330 Mr. Galbraith on the Figure of the Earth. 



exact quantity of compression by the various arcs on the me- 

 ridian, and the parallels now executing throughout Europe; 

 though I am inclined to believe, that measurements of arcs of 

 the meridian near the equator, and as close to the poles as 

 convenient, will be more decisive. In the execution of these, 

 however, care should be taken to select proper portions of the 

 meridian under uniformity of geological character. Some of 

 the extensive plains in the North of Russia and in South 

 America, appear to me to be the most eligible ; though I have 

 seen Spitzbergen recommended, from the facility it affords of 

 executing the necessary operations. Yet for these very rea- 

 sons I am disposed to think that from its irregular and broken 

 character, by extensive Jiords, as they are called, running 

 amongst the islands, it is to be feared that very irregular lo- 

 cal attractions will be found to prevail ; so that each series of 

 zenith distances would be something like the Schihallien ex- 

 periment; and the irregularities thence produced, would rather 

 tend to throw a doubt over the true compression, than to point 

 out the proper quantity. 



Edinburgh, April 1827*. WlLLIAM GALBRAITH. 



P.S. In the foregoing remarks, it will be seen that I have 

 endeavoured to introduce a few small corrections into the usual 

 formulae for obtaining the ellipticity, which may perhaps be 

 thought by some, to be too minute to deserve much attention 

 in the present state of the problem, as being much within the 

 probable errors of observation. For instance, instead of taking 

 the ratio of the centrifugal force to gravity at the equator at 

 2 i^ I have adopted g iy . nearly, as it ought to be ; and for the 

 coefficient | = 2*5, it is assumed at about 2*49. These, no 

 doubt, appear trifling ; but nevertheless their adoption reduces 

 the constant 0*00865 to 0*00861, and this small modification 

 diminishes the ellipticity in an equal degree. I have also pre- 

 ferred the reduced latitudes to the apparent, or those got di- 

 rectly from observation ; and this removes an irregularity which 

 at one time I was persuaded occurred in the elliptical figure 

 of the earth ; namely, a protuberance at about the parallel of 

 45° N., which I am now disposed to attribute to a slight error 

 in the approximate formula usually employed. It has also 

 been thought advisable to apply the method of the least squares 

 with caution. I am perfectly aware that this method is the 

 best that can possibly be applied in many cases ; but that there 

 may be particular instances where, by employing it without 

 discrimination, it may, from the manner in which it must be 

 employed, be the means of leading to more erroneous conclu- 

 * So in the MS.— Edit. 



sions 



