1886.] Mr H. Gadoiv, On some Caves in Portugal. 381 



(4) A Verification of a transformation in Elliptic Functions. 

 By J. Chevallier, B.A. 



The author contributed the details of a verification, by direct 

 algebraical methods, of the following theorem : 



where X = x 5 - 2 Ace' + Bx 3 - Cx 2 + Dx-E, 



Y = x*-Ax + A', j = ±(-l+ijl9), 



A=-%(Jl9+i), A' = ■& (11 + %Jl»), 



B = h(25 + 5ijl9), C=-%(JT§+6i), 

 D = \ (21 + 9iJW), E = -\ (Jl§ + 1 li), 



then V - g 2 y - g 3 = J\P (4a 3 - g,x - g a ) (*fj 



where g 2 = 8, g 3 = >Jl9. 



(5) On some Caves in Portugal. By H. Gadow, M.A. 



In the spring of 1884 I made a zoological excursion through 

 the Algarve, my chief object being to explore the fauna of certain 

 large subterranean caves. According to Murray's Handbook for 

 Portugal, and von Maltzan's Reise nach Algarve, these caves are 

 situated somewhere near the little village of Alte, nearly in the 

 centre of the Algarve. Whilst travelling northwards from Faro to 

 Louie I was told of the existence of some other caves in the 

 neighbourhood. 



Leaving the high road from Louie towards Salir, I followed a 

 mountain path leading eastwards over densely wooded very 

 picturesque hills for about two miles, and came to a wild ravine 

 through which dashed the Rio Secco, one of the eastern tributaries 

 of the poisonous Bio Quarteira. According to the geological maps 

 published by the Portuguese Government, the Bio Secco runs 

 through Jurassic and Keuper formations. Its banks are steep, 

 with an incline of 60°, about 200 feet high near the caves, and 

 strewn over with innumerable large and small, but extremely 

 rough boulders, between which grow plenty of locust trees, olives, 

 a few oaks (Q. suber and robur) and shrubs. Alongside, and in 

 the bed of the river a dense and luxurious vegetation of oleander, 

 olives, vines, cork trees and sarsaparilla delights the eye. On the 

 eastern side there is a plateau, nearly flat, with a few olive trees 

 and dwarf palms (Chamaerops humilis). Cultivation of corn has 

 been attempted, but yields very little, because the plateau is 



