276 



of a year at 4 per cent., so that, at the end of the year, it shall, by 

 accumulating in the same way, amount to L.l. 



Let the interest of L.l for a year, payable at the end of the 

 year, be i ; and let the interest for the first ccth. portion of a year, 

 payable at the end of the period, be I^;, then, we ought to have — 



or, lx + h'^i-x = ^i • . . (1.) 



To solve this equation, substitute 1 — x for x, and there results 



whence, by subtraction, 



xi^l^^(l-x)i-Ii_^ . . . (2.) 



This equation shows that the excess of the proportional part of the 

 year's interest above the sum payable is the same for complementary 

 portions of a year. 



Substituting the value of Ii_a. from equation (2), we get 



I_^2 -fl^ I 1 4- (l—x)i — xi \ =zxi 

 I^ = i|2^^-(l^-^)| ■hi\/{l+if-4:xi(l~x)i 



The follov^^ing Gentleman was duly elected an Ordinary 

 Fellow : — 



James B. Fraser, Esq., Glasgow. 



The following Donations to the Library were announced : 



Flora Batava. 176 Aflevering, 4to. — From the King of Holland. 

 Transactions of the Architectural Institute of Scotland. Vol. III., 



Part 1. 8vo. — From the Institute. 

 Magnetische Ortsbestimmungen ausgefiihrt an verschiedenen Puncten 



des Konigreichs Bayern und an einigen auswartigen Stationen. 



Von Dr J. Lament. 1 Theil. 8vo. 

 Annalen der Kbniglichen Sternwarte bei Miinchen. VI. Band. 



3vo. — From the Observatory. 

 A Monograph of the British Nudibranchiate Mollusca ; with figures 



of all the species. By Joshua Alder and Albany Hancock. 



Part 6. 4to. — From the Ray Society. 



