I4j2 Mr. Troughton o/i dividing Instruments , 
"the regularity of the whole operation would thereby be 
destroyed. 
It may not be improper to remark, that dividing by the eye 
does not require a more expensive apparatus than the opera- 
tion of dividing by hand ; and, indeed, less so when the scale 
of inches is deemed necessary. The method by adjustment 
is still more expensive, requiring whatever tools Bird’s me- 
thod requires, and, in addition to these, a frame and micro- 
scopes, somewhat similar to those for dividing by the eye. 
It is somewhat more difficult to give a comparative estimate 
of the time which the different methods of dividing require. 
I know that thirteen days of eight hours each, are well em- 
ployed in dividing such a circle by my method ; about fifty- 
two days would be consumed in doing the same thing by 
Bird’s method ; and I think I cannot err much when I state 
the method by adjustment, supposing every dot to be tried, 
and that two-thirds of them want adjusting, to require about 
one hundred and fifty of such days. 
The economy of time ( setting aside the decided means of 
accuracy) which the above estimate of its application offers to 
view, will, I think, be considered of no little moment. By the 
rising artist who may aspire at excellence, it will at least, and 
I should hope, with gratitude, be felt in the abbreviation of his 
labours. To me, indeed, the means of effecting this became 
indispensible ; and it has not been without a sufficient sense 
of its necessity, that I have been urged to the progressive im- 
provement and completion of these means, as now described. 
It is but little that a man can perform with his own hands 
alone ; nor is it on all occasions, even in frames of firmer 
texture than my own, that he can decisively command their 
