322 



a known law of compensation exists ; and those in which the sepa- 

 rate observations and their errors are independent of each other. 



Thus, when we repeat the measurements of an angle upon 

 different parts of a circle, we are certain that, however erroneous 

 the division may be, the entire circumference is 360, and that, 

 therefore, an error of defect in one part, implies one of excess in 

 another part of the limb. Again, if we read at three or five places 

 equidistant from each other, we know that that part of the inaccu- 

 racy which arises from the eccentricity of the fittings, is eliminated. 

 Or if we take an altitude face East and then face West, we know 

 that the two errors arising from a misplacement of the zero com- 

 pensate for each other. But in all those cases where the compen- 

 sating principle exists, a result from which any of the compensating 

 quantities is excluded, cannot be considered as that of a complete 

 observation ; thus an altitude face East, without its complementary 

 altitude face West, could not be used to found upon ; and those only 

 in which the compensating principle has had full scope, can be ad- 

 mitted to be observations. 



Thus it seems that our attention need only be given to those 

 cases in which no law of compensation is known to exist: of which 

 our example is one. 



As there existed no particular reason why one set of stars should 

 have been taken rather than another. Signer Santini might have 

 chanced to make only observations I. and IV., and he would have 

 had strong reason to believe the latitude to be 45° 23^ 56"; or 

 if the weather had permitted him to make only observations III., 

 IX., XII., and XIII., he would have concluded that the true lati- 

 tude is 45° 24' 04". Within the limits of the errors to which the 

 particular class of observations is liable, it is diflScult to adduce any 

 argument in favour of one rather than another, in fact, it is a matter 

 of accident, what result is arrived at. 



That we may have a clear view of the subject, suppose that, in 

 order to measure a given angle, a circle is used of, say, 30 inches 

 diameter, divided to 10", and carrying a telescope powerful enough 

 to render an angle of 1 0" quite appreciable ; suppose also, that the 

 graduation is perfect, and that by the first observation the angle 

 comes out so many degrees, minutes, and say 40". If we measure 

 the angle again we shall obtain the same result 40", and if again 

 and again, and again, still the same 40"; and it is quite clear, that 



