IV PREFACE. 



cially of the doctrine of Elimination, and of the solution of Equa- 

 tions containing more than one unknown quantity. Preliminary 

 information upon the subject-matter will be found in the special 

 treatises on Probabilities in " Lardner's Cabinet Cyclopaedia," 

 and the " Library of Useful Knowledge," the former of these by 

 Professor De Morgan, the latter by Sir John Lubbock ; and in 

 an interesting series of Letters translated from the French of 

 M. Quetelet. Other references will be given in the work. On a 

 first perusal the reader may omit at his discretion, Chapters x., 

 xiv., and xix., together with any of the applications which he 

 may deem uninviting or irrelevant. 



In different parts of the work, and especially in the notes to 

 the concluding chapter, will be found references to various writers, 

 ancient and modern, chiefly designed to illustrate a certain view of 

 the history of philosophy. With respect to these, the Author 

 thinks it proper to add, that he has in no instance given a cita- 

 tion which he has not believed upon careful examination to be 

 supported either by parallel authorities, or by the general tenor 

 of the work from which it was taken. While he would gladly 

 have avoided the introduction of anything which might by pos- 

 sibility be construed into the parade of learning, he felt it to be 

 due both to his subject and to the truth, that the statements in 

 the text should be accompanied by the means of verification. 

 And if now, in bringing to its close a labour, of the extent of 

 which few persons will be able to judge from its apparent fruits, 

 he may be permitted to speak for a single moment of the feelings 

 with which he has pursued, and with which he now lays aside, 

 his task, he would say, that he never doubted that it was worthy of 

 his best efforts ; that he felt that whatever of truth it might bring 

 to light was not a private or arbitrary thing, not dependent, as to 

 its essence, upon any human opinion. He was fully aware that 

 learned and able men maintained opinions upon the subject of 



