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VIII. " On the Application of the Calculus of Probabilities to 

 the results of measures of the Position and Distance of 

 Double Stars." By THE LORD WROTTESLEY, V.P.R.S., 

 &c. Received May 27, 1859. 



In a communication addressed to the Royal Society "On the results 

 of Periodical Observations of the Positions and Distances of certain 

 Double Stars," printed in the Philosophical Transactions for 1851, I 

 took occasion to remark that the differences between mean results ob- 

 tained on different evenings were greater in proportion than those of 

 the separate or partial measures obtained on the same evening, which 

 arise from chance errors of observation, and that this circumstance 

 rendered the application of the Formulae of the Calculus of Probabi- 

 lities to the reduction of the observations embarrassing and difficult. 

 In other words, the differences between the mean positions and dis- 

 tances obtained on different nights were greater than would have 

 been anticipated by one who had merely computed the probable error 

 of a single measure in the usual manner from the data furnished by 

 the sums of the squares of the partial differences from the mean. 



The observations made since 1851 fully confirm the anomaly in 

 question. It is probable, therefore, that there is some cause which 

 modifies sensibly and in some unknown manner the results obtained. 

 It may be temperature acting on the micrometer screw ; it may be 

 the state of the atmosphere or the method of making the observation ; 

 but whatever it be, the observations show conclusively that such 

 causes are sometimes in operation. 



For the purpose of obtaining some numerical expression, however 

 imperfect, of the effect produced, I adopted the following method : 

 I took the difference between two mean results of position obtained 

 on two different nights, where not more than about two months in- 

 tervened between the observations ; and I ascertained also the mean 

 of the probable errors of such positions as computed in the ordinary 

 method. In order that each star might be subjected to exactly the 

 same treatment, I selected always the observations of the first two 

 nights on which it was observed, except when the two consecutive 

 means were obtained at too long an interval apart. Now as the 

 number of partial measures of angle obtained on each separate night 

 very often did not exceed six, these probable errors are certainly not 



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