72 ROUGH WAYS MADE SMOOTH. 



give about the fairest final mean value. We have seen, how- 

 ever, that the results of observations by seven distinct 

 methods give values ranging only between 92,250,000 miles 

 and 92,850,000 miles, the six best methods giving 

 values ranging only between 92,250,000 miles and about 

 92,480,000 miles. The new value thus lies 500,000 miles 

 above the largest and admittedly the least trustworthy of the 

 seven results, 870,000 miles above the next largest, a million 

 miles above the mean value, and i, 100,000 miles above the 

 least value. It certainly ranges 500,000 miles above the 

 largest admissible value from those seven trusted methods, 

 dealt with most skilfully, cautiously, and laboriously, by such 

 mathematicians as Newcomb and Leverrier. 



Can we hesitate as to the inference we should deduce 

 from this result ? We need not for a moment call in ques- 

 tion the skill or care with which the British observing parties 

 carried out their operations. Nor need we doubt that the 

 results obtained have been most skilfully and cautiously in- 

 vestigated by those to whom the work of supervision and of 

 reduction has been entrusted. We need not even question 

 the policy of devoting so large a share of labour and expense 

 to the employment of a method held in little favour by most 

 experienced Continental and American astronomers, and 

 objected to by many in England, including some even among 

 official astronomers. It was perhaps well that the method 

 should have one fair and full trial. And it is certain that 

 all who have taken part in the work have done their duty 

 zealously and skilfully. Captain Tupman, to whom Sir 

 George Airy, our chief official astronomer, entrusted the 

 management of the calculations, has received, and justly, 

 from his official superior, the highest commendation for his 

 energy and discrimination. But beyond all manner of doubt 

 the method employed has failed under the test thus applied 

 to it. I do not say that hereafter the method may not 

 succeed. Some of the conditions which at present render it 

 untrustworthy are such as may be expected to be modified 

 with the progress of improvement in the construction of 



