6 Ratherfurd Photographic Measures. 



correspond to increasing focal length of the telescope. To calculate 

 the focal length, we have the following: 



Linear scale value* = 0.020859 Ji^ches, 

 Mean angular scale valuef = 28". 01 24 

 from which : 



Focal length = 153.59 inches. 

 Now putting : \ 



f ^ reading of the focal micrometer for any given plate, 



I find from the above focal length and pitch of the micrometer 

 screw that the numbers given in table IV. A require an additional 

 correction of: 



+0-0325 (/— 7-86) 



to reduce them to the mean focal reading (7.86). Accordingly, this 

 correction has been applied to the means in the sixth column, thus 

 obtaining the corrected means of the seventh column. From these 

 latter it is possible to discuss the effect of temperature, indepen- 

 dently of the focal readings, provided we assume that the zero 

 point of the scale attached to the focal micrometer always retained 

 exactly the same distance from the optical centre of the lens, except 

 as influenced by changes of temperature. Now this assumption 

 can hardly be regarded as altogether justified a priori in the case 

 of the RuTHERFURD tclcscope. I have therefore made two separate 

 least square adjustments of the quantities given in the columns 

 mean and mean corrected. 



Representing these quantities by equations of the form : 



^ -hy (i — to) 

 where t is the observed temperature for any plate, and tg the mean 

 temperature, I find : 



Column mean = — .0027 =h .00063 — .000372 (t — 58°. 4) 



± .000029 



Column mean corr'd = — .0027 =b .00057 — .000424 (t — 58°. 4) 



zh .000027 



The attached probable errors show that the observations are 

 represented better if we take the readings of the focal micrometer 

 into account. This would seem to justify the assumption of con- 



* Rogers' determination, Ann. N. Y. Acad. Sci., vol. vi, p. 249. 

 ] The Pleiades result, ibid., p. 270. 



