354 Proceedings of the Royal Society 
= 500,522,804; and by another mode 500,482,296 British inches. 
The Proceedings' author does indeed considerably confuse his ex- 
planation of the principles of each method ; and wherefore the final 
difference out of the same observational quantities to begin with, 
— but his numbers are correct, and are probably derived from my 
own pages with their peculiar mode of expressing Captain Clarke’s 
results of feet or yards, in inches, and showing them, sometimes 
for the whole axis (vol. iii. p. 134) and sometimes for the semi- 
axis (as in vol. ii. p. 450.) 
Now, Captain Clarke himself does not attempt (as I had already 
shown in “Life and Work,” vol. ii. p. 451) to decide entirely between 
the two calculated results he has given, — but he states each of 
them, and seems to leave his readers to do as they like between the 
two. Anywhere between the limits of his two quantities, therefore, 
is to be looked on as derived from him, and as, in fact, his deter- 
mination, rather than any one else’s, especially if with some refer- 
ence to his limits of error or variation. 
Now the exact arithmetical mean of the Captain’s two published 
quantities, stands thus — 
First computation, 500,482,296 
Second ,, 500,522,804 
Mean, 500,502,550 
or differing from 500,500,000, by only ^gth of the amount of the 
debateable ground between the two almost equally important 
factors given by him. If, moreover, a very little increase of weight 
be extended to the first result, on account of the rather higher- 
analysis by which it is brought out by Captain Clarke, the ten- 
dency is to reduce even that small difference, or perhaps throw it 
to the opposite side. Wherefore, if any one will only trouble him- 
self with as many rough digits as he can be certain of, — Captain 
Clarke’s whole result may be stated in a compendious manner as 
500,500,000 with a probable error of 20,000 British inches. 
If then I had stated the length of the earth’s axis as outside 
all Captain Clarke’s debateable ground between his two results, say 
at 500,550,000 or 500,450,000 inches, — the Proceedings' author 
might have truly said that I had stated it at a figure which Captain 
