Mr. Galbraith on Determining the Figure of the Earth. 49 



advantages of those adjacent. If two arcs, for example, are 

 chosen near the equator, a very small error in the measure- 

 ment of the length of a degree may be productive of a consi- 

 derable error in the compression. On comparing a degree 

 measured in India, in latitude l.S° 6' Si" N., with that in Peru, 

 in latitude 1° 31' 0" N., the compression by the usual formula 

 given for that purpose will be -~^-^, much less than that usually 

 received as most entitled to confidence. The difference of the 

 leno-th of a degree measured in these two parallels is only 

 about 25 fathoms, and consequently a small error committed 

 in the measure of either, amounts to a considerable part of the 

 whole, and must, by that means, affect the compression in a 

 similar manner. In fact, the increase of this difference by a 

 single fathom would increase the compression considerably, 

 or from ^l-u to -^l-r. To avoid this circumstance, distant de- 

 grees have'frequently been chosen, where the difference ot their 

 lengths is considerable, and consequently a small error in the 

 measure of either has but little effect on the resulting com- 

 pression. But this artifice cannot be employed when recourse 

 is had to the method of the least squares ; for in that case all 

 the arcs are combined, the favourable with the unfavourable, 

 and it is difficult to estimate what effect this has on the final 

 result. In general I have remarked that the conclusions de- 

 rived fi'om it lately, give a greater compression than that usually 

 received, and it would require some consideration to show why 

 this has been the case. 



Again, if the compression be deduced from the English and 

 French degrees, it will be about ^^5; and it would require the 

 difference of the lengths to be increased about five fathoms to 

 bring it to ^ j^, the more usual quantity. In truth, it may be 

 readily inferred by consulting any table of lengths of degrees, 

 such as those given by Cagnoli and Lambton, that a small 

 error committed in the measurement of arcs either near the 

 equator or near the poles, when compared together may have 

 a considerable effect on the accuracy or inaccuracy of the re- 

 sulting compression. 



If two arcs are therefore compared at no great distance from 

 the equator, such as one at about 10° S. with another at the 

 same distance nearly N., a very small error in the measure- 

 ments of the arcs will have a great influence on the compres- 

 sion, by whatever mode it may be obtained. The same thing 

 nearly will happen when a degree upon the equator is com- 

 pared with one about ten or fifteen degrees from it. This in- 

 ference also applies to those similarly situated with respect to 

 the pole. It also appears that the lengths of degrees vary 

 most rapidly at 4-5°, and consequently it is on this account that 



iVfTc6V;7><?. Vol.2. No. 7. J«/7/1827. H the 



