UTILITY OF A SERIFS IN FINDING A FLIT F.N T. $13 



must produce such a curvature, not to mention some degree 

 of resistance, which these particles may experience in space, 

 though with respect to large bodies it is imperceptible. Fi- 

 nally, the tail will extend so much farther to our eyes, in 

 proportion as the production of this fluid is more abundant, 

 and its decomposition more slow; both which circumstances 

 may vary, not only in different comets, but in the same 

 comet at its different returns. Combining these different 

 considerations therefore, may it not happen, that a comet 

 observed with a very long tail, and of considerable appa* 

 rent diameter, from the greater spread of its envelope of 

 lucifcrous vapours to a determinate distance from its body, 

 shall return with very little tail, and a much less apparent 

 diameter; that its light even shall 'be weaker; and that thus 

 it shall not be known for the same as was expected from cal- 

 culation, though in reality it is so? 



Here let me stop. He who coasts along the shore by the Conclusion, 

 help only of the lead and the log, without a compass and 

 without a quadrant, must not set up for a geographer, but 

 contine himself to hints. In conjectures like the present, 

 the analogies on which they are founded can furnish oaly 

 germes of a theory : time alone can show by repeated ob- 

 servations, whether they be capable of becoming fruitful ; 

 but at least they atford matter for reflection and inquiry, 

 and the first ideas I communicated to you have already been 

 corrected and extended by your remarks. At your desire I 

 now deliver them to you, such as they are^ in testimony 4>f 

 my respect, &c. 



Berlin, 2 June, 1799, ^ 



XII. 



4n Example of the Utility of a Series in finding a Fluent. 

 By a Correspondent. 



To Mr. NICHOLSON. 

 SIR, 



T sometimes happens, that great mathematicians give Difficulty of dU 

 themselves no inconsiderable pains to untie a knot, which rect solutions, 

 they might cut with ihe greatest ease. As an instonctvof 



this 



