353 
of Edinburgh, Session 1867-68. 
pare its measured size in parts, with definite portions of the length 
of the earth’s axis of rotation. The length of that axis I have 
taken, successively, from means of the best determinations thereof 
by the greatest geodesists of the age, giving their names, and gene- 
rally their original quantities ; and my adopted mean has always 
been within the limits enclosed by their several measures ; these, 
slightly differing from each other in the smaller numbers — but so 
slightly as not to prevent the earth’s polar axis being now con- 
sidered an exceedingly well determined quantity. That is, it is 
known within a very small fraction of the whole length ; which is 
all that man with his merely finite powers can expect to attain to 
in any practical problem, whether it refers to the length of a 
moderate bar of metal, or the dimensions of a cosmical globe. 
Accusation First . 
Nevertheless, th e Proceedings' author accuses me of having acted 
so flagrantly as to have used in my researches “a supposititious 
polar axis of the earth,” p. 261 ; also a something which Captain 
Clarke (an admitted authority) “ did not find it to be ; ” and 
finally he states, on his p. 263, that the polar axis of the earth 
“ is still itself an unknown and undetermined linear quantity.” 
This is the three-fold charge, and now I have to show that each 
item is utterly erroneous, and is followed by worse things still. 
1. As to having used a “ supposititious,” instead of the measured, 
length of the earth’s polar axis, — I point to p. 450, vol. ii. of my 
“ Life and Work,” — where I have quoted at length, and have fol- 
lowed in vol. iii. the results of calculations based on all the best 
known measures of the earth, from the worthily authoritative quarto 
recently published by the Ordnance Survey Office under Sir H. 
James, —chiefly computed by his excellent mathematical assistant 
Captain Clarke. 
Accusation Second . 
2. But it is next said by the Proceedings author, that I, having 
employed 500,500,000 British inches for the length of the polar 
axis, — have used fur it, that “which Captain Clarke did not find it 
“ to be.” Let us see if this charge is true, from the pages of the 
Proceedings' author himself. He states that Captain Clarke found 
the length of the earth’s polar axis by one mode of computation 
