IMPROVED CURSORS.—In some slide-rule operations, notably in those involved in solving quadratic and cubic equations, it not infrequently happens that readings are obscured by the frame of the cursor. Frameless cursors have been introduced to obviate this defect. A piece of thick transparent celluloid is sometimes employed, but this is liable to become scratched in use. Fig. 37 shows a recent form of frameless glass cursor made by the Keuffel & Esser Company, Hoboken, N.J., which is satisfactory in every way. Cursors having three hair lines are now fitted to some rules, the distance apart of the lines being equal to the interval 0·7854–1 on the A scale. THE DAVIS-PLETTS SLIDE RULE.—In this rule a single log.-log. scale and its reciprocal scale are arranged opposite the ordinary upper log. scale. Thus, common logarithms can be read directly, while by taking advantage of the properties of characteristics and mantissas of common logarithms, the scale can be extended indefinitely. As 10 is the highest number on the log.-log. scale, it is carried down to within 0·025 of unity. The reading of log.-log. values above 10 is effected in a very simple manner. There is also a scale in the centre of the slide which, used in conjunction with the upper log. scale enables the natural logarithm of any number between 0·0001 and 10,000 to be read direct, while any number on the upper log. scale can be multiplied or divided by _e^x_ if the latter is between these limits. On the back of the slide are scales for all circular and hyperbolic functions, these being used in conjunction with the upper log. scales. THE CROMPTON-GALLAGHER BOILER EFFICIENCY CALCULATOR has a stock in the thickness of which is a slot admitting a chart which can be moved at right angles to the two separate slides. On the bevelled edge of one slide, the graduations are continued so as to read against curves on the chart, through an opening in the stock. THE DAVIS-GRINSTED COMPLEX CALCULATOR.—This slide rule is of considerable service in connection with calculations involving the conversion of complex quantities from the form _a_ + _j_ _b_ to the form R∠θ, and _vice versa_. The usual process of conversion necessitates repeated reference to trigonometrical tables, and is both tedious and time-taking. The Complex Calculator enables the conversions to be effected without reference to tables and with the minimum expenditure of time and labour. The rule, which is about 16 in. long, has five scales. The upper one (A) is an ordinary logarithmic scale thrice-repeated. The adjacent scales on the slide comprise (1) a logarithmic scale of tangents (B) ranging from 0·1° to 45°, and (2) a logarithmic scale of secants (C) from 0° to 45°. The lower scales D and E are identical with the A scale, and are provided to enable multiplication, etc., to be performed without the need for a separate slide rule. Readings can be transferred from A to the lower scales by means of the cursor.