318 Intelligence and Miscellaneous Articles. 



and some space is given to their graphical representation. We 

 then have (rv.) the addition and subtraction formulae for func- 

 tions of two or more angles, and (v.) the functions of sub- 

 multiple angles. The next chapter (vi.) is to our mind the most 

 valuable of the elementary chapters for readers for Scholarship 

 papers. The collection of worked-out examples will be of material 

 use to such readers on account of the many beautiful artifices used 

 in their solution. At a somewhat earlier stage than is usual, Mr. 

 Hobson discusses (vn.) the expansion of functions of multiple 

 angles. He does so because " they are merely algebraical conse- 

 quences of the addition theorems." In vin. and ix. the reader is 

 introduced to the relations between the circular functions and 

 circular measure of an angle and the formation of Trigonometrical 

 Tables, it being assumed at this latter stage that the student has 

 acquired a knowledge of logarithms from some work on Algebra. 



Properties of triangles and quadrilaterals occupy chapters x., xi., 

 xn. These are treated in some detail, references to the modern 

 geometry of the triangles being in the main purposely excluded. 



The Analytical side of the subject occupies chapters xiii. to the 

 end. In xiii. is an account, with applications, of complex quan- 

 tities, which is preliminary to the (perhaps) distinctive feature of 

 Mr. Hobson's book — the rigorous discussion of the theory of infinite 

 series. The corresponding portion in Mr. Hobson's Encyc. Brit. 

 article has recently elicited commendation from Prof. Chrystal, and 

 the work before us, we believe, presents the proofsineven fuller detail. 



The exponential function, and what the author calls the 

 " generalized logarithm " (" the doubly infinite series of values of 

 the logarithm of a quantity"), form the subject-matter of xv. ; 

 hyperbolic functions of xvi. ; infinite products of xvn. ; and the 

 closing chapter gives a proof of the irrationality of tt, with other 

 applications of continued fractions to the subject. We have noted 

 few errors: p. 83, line 4, for h read 6; p. 103, line 4, for (29) 

 read 40 which depends on (29) of § 49 ; p. 123, line 15, for second 

 sin0 read tan ; p. 132, line 7 up, for (7) read (11); p. 311, 

 line 10 up, for sin (a?— uy) in denominator read cos {x— iy). There 

 is a beautiful and numerous collection of exercises which will 

 interest any one who has a taste for the subject. The figures and 

 the " get up " are all that one could wish for. 



XL. Intelligence and Miscellaneous Articles. 



EDITOEIAL NOTE ON MR. PARKER'S PAPER ON THE ABSURDITY 

 OF DIAMAGNET1SM. 



IF I had seen Mr. Parker's paper in last month's Philo- 

 sophical Magazine before publication, I would have 

 referred it back to him for some important alterations. I 

 could hardly, however, have foreseen, when publishing a paper 

 by a Fellow of St. John's College, Cambridge, that it was 

 likely to contain such statements as, 1st, that there is anything 

 new in the theory that diamagnetic action is really due to the 

 paramagnetism of the air ; and, 2nd, that no theory of dia- 



