618 



SCIENCE. 



[N. S. Vol. IV. No. 95. 



The lectureship in chemical physiology is va- 

 cant by the resignation of Dr. A. Sheridan Lea, 

 F. R. S., on account of ill health. 



Prof. Bubnof, of Dorpat, will succeed Prof. 

 Erismann in the chair of hygiene in the Uni- 

 versity of Moscow. Dr. S. Bianchi has been 

 appointed full professor of anatomy at Vienna, 

 and Dr. B. Boccardi associate professor of micro- 

 scopical anatomy in the University at Naples. 



DISCUSSION AND CORRESPONDENCE. 



COMPARISON BETWEEN THE USE OF FIXED AND 



MOVABLE CIRCLES, IN THE DETERMINATION 



OF DECLINATIONS BY MERIDIAN 



CIRCLE. 



One advantage claimed for the use of a mov- 

 able circle is, that it tends to eliminate the effect 

 of graduation errors. 



This effect will not be entirely eliminated by 

 any number of changes in the position of the 

 circle ; but considering it as one of the sources 

 of accidental error, the mean of a large number 

 of observations will be affected by the mean of 

 the errors of graduation for the increased num- 

 ber of divisions. 



The relation of this error, to that due to other 

 conditions, should also be considered ; and in 

 establishing the advantage of using the movable 

 circle, in so far as graduation errors are con- 

 cerned, one should be confident that no other 

 sources of error are introduced. 



In dealing with instrumental errors it is un- 

 doubtedly sounder policy to arrange observa- 

 tions so that they may be eliminated, rather 

 than to determine the effect of such errors and 

 correct for them. 



But this policy refers to errors tbat can be 

 actually eliminated, and without introducing 

 others of unknown character or amount. Where 

 both methods may be used, actual elimination 

 of error, and, its determination and subsequent 

 correction, the advantage is recognized, in the 

 knowledge thus gained of the general laws 

 governing errors and their correction. 



In the case of a fixed circle the instrument is 

 a homogeneous one throughout a series of ob- 

 servations, which may extend over many years. 

 The laws of flexure may be studied by consecu- 

 tive determinations, as part of a united series; 



and, in general, the performance of the instru- 

 ment can be investigated, under the varied 

 conditions arising from extended use, with the 

 certainty that some errors are truly systematic 

 in character. 



With a movable circle there is the advantage 

 of variation of conditions, which may produce 

 results nearer the truth, in the average, by ab- 

 sence of certain systematic errors. 



It will always be a matter of judgment based 

 upon experience, whether one can deal better 

 with results affected by systematic errors, or 

 with observations in which they are replaced by 

 accidental ones. 



In practical observing one method is usually 

 adopted for general work. While there are 

 other conditions that may determine which 

 method will be used, a comparison of their re- 

 spective accuracy is not without interest, using 

 such material as may have a bearing upon such 

 a test. 



For the purposes of illustration the probable 

 error of graduation, for the mean of four divis- 

 ions, may be assumed to be =b 0^^.15, the value 

 obtained in the measurement of the 1° arcs, of 

 the Repsold Meridian Circle of the Lick Ob- 

 servatory. If this error were entirely acci- 

 dental, throughout, a reading made upon two 

 adjoining divisions should have a smaller error ; 

 but as there appears to be evidence of a peri- 

 odic character in the graduation, this value 

 may be adopted for the present comparison. 



Representing by g the probable error due to 

 graduation, for the general case of a measure 

 of zenith distance we should have to consider 

 the error of the Nadir reading, and g would be 



With a fixed circle, however, if the value of the 

 latitude, used in determining star declinations, 

 is that obtained by observations of standard 

 stars with the same instrument, the graduation 

 error of the Nadir reading is actually eliminated 

 from the results. Or, if when the instrument 

 is reversed the same divisions come under the 

 microscopes at the Nadir reading, the gradua- 

 tion error of those divisions is then eliminated 

 from the measurement of any particular zenith 

 distance in both positions. Under these condi- 

 tions, the probable error gr of a determination 

 of a star's declination, by means of reading on 



