56 RESEAECHES ON II. 



we perceive that it is not so, but that it varies with d. It is true that these 

 deviations are small, and perhaps within the limits of inevitable errors in the 

 observations until d does not exceed 30°, but for 60° there is more than a unit 



of difference in the ratio between the tangents and —^'^ '^^ ^^J therefore rest 



assured that this law is not exact except for small deviations ; still, the proportion 

 between the length of the needle and the radius of the circle is very small, viz., 

 about Tith, and the divergency would be much greater, if that proportion itself 

 were greater. This may be clearly seen on comparing the preceding tables (pages 

 54, 55) with the proportions of the relative tangents, and they will be found very 

 different. 



Conclusion. 



Those who have had sufficient patience to follow me in the aggregate of the 

 calculations and experiments contained in this paper, will be convinced that certain 

 branches of physics seem to be easy only when seen from a distance, but upon a 

 closer inspection it will appear that great labor is requisite if we wish thoroughly 

 to fathom them. It is, however, pleasing to observe that the most complicated 

 phenomena are subject to invariable mathematical laws, which, though difficult to 

 discover, are not the less interesting because they belong to a class of phenomena 

 less splendid than the great planetary systems. 



I am far from supposing that this memoir has sufficiently corresponded to the 

 object intended. I rather look upon it as a mere sketch, which can be completed 

 by such as are furnished with more accurate instruments ; and I hope to be able to 

 return to the subject myself, when I shall be less occupied than at present with the 

 duties of my situation. 



