Notices respecting New Books. 465 



mine their form, and gives rules for describing cycloidal and invo- 

 lute teeth. He then takes the question of the strength of teeth, 

 goes on to give rules for the construction and proportion of wheels, 

 and ends the chapter with some articles on screw-gearing. This 

 very brief account of the contents of a single chapter will perhaps 

 serve to indicate the sort of treatment which the subject receives 

 at our author's hands, as well as to show how much is taken up 

 directly with the question of strength, viz. about a fourth part in 

 the case of the present chapter. A similar remark would apply to 

 other chapters. 



The work seems to have been executed with great care and with 

 an ample knowledge of the subject. It will doubtless be very useful 

 to students of mechanical engineering ; and those whose interest 

 in mechanics is of a less practical kind will find a good many inter- 

 esting questions worked out clearly and accurately. 



The author of such a w 7 ork as that before us has one great diffi- 

 culty to contend with. He is obliged to consider the extent of the 

 mathematical knowledge w'hich his readers may be presumed to 

 have ; and in order to render his work useful to as large a class 

 as possible, he is obliged to take some things for granted which 

 admit of being proved. What should be taken for granted and 

 what proved is a question that must be settled by a sort of com- 

 promise ; and as the author may be presumed to have given it a 

 great deal of attention, his opinion, as expressed in the selection 

 that he makes, is prima facie entitled to great weight; we do not, 

 however, think that in the present case Mr. Unwin has been 

 always very happy. At all events, we think that we were entitled 

 to expect that the omissions should be obviously consistent with 

 each other, that where matters are not referred to their ultimate 

 principles they should, at all events, be referred to important pro- 

 positions (to what may be called secondary principles), and that 

 when algebraical formulas are given without proof they should be 

 accompanied with sufficient explanations to ensure their being 

 understood. It would be easy to point out examples of failure in 

 each of these respects, which might with advantage be rectified in 

 a second edition. Thus, on p. 186 it is taken for granted, with- 

 out so much as a reference, that the work lost in the friction of 

 teeth is proportional to p H (E 2 + E 2 ) -=- E x E 2 ; while on p. 207-8 

 the formula for the tensions of a rope stretched over a fixed 

 cylinder (T x = T 2 e^ ) is proved at full length. It is hard to see 

 why both should not be assumed, or both proved. In the former 

 case the reader's attention should be drawn to the fact that a 

 point capable of proof is being taken for granted ; this, however, 

 is not done on p. 186. Again, on p. 30, where the subject dis- 

 cussed is the strength of a beam subject to simple bending, we are 

 told that the beam will be of adequate strength when the bending- 

 moment equals fZ, Z being " the modulus of the section — that is, a 

 function of the dimensions of the section which is proportional to 

 the moment of resistance of the section ;" and on p. 35 a table is 

 given of the values of Z for certain forms of section. Here every 



Phil Mag. S. 5. Vol. 3. No. 20. June 1877. 2 H 



