The iso-MAC charts show clearly how patient age can be used to guide the choice of end-expired agent concentration. They also allow a consistent total MAC to be maintained when changing the inspired nitrous oxide concentration, thereby reducing the chance of inadvertent awareness, particularly at the extremes of age.

The cubic holds a double fascination, since not only is it interesting in its own right, but its solution is also the key to solving quartics. This article describes five fundamental parameters of the cubic (δ, λ, h, xN, and yN), and shows how they lead to a significant modification of the standard method of solving a cubic, generally known as Cardan’s solution.

An appreciation of the geometry underlying algebraic techniques invariably enhances understanding, and this is particularly true with regard to polynomials. With visualisation as our theme, this article considers the cubic equation and describes how the French mathematicians François Viète (1540–1603) and René Descartes (1596–1650) related the ‘three-real-roots’ case (casus irreducibilis) to circle geometry. In particular, attention is focused on a previously undescribed aspect, namely, how the lengths of the chords constructed by Viète and Descartes in this setting relate geometrically to the curve of the cubic itself.

The central role of the resolvent cubic in the solution of the quartic was first appreciated by Leonard Euler (1707-1783). Euler's quartic solution first appeared as a brief section (§ 5) in a paper on roots of equations [1, 2], and was later expanded into a chapter entitled ‘Of a new method of resolving equations of the fourth degree’ (§§ 773-783) in his Elements of algebra [3,4].

SummaryA new percutaneous infraclavicular approach for rannulating the axillary vein is described. The technique was devised using surface landmarks established by cadaver dissection. This is a relatively safe procedure with no risk of pneumothorax, provided that the tip of the needle remains inferior to the clavicle. Key wordsVeins; cannulation.Direct percutaneous cannulation of the large central veins is most commonly achieved using either the internal jugular or the subclavian vein.' However, these techniques are not without hazard. Indeed, in view of the proximity of the thoracic inlet, these two routes probably have the most potential for serious acute complicat i o n~, ' -~ particularly pneumothorax and haemothorax. While a pneumothordx can be effectively treated by inserting a chest drain, a vascular laceration (artery or vein) sufficient to cause a haemothorax usually requires surgical exploration.Thc more distal axillary approach to the axillary vein avoids these particular complications, although thcrc is a risk of damaging the medial cutaneous nerve of the arm, since this nerve lies immediately medial to the vein in the axilla.1° Access to the central veins via the external jugular vein is sufficiently unreliable for it not to be considered a route of first choice, although it is being increasingly used surgically for tunnelled Hickman catheters,14 as well as for central venous pressure monitoring.'5 There are also complications with this approach. 16,17 Access via the femoral vein is complicated by the potential for thrombo-embolism and therefore only tends to be used when the usual central venous access routes are particularly difficult. The basilic vein can only be used with long narrow cathctcrs, which are sometimcs vcry difficult to thread centrally.There are, therefore. sufficient problems associated with the commonly used routes for cannulation of thc large central veins, to stimulate a continued search for safer routes of access. One approach is to consider different ways of using existing routes; for example, the 'half-way' catheter concept,18-2' whereby a pcriphcral arm-catheter is advanced only as far as the axillary vein. Although not suitable for central venous pressure monitoring, such a technique is satisfactory for intravenous feeding. Alternatively, new routes of access can be sought. To this end, the infraclavicular region was explored in the dissecting room (adult female cadaver) with a vicw to establishing suitable surfacc landmarks to facilitate an infraclavicular approach to the axillary vein. AnatomyThe axillary vein is the continuation of the basilic vein and extends from the lower border of teres major to the outer border of the first rib. where it continues as the subclavian vein (Fig. 1). The axillary vein is crossed immediately anteriorly by pcctoralis minor, which divides the vein topographically into three parts. namely proxirnal. posterior and distal to pectoralis minor.2' The medial border of pectoralis minor extends from the coracoid process along a line roughly a...