Archdeacon Pratt on the Figure of the Earth, 17 



cases of this kind by way of illustration in my last-published 

 paper already referred to. 



I hope that the above comprehensive survey of the differential 

 equations relating to Entropy and Energy may contribute to 

 make mathematicians and physicists better acquainted with 

 magnitudes which play so important a part in the mechanical 

 theory of heat, and to render the employment of them easier to 

 them. In particular, I consider that the parallel treatment 

 throughout of these two magnitudes presents the advantage of 

 rendering distinctly evident how far they resemble each other, 

 and wherein they differ. 

 Zurich, July 24, 1865. 



II. Archdeacon Pratt's Reply to Captain A. R. Clarke's 

 Remarks on his Determination of the Figure of the Earth from 

 Geodetic Data*. 



I HAVE read the remarks of Captain Clarke, in your Num- 

 ber for March, on my method of determining the mean 

 figure of the earth from geodetic data, as set forth in the third 

 edition of my e Figure of the Earth/ with the care which any- 

 thing proceeding from such an authority on such a subject 

 justly demands; but I see nothing in them to convince me that 

 BessePs method is not erroneous. In the present communica- 

 tion I hope to make this matter clear. I propose, first, to point 

 out in what BessePs method is erroneous; secondly, to explain 

 my own method, as already published ; thirdly, to suggest an 

 improvement of my method. 



I. To point out in what BesseVs method is erroneous. 



2. In obtaining by geodesy the figure of the earth, there are 

 two classes of errors which we have to diminish as much as pos- 

 sible — those arising from observation and measurement, and 

 those arising from the irregularities of the actual surface and 

 mass of the earth, as far as it differs from being a perfect sphe- 

 roid of equilibrium. The latter class is, as all now acknow- 

 ledge, much the most important. Captain Clarke says of these 

 errors, that they et are in their average magnitude very much 

 larger than the probable errors of astronomical determinations of 

 latitude, and indeed overwhelm the errors of the geodetical ope- 

 rations." BessePs method for diminishing both classes of errors, 

 which he attempts to do by one process, Captain Clarke explains 

 with great perspicuity. Each arc is subdivided into subordinate 

 arcs, and corrections, 



x, m-\-uu + {3v-\-x, . . . ., 

 * Communicated bv the Author. 



Phil. Mag. S. 4. Vol. 32. No. 213. July 1866. C 



