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 a;th portion of a year, 

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



or, I^+I^Ii_;, = a;i . . . (1.) 



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



Ii-x + I. Ii-x = (l-^)« 

 whence, by subtraction, 



.r,:-I^ = (l-^)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 I]_.^ from equation (2), we get 



1/ + I^ I 1 + (\-x)i-xi\ =xi 

 I, = i I 2 X i - (1 + I + ^V{l + if-4:xi(l-x)i 



The following Gentleman was duly elected an Ordinary 

 Fellow ; — 



James B. Fraser, Esq., Glasgow. 



The following Donations to the Library wei'e 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 Koniglichen Sternwarte bei Miinchen. VI. Band. 



8vo. — 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. 



