Observations of 500 Nebula. 



I often observed by moonlight, and did not shrink from other unfavourable 

 circumstances, it soon appeared, that the work required so much time, that 

 the original plan could not be carried out. It is then no longer my inten- 

 tion sensibly to extend the compass of the observations beyond the limits 

 of the 500 observed but indiscriminately chosen nebulae, but only in the 

 course of the following years to endeavour to consolidate the results already 

 attained. In order to avoid being obliged by the above mentioned circum- 

 stances entirely to abandon the observation of nebulas and presserve an in 

 some degree consistent plan of operations. I found it best, as I have else- 

 where lately explained, to modify the original plan as regards objects to be 

 observed, so that it has now for some years even included the micrometri- 

 cal measurement of telescopic clusters, a work which can at least partially 

 be performed in spite of moonlight, and indeed generally under circumstan- 

 ces unfit for the observation of nebulas. 



If then on the one side I have arrived by experience at the discoura- 

 ging conclusion, that a single person's powers are very limited in turning 

 to account on a more extensive scale, though only in one special direction, 

 the vastly rich material . which the nebular world offers ; I have nevertheless 

 on the other hand fully convinced myself that a relatively great accuracy, 

 not in only a few but in fact in most cases, can be attained in the deter- 

 mination of the nebulae's positions. 



From a number of arbitrarily chosen differences between the evening- 

 means of the observed quantities and the respective media of them I have 

 in the following manner approximative^ computed the outstanding errors 

 in the results. Considering a number p of nebulae, let e be one of the dif- 

 ferences in question and X e 2 the sum of the squares of the differences in 

 the y«. nebulae; n the number of nights any one of the nebulae was observed, 

 Xn the whole number of nights for all the p nebulae: and r the mean error 

 in the result of one night, all the results being supposed to have the same 

 weight: we have 



Meanwhile, as each nebula is here only observed very few nights , the right 

 use of this formula in the present case may seem doubtful, because p 

 must obtain too great a weight in regard to X n , for it to be possible that 

 the resulting values should become very trustworthy. Under such circum- 

 stances it would no doubt give a nearer approximation to the truth simply 

 to put ft = 1, although in this way r should come out a little too small, 



