of the Rutherfurd Photographs. 219 



on the scale will lie between 9/0 and n. r o because a whole space 

 of the scale corresponds to two turns of the micrometer head ; 

 consequently the correction to the difference of the readings on 

 scale and star will be proportionate to that difference, that is to 

 \ m ; the correction to the latter is easily seen to be 

 — (2 *w) X 0.0010 millimetres. 

 Adding this to the correction for runs we obtain 



(? m ) ( 0.00010 -| ) millimetres. 



As an example let us correct the first observation given on the 

 specimen sheet on page 199. The date being March 25, we get 

 from Table II, 



B = + 0.0045. 

 Consequently the correction for runs and screw errors is 



— {i >») X 0.0019 millimetres. 

 A table may now be constructed with the argument \ m which 

 applies to all observations taken on March 25. 



% m. Correction. 



0.0 0.0000 millimetres. 



o. I — 0.0002 



0.2 — 0.0004 



0.3 — 0.0006 



0.4 — 0.0008 



0.5 , . — O.OOIO 



0.6 — O.OOII 



0.7 — 0.0013 



0.8 — 0.0015 



0.9 — 0.0017 



1.0.. — 0.0019 



For the star given on the specimen sheet the correction is 

 — 0.0009. During the second half of each morning's observations 

 when the micrometer head is set at 9/5 instead of at 9/0 it some- 

 times happens that the reading on the scale exceeds 11. r o, in 

 which case the correction will not be exactly proportionate to 

 ijr m; but the error committed by using the same table throughout 

 will never reach o/^, and in most cases is entirely negligible. 



3 . Having applied the corrections given above we have now to 

 change the measures into rectangular coordinates x and y, referred 

 to the central star 15 as origin, one axis being parallel to 

 the cylinder and the other at right angles to it. For this purpose 

 we subtract the mean of all the readings on the central star for 



