14 J. H. Alexander on a New Formula for Interpolations. 



A river valley should thus be surveyed from its mouth to the 

 heads of all of its tributaries. The Connecticut in our own coun- 

 try affords a most interesting region for investigation ; for the 

 terraces are on a magnificent scale, and may be traced, as the 

 writer has seen, even among the White Mountains. One river 

 thus studied, will be a standard of comparison ; and when a whole I 

 country has been carefully examined from the shores to its higher 

 summits, we shall have certain and satisfactory data for some 

 grand deductions. We may then hope to learn which terraces 

 belong to one and the same epoch, and to what extent they are 

 measures of the elevations of a country. After these points are 

 determined, we may look for a full elucidation of. the former 

 changes of level a continent has undergone during the period in- 

 cluded, or perhaps may prove coincidences between distant coun- 

 tries that will point to some principles in geological dynamics yet 

 but half acknowledged. W 



The writer has said nothing upon the effects of glaciers, as 



they will be better learned from those who have made them their 

 study. The course of investigation pointed out precedes the 

 application of any theory to account for the facts. 



We do not attempt a review of the known facts relating to 

 terraces in this country, since they can establish little more than 

 the general truth of their existence, until a systematic series of 

 observations is carried out. 



New Haven, November, 1848. 



Art. II. — On a New Formula for Interpolations ; by J. H. 



Alexander, Esq. 



as claiming any thing for it in that behalf; for, in so far, it is 

 neither the better nor the worse : but simply, because it was new 

 to me at the time I developed it for my own use. That it will 

 be new to others now, by no means necessarily follows ; indeed, 

 from the readiness with which the elements submit themselves to 

 the requisite decompositions and transformations, rather the oppo- 

 site is to be presumed. The principle of the method is certainly 

 as old lis Descartes; and the form of it, even, may occur in some 

 of the mathematical writers, not long after him but now ancient 

 for us ; although, from comparatively slight familiarity with those 

 writers, I am not aware of its existence. At all events, how- 

 ever, it does not appear in some of the most recent treatises on 

 the special subject, where one would naturally expect to find the 

 fruits both of ingenuity and of research ; and therefore having 



recognized, for a good while and frequently, the ease and fecun- 











new, not ( 





