## Transactions of the Cambridge Philosophical Society.. |

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### Common terms and phrases

A₁ angle arbitrary functions B₁ b₂ bodily forces circles touching circumspheres coefficients concyclic concyclic points corresponding cos kt cos² denote derived differential equations displacements equilibrium expression five formula four circles given H₁ harmonics Hart tetrads Hence hyperspheres intermediary integral intersection inverse tetrad k²pa² L₁ Latin Squares latitude line geometry linear complex magnitude meet multiples notation obtain operators P₁ P₂ partial differential equations permutations planes Prop PROPOSITION prove radial ratio Rectangles respectively result satisfied scale sin e sin² sin³ solution surface forces symmetric function tangential tetrad of circles tetrahedron theorem U-conics u₁ u₁y U₂ V₁ values vanish vibrations w₁ X₁ y₁ zero αλ απ ӘА ди ди дх

### Popular passages

Page 99 - ... a, b' and b, c' and c, d' and d' are the exterior-interior or corresponding angles.

Page 66 - ... 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 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 15 - ... 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 261 - ... different letters appearing in each row and in each column. He and subsequent writers have called such squares " Latin Squares," and we have the question as to their enumeration for a given order. In regard to this matter he writes...

Page 236 - It is required to prove that if A, B, C, D are four magnitudes of the same kind, and if (A :B) = (C: D), and if A > C, then (AC:BD) = (A :B).

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...