Transactions of the Cambridge Philosophical Society, Volume 16University Press, 1898 - Philosophy |
Other editions - View all
Common terms and phrases
a₁ A₂ aa aa abcd algebraically independent angles arbitrary functions B₁ b₂ circles touching circumspheres coefficients concyclic concyclic points conics constants corresponding cos² cosec denote derived differential equation displacements expression five four circles four spheres geometry given Hart tetrads Hence hyperspheres intermediary integral intersection inverse tetrad Latin Squares latitude line geometry linear complex magnitude meet multiples notation obtain operators orthogonal P₁ pairs partial differential equations permutations planes Prop PROPOSITION prove radial ratio respectively result satisfied scale sets of four sin² solution supplementary angle surface forces symmetric function tetrad of circles tetrahedron theorem U-conics u₁ u₁y U₂ V₁ values vanish X₁ y₁ απ аф ӘА ӘФ ди ди дх
Popular passages
Page 64 - ... surface varies as the cosine of the angle between the normal to the surface and the direction of the radiation.
Page 232 - ... a therefore and b are not unequal ; that is, they are equaL. Next, let c have the same ratio to each of the magnitudes a and b ) a is equal to b. For, if they are not, one of them is greater than the other ; let a be the greater ; therefore as was shewn in Prop.
Page 56 - The object of this paper is to express in the form of an harmonic series the amount of heat due to the earth in any latitude, or for a zone of any extent , from solar radiation at any period of the year. In the main...
Page 249 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 13 - ... 14, p. 308, and applies them to two classes of cases in which results of a general character are obtainable, the first class consisting of the vibrations of a solid sphere due to forces whose frequency is small compared to that of the fundamental free vibration of the same type , the second class of the forced vibrations of any frequency in a very thin spherical shell (p. 14 — 57). U 10 a. R.
Page 152 - ... spheres with 8 points on every sphere and 5 spheres through every point. Grace went on to show that starting from six spheres through a point we obtain a figure of 72 points and 27 spheres; and starting from seven spheres through a point we obtained a figure of 576 points and 126 spheres; and he remarks: 'Similar sets of points probably exist in which there are eight, nine . . . spheres through each point, but as the number of points increases the difficulties as to notation become very great.
Page 249 - ... required. Again, if we wish to find the ratio of two solids, A and B, we seek some unit of measure which is contained an exact number of times in each of them. If we take a cubic inch as the unit of measure, and we find it to be contained 9 times in A, and 13 times in B, then the ratio of A to B is the same as that of 9 to 13.
Page 317 - Laplace's equation, and equat-ing to zero the coefficients of the various powers of x, y...
Page 260 - Magiques." He commences as follows : " Une question fort curieuse qui a exercé pendant quelque temps la sagacité de bien du monde, m'a engagé à faire les recherches suivantes, qui semblent ouvrir une nouvelle carrière dans l'Analyse et en particulier dans la doctrine des combinaisons. Cette question rouloit sur une assemblée de 36 officiers de six différens grades et tirés de six...
Page 263 - 2 + n — 2 relations between the coaxial minors of any determinant of the «th order (A certain class of generating functions in the theory of numbers, Phil. Trans., Vol. CLXXXV, p. 111 — 160). The relations are put in evidence for a particular determinant (p. 537—541). T 4 a , U 10. EP CULVERWELL. A Mode of Calculating a Limit to the Direct Effect of Great Eccentricity of the Earth's Orbit on Terrestrial Temperatures , showing the Inadequacy of the Astronomical...