180 On a new graphical Method 
sponding refraction, it will be brought sufficiently near the truth 
for our present purpose almost at ‘the horizon. 
Let AB and C D be two parallel 
lines of sines whose zeros are at A A D 
and C. Join AC, as also F and H I 
the two altitudes increased as above, 
to cut ‘AC in E. Then it is plain 
that the line joining any other alti- Si iH 
tudes whose sines are inthe ratioof F oe | 
AF to CH must also pass through \] 
KE. If, therefore, EI be the effect B Cc 
of refraction on a given distance in 
the first case, it will be so whenever the sines haye the same ra- 
tio: reckoning always the greater altitude on A B. 
" ‘The construction of this part is as follows:—Having drawn 
and divided the lines of sines, take any distance which we shall 
imagine to be an are ina vercicet circle, in order that the effect 
of refraction may be had at once from a table of refractions ; since 
in that case it is the sum or difference of the refractions corre. 
sponding to the altitudes ; and having laid a ruler to join these 
altitudes, let this effect be set off in a straight line as from E 
to I. 
Suppose again that we shift round the same are of distance, still 
keeping it in the verticai. circle, till the sines of the altitudes have 
a different ratio; we may then find the effect of refraction as 
before; and proceeding in this way for all ratios of altitude 
with the several distances, the linear table nay be completed to - 
a considerable degree of accuracy without requiring any other 
calculation. The effect of refraction might be expressed i in va- 
rious ways; but perhaps one of the most convenient is to do it 
by parallel straight lines such as ET reaching from AC to a eurve 
which belongs to the corresponding distance. The arguments 
of this table are simply the apparent altitudes and apparent di- 
stance; because the numbers for the apparent altitudes are to 
be placed PEPE Ste the sines of the apparent altitudes increased 
by thrice the refraction. The correction for refraction is’ thus 
obtained in any given case, by merely applying a ruler to the al- 
titudes; this will cut AC in a point between which and the curve 
corresponding to the distance, the required correction is con- 
tained on a straight line such as EI. It is always additive. 
I shall next explain the principles of the part that relates to 
parallax: Let MN and PQ be two parallel straight lines, of 
which MN is the greater; join MP. Take ms = cos. d, the 
distance being denoted by d ; join NK, producing it to meet the 
extension of MP in T. T hrough T draw TL parallel to PQ; 
Boe make 
Se ngs thy 
Foes. ae 
