466 On the Rotary Power which the Essence of Turpentine 



putting for Q*, the probability of throwing, in one trial with the 

 s dice, r different doublets, and s — 2?- numbers not repeated. 

 Now the calculation of this probability is easily seen to be merely 

 the problem of art. 2 in" a different form. In general, the pro- 

 bability of throwing a single numbers^ b doublets, c triplets, &c. 

 in one trial, will be 



t{t-l){t-2) . . . [t-a-b-c- . . . +1) 



1.2.3...S 



^ (1.2)*(1.2.3)''...1.2...fl.l.2...6.1.2...c..- 



(where s must not be confounded with the s of art. 2). In the 

 case of r doublets and s — 2r single numbers, the denominator 

 of the second factor becomes 



(1.2)''1.2.3...?-.1.2.3...(s-2r). 



16. Having thus obtained an expression for Q*., we are in 

 possession of all the elements necessary for the approximate 

 solution of the general problem. But I should consider it a 

 great waste of time and laboiir to attempt anything like a nu- 

 merical result in the actual case. All that I have aimed at is to 

 show that there is no real difficulty of principle in applying the 

 theory of probabilities to this and similar questions, however 

 impracticable it may be to obtain a complete numerical solution. 

 If it be said that such a conclusion is vague and unsatisfactoiy, 

 I reply that the same thing happens in every branch of applied 

 mathematics. The theory of dynamics can hardly furnish the 

 exact numerical solution of a single problem suggested by actu- 

 ally existing cases of motion; still less do the mathematical 

 processes employed in hydrodynamics, the theory of heat, &c., 

 correspond to the facts of nature. But in all these cases the 

 consideration of principles is not the less interesting and instruct- 

 ive ; and the discussion of problems depending upon data more 

 or less fictitious, may be, and often is, of the highest practical 

 importance. 



AprU 14, 1851. 



LXIV. On the Rotary Power which the Essence of Turpentine 

 and Saccharine Solutions exercise on Heat. By MM. F, De 

 tA Provostaye and P. Desains*. 



MM. BIOT and Melloni have demonstrated in a memoir 

 printed in the Comptes Rendus, vol. ii., that quartz, cut 

 perpendicular to its axis, exercises a similar rotary action upon 

 polarized heat to that which it exercises upon polarized light. 

 * Translated from the Annales de Chimie et de Physique for Nov. 1850. 



