Notices respecting New Booh. 367 



case. Tims it is found that 



v 



i8 =1 _i__i i_ _i__i__L J__L J L_ 



7 ' 1+ 1+ 1+ 1+ 10+ 1+ 1+ 1+ 1+ 2+... 



* . * 



From this the following convergeuts can be derived in succes- 



,, , , . 1 2 3 5 8 85 ,, , . 449 x1 4 . a 



sion: — the first si.r, -, -, -, -, -, — - ; the tenth, ___; the twentieth, 

 1 1 2 6 5 53 280 



403201 



§fi1 44-0 ' anc ^ so on *° * n ®/ or ^^j eightieth, &c. Mr. Muir investi- 

 gates in detail the properties of the successive convergeuts by which 

 these and similar results are obtained. The notation used iu the 

 pamphlet is unusual ; and though it is easy to imagine the reason 

 for its adoption, that does not prevent its being cumbrous ; e. g. if 

 the fraction written at the beginning of this article is under consi- 

 deration, the equation, which is commonly written thus, 



jMV-i— p n -iq n = (-l) n+l , 



assumes in Mr. Muir's notation the following form :—- 



K(A, a 1 ...a n )K(a 1 ...a n _ 1 )~K(A, a 1 ...a n _ 1 )K(a 1 ...a n ) = (-iy+K 



The pamphlet is designed for the use of students, who will 

 doubtless find it a useful supplement to their text-books. 



The Universe and the Coming Transits. By Richard A. Proctor, 

 B.A. Cantab. London : Longmans, Green, and Co. 1874. 

 We shall not easily forget the intense delight with which we 

 perused many of the essays, on their first appearance, that Mr. 

 Proctor has collected in the present volume ; and it is with some 

 regret that on reperusing them in their collected form we have 

 not experienced the same pleasure as on the occasions alluded to. 

 Perhaps it is inseparable from the mode of publication adopted 

 that a considerable amount of repetition occurs, so much so as to 

 be painful in reading essay after essay on the transcendental sub- 

 ject of the " construction of the universe ;" and we cannot help 

 thinking that Mr. Proctor would have much better served this the 

 highest branch of astronomy had he given us the cream of each 

 essay in consecutive order, commencing with a brief history of its 

 development instead of including this essential part in one of the 

 later essays of his series. 



The greatest problem connected with an exposition of the uni- 

 verse as illustrative of the construction of the heavens is doubtless 

 that of the constitution of the Milky Way. We have experienced 

 some little difficulty in ascertaining clearly Mr. Proctor's views of 

 the Via Laetea, principally on account of the fragmentary character 

 of the work before us ; but we have marked a few passages in which 

 w T e apprehend Mr. Proctor's views are definitely stated. On p. 83 

 w T e read : — "All these phenomena point to the conclusion that the 

 Milky Way, in this neighbourhood at any rate, is really what it 

 appears to be, — a belt or zone of stars separated from us by a com- 



