three Degrees of the Meridian. 91 



some fault in the instrument, with respect to vertical posi- 

 tion, constraction, or some accidental derangement, there 

 is an error of some seconds in the observations of the fixed 

 stars. How is this to be discovered ? This is not to be 

 done bv comparing the value of a degree on the meridian, 

 as deduced from these observations, with the results of other 

 measurements in distant parts of the globe. For if we find 

 that these degrees so taken do not agree in giving the same 

 ellipsoid, we are not to attribute all the differences to irre- 

 gularities of the earth, wiihout supposing any error on the 

 part of the observer, of his instrument, or of other means 

 employed in his survey. 



But this, in fact, is what has generally been done. It 

 must, however, be acknowledged, that the majority of ob- 

 servers have not been in fault, as they could do nothing 

 better ; but too much reliance has been placed on the good- 

 ness of their instruments, their means, and other circum- 

 stances. It is true that irregularities of the earth and local 

 attractions may occasion considerable discre|iancies which 

 are even inevitable ; but before we decide that these are 

 the real source of disagreement, we ought carefully to as- 

 certain that there are no others. 



But to return to our subject, of the English measure- 

 ment. If the unpertainty which yet subsists, with respect 

 to the exact figure of the earth and its dimensions, occa- 

 sions some small errors in the calculation of the series of 

 triangles, the sum of these errors will be found in the esti- 

 mate of the entire arc, and will increase in proportion to 

 the extent of the arc measured. Now, in the English 

 measurement, we find exactly the reverse of this. For the 

 diflerence between the results of calculation and observation 

 is only l",.S8 on the whole arc j but is even as high as 

 4",77 on one of the smaller arcs. So that, whatever error 

 we may suppose to have been introduced into the calcula- 

 tion by assuming a false estimate of the spheroidity of the 

 earth, or of other elements emplnved in the calculation, it 

 ■ is very evident thai the zenith dis'ancss of stars taken at 

 Arbury Hill are affected by some considerable error, wholly 

 independent of these elements. 



It was not till the date of the measurement of the me- 

 ridian in France, that M. Delambre published and ex- 

 plained, with admirable perspicuity and elegance, all the 

 i'ormidae and methods relative to the calculation of sphe- 

 roids, and put it in the power of astronomers in general to 

 make usc of the elliptic elements in verifying the results of 

 their observations. In the present stale of science thcs^i 



elements 



