, OF ARTS AND SCIENCES: SEPTEMBER 20, 1864. 359 



United States Coast Survey, and which has been adopted by the Nautical 

 Almanac. They seemed well selected, their places were derived from 

 observations up to 1851 by an American astronomer entitled to con- 

 fidence, the investigations were published in detail, open to criticism, and 

 inviting it, thus satisfying all the conditions of a safe catalogue to be 

 adopted by the Nautical Almanac. It was expected that the places 

 would be improved from time to time by the aid of later observations, 

 but I can see nothing in the paper of Mr. SafFord, in which he uses the 

 additional observations of the last ten years, to convince me that the 

 place of this star should now be changed from that adopted. And cer- 

 tainly the necessity of such a minute change cannot be considered as 

 demonsti'ated. There are so many nice points in the combination of 

 the work of different observers and different instruments, and so much 

 is arbitrary, or dependent on the judgment of the computer, that the 

 existence of a magnitude which is less than the personal equations of 

 the observers, especially when it is not visible with the aid of the in- 

 struments employed, is extremely difficult to prove, and it is much 

 more difficult to measure such a magnitude. In fact, the accuracy that 

 appears to be reached by such a combination of observations by the 

 method of least squares is often illusory, and is over-estimated by many 

 astronomers. I doubt the possibility of measuring with any degree of 

 accuracy a quantity which cannot be distinguished from zero by the 

 sense employed in measuring it. The limit of exactness of measuring 

 must lie very near the limit of distinct perception, and no repetition of 

 observations can carry our knowledge much beyond it ; and if, in the 

 record of observations, a show of precision is kept up beyond this limit, 

 nothing is added to the probability of the resulting value, but the 

 reverse. This is not inconsistent with the doctrine of probabilities em- 

 bodied in the method of least squares. The rigorous theory assumes 

 continuity of error ; and it also implies that in each observation there 

 is some tendency or attraction toward the true value sought. Now this 

 effect or attraction of the thing observed can only be operative within 

 the limit of sensibility, and that part of each observation which is under 

 this limit, and which we cannot know to be produced or influenced in 

 some way by the object observed, might as well be appended arbitrarily 

 or by the cast of a die. To expect to add anything to our knowledge by 

 taking the mean of these would be hoping to coin pure ignorance into 

 knowledge by the method of least squares. 



And furthermore it is obvious from these considerations, and from 



