[ I0 3 ] 
of the logarithm fine of half that arc, rejecting the 
Indices. 
But, as thefe differences give the divifions to the 
fupplements of the real verfed fines ; therefore the 
arithmetical complement of the logarithm fine of any 
arc being doubled, will give the difiance of the di- 
vision for the Supplement of twice that arc on the 
line of verfed fines. 
Thus, for 70°, the logarithm fine is 9,97295) 
The arithmetical complement is 0,02701 
Its double is 0,05*402 
Which is the number in the foregoing table fiand- 
ing againfi 140°, and is the Supplement verfed fine 
of twice 70 degrees. 
Now, as the arithmetical complement of the log. 
fines of arcs, are the difiances on the line of fines be- 
tween 90°, and the divifions to thofe arcs ; there- 
fore the diftances between 90° and any arc, being 
twice repeated, will give the division of the Supple- 
mental verfed fine to twice the co-fine of that arc. 
XIV. A Letter from Mr. John Dollond to 
Mr. James Short, F. R. S. concernmg an 
hnprovement of refradting Telefcopes. 
Read March 
* 753 - 
I 
S I R, 
T is well known, that the perfec- 
tion of refracting telefcopes is very 
much limited by the aberration of the rays of light 
from the geometrical focus ; which arifes from two 
very different caufes $ that is, from different de- 
grees 
