434 Mr. Ivory on the Longitudes of the Trigonometrical Survey. 



With the data at Beachy Head and Duonose, and making 



— = '00324, I have deduced these values of eo, viz. 



co = 1° 26' 58"*3 

 co = 1 27 0-8 



These results approach near the true quantity, but they do 

 not agree, which shows that there is some inconsistency in 

 the observed quantities. If we add 0"*6 to the difference of 

 latitude, the formulas will give results very nearly equal to 

 one another and to the true quantity. Thus, making 



X = 50° 44' 2l"'3 



M =50 37 4 -7, 



I have found eo = 1 27 3 *8 



eo = 1 27 7-2, 



and the mean of these values almost coincides with the exact 

 quantity. 



What has now been said is decisive of this question. The 

 equations to which the problem has been reduced, which are 

 rigorously exact, prove that the excentricity has an influence 

 on the difference of longitude, however minute that difference 

 may be, and however difficult to bring it to an exact valua- 

 tion. The investigation we have employed is drawn from the 

 principles of elementary geometry. We have advanced no 

 vague reasoning about the well-known properties of spheroidi- 

 cal triangles and geodetical lines, in a case where, in fact, 

 there is neither any such triangle nor any such line. 



If we combine the two equations (A) so as to exterminate 

 the excentricity, we shall obtain the following equation ; viz. 



/ COS A' COS A, V 



= sin eo ( ; r ) 



\ cos A tan m cos A' tan rw / 



+ cos to (cos X' tan X + cos X tan A') — (sin X -f- sin X'). 



Here, then, we have an equation which is independent of 

 the excentricity, and which therefore expresses a property 

 common to the sphere and to any spheroid. But if any one 

 should imagine that, now certainly by this exact equation, 

 the difference of longitude may be found independently of 

 the excentricity, he is advised to consider well the principles 

 on which he proceeds before he begins to calculate, lest he 

 should lose his labour. 



Dr. Tiarks has treated of this subject in the last Number of 

 this Journal. He is fortunate enough to take the right side 

 of the question, standing forth as the champion of the method 

 in the Survey. But he has entirely mistaken the nature of the 

 problem and the difficulties that must be overcome in solving 



it. 



