TRANSACTIONS OF THE SECTIONS, 19 
them into rows and columns shall form a network such that the sum of the 
squares of all these joining lines shall be a minimum, the first and last points of 
the first and the last row being any four points given in space. The network may 
be regarded as a kind of extensible surface, each thread of which has a tension 
proportional in each segment to the length of the segment. 
The problem is thus expressed as a statical problem, but the direct solution 
would involve the consideration of a large number of unknown quantities. 
This number may be greatly reduced by means of the analogy between this 
problem and the electrical problem of determining the currents and potentials in 
the case of a network of wire having square meshes, one corner of the network 
being kept at unit potential while that of the other three corners is zero. 
This problem having been solved by Kirchhoff’s method, the position of any point 
P in the geometrical problem, with reference to the given points A, B, C, D, is deter- 
mined by finding the values of the potentials p , p,, py p, of the corresponding point 
in the electric problem when the corners a, b, c, d respectively are those of unit 
potential. f 
The position of P is then found by supposing masses p ,p,,?, Pp, placed at 
A, B, C, D respectively, and determining P as the centre of gravity of the four 
masses, 
On the Calculation of Exponential Functions. By Prof. F. W. Newman. 
This paper consisted of certain tables of e~*, with an account of the mthod of their 
construction, The author placed them at the disposal of the Committee on Mathe- 
matical Tables, that they might be used to supplement or verify the tables of e~* 
mentioned in the Committee’s Report (Brit. Assoc. Report, 1878, pp. 2 and 167). 
On Bitangents to the Surface of Centres of a Quadric. By Prof. F, Pursmr. 
On Multiple Contact of Quadrics and other Surfaces, 
By W. Srorriswoopz, M.4., PRS, 
—- 
Explanations of Mr. M‘Clintock’s Method of finding the Value of Life Annuities 
by means of the Gamma Function, By T. B, Spraeur, M.A, 
ASTRONOMY, 
Photographic Operations connected with the Transit of Venus. 
By Capt. Asnry, RL, PRAS., FOS, 
Tn this es an account was given by the author of the means adopted for 
insuring, at the different stations which would be occupied by the parties sent out 
to observe the transit of Venus, photographic observations of the phenomenon in 
question. It had been determined that at every station a photograph should be 
taken every two minutes during the transit, and it has been a matter of consider- 
able labour to work out a process that would admit of such a large number of 
negatives being taken in a hot climate. In Kerguelen’s Land it would be perfectly 
feasible to adopt the ordinary wet process, the low temperature admitting of it ; 
but in a temperature of 90° FY the evaporation of the volatile constituents of the 
collodion would render such a process inapplicable, as all photographers will 
admit. In India, where the author had worked, a large-sized tent had often 
proved injurious, and it would have been madness to have trusted to the wet 
method. It was therefore determined to use a dry process if practicable; and 
after much deliberation it was decided to employ an tongs dry process, using a 
