244 Prof. Henuessy on the Distribution 



with the conditions of the ocean in which the island is situated. 

 If the surface of the ocean is warmer than the air over the island, 

 the latter will gain in temperatui-e by the interchange of currents 

 of air over both. If we abstract all other causes, it is obvious 

 that a point on the island would in this case be warmer, the 

 closer it happened to be to the sea ; in other words, its tempe- 

 rature would be a function of its distance from the coast. The 

 isothermal lines of the island would be a series of nearly concen- 

 tric curves, having some relation in their shapes to the outline 

 of the coast. If the influence of the amount of heat gained by 

 sunshine above what is lost by radiation be now considered, it 

 appears in general that the positions and shapes of the isother- 

 raals will be changed. 



This change may be represented by transporting the centres of 

 the isothermals towards the nearest pole of the earth. 



For if H represent the efi"ective amount of heat gained by a 

 point in the island, its expression will be made up of two prin- 

 cipal terms, of which the first, as we have just seen, must be a 

 function of the distance c from the coast. The second would 

 obviously be a function of the latitude X, whether we take into 

 account the absorption of the sun's rays in passing through the 

 atmosphere or not. In the latter and more simple case /(X), 

 can be found in terms of the latitude of the place, the sun's lon- 

 gitude, the inclination of the echptic to the equator, and the 

 excentricity of the earth's orbit. I have treated the problem of 

 isothermal lines with the form of /(X) so found, and have arrived 

 at the same conclusion as that which is here deduced, in a paper 

 read before the Royal Irish Academy. 



If we take into account the resistance of the atmosphere to the 

 passage of sunshine through it, whatever knowledge we already 

 possess shows that the loss of heat from this cause will increase 

 with the obliquity of the sun's rays, and therefore it will be such 

 a function </)(X) as to possess the property of increasing with X, 

 and its minimum value will be ^(0). 

 We may therefore write 



H = F(c)+/(X)-(/>(X), 

 or simply, 



H=F(c)+/(X), 



with the conditions that F(c) continuously increases as c dimi- 

 nishes, down to c = 0; and that /(X) continuously increases as 

 X diminishes, down to X=0; so that the maximum value of H 

 would be 



F(0)+/(0). 



If another point whose distance from the coast is c,, and lati- 



