1878.] "Facility of Production" of Chemical Combinations. 55 



84, 126, 126, 84 36, 9, 1."* These numbers, it will be observed, are 

 the numerical coefficients of the several terms in the expansion of 

 (a + /c) 9 and the symbols in the corresponding squares the symbols 

 corresponding to those coefficients. Thus, for example, in the case of 

 the fourth base, which passes through the numbers 1, 3, 3, ], we have 

 (a -f k-) 3 = a 3 + 3a 2 k + 3a/c 2 -f k z . The numerical coefficients, as is 

 well known, express the number of ways in which the letters in the 

 corresponding symbols may be permuted. Now, the " facility of pro- 

 duction" of the hydrocarbon varies with the number of these permuta- 

 tions, so that in each square the symbol is associated with the number 

 expressing its " facility of production." If experience be concordant 

 with theory, the actually existing hydrocarbons which appear on the 

 several base-lines (between which it is our object to effect the com- 

 parison in question) will be found in those squares in which the 

 highest numbers appear. Now, if a perpendicular be let fall upon 

 any base from the upper left-hand corner of the square in the top 

 horizontal row, this line will either pass through the square con- 

 taining the greatest number or will pass between two such squares, the 

 numbers equally diminishing on each side. The perpendicular drawn 

 through all the bases will be termed the axis or main diagonal of the 

 system. 



The squares in which the actually existing hydrocarbons appear 

 are in the map shaded; there are no known hydrocarbons corre- 

 sponding to the plain squares. If we follow the course of the axial 

 line, it will be perceived that, up to the twentieth base, the squares 

 through which the axis passes and the squares which lie immediately 

 to the right and to the left of the axis, with one exception, are coloured 

 grey, so that, up to this point, all the hydrocarbons which have theo- 

 retically the greatest "facility of production" have actually been 

 produced. Further, a close inspection will show that there is a decided 

 tendency in the system to approximate to this central line. 



It does not follow, from these considerations, that " facility of pro- 

 duction " should be the only cause determining the actual existence of 

 the hydrocarbons. The case is not so simple as that of drawing white 

 and red balls from an urn or cards from a pack. At one time the 

 efforts of chemists may be mainly, although even unconsciously, 

 directed to filling up one part of this system ; at another time to filling 

 up another part ; efforts which may have their origin in testing the 

 truth of speculations or possibly in the discovery of some one method 

 or one hydrocarbon ;f but the remarkable fact remains that, notwith- 

 standing the operation of these multifarious causes acting in various 



* Vide Todhunter, " History of the Theory of Probability." 



f Thus the great attention which has of late been paid to the derivatives of 

 phenyl has caused what may be considered as an exaggerated growth of the system 

 to the right of the main diagonal. 



