304 Intelligence and Miscellaneous Articles. 



remainder in Lagrange's series in the form of a definite integral. 

 This result, which seems to be due to M. Popoff, is given here in 

 the way in which it is demonstrated by M. Zolotareff. The next 

 point to which we would call attention is in connexion with the 

 interesting subject of the areas of roulettes, to the study of which 

 Steiner has contributed so many beautiful results. The additions 

 are to what is now well known as Holditch's theorem, first pub- 

 lished in the 'Lady's and Gentlemen's Diary 'for 1858, in the 

 appendix to which volume an elegant extension of the theorem 

 was given by the Editor, Mr. Woolhouse. For the substance of 

 the recent extension our author is again indebted to Mr. E. B. 

 Elliott, whose paper appeared in the ' Messenger of Mathematics ' 

 for February 1878. This paper was fruitful in results, as it 

 suggested further extensions by Mr. Leudesdorf and Mr. Kempe. 

 In our text we have Kempe's "singularly elegant" theorem; 

 but it strikes us that full justice has hardly been done to Mr. 

 Kempe, or a part only of his results is given; this oversight 

 can easily be remedied, should the author see fit, in his next issue*. 

 The whole subject is just now occupying attention : we have 

 noted a paper by M. Darboux in the Bulletin des Scieiices Mathema- 

 tiques et Astronomiques, and some short notes by Prof. Minchin. 

 This latter gentlemen, we believe, is preparing an extended paper on 

 the subject of roulettes ; and Mr. Elliott is prosecuting his researches 

 in the direction of kinematics on a sphere. But we have exceeded 

 our limits, and must refrain from referring to the additions in the 

 last two chapters. Mr. Williamson still excludes the " change of 

 the variables in a multiple integral ;" perhaps in a future edition he 

 may say something upon this matter, and bring forward to notice 

 the method employed by Mr. McColl (cf . his paper on the " Calculus 

 of Equivalent Statements and Integration Limits," in the Proceedings 

 of the London Mathematical Society, No. 124, and questions in the 

 ' Educational Times '). The admirable manner in which the more 

 ordinary parts of the subject, and notably the chapters on the geo- 

 metrical applications, are handled thoroughly merits the approbation 

 it has received ; and we take our leave of Mr. Williamson, wishing 

 his work bon voyage and himself " more power " still to write his 

 promised (if we mistake not) treatise on Differential Equations. 



XLIV. Intelligence and Miscellaneous Articles. 



ON STEADY MOTION IN AN INCOMPRESSIBLE VISCOUS FLUID. 



To the Editors of the Philosophical Magazine and Journal. 



U.S. Coast and Geodetic Survev Office, 

 Gentlemen, Washington, Feb. 15, 1881. 



IFIXD today in the February number of the Philosophical Maga- 

 zine a letter from Dr. A. Oberbeck, of Halle, on the subject of 

 my paper published in the November number of the Magazine, 

 * Cf < Nature,' vol. xviii. p. 148, June 6th, 1878. 



