224 Messrs. W. K. Dunstan and T. A. Henry. 



(c.) The solution of the problem in both the cases of long shafts and 

 short axles depends upon the discovery of a series of discon- 

 tinuous functions. These functions would appear to have con- 

 siderable interest for the mathematician. Like functions first 

 appear, I think, in a paper by Boussinesq,* and they offer ;in 

 alternative to the usual solution of problems in vibration by 

 Fourier's series. The latter in such cases often give easy ana- 

 lytical expressions, which, however, may be almost useless for 

 the purposes of numerical calculation owing to the slowness 

 of their convergence. In the course of the paper the numerical 

 solution by the use of discontinuous functions, is compared 

 for one case with the solution obtained by a Fourier's series. 

 A verification of the work is thus obtained, and the advantages 

 of the novel functions illustrated. 



(d.) There are many points in the memoir which suggest possibilities 

 for physical research, and it seems to me that both from the 

 purely scientific and the engineering sides a well-devised 

 series of experiments on continuously and on abruptly varying 

 torsional loads would lead to results of much interest and 

 practical value. 



The memoir endeavours to complete as fully for torsional loading the 

 theory of a changing load as the latter has been completed for longi- 

 tudinal and transverse loading by de Saint- Venant, Boussinesq, and 

 Flammant. The methods, analytical and graphical, are analogous, but 

 the whole of the results, algebraic and mimerical, are, I believe, novel, 

 and apply to a series of cases which, if possible, have even greater 

 practical importance. 



" The Nature and Origin of the Poison of Lotus Arabiais. Pre- 

 liminary Notice." By WYNDHAM R. DUNSTAN, M.A., F.R.S., 

 Sec.C.S., Director of the Scientific Department of the Im- 

 perial Institute, and T. A. HENRY, B.Sc. Lond., Salters' 

 Company's Kesearch Fellow. Received June 7 Head June 

 14, 1900. 



IjOtus Arabicus is a small leguminous plant resembling a vetch, with 

 pink flowers, indigenous to Egypt and Northern Africa. It grows 

 aliundantly in Nubia and is especially noticeable in the bed of the Nile 

 from Luxor to Wady Haifa. It is known to the natives ;is " Kh.mb.er," 

 and old plants with ripe seed are used as fodder. The dried plant is 

 unusually green, and possesses the aroma of new-mown hay. At 



See ' History of Elasticity ' vol. 2, arts. 401, 402. 



