778 



NA TURE 



[June 17, 192: 



Further, it may be confidently anticipated that the 

 men of science and scientific institutions of the Czecho- 

 slovak republic will accomplish much in the way 

 of scientific advancement in the future, and con- 

 sequently will receive more adequate notice in 

 British journals than has hitherto been the case 

 (compare Prof. Brauner's own resume of " Science 

 in Bohemia " in Nature, May 13). 



Finally, many Russian authors now publish in 

 Czech journals and consequently use the Czech 

 transcriptions for their own names. 



J. G. F. Druce. 



May 24, 1922. 



Immediate Solution of Dynamical Problems. 



A DISCUSSION is submitted here in the manner 

 called elementary, where the theorems of the gravita- 

 tion of a sphere are proved for any portion of a 

 spherical surface, such as a bowl, before proceeding 

 to the result for a complete sphere (see letter by Prof. 

 Andrew Gray in Nature, May 20, p. 645). 



Consider the potential (Fig. i) at P, dVi , and attrac- 



tion to the centre, rfF, of a small element rfS at E, of the 

 surface of a sphere, centre C and radius QK — c, taken 

 of superficial density a, g/cm^, with G the gravitation 

 constant. Then 



rfU rfS . __ ^_ 



/- ""EP' with EP = CE cos (/i + CP cos 0, so that, 



with CP — y, and P' the inverse point to P in the 



sphere, CP' = r' = ^' , ^^ = :f^, (CE cos ^ + CP cos 0) 



V EP EP^ 

 _ d^ cos <p dS cos e ( CP _ EP^ \ 



~ EP^ EP^^ ^because CP'EP'^/ 



- CEd(>3 + CP'd(^' = cdu + r'du}' - cdw + -dw' , 



reckoning the solid angles rfw, rfw' subtended by (iS at 

 P, P' as positive when the aspect of the surface is the 

 concave side. 



Then by summation over any finite portion of the 

 spherical surface, 

 U 

 ^ =cw-fy'w, not restricted to the spherical bowl 



result in Maxwell's "Electricity and Magnetism." 



And for F, the radial component acting along PC 

 of the attraction at P, 



dY dS cos d CP' dS cos e _ r' c" F c" 

 -^^d.^^M. 



G<r 



EP'' 



CP EP' 



Go- y2" 



These two or three lines of geometry can thus re- 

 place some pages of analysis in Maxwell's " Electricity 

 and Magnetism." 



NO. 2746, VOL. 109] 



For a complete sphere, and P inside, w =47r, w' = o, 

 Q- = 47rc, F-o, and P outside, w = o, w'=:47r, ^-iprf' 



Atrc^ F 47rc^ 



V' G^~ y* ' ^ well-known theorems for a 



complete spherical shell, and thence for a solid sphere, 

 given first by Newton in the " Principia " (i, 41), and 

 of pioneering interest in justifying his theory of 

 gravitation for a body, like an apple, brought from 

 the moon down to the surface of the earth. 



A recent article by Florian Cajori, on Newton's 

 discover}^ of Gravitation, in the University of Cali- 

 fornia Chronicle, April 1922, is worth the attention 

 of Prof. Andrew Gray, in its bearing on his own 

 historical reflexions on the importance of the attraction 

 of a sphere in Newton's theory of universal gravity. 



The further theorem, that the mean potential over 

 the sphere of any body M outside the sphere is equal 

 to the potential of M at the centre, is obvious by 

 transferring an element of M at P to the other end 

 of the vector PE. Or if M is inside the sphere, the 

 mean potential over the surface is M/f . 



In hydrodynamical analogy, the flux across any 

 surface fixed in an incompressible liquid is the equi- 

 valent of liquid supplied to the interior from outside, 

 and so interpreting and justifying the theorem of 

 Gauss, between the surface integral of normal force 

 and the attracting body M, inside or outside. 



In this way the precept of Poinsot can be followed, 

 to examine the nature of things in themselves by 

 direct vision, and not through a mist of equations 

 and formulas. G. Greenhill. 



I Staple Inn, London, W.C.i, May 27. 



Arabic Chemistry. 



In a manuscript in my possession of the " Rutbatu '1- 

 Hakim " of Maslima ibn Muhammad Abu '1-Qasim 

 al-Majriti (f 1004 a.d.) the author claims to have 

 written the section on chemistry in the celebrated 

 " Letters " of the Ikhwanu's-Safa (Brethren of 

 Purity), the well-known Encyclopaedists of Islam in 

 the tenth century a.d. I believe this fact to have 

 been hitherto unknown, as it is not mentioned by 

 Dieterici or Brockelmann nor by Shahraziirl, all o^, 

 whom give as the names of the authors of thai 

 " Letters " only the following five : Abii Sulaiman 

 Muhammad ibn Na.sr al-Busti, Abu '1-Hasan 'Ali ibn 

 Harun az-Zinjanl, Abu Ahmad an-Nahrajiiri, al- 

 'Aufi and Zaid ibn Rifa'a. 



Maslima al-Majriti was an accomplished chemist, 

 and his work the " Rutbatu '1-HakIm " was mentioned 

 by Ibn Khaldijn in the " Prolegomena " to his 

 history. Although much of the " Rutba " is, as Ibn 

 Khaldun observes, very enigmatical, yet there are 

 certain passages in it of considerable historical 

 interest to chemists. Two of these I give below. 



1. "I took natural quivering mercury, free from 

 impurity, and placed it in a glass vessel shaped like 

 an egg. This I put inside another vessel like a 

 cooking-pot and set the whole apparatus over an 

 extremely gentle fire. The outer pot was then at 

 such a temperature that I could bear my hand upon 

 it. I heated the apparatus day and night for 40 days, 

 after which I opened it. I found that the mercury 

 (the original weight of which was \ lb.) had been 

 completely converted into a red powder, soft to the 

 touch, the weight remaining as it was originally." 



2. [On the refinement of gold and silver.] " Silver 

 alloyed with lead may be separated from the latter 

 by placing it in a cupel made from bones (called the 

 ' dog's head ' or commonly the kuraja ; it is a 

 crucible made from burnt bones) and fusing it by 

 means of a strong fire. The lead is removed and 

 absorbed by the cupel and the fire makes manifest 



I 



