The purpose of the essay is to show the advantages of hyperbolic functions in restricted relat:ivity. Based on the work of Fontend and others, the author has further developed the use of rapidities in place of velocities and has introduced festinations in place of accelerations. A simple universa1 distortion factor is deduced in hyperbolic notation, and symmetrical expressions are derived for mechanica1 force, momentum, and energy. The theories of aberration of light and of Fizeau's experiment are used further to demonstrate the advantages of hyperbolic functions in relativity. The invariance of Maxwell's equations for the two observers in relative motion is proved in two different and independent ways: (a) by the method of paired functions, and (b) by using divergence and curl in a semihyperbolic four-dimensiona1 space. A list of references to books on restricted relativity and to the author's previous contributions on the subject is appended.* Reference 12, p. 63.

OF PAPER A condenser is charged from a source of direct voltage. and then is used as a booster in series with this source to charge another condenser. By repeating this process a large number of times the second condenser is finally subjected to twice the voltage of the source. This is the principle of the Delon apparatus for testing cables, and is explained in a numerical example. Then the more general case of two or more "pre-charged" condensers in series is considered, when these condensers are connected to some source of direct voltage; it is shown how to determine the final distribution of voltages among them. A similar problem is solved for pre-charged condensers in parallel. Final]y a general network of pre-charged condensers is considered, and equations are derived similar to Kirchoff's laws, from which the final distribution of voltages and charges may be computed knowing the initial distribution.IN A paper presented before the Institution of Electrical Engineers (British) in February 1916, Mr. 0. L. Record described Delon's apparatus for testing the insulation of a high-tension cable.' While endeavoring to make clear to himself the theory of this ingenious device the present writer has investigated in general the action of a pre-charged condenser used as a booster in series with some source of e.m.f. for charging another condenser. This led him further to deduce the equations of a general network of such condensers. Before giving these more general relationships it is of interest to explain the principle of Delon's apparatus in a simple numerical example.The diagram of connections is shown in Fig. 1, in which C is a two-conductor cable under test, T is the testing transformer, R is a synchronous revolving rectifier arm, and C1, C2 are two "booster" condensers. The theory of the apparatus, confirmed by actual experience, shows that the cable is subjected to a continuous voltage which is numerically equal to twice the ampli-1. Journal Inst.

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