494 Proceedings of the Royal Irish Academy. 



tions -^ith a transit instrument. The greater number of observations 

 whicb may be consulted for tbis purpose allow us to enter more fully 

 into this research. 



When we want to find a general expression for the probable error 

 of a personal equation, deduced from simultaneous observations of a 

 single star across the two halves of the system of wires, we must take 

 into account a circumstance which has been experienced in nearly 

 every series of observations. AVe allude to the fact that a far greater 

 uncertainty in the value of the equation is found by comparing the 

 results of different stars with one another, than might be expected 

 •from the accordance between the transits of one star over the different 

 wires. It must be supposed that a new cause of errors arises from 

 the observer's passing from one star to another, or that the observer, 

 in the intervals between the observations, gets out of practice, and 

 each time has to fonn for himself a new habit of estimating the tran- 

 sits. C. A. F. Peters finds, for instance, as mean of five results, the 

 probable error of a personal difference :^'' — 



By comparing the By comparing the 



single -wires reduced to the results of different stars 



middle M-ire. with the mean of them. 



Eye & Ear. Chronograph. Eye & Ear. Chi-onograph. 



±0^-071. ±0^-051. ±0^-141. ±0^-061. 



It has, besides, been remarked by experienced astronomers, that 

 the transit over the first wire often does not agree as well as the 

 others do, after having been reduced to the middle one, audit is, there- 

 fore, not improbable that zone observations, which sometimes only are 

 made over one or two wires, may be affected by constant eiTors.f 



For these reasons we cannot but approve of the expression for the 

 probable error of a personal equation found by one star, which has- 

 been proposed by Dr. Albrecht:]: 



in which A is the probable error, found by comparing the transits over 

 the single wires with one another, and ^ the error produced by the 

 variation of the equation in going from one star to another. As we 

 here only consider the most common method of finding a personal 

 equation, we may suppose that each observer observes n wires, and 



* Astronomische Nachiichten, vol. sHx., page 27. 



t See Argelander's remarks in " Yierteljairsschrift der Astronomischen Gesell- 

 echaft," vii. (1872), page 16. 



+ Ueber die Bestimmung von LangendifFerenzen mit Hiilfe des Elektrischen 

 Telegraphen, Leipzig, 1869, page 26. 



