28 



the compass is more costly than a common sextant and mercu- 

 rial horizon. 



2. The observations of the dip and variation of the compass 

 are more difficult to be made with accuracy than a common 

 lunar observation. 



3. The reduction of these magnetic observations, on the Doc- 

 tor's hypothesis, would be more laborious than the working of 

 a lunar observation. 



4. Mr. Walker proceeded to show, in conformity with the 

 remarks of Dr. Patterson, that Dr. Sherwood's assertion that 

 he can determine the latitude and longitude from the dip alone, 

 or from the variation alone, was contrary to the first principles 

 of the geometry of position; since a point, in order to be deter- 

 mined, in space, must be referred to three given surfaces. If 

 one of them is the surface of the spheroid as in geography, then 

 the point must be referred to two other given surfaces; where- 

 as, by the dip alone, Or the variation of the compass alone, a 

 point can only be referred to one of these two surfaces, and the 

 resulting locus is a line and not a point. Hence, if latitude and 

 longitude are determined by magnetic observations, it must be 

 by both the dip and variation. Dr. Sherwood's method, there- 

 fore, could be of no use for nautical purposes, from the im- 

 possibility of observing the variation of the compass at sea with 

 any tolerable degree of accuracy. 



5. Dr. Sherwood's assertion that the magnetic method could 

 be used in cloudy weather is inaccurate; since the variation of 

 the compass cannot be ascertained without astronomical obser- 

 vations. 



6. Restricting then the use of magnetic observations to those 

 made on land in fair weather, still, owing to local pertur- 

 bations, the probable discrepancy of the mean of many obser- 

 vations at one place from the theoretic dip and variation, may, 

 at a low estimate, be assumed to be ten minutes of space, and, 

 as the resulting errors of latitude are of the same order, we 

 should have ten miles for its probable error, which is twenty 

 times that of a common sextant and mercurial horizon. 



7. Owing to the proximity of the north pole to Dr. Sher- 

 wood's assumed magnetic pole, the probable error in the result- 

 ing longitude would far exceed that of the dip and variation 



