192 The Rev. Dr. Robinson on the Constant of Refraction. 



drawing the instrument from the pier, and pushing it toward it, makes only a 

 change of 0".02 ; of 30 sets taken round the circle at different times, the 

 greatest I have found is 0".75, and the least 0".00 ; and during the last three 

 years that at 360° (which equals the mean of the 30 sets) has been within the 

 limits of 0".25 and 0".54. In respect of its division, after a careful examination 

 of 288 diameters in four positions, I have stated, that I considered It good ; trifling, 

 however, as the resulting error may be. It is obviously always necessary to correct 

 for It when it is known. I have not, however, obtained my con-ections in the pre- 

 sent Instance by the method described in that memoir. The errors which I found 

 were absolutely casual, so that it was Irapessible to Interpolate between them ; 

 the Individual research of each would have demanded an impracticable sacrifice 

 of time ; and even could this have been afforded, the value of the result appears 

 to me at least doubtful. All such modes of examination assume, that the divisions 

 keep the same relative position while the circle is turned through any arc ; but 

 it is found in actual experience, both with this and other circles, that occasionally 

 the correction of a diameter varies with its situation to a whole second or even 

 more. I have, therefore, applied twelve equidistant microscopes to the circle ; 

 and presuming (as is also shown by the table of errors which I had constructed 

 by my first method of correction) that their mean is free from sensible error, I 

 use It to correct that of the four reading microscopes. In a way as simple as I 

 believe it to be effective. Let m^ m^ be the means of the reading microscopes, 

 and of the twelve when any number x is at the index. Then, on this supposi- 

 tion, we have, 



m, — 'm„ = u, — u„-\-e{x) — e (o). 



We may assume the reading of the four at o to be a zero to which all others are 

 referred, and therefore, 



e {x) = (m, — m„) — (m, — M„), 



which only implies the permanence of the microscopes while the readings are 

 taken. Out of more than 100 of these -corrections most are negative, which 

 arises from the zero reading m„ requiring, according to my former mode of 

 examination, a correction of-|-0".93; about one-fourth of the number differ 

 from this more than ± 0.49, and in some I have found reason to suspect a 

 minute change depending on the temperature. As, however, it can be deter- 



