600 
NATURE 
[April 26, 1883 
On Differential Resolvents (vol. vi. 1863). A subject first 
brought into notice by Mr. J. Cockle, subsequently dis- 
cussed by Rey. R. Harley. The functions considered are 
derived from equations in a factorial form; see also 
Manch. Phil. Soc. Memoirs, ii. 1865. [In the R. S. 
Catalogue these are also numbered (33)]. (37) Note 
on the Contact of Curves (vol. vii. 1866). “In my 
former paper” (P/z/. Trans. 1862, see infra) “one 
set of expressions is unsymmetrical with respect to the 
variables; the other, although symmetrical, involves 
certain arbitrary quantities which remain to be eliminated 
by special methods in the course of the developments ’’— 
the object of the note is to establish general expressions 
which are both symmetrical and free from arbitrary 
quantities. (38) Note on the Resolution of a Ternary 
Cubic into Linear Factors (7. 1866) is in effect a note on 
a paper by Mr. J. J. Walker in the previous volume, 
entitled “ Un the Resolution of Composite Quantities into 
Linear Factors.” 
Crelle’s Journal—(5) Mémoires sur les points singu- 
liers d’une courbe a double courbure (vol. xlii. 1852). (6) 
Mémoire sur quelques formules relatives aux surfaces du 
second ordre (zd, 1852). (12) Correspondence between 
Prof. Donkin and Mr. Spottiswoode (vol. xlvii. 1854) ; 
extracts from letters (one from each) on a Method for 
Determining Two Cyclic Sections of a Surface of the 
Second Order. (14) The Memoir on Determinants (vol 
li. 1856). (25) Sur quelques formules générales dans 
le calcul des opérations (vol. lix. 1861), connected with 
a Phil. Trans. paper (17). In this he shows the method 
by which he obtained the formule in (17). (32) Note 
sur la transformation de la cubique temaire en sa forme 
canonique (vol. lxiii. 1864). 
Tortolint Annali di Scienze.—(8) Sulla trasformazione 
delle equazioni differenziali lineari dell’ ordine secondo 
(vol. iii. 1852). 
R. Soc. Proci—(13) Researches on the Theory of In- 
variants (vol. vii. 1854). ‘‘The view of invariants here 
taken has suggested a series of other functions of which 
invariants form the last term. These functions I propose 
to call variants. With the exact relation between these 
functions and covariants I am not at present acquainted.” 
(17) On an Extended Form of the Index Symbol in the 
Calculus of Operations (vol. x. 1859, PAz/. Trans. 1860). 
A more detailed form of (9). (20) On the Calculus of 
Functions (vol. xi. 1861). (21) On Internal and External 
Division in the Calculus of Symbols (z4.). Connected 
with a paper by Mr. W. H.L. Russell (P/z/. Trams. 1861), 
a generalisation and an extension. (30) On the Equations 
of Rotation of a Solid Body about a Fixed Point (vol. 
xiii. 1863). In treating the equations of rotation of a 
solid body about a fixed point it is usual to employ prin- 
cipal axes of the body as the moving system of co- 
ordinates. Cases, however, occur in which it is advisable 
to employ other systems. The object of the paper is to 
develop the fundamental formule of transformation and 
integration for any system. [This is also given as (34) in 
the &. S. Caz]. (35) On the Sextactic Points of a Plane 
Curve (vol. xiv. 1865 ; Phz/. Trans. 1865). (40) On the 
Contact of Conics with Surfaces (vol. xviii. 1870; Pz? 
Trans. 1870). (43) On the Contact of Surfaces (vol. xx. 
1872 ; Phil. Trans. 1872). (45) On the Rings Produced 
by Crystals when Submitted to Circularly Polarised Light 
(vol. xx. 1872); 1874 (2) On Combinations of Colour by 
Polarised Light; 1874-5 (6) On Stratified Discharges 
through Rarefied Gases ; 1875-6 (c) On Multiple Contact 
of Surfaces; (@) An Experiment in Electromagnetic 
Rotation ; 1876-7 (e) On Stratified Discharges (ii.) ; Ob- 
servations with a Revolving Mirror (iii.) ; (7) Ona Rapid 
Contact Breaker and the Phenomena of the Flow; 
1877 (g) On Hyperjacobian Surfaces and Curves; (/) 
Stratified Discharges (iv.): Stratified and Unstratified 
_* When there is a paper in the PAi?, Trans. as well, the reference is also 
given under this head. 
by Crystals submitted to Circularly Polarised Light (vol. 
Forms of the Jar-Discharge; (7) Photographic Image of 
the Stratified Discharge; 1878 (7) Stratified Discharge 
(v.); Discharge from a Condenser of Large Capacity ; 
1879 (£) On the Sensitive State of Electrical Discharges 
through Rarefied Gases [with J. F. Moulton], PAz/. Trans. > 
1879-80 (7) On some of the Effects Produced by an In- 
duction Coil with a De Meriten’s Magneto Electric 
Machine ; (vz) On the Sensitive State (ii.) (with J. F. M.), 
Phil. Trans. ,; 1880-1 (#) On the 48 Coordinates of a 
Cubic Curve in Space (Phz/. Trams.) ; 1881 (0) On Strati- 
fied Discharges (vi.), Shadows of Striz (with J. F. M.); 
and (#) Multiple Radiations from Negative Terminal ; 
1881-2 (g) Note on Mr. Russell's Paper on Definite In- 
tegrals ; (7) Note on Mr. Russell’s Paper on Certain 
Geometrical Theorems ; (s) On the Movement of Gas in 
Vacuum Discharges (with J. F. M.)2 
R. Asiatic Soc. Journal—(18) Note on the supposed 
Discovery of the Principle of the Differential Calculus by — 
an Indian Astronomer Gol: xvii. 1860). While not grant- 
ing that Bhéskardcharya had discovered the principle, “it 
must be admitted that the penetration shown by him in 
his analysis is in the highest degree remarkable, and that 
the formula which he establishes and his method of esta- 
blishing it bear more than a mere resemblance—they ~ 
bear a strong analogy—to the corresponding process in 
modern astronomy.”’ (28) On the “Stirya Siddhdnta ” and 
the Hindoo Method of calculating Eclipses (vol. xx. 
1863). It had been suggested that Mr. Spottiswoode 
should undertake an edition of the above work. For 
reasons stated, the attempt was not made; but the object 
of this paper is the translation into modern mathematical 
language and formule of the rules of the work in 
question. 
Rk. Geog. Soc. Proc—i19) On Typical Mountain 
Ranges : an application of the Calculus of Probability to 
Physical Geography (vol. iv. 1861 ; Journal, vol. xxxi. 
1861). 
peta Soc. Memoirs.—(22) On a Method for de- 
termining Longitude by Means of Observations on the 
Moon’s greatest Altitude (vol. xxix. 1861; also in Geog. 
Soc. Proc. vol. v. 1861). 
British Assoc. Report—(24) On the Reduction of the 
Decadic Binary Quantic to its Canonical Form (1861, 
part 2); (36) Address to Section A (1865); (a) Address 
to the Association (1878). 
Phil. Trans.—(26) On the Contact of Curves (1862) ; 
(27) On the Calculus of Symbols (1862); 1874 (a) On the 
Contact of Quadrics with other Surfaces. See also above 
under 2. Soc. Proc. | 
Comptes Rendus.—(39) Note sur V équilibre des forces — 
dans l’espace (vol. Ixvi. 1868); (48) Note sur la repré-_ 
sentation alyébrique des lignes droites dans l’espace 
(vol. Ixxvi. 1873); (49) Sur les plans tangents triples a 
une surface (vol, Ixxvii. 1873) ; 1874 (a) Sur les surfaces | 
osculatrices ; 1875 (4) Sur la représentation des figures 
de géométrie & #z dimensions par les figures corréla- 
tives de géométrie ordinaire; 1876 (c) Sur le contact 
dune courbe avec un faisceau de courbes doublement 
infini. | 
R. Inst. Proc.—(44) On Optical Phenomena produced 
a 
vii. 1872. See also Phil. Mag. vol. xliv. 1872); (46) On 
the Old and New Laboratories at the Royal Institution 
(vol. vii. 1873) ; (47) On Spectra of Polarised Light (20. | 
1873) ; 1574 (2) On Combinations of Colour by Polarised 
Light ; 1878 (6) A Nocturne in Black and Yellow ; (c) 
Quartz: an old chapter rewritten; 1880 (¢) Electricity in 
Transitu; 1882 (e) Matter and Magnetoelectric Action. 
Musical Society Proc.—1879 (a) Lecture on Beats and 
Combination Tones. | 
Royal Society.—Presidential Addresses for the Years _ 
1879, 1880, 1881, 1882. | 
* For analyses of the papers on ‘‘Sensitive Discharges,” &c., consult — 
vol. ii. of ‘‘A Physical Treatise on Electricity and Magnetism,”’ by J. E. H. 
Gordon, 1880 (see pp. 47-50, 71-81, 88-111). 
