The four dimensional classification of globular dusters with the parameters, Z, Y, age and HB type is presented defining two new parameters. ( B − V ) 1 / 2 a n d S 3 / 2 which are shown to be tightly correlated with Kinman's spectral types and the helium abundances obtained from the R-method, respectively. The Z- and Y- abundances are derived from ( B − V ) 1 / 2 a n d S 3 / 2 , respectively, and the latter parameters determine the age class of clusters with help of Dickens' HB type, which is a function of Z. Y and age. For the examined forty two globular clusters the computed range at Z and Y are 1.5×10 -4 ≤ Z ≤ 4.5×10 -2 and 0.23 ≤ Y ≤ 0.41. The age difference between the oldest (HB type 1) and the youngest (HB type 7) clusters is roughly estimated to be 2 − 4 × 10 9 years. Using these four parameters the known anomalous C-M diagrams seem to be reasonably interpreted without taking into account some complicate parameters such as unusually overabundant heavy elements, mass loss and mass spread, etc. The four dimensional scheme strongly suggests the slow successive collapses of the proto-Galaxy rather than a single fast collapse, and by this slow collapse model the inversion of chemical abundance gradient in the Galaxy can be explained. It is also shown that the clump position along the RGB near the HB level removes down to the fainter magnitude as the Z(Y)- abundance increases (decreases).

To reduce the instrumental and calibration errors in the photoelectric photometry as much as possible it is necessary to select the optimum photocell voltage and energy attenaution and to observe as many standard stars as possible over the wide range of color, spectral type and air mass.

A hyperbolic orbit is expanded in terms of F analogous to the eccentric anomaly of an elliptical orbit: τ p s i n q υ a n d τ p c o s q υ are expressed in terms of F. The true anomaly υ is expressed in terms of F, and F in terms of υ .

The gain of internal energy of a star cluster caused by the tidal attraction of our Galaxy is examined. Expressions are derived which include the effects of a two-body orbit and internal motions of the cluster. These formulae are compared with previous results based on (i) uniform rectilinear motion and (ii) neglect of internal motions induced by cluster gravitation(i.e., impulsive approximation), and it is found that these simplifying assumptions generally introduce significant uncertainties.

On the instantaneous tidal relaxation approximation, formulae are derived for the ellipticities and virial theorem of a slightly flattened homogeneous rotating cluster (the largest axis of the cluster is directed towards the Galactic center), in terms of the Galactic tidal force and the characteristic intrinsic plus orbital angular velocity. The expression for a purely tidally-determined ellipticity is identical to that for an incompressible fluid body of uniform density. Orbital motion generally contributes significantly to the shape of the cluster. The virial theorem is identical to that for an isolated cluster except that the gravitational potential energy is multiplied by (1- χ ), where χ is a positive tidal correction term. To obtain the actual mass of a cluster, the virial theorem mass based on an isolated cluster should be multiplied by the factor 1/(1- χ ). The formulae are applied to open star clusters, the globular cluster ω Centauri, and dwarf elliptical galaxies in the Local Group.