72 Royal Society : — 



equal," it would surely have been more profitable to have enume- 

 rated the several axioms which Euclid tacitly assumes. Instead of 

 showing, in a very questionable manner too, how the 11th and 12th 

 propositions of the third book might have been proved directly had 

 they been placed after the 18th proposition, would it not have been 

 better to have proposed a rearrangement of the whole book — to 

 have given a sketch, in fact, of a better treatment of the many beau- 

 tiful properties of the circle ? 



The collection of geometrical exercises given by Mr. Potts is an- 

 other characteristic feature of his work, and has also been improved. 

 In order to give to exercises their full value, however, and to prevent 

 them from degenerating into mere riddles, they should be made sub- 

 ordinate to, and illustrative of geometrical methods-, and this, it 

 must be admitted, Mr. Potts has not been able to do fully, since, for 

 other and good reasons, he has preferred selecting his exercises from 

 college and university examination-papers. Comparing his selections 

 with others, however, we cannot but agree with the Reviewer whom 

 Mr. Potts himself quotes in his preface. With respect to the first 

 of the exercises " on tangencies," we will merely caution the student 

 against accepting the author's analysis, either as a model for imitation 

 or as a specimen of Mr. Potts' ability ; it is unusually defective. 

 The very enunciation of the problem is objectionable, disfigured as 

 it is by the introduction of the perfectly irrelevant datum " of a line 

 given in position." 



We do not care to dwell longer upon imperfections w T hich, if not 

 trivial, are certainly far outweighed in importance by the many 

 excellent features of the book. We will merely repeat, then, that 

 although we trust the work, considered as an introduction to the 

 science of geometry, will some day be superseded, we are convinced 

 that as a carefulEnglish reproduction of Euclid's Elements, illustrated 

 by the notes of an able and judicious teacher, and enriched by a 

 large collection of very useful exercises, it will long maintain its 

 ground. 



XL Proceedings of Learned Societies. 



ROYAL SOCIETY. 

 [Continued from vol. xxii.] 

 April 11, 1861. — Major-General Sabine, R.A., Treasurer and Vice- 

 President, in the Chair 

 THE following communication was read : — 

 " On the Motion of a Plate of Metal on an Inclined Plane, when 

 dilated and contracted ; and on the Descent of Glaciers." Bv the 

 Rev. Henry Mosely, M.A., Canon of Bristol, F.R.S., Inst. Sc. Paris 

 Corresp. 



The case in which the upper edge of such a plate (supposed rec- 

 tangular) is fixed is first discussed ; and then that in which the lower 

 edge is fixed. Each of these cases is considered subject to the con- 

 dition of friction ; first, when the plate is dilated, and secondly, when 



