371 
of Edinburgh , Session 1867 - 68 . 
perfect : but a learned man who measures their respective lengths to 
T'o'o o"o °f an inch, can seldom or never reach perfect decision 
in his last place of figures; and finds anomalies of expansion, imper- 
fections of the eye, or the touch, plasticity of the hardest metals, 
and all the powers of nature interfering between him and his pro- 
posed goal of perfect accuracy. 
Well therefore has one of the best men whom Cambridge has 
sent forth within this century, summed up these ruling facts of 
all the higher natural philosophy, — by stating “ that no human 
“ hand or machine ever yet drew a straight line, or erected a per- 
“ pendicular, or fixed an instrument in perfect adjustment.” And 
in truth it is an attribute higher than man’s, to perform any prac- 
tical mechanical operation with perfect exactness. 
To acknowledge this fact and work within it, — tends to lead men 
on to that old and beautiful confession of Sir Isaac Newton, i.e., that 
all that even he had been able to do, through a long life spent in 
scientific observation, — was, to pick up a few pebbles on the shore 
of the boundless ocean of knowledge. It tends, in fact to keep 
man in his proper place, in humility of mind, but in earnest con- 
templation of a high ideal, and in efforts always to rise above his 
last endeavour, — assured that there is hope for some further im- 
provement, when the distance between himself and ideal perfection 
is infinite. 
But to deny the fact of man’s incapacity for perfect performance 
of problems in practical science, and to refuse its evidences— -is 
either to exhibit an uneducated ignorance of what accuracy is, — 
or to endeavour to apply to the creature that which is an attribute 
of the Creator. 
Hence, when the Proceedings' author (at p. 265) lays it down, that 
“ Measures, to be true counterparts, must, in mathematics, be 
“ not simply 1 near ’ or ‘ very near,’ which is all that is generally 
u and vaguely claimed for the supposed pyramidal proofs ; but 
“ they must be entirely and exactly alike, which the pyramidal 
“ proofs fail altogether in being. Mathematical measurements of 
“ lines, sizes, angles, &c., imply exactitude and not mere approxi- 
“ mation ; and without that exactitude they are not mathema- 
“ tical, ” 
we may well ask, Is the gentleman showing simple ignorance of 
