138 Transaetions.—Miscellatrteous. 
portionately better results, the longer the distance, as I estimate it as subject 
to an average error of 5” or 6’ which is equivalent to about 10 chains, and 
this error is the same for all distances. Thus, in finding the distance 
between two hills 50 miles apart, this would only introduce an error of 
21 links per 10 chains, thus nearly approaching in accuracy to a chained 
measurement, besides being free from accidental errors and omissions which 
all chained measurements are liable to. 
But although the errors of observation do not affect the results in pro- 
portion to the distance, still, any error in the estimated refraction will do so; 
therefore this method is only suitable for hilly country, where other methods 
are not available; as, whenever the line of sight between the two stations 
passes for any considerable distance close to the surface of water or level 
land, the refraction is generally very variable and uncertain, and the results 
obtained by this method will then be unreliable. 
In my own practice, using an 8-inch transit theodolite, reading to 10", 
and noting the level readings at each observation, the distances found by 
this method have an average error of half-a-chain to the mile. 
For instance, in a circuit of 50 miles between two known points, 
average distance of stations 10 miles apart, the error was found to be 23 
chains, or less than half-a-chain per mile. In another case, there was an 
error of 31 chains in 60 miles, or about half-a-chain per mile. 
It is requisite, in this method, to use only the corrected vertical angles, 
that is, they must be corrected for the height of the eye and object. 
Rules for calculating the correction are given in most books on survey- 
ing, but the following blank form will be convenient when the difference of 
heights of the eye and object is given in feet and inches, and the distance 
between the stations in links :— 
Blank Form. 
Difference of height of eye and objesi HEHcheklog 42.790 e a 
Distance between stations in lin AA a 
Colog tang 1'—log 7:92 — REDE log 4°41570 
Correction in seconds of are — log .*..... 
Note.— When the height of the eye exceeds the height of the object, the 
correction is to be added to an elevation or subtracted from a depression. 
When the height of the object exceeds the height of the eye, the cor- 
rection is to be added to a depression, or subtracted from an elevation ; 
Or the rule for applying the corrections may be simplified thus : 
Mark angles of elevation + mark angles of e eque 
Mark he ight of eye -- mark height o of obje 
Then take the algebraical sum of the heights of the eye did object, to com- 
pute the correction, to which prefix the same sign; then the algebraical 
sum of this correction, and the observed vertical angle, will give the true 
vertical angle, 
Uma 
