd Photographic Plates. 203 



of these quantities will therefore give us the errors of the screw 

 at the various points observed. The method of computation will 

 be plain from the following table. We have : 



Second Series. 





FiRST Series. 



J, 





Error. 



Sum. 



5- 



- 7 



+ 48 



+ 48 



7- 



- 9 



+45 



+ 93 



9- 



-II 



+59 



+152 



:i- 



-13 



+40 



+192 



:3- 



-15 



+ 7 



+199 



5- 7 



+37 



+ 37 



7- 9 



+53 



+ 90 



9-1 1 



+51 



+ 141 



11-13 



+46 



+ 187 



13-15 



+ 5 



+ 192 



The numbers in the column " Sum " are evidently the errors of 

 the screw at the successive points : 







r 



, 9% II^ 13% 



15'' • 





We may therefore proceed as follows : 







First Series. 





Second Series. 





Eead. of 



Error of 



Prog. 



Final 



Kead. of Error of Prog. 



Final 



screw. 



screw. 



corr. 



error. 



screw. screw, corr. 



error. 



5 



7 



9 



II 



13 

 15 







+ 48 

 + 93 

 + 152 

 + 192 

 + 199 







— 40 



— 80 

 • — 120 

 — 160 

 —199 







+ 8 

 +13 



+32 

 +33 

 + 



5 00 



7 +37-38 



9 +90—77 



II +141 —115 



13 +187 —153 



15 +192 —192 





 — I 



+13 

 +26 



+34 

 



The quantities in the column headed " Error of Screw " are 

 the summed errors from the preceding table. The next column, 

 headed '' Progressive Correction," contains a correction which 

 varies uniformly as we proceed along the screw. It is intended 

 to make the errors.of the screw zero at the ends, and amounts to 

 no more than changing our standard of length. Up to this point 

 we used as our standard of length the mean millimetre of the scale. 

 The application of the progressive correction makes the total 

 length of the screw the standard, and the quantities in the last 

 column, headed " Final Error," will therefore serve to reduce 

 readings taken with this screw to what the}^ would ha,ve been if 

 the screw had no progressive errors. The signs will have to be 

 changed in order to get the corrections that must be added to 

 observed readings of the screw. We thus get the following final 

 table of corrections that must be added to observed readings of 

 the screw, in order to reduce them to what they would have been 

 if the screw were free from non-periodic errors. 



