TRANSACTIONS OF THE SECTIONS. 5 



vrliere 



I F(p, y)= ^i^Ly). i>(p,y)=(f(p,yyp (4«) 



Botli formulse are of use in the integral calculus. 



Proof of the Binomial Theorem. By the late Ja^ies Lindsay. 

 Communicated by W. B. Geant. 



On the Approximate Drawing of Circular Arcs of given lengths. 

 By Professor W, J. Macqtjorn Raxkine, LL.D., F.B.S. 



This paper contains rules for use in meclianical drawing', founded on the prin- 

 ciple, that if a straight line and an indefinite number of circles in one plane touch 

 each other at one point, the curve which cuts oif parts of a given uniform length 

 from the straiglit tangent and from all the circles, approximates, in the neighbour- 

 hood of the place where it cuts the straight tangent, very closely to a circular arc 

 "whose radius is three-fourths of the given uniform length. The arcs laid otf 

 according to the rules are somewhat longer than the exact length ; but in an arc 

 subtending 3CF the error is only tts o^ P^i"'' o^ ^^^ length of the arc ; and it varies 

 nearly as the fourth power of the angle subtended by the arc. 



ASTROSOMT. 



Preparations for Observing the Total Solar Eclipse of August 18, 1868. 

 By Major J. F. TexXxaxt, R.E., F.B.A.S., F.R.G.S., F.M.S. 



In January last I drew the attention of the Royal Astronomical Society to the 

 Total Eclipse of 1868, August 18, which will be visible in India, and in the March 

 Number of the ' Notices' of the Society will be found a paper in which I proposed 

 that the Government of India should be solicited to make arrangements for maldng 

 use of this very favourable opportunity for examining the prominences. 



I am happy to say that, at the suggestion of tlie Astronomer Royal, the Secretary 

 of State for India has sanctioned the preparation of an ec[uipment, and I propose in 

 this note to mention what is in progress. 



First. It is intended to photogi-aph the appearances of the total phase. For 

 this purpose a 9 j-inch " silver-on-glass" reflector, equatoiially mounted and driven 

 by clockwork, is being prepared. The photographs will be taken in the focus of 

 the speculum, and it is estimated that the exposure to produce an image of the 

 prominences will not exceed half a second. Provision is being made for a consi- 

 derable field, in order that, if possible, some record may be obtained of the struc- 

 ture of the corona. 



Secondly. It is proposed to examine, as well as may be, the spectra of the pro- 

 minences and corona. For this, one of the old collimators of the Greenwich Transit 

 Circle has been kindly lent by the Astronomer Royal. It is being equatorially 

 mounted in a rough way, and Avill be provided with a spectroscope permitting the 

 observations to be referred to the lines of the solar spectrum. 



Lastly. The Astronomer Royal has lent a -ii-iuch telescope, moimted firmly, to 

 which is being adapted an ej'epiece for examining the state of polarization of the 

 lights of the prominences and corona. An an-augemeut is being made by which 

 one test may be rapidly changed for another, and it is hoped that in this way a 

 more satisfactory result will be obtained than by any single test. 



1 trust that all the instruments will be in India early in next year, and that they 

 will be in position in time to allow experiments to be made, so as to secure tho 

 success of the photogi-aphic operations. 



