316 SECTIONAL TRANSACTIONS.— A. 



Mr. W. M. H. Greaves. — The Colour Temperature of Early Type Stars. 



The observational methods used in determining colour temperatures by measures 

 of the optical densities of photographed spectra are described briefly in this paper. 



CJ/. -C.2 



It is shown that by stellar observations alone the quantity i— m / ( (I— e X^T 



can be determined for each star where A; is a constant, T is the colour temperature, 

 C2 ( = 14320) is the well-known constant in Plunck's formula, and X„i (measured in 

 microns) is the mean wave-length of the spectral range used. The constant k can 

 only be determined by spectro-photometric comparisons of one or more stars with a 

 terrestrial source. 



The observations which have been obtained for early type stars give temperatures 

 which in many cases conflict with those predicted from the ionisation theory. Most 

 stars of type and many stars of types BO to B2 have colour- temperatures lower than 

 the average star of type AG, whereas the ionisation theory leads us to expect 

 considerably higher temperatures for the and B type stars. Two possible explana- 

 tions are suggested : viz. (I) a reddening of the star light by passage through an inter- 

 stellar cloud, and (2) considerably reduced pressures in the reversing layers. 



Dr. H. L. Alden. — Programme of the Yale Southern Station. 



Dr. Dorothy Wrinch. — Generalised Solutions of Laplace's Equation. 



A large class of problems in mathematical physics require for their solution the 

 construction of a function V which satisfies Laplace's equation 



V2V=0 



is evanescent on S the sphere at infinity, has no singularities between S and a certain 

 closed surface s, and on this surface takes a specified form. This general class 

 includes problems of electrostatics, such as the distribution of electricity on con- 

 ductors, both when they are freely charged and when electrification is due to an 

 external field of force and problems of hydrostatics, as for example when there is 

 streaming past an obstacle or when the surface in question has uniform translational 

 or rotational motion in an infinite fluid. 



In this paper the author explains a method of constructing a harmonic function 

 V to solve problems associated with surfaces of revolution s of various types. Pro- 

 blems associated with spheroids (already, of course, soluble in terms of spheroidal 

 harmonics) yield more easily to this technique, and problems associated with surfaces 

 of revolution whose generating curves are nodeless epicycUcs of retrograde type 

 given parametricaUy by 



x = a (cos u+ k cos 2m) a ^ ^ 1 

 y = a (sin u — k sin 2m) ^ ^ 2 



which range from the circle for k=o to the three-cusped hypo-cycloid for k=^ admit 

 simple treatment on these lines. 



The essential point of the method is that it allows the construction of harmonics 

 suitable for a large variety of surfaces of revolution. The author will give some 

 further examples of surfaces of revolution to which it is applicable. 



Mr. F. PuRYER WmiE.—Clebsch's Contact Problem. 



The problem deals with the configuration of the sets of ^—1 points upon an 

 algebraic curve of genus p which, each counted twice, make up a canonical set, and 

 which are thus the points of contact of the curve with a primal in the space con- 

 sidered. If the curve is the most general of its genus we may take it to be the 

 canonical curve of order 2^—2 in space of ^—1 dimensions; and the problem is 

 that of determining the (p—1)- tangent primes. The theory of the Riemann theta 

 function provides a certain amount of general information with regard to this case, 

 e.g. the number of such primes is 2i>-i (2/' — 1), but from the geometrical point of view 

 the only case which has been completely worked out is the first, p=3, the bitangents 

 of the plane quartic curve. 



