ON ASTRONOMY. 97 



tudes by astronomical observation, bas been executed, and tbe com- 

 putations performed by wbicb the results of the mechanical work are 

 made available. The calculations of the elements of a survey from 

 given data are founded on mathematical formulae, and are susceptible 

 of rigid accuracy ; but the mechanical work in tbe field depende for 

 its precision upon tlie means employed, and on the skill and care of 

 the operator. In some of the early attempts, as we have before stated, 

 to measure great distances on the earth's surface, the only means em- 

 ployed was counting the revolutions of a carriage wheel, of known 

 periphery, in travelling over the distance. 



When the method of triangulation was invented tlie line to be 

 determined mechanically was shortened so that, without too much 

 labor, the whole length could be measured by rods or cluiins; and, 

 finally, an apparatus was constructed especially for the measurement 

 of base lines. 



Any simple material of whatever form is liable to change its dimen- 

 sions with a change of temperature, so that a line measured on the 

 ground by a steel or glass rod, or a chain, would appear to have a 

 different length if measured in summer, from that which it would have 

 if measured in winter with the same apparatus. This was found to be 

 the chief source of error, and although the changes in length of a rod 

 caused by a given change of temperature may be calculated and a cor- 

 rection applied to the measurements, yet for primary base lines a more 

 accurate measuring apparatus was devised, by combining two metallic 

 bars upon the compensating principle, illustrated in the compensation 

 pendulum. 



This method was first applied by Colonel Colby, in the ordnance 

 survey of Great Britain. It has been brought to groat perfection in 

 this country by Professor Bache in the base apparatus of the Coast 

 Survey. 



The great object to be attained in a measuring apparatus of this 

 kind is such a combination or arrangement that the extreme points of 

 the compound bar used as measuring limits shall remain at an invari- 

 able distance apart under all degrees of temperature, and even while 

 the temperature is changing. 



This is effected in the Coast Survey base apparatus by two bars, one of 

 brass and the other of iron, each a little less than twenty ieet in length, 

 placed side by side so as to be cai>able of independent parallel motion 

 on rollers. At one end, the two bars are firmly attached to each other 

 by means of a block to which they are fastened by screws, the 

 medium of connexion at the other or free ends of the bars is a lever of 

 compensation. The brass bar is attached to the lever by a hinge pin, 

 and the iron bar abuts against the lever, the free end of which is 

 the point that remains fixed during any change in the length of the 

 bars ; the points of attachment of the bars to the lever being adjusted 

 at such a distance from the end of the lever that the motion will be 

 about this end as a centre. These points are determined by the rela- 

 tive expansions of the brass and iron, and the cross sections of the 

 bars are so calculated that they will undergo tbe same changes of 

 temperature from the same source of heat in the same time. The end 

 of the lever of compensation abuts against a small secondary rod or 



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