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XL VII I. Notices respecting New Books. 



Explanatory Mensuration for the use of Schools. Containing numerous 

 examples, and (by the kind permission of the Oxford Delegates) em- 

 bodying nearly all the questions set in their local Examination Papers. 

 By the Rev. Alfred Hiley, M.A. London ; Longmans and Co. 

 1871. Pp. 158. 



TT is much to be regretted that the Oxford Delegates gave Mr. 



-*- Hiley permission to use their questions. By doing so they have 



given a sort of informal authority to a very poor book. Several 



parts of the subject are included that are very ill adapted for 



boys whose knowledge of mathematics is limited to arithmetic — - 



such as the Mensuration of Segments of Spheres, Frustums of 



Wedges, &c. But this is by no means the worst point of the book. 



Mr. Hiley' s statements and explanations are frequently awkwardly 



expressed and inexact. Thus he defines a right-angled triangle as 



one " that contains a right angle" (p. 3). He classifies lines in the 



following queer fashion : — *'■ Lines may be either straight, curved, or 



parallel" (p. 1). He lays it down that "The circumference of any 



circle is divided into 360 parts called degrees" (p. 6), instead of 



"360 equal parts." If an arc ACB subtends at the centre of a 



circle an angle AEB, he tells us that " the arc ACB bears the same 



ratio to the circumference of the circle that the angle AEB does 



to 360°" (p. 70), instead of " the number of degrees in the angle 



AEB;" and so on in many other cases. 



Occasionally his inexactness wanders into inaccuracy, as in the 



following case (p. 80) : — " To find the circumference or perimeter 



of the ellipse. Multiply half the sum of the two diameters [he 



22 

 means the two principal axes'] by — -.." If Mr. Hiley will apply his 



rule to the case in which the minor axis is indefinitely small, 

 when the perimeter will equal twice the major axis, he will easily 

 deduce the curious arithmetical theorem that 



14=11, 



or, in accordance with the rule provided " when greater accuracy is 

 desirable" (p. 81), that 



4=3-1416. 

 Mr. Hiley's account of the prismoid is given in such a form that 

 no one who comes fresh to the subject could apply it to the deter- 

 mination of the volume of a portion of a railway-cutting ; yet three 

 of his examples contemplate this application. He is particularly 

 unfortunate in these examples. One of them (which is due to 

 the Oxford Delegates) is correctly set, and the answer is correct. 

 The two other examples were apparently drawn up by Mr. Hiley 

 himself. But if he made a model of the solids referred to in his 

 questions, he would find that one or both of the slant faces of the 

 cuttings would be not planes but curved surfaces of some kind or 

 other, and, as these curved surfaces are not defined, the questions do 

 not admit of answers. 



