444 Mr. W. J. M. Rankine on simultaneous Observations of 



It is replied, that this necessity may be regarded as merely 

 posterior to some act of limitation by which the events s, t, &c., 

 previously of larger comprehension, became restricted to that 

 particular interpretation in terms of sc, y, &c. which they bear in 

 the problem, and which is the foundation of the logical necessity 

 referred to. What that larger ccTmprehension is, it is wholly 

 unnecessary to attempt to define. It suffices, upon the general 

 grounds of symbolical algebra, to apply to the inverse process of 

 the removal of a nexus, the formal laws which are derived from 

 the direct and always interpretable case of its imposition. I 

 regard this as a principle, which, though capable of verification 

 in innumerable instances, does not rest simply upon the cumu- 

 lative evidence afforded by such instances, but has a real foun- 

 dation in the intellectual constitution. 



Finally, as respects the mode in which the aforesaid logical 

 necessity has been represented in the example of the urn, it may 

 be remarked that it involves no more than is implied in the 

 various figures by which, in difl*erent languages, the idea of ne- 

 cessity has been symbolized. For in each of those figures we 

 have presented to us the notion of something which has once 

 been free, but has ceased to be so through a material act, or a 

 positive determination*. And any one of these modes of illus- 

 tration might with equal propriety have been adopted. 



The verification of these results will be considered in my next 

 paper. 



Lincoln, Sept. 30, 1854. 



LV. On some simultaneous Observations of Rain-fall at differ- 

 ent points on the same Mountain- Range. By W. J. Macquorn 

 Rankine, Civil Engineer, F.R.SS. Lond. and Edinb. ^-c.f 



1. npiIE question of the relative proportions of rain which fall 

 A at points having different situations, levels, and aspects 

 on the same mountain-range, is one which, besides its scientific 

 interest, is of great practical importance, especially with reference 

 to the water-supply of large towns. 



2. The observations here recorded are intended as a small 

 contribution to our knowledge of this subject. They were made 



♦ Witness the supposed derivation of the Latin necesse from nexus, of 

 the Greek (IfiapufVTf, from a verb signifying division by the casting of lots, 

 of the \>ord/(:/^e, &e. The higher limitation implied by the addition of 

 such terms as absolute {e. g. absolute necessity) is curiously derived, not 

 from the direct idea of physical restraint, but from the converse one of the 

 removal of all restraint upon the restraining power. 



t Communicated by the Author; having been read to the British Asso- 

 ciation for the Advancement of Science, Section A, at Liverpool, Sept. 1854. 



