166 



the Massachusetts Survey. He deemed it his duty, however, to say that the 

 observers, Messrs. Borden and Paine, had made amends for the inferiority of 

 their instruments by the application of extraordinary tact and skill, and had 

 produced a survey adequate for all the purposes originally contemplated by 

 the Legislature of Massachusetts. The discrepancies between the astronomi- 

 cal and topographical results in the tables referred to by Mr. Hassler, except 

 for the stations of Piltsfield and Williamstown, are not much greater than 

 those which the European surveys present. And the close agreement of the 

 Vtilue of the degree perpendicular to the meridian, obtained by chronometric 

 differences of longitude, with the most approved values of this element, shows 

 that these instruments may be employed as an important auxiliary of a trigo- 

 nometric survey. Indeed, from a comparison of the final results, for this small 

 survey, (more extensive, however, than any other yet made, as far as regards 

 the use of chronometers,) it must be manifest to any one that an extension of 

 a similar comparison of chronometric and trigonometric results over the entire 

 surface of the United States, besides furnishing all the requisites for topogra- 

 phy, would form a valuable contribution to science, and perhaps go far to 

 settle the question, how far the shape of the surface of this portion of the 

 western continent conforms to the measures of the eastern. Mr. Borden had 

 omitted no expedient for obviating the errors of the eccentricity of his repeat- 

 ing circle, and his complete success may be inferred from the fact that the sides 

 of twenty miles length, derived from the original base by different series of tri- 

 angles, conformed together within three feet on the average, and never differed 

 more than five feet. 



Mr. Walker stated that he differed in opinion from Mr. Hassler, in refer- 

 ence to the precision of the latitudes furnished from sextant observations by 

 Mr. Paine. The 8J inch sextant by Troughton was a choice instrument of its 

 kind, and though absolute angles could not be measured by it without an 

 error of perhaps 6", yet, this error disappears, by observing, as in Mr. Paine's 

 case, north and south stars of the same altitude on the same evening. There 

 is not any necessary error outstanding, but that of the star catalogues. The 

 others may vanish in the mean of a great number of observations. The same 

 method was used with eastern and western altitudes for rating his chronome- 

 ters; and being all executed by himself, there was no personal equation neces- 

 sarily outstanding. It is to this compensation of small errors in the mean 

 result that Messrs. Paine and Borden are indebted for the close agreement, 

 (quite unexpected even by themselves,) of their spheroidal elements, derived 

 from so small a survey, with the standard values of those elements derived 

 from European triangulations. Mr. W. remarked that the publication of the 

 statistics of the expense of the survey was useful to others, who contemplate 

 similar undertakings, and had its example in the Transactions of other Aca- 

 demies. 



Mr. W. then proceeded to notice Mr. Borden's answer to 

 Mr. Hassler's objections to the Massachusetts Survey. 



1. Any reader will understand the phrase " Chronometric Survey." 



2. The Act of the Legislature ordering the Massachusetts Survey was 



passed in March, 1830. 



