n/[pi])[theta].x.

Hence our instrument draws a curve which gives the integral (1) in the form

y = 2/[pi] [Integral,0:[pi]] f(x)cos((n/[pi])[theta]x) dx

as a function of [theta]. But this integral becomes the coefficient a_m in
the cosine expansion if we make

[theta]n/[pi] = m or [theta] = m[pi]/n.

The ordinates of the curve at the values [theta] = [pi]/n, 2[pi]/n, ...
give therefore all coefficients up to m = 80. The curve shows at a glance
which and how many of the coefficients are of importance.

The instrument is described in _Phil. Mag._, vol. xlv., 1898. A number of
curves drawn by it are given, and also examples of the analysis of curves
for which the coefficients a_m are known. These indicate that a remarkable
accuracy is obtained.

(O. H.)

[1] For a fuller description of the manner in which a mere addition machine
can be used for multiplication and division, and even for the extraction of
square roots, see an article by C.V. Boys in _Nature_, 11th July 1901.

CALCUTTA, the capital of British India and also of the province of Bengal.
It is situated in 22 deg. 34' N. and 88 deg. 24' E., on the left or east bank of
the Hugli, about 80 m. from the sea. Including its suburbs it covers an
area of 27,267 acres, and contains a population (1901) of 949,144. Calcutta
and Bombay have long contested the position of the premier city of India in
population and trade; but during the decade 1891-1901 the prevalence of
plague in Bombay gave a considerable advantage to Calcutta, which was
comparatively free from that disease. Calcutta lies only some 20 ft. above
sea-level, and extends about 6 m. along the Hugli, and is bounded elsewhere
by the Circular Canal and the Salt Lakes, and by suburbs which form
separate municipalities. Fort William stands in its centre.

_Public Buildings._--Though Calcutta was called by Macaulay "the city of
palaces," its modern public buildings cannot compare with those of Bombay.
Its chief glory is the Maidan or park, which is large enough to embrace the
area of Fort William and a racecourse. Many monuments find a place on the
Maidan, among them being modern equestrian statues of Lord Roberts and Lord
Lansdowne, which face one another on each side of the Red Road, where the
rank and [v.04 p.0982] fashion of Calcutta take their evening drive. In the
north-eastern corner of the Maidan the Indian memorial to Queen Victoria,
consisting of a marble hall, with a statue and historical re