142 Notices respecting New Books. 



We have dwelt so long upon the man, that our remarks upon his 

 writings must be brief. The title-page of the present volume would, 

 we think, justify the expectation that it contains at least all Mr. Ellis's 

 printed works ; this, however, is not the case. That part of his 

 writings which is contained in the edition of Bacon's works is not 

 given here, an omission not to be wondered at, but to be regretted ; 

 at least we should be glad to see the General Preface to Bacon's 

 philosophical works printed separately. We quite agree with Dr. 

 Goodwin that it is the most valuable of his writings. We may add 

 that it contains a singularly able exposition of the more difficult 

 points of Bacon's philosophy, and particularly of the meaning of his 

 chief technical terms. 



The most important article in the present volume is perhaps the 

 •' Report on the Recent Progress of Analysis " (pp. 238-323), pre- 

 sented to the British Association in 1846. It contains an account 

 of the progress made in the Theory of Elliptic Functions and the Com- 

 parison of Transcendentals in the twenty years preceding the writing 

 of the Report. Next in prominence, if not in importance, is a series 

 of articles on the Theory of Probabilities, and on the Method of 

 Least Squares. These articles Dr. Goodwin considers to represent 

 Mr. Ellis's special tendency in regard to mathematics : — " He de- 

 lighted to discuss the principles of investigations already known, to 

 trace the history of processes, to examine the philosophy of a sub- 

 ject, to hunt up its literature, or to simplify its treatment." They 

 also illustrate the influence which the writings of Dr. Whewell 

 exerted on the formation of his philosophical views, an influence 

 which may be noticed in several of his other writings. The first, 

 " On the Foundation of the Theory of Probabilities," is devoted to 

 an attempt to show that James Bernoulli's theorem, viz. that in a 

 long series of trials events tend to recur in numbers proportioned to 

 their individual probabilities, is not really susceptible of proof, but is 

 a fundamental and self-evident principle. He does not seem to have 

 been quite satisfied with this article ; and eight years after, in order 

 to strengthen his view, he wrote a sort of Appendix to it, entitled 

 " Remarks on the Fundamental Principle," &c. The next is a review 

 of the methods that have been proposed for proving the principle of 

 least squares ; this is followed by remarks on " an alleged proof" of 

 the same principle " contained in a late Number of the Edinburgh 

 Review." In one respect the article, which is written with great 

 spirit, is remarkable, as he composed it twelve months after the com- 

 mencement of his last illness. The author of " the alleged proof" 

 was Sir John Herschel, who has since republished the article ; and 

 we surmise that the short note on page 399 of Sir John Herschel's 

 'Essays' is intended to meet one of Mr. Ellis's objections. The 

 last is the solution of a detached problem in probability. 



The remainder of the mathematical part of the volume contains 

 about thirty-five articles, mostly devoted to the solution of isolated 

 questions in several of the higher branches of the science ; some of 

 them were dictated to an amanuensis during his last illness. These 

 exemplify a power, which Mr. Ellis possessed in great perfection, of 



