SURVEY OF MASSACHUSETTS. 43 
the refractions from right to left and from left to right succeed each other with such 
rapidity that all further appearance of distinct outline disappears, and in proportion as 
their apparent size increases, their distinctness diminishes until, if the objects be small 
and far off, no traces of them can be seen. 
If we suppose a diminution of heat, from the temperature of distinct sight, in the same 
ratio that we have been supposing an increase, (which frequently takes place in the after- 
noon of a cold day,) objects will present similar appearances and vanish in the same 
manner. 
In the foregoing remarks, I have supposed the atmosphere to possess, during the time 
of observation, the same degree of transparency. 
Respecting the process of determining the azimuths of the stations, I would state that 
the system adopted in preparing the work for the map, is the same we use in all our cal- 
culations. I shall therefore describe it in connexion therewith. 
First, we divided the state into sections of about fifty miles square each, and determined 
the direction of meridians through the most central trigonometrical station in each section, 
Two of these meridians were determined by direct astronomical observations, and the other 
meridians were calculated. Angles were carefully measured from the two observed me- 
ridians with all the most conspicuous signals, which were in sight from the stations, 
(which we shall call for the sake of distinction a,) through which the meridians pass. The 
direction of the sides of the triangles radiating from the @ stations were determined from 
the angles measured directly with the meridians. The azimuths of the sides of the trian- 
gles radiating from the stations seen from stations a, (which we shall call 0,) were predi- 
cated upon the angles measured at the stations d, from the signals standing upon stations a. 
The azimuths of the sides of the triangles radiating from the stations seen from station 8, 
(which we shall call c,) were determined from the angles measured at station c, from the 
signals standing upon stations J; and in like manner the same system was continued until we 
reached the extreme station of the section, or any desired station within the limits of the 
survey. ‘The same system was carried forward between the two observed meridians, 
making each meridional station alternately station a. The difference in the azimuth de- 
termined by computing from a series of angles, from one meridional station to the other, 
with that determined from astronomical observations, gives the inclination of the meridians. 
I would here remark, that carrying forward the computed azimuths upon this system, 
supposes that the meridians of the stations a, d, c, &c., are all parallel. I would further re- 
mark, that the azimuths of the sides of the triangles determined from the stations a, remain 
unaltered, for the reason that they have been carefully determined directly from the meri- 
dian, which must be considered of the highest possible authority, and they may for that rea- 
son be called standard lines. A line or side of a triangle extending from one station 4, to 
another station 0, is considered differently. ‘Thus the azimuth of a line or side of a trian- 
gle extending from station 0, No. 1, to station , No. 2, (using the numbers merely for 
distinction’s sake,) should be exactly the reverse of each other; that is, if the azimuths of 
the line determined from station 3, No. 1, to station b, No. 2, is South 40° 10’ 20” West, 
the azimuth of the same line, determined from station 4, No. 2, should be N orth 40° 10’ 
20” Kast. But we will suppose that the azimuths do not exactly agree, (as it frequently 
* IT would wish to have it understood that the objects selected are slender poles, spires of churches, or something of 
the kind, because the reasoning will apply more readily to objects of that form. 
