348 ADDRESS ON PRESENTING THE GOLD MEDAL OF THE [45 



already ascertained, we can at once obtain the value of the mean of the 

 squares of the differences between those places, supposing the differences to 

 be entirely due to casual errors of observation. The actual mean of the 

 squares of the differences is found to be greater than the above-mentioned 

 mean, and the excess is due partly to the proper motions of the nebulae in 

 the interval, partly to the differences in the star-places employed, and, very 

 probably also partly to constant differences in the mode of observing the 

 same nebula by the two observers. Hence Professor D'Arrest concludes that 

 the probable amount of the annual relative motion of the nebulae with 

 respect to the sidereal system is less than 0"'4 measured in arc of a great 

 circle. 



I may appropriately conclude my remarks on Professor D' Arrest's Resultate 

 aus Beobaclitungen der Nebclfleckcn und Sternhaufen by a quotation from 

 one who has himself done much in the same line of research. Speaking of 

 Laugier's and D'Arrest's observations, Dr Schultz says : " These works have 

 the high merit of having originated a new and important branch in the 

 study of the nebulae ; and D'Arrest has done especial service to this study 

 by shewing that, when what is required is simply good determinations of 

 positions, a much greater number of nebulae than has been usually supposed 

 may be advantageously observed with instruments of but very moderate 

 dimensions. But his series of observations is chiefly and especially important 

 as proving beyond s the possibility of a doubt that the positions of nebulae 

 in general are determinable with far greater accuracy than it had been 

 previously usual to suppose ; and D'Arrest's work thus made an epoch in the 

 study of nebulae, by freeing it from the deterring prestige which had before 

 that period been attached to it." 



Many other observers have since followed up the work thus begun by 

 Professor D'Arrest. Very accurate positions of nebulae have been observed 

 by Auwers, Schmidt, Schonfeld, Vogel, Riimker, Stephan, Schultz, and others. 

 I may particularly mention Schonfeld's Mannheim Observations of 235 Nebulae, 

 which appear to be extremely accurate and are published in a form that 

 leaves nothing to be desired. This work also enjoys the immense advantage 

 that the places of all the stars of comparison have been newly determined 

 by the meridian observations of Professor Argelander. But a still more 

 extensive work in the same field, and which promises to attain even a 

 greater degree of accuracy, is that by Dr Schultz, from whom I have quoted 

 above. This work consists of micrometrical observations of 500 nebulae made 



