158 ANNUAL OF SCIENTIFIC DISCOVERT. 



new focus, which was proportionally further from the object-glass as 

 the object was nearer, the angle which the hairs subtended from the 

 centre of the object-glass must be variable, diminishing as the dis- 

 tance was diminished. Hence a correction was necessary, and this 

 the theory of refraction by lenses furnished. It showed that the error 

 was constant at all distances, amounting in every case to the focal 

 length of the object-glass for parallel rays. This constant was to be 

 added in reading the staff, by bringing the lower cross hair near any 

 even division of feet, but exactly two-hundredths of a foot above it, 

 corresponding with the two links from the centre of the instrument to 

 the anterior focus, in the cases of a five-inch theodolite and ten-inch 

 level. Then, by reading the upper distance hair, and deducting the 

 even number of feet at the lower hair, the difference was the distance 

 in chains and links. If the compass was sufficiently delicate, any 

 operation of contouring, or running trial levels, could be performed 

 with rapidity and accuracy. When provided with the two distance 

 hairs, the level of the ground could be taken above and below the 

 ordinary range of the instrument. The use of these distance hairs 

 for eighteen years had proved their practical value. In taking the 

 widths of rivers or deep ravines, distances of twenty chains had been 

 read in favorable weather ; and when the hairs were accurately fixed 

 on the diaphragm, they might be used for even fractions of a link, in 

 taking widths incapable of direct measurement. 



When applied to a theodolite, they could be used for measuring 

 distances on sloping ground. But in that case, since the line of sight 

 was no longer perpendicular to the staff, a correction was necessary, 

 for which a table was given, showing the angles of elevation of the 

 various heights, which were simple fractional parts of the horizontal 

 distance. When the horizontal distance to the staff had been ascer- 

 tained, the theodolite was to be elevated to the tabular angle corres- 

 ponding to the fractional rise nearest to the slope of the ground ; then 

 that fraction of the horizontal distance, less the reading of the staff, 

 would be the correct rise. With the theodolite, it was convenient to 

 have another set of hairs, for reading the distance in feet, as well as 

 in links. In clear weather, with a distinct reading staff, a distance of 

 forty chains had been read between the foot and link hairs. 



DEW-BOW SEEN ON THE SURFACE OF MUD. 



Professor Rankine, in a letter to the London Philosophical J^faga- 

 zine, says: There was seen to-day (February 13, 1862), by myself 

 and some other persons in this neighborhood, a very beautiful phe- 

 nomenon, of which the cause is obvious, and of such a nature that 

 one would expect the phenomenon to occur frequently ; but I dp not 

 remember to have yet seen any instance of it recorded in any Scien- 

 tific publication. I refer to a prismatically-colored hyperbolic ins, or 

 bow of the first order, exactly resembling that sometimes seen on a 

 field of dewy grass ; but in this case it was displayed on the muddy 

 surface of a by-road, and on the less trodden parts of an adjoining 

 turnpike road, throughout a distance of more than a mile. The time 

 was between half-past twelve and one P. M. ; the morning had been 

 hazy, but the mist had cleared away, and the sun was shining brightly. 



