( 693 ) 



The parallactic p. m. shall then be : 



— sin A = I' — p . 

 Q 



If this equation is written out for each individual nebula and if, 



after that, we take the mean of all the equations, the quantities p will 



h 

 disappear and we obtain the mean value of - , which is the secular 



Q 

 parallax. 

 Or rather : 



As we may treat the quantities p as if they were errors of obser- 

 vation, which mix up with the i-eal errors of the observed quantities 

 1', we may write out for each nebula an equation of the form 



A 



- sin X = v ( 1 ) 



Q 



If then we assume that the distance q is the same for all the 

 nebulae, we may solve the whole of the equations (J) by the method 

 of least squares. 



I have long wished to apply this method in order to get some 

 more certainty about the position of the nebulae in space, but I have 

 been restrained by the extent of the work connected with such an 

 enterprise. 



The difficulty has disap{)eared since the i^ublication, a few years 

 ago, of a paper by Dr. Mönnichmeyer assistant at the Observatory of 

 Bonn {Veröff. der Kón. Stermv. zu Bonn. N°. 1). In this paper all 

 the materials available at the time of its appearance have been 

 brought together in a way which, for my purpose, leaves little to 

 be desired. 



This paper contains the observations of Dr. Mönnichmeyer himself. 

 Tliey bear on no less than 208 objects, mostly chosen among such 

 nebulae as can be measured with considerable or at least moderate 

 precision. Dr. Mönnichmeyer has collected besides, all previous obser- 

 vations of these objects. I have confined myself to the observations 

 of those nebulae for which all the observers have used the same 

 star or stars of comparison. I have further rejected the observations 

 of those objects for which Mönnichmeyer did not succeed in deter- 

 mining the personal errors. The observations which thus have served 

 for the investigation are those of Mönnichmeyer's paper pages 59 — 70, 

 from which have been excluded, in the first place, those objects 

 which in the list of pages 15 — 17, second column, have been denoted 

 by the letter M ; further the planetary nebulae, the clusters and the 

 ring-nebula h 2023. 



