Catalogue of the Fishes of Connecticut. 55 



Putting the differential of (13) equal to zero, we have 



r — rV''=0. 

 Taking the logarithms and reducing, we find 

 I02:. r — log. r' 



, ^-=-^-7, — ^- (14). 



, r log. e ^ ^ 



By using the foregoing values of r, r', and e, we find 

 ^=0-5025, 

 which is a little more than half a year. Substituting this value 

 of t in the expression (13), it becomes |0-000592. Hence the 

 greatest difference which can possibly occur is when the given 

 sum has been on interest a little more than half a year ; this dif- 

 ference is then less than six tenths of a mill on one dollar. 



If this interest is found to be too great, we may take the rate 

 per cent, per annum as much smaller as we wish ; all that I have 

 wished to show is, that this method of instantaneous compound 

 interest is practicable. 



Before closing this subject, it may not be amiss to remark, that 

 the values of the third column of our table could have been cal- 

 culated by formula (5), by calling r=0-07. This is obvious, 

 since we determined r'= 0-0676587 from the condition that equa- 

 tions (4) and (5) should be identical. 



Ulica, January 27th, 1844. 



Art. IV. — Catalogue of the Fishes of Connecticut, arranged 

 according to their natural families ; prepared for the Yale 

 Natural History Society, by Rev. James H. Linsley, A. M. 



To THE Secretary of the Yale Natural History Society: 



My dear Sir — In continuation of the plan of furnishing a reg- 

 ular series of catalogues of the zoology of Connecticut, I here- 

 with, as next in order, transmit a list of the fishes, or fourth class, 

 which I hope may prove acceptable to the Society. 



The following catalogue embraces the names of all the species 

 I have yet ascertained to be found in our waters, together with 

 the names of a very few whose residence therein can scarcely be 

 doubted, from the circumstance of their having been obtained in 

 adjoining States. 



I would improve this opportunity to tender my thanks to those 

 gentlemen and friends, who have kindly furnished me specimens 



