42] ROYAL ASTRONOMICAL SOCIETY TO M. PETERS. 319 



I cannot but regard this work of M. Peters as a perfect model of 

 excellence, evincing consummate skill in the observer, as well as admirable 

 power of turning the observations to the best account. It shews that it 

 is possible by meridional observations to obtain absolute parallaxes almost 

 as small as the relative parallaxes that can be measured by the heliometer, 

 or by similar means ; though to do so requires a most rare union of instru- 

 mental advantages, care and judgment in the observer, and analytical skill 

 in combining in the best manner the results of observation. 



No one can read the papers of M. Peters, or those of the Russian 

 and German astronomers generally, without being struck with the constant 

 employment of the method of least squares. It is to be wished that this 

 method were more in use among English astronomers, as I believe not a 

 little of the precision of modern determinations is due to it. We seem 

 to entertain a distrust respecting the results of the calculus of probabilities, 

 more particularly with regard to the estimation which it affords of the 

 probable amount of error in any determination. 



It should be borne in mind, that when we speak of the probable error 

 being of a certain amount, it is not meant that it is improbable that the 

 error should exceed that amount, but only that it is as probable a priori 

 that the error falls short of, as that it exceeds it. If we know by inde- 

 pendent means that the error of any determination is much greater than 

 the probable error given by the observations, we may infer, with great 

 probability, that some constant cause of error has occurred in the obser- 

 vations employed. In the estimation of probable error, only fortuitous causes 

 of error are taken into account. The employment of the method of least 

 squares does not render it less necessary to avoid all sources of constant 

 error: it is not a substitute for, but an auxiliary to good observations, 

 and enables us to obtain from them all that they are capable of yielding. 



I cannot conclude without congratulating the Society on the improved 

 prospects of that very delicate branch of astronomy which relates to the 

 research of stellar parallax, especially as there is every reason to believe 

 that this country will contribute its full share to the advancement of it. 

 We may hope that the beautiful reflex zenith telescope of the Astronomer 

 Eoyal, the magnificent heliometer which is in the able hands of Mr Johnson, 

 and the improved method of recording star transits by means of galvanism, 

 will enable us ere long to take many firm, though long-reaching, steps 

 into regions of space hitherto untrodden. 



