PACE (Passus), a measure of the Roman system, being in fact their unit of itinerary measure, to which the mille passus, or Mile, was referred. The word passus is connected with the root of pandere, to extend, and Paucton curiously enough derives it d passis manibus, from the length between the extended hands, instead of a passis pedibus. There is however reason to believe that the mille passus came into use from the practice of measuring distances in new countries from the number of paces marched by the soldiery, of which a rough reckoning was kept, but whether by actually counting the paces, or by the time of marching compared with the previously known number of paces in a given time, is not known. It is well known that with disciplined soldiers either method would give very good practical results. Vitruvius describes a machine to be fastened to the wheel of a chariot (an invention revived in our own day), by which its number of revolutions was registered; but this was probably a late invention. The pace was not, as persons in general suppose, the step, or tbjfi distance from heel to heel when the feet are at their utmost ordinary extension; this, which the French metrologists call pas simple, was the gradus or gressus. The passus, or pas double of the same writers, was two gradus, or the distance from the point which the heel leaves to that on which it is set down. Assuming the Roman foot at 11-62 English inches, the pace, which was five feet, must have been 58" 1 inches or 484 English feet. Here we might have stopped, if it had not been necessary to explain something relative to what it pleased the writers of the middle ages to call the geometrical pace, composed of five geometrical feet. What they meant by this measure is not easily understood, except by the supposition (which some of their writings confirm) that they imagined a fixed and universal measure of length to exist in nature, and to have been actually obtained. At the beginning of the sixteenth century the Roman mile, at least the mile of 5000 feet or 1000 paces, was generally used by writers [mile], and itinerary measures were more often written about than verified. The stadium, or eighth part of this mile, had also been introduced (into books) from the Greek system, and it was the common opinion, derived from Ptolemy, that the degree of latitude was exactly 500 stadia, or 62J miles. This mado the pace, or the 126th part of the stadium, stand forward as a proper universal measure, being the 62500th part of that which all believed the degree of latitude to be. But though this may be a probable origin of the geometrical pace, it is certain that writers did not adhere uniformly to it, so that the later metro'o^ists have formed different notions of its length. We shall give the accounts of several modern writers. Dr. Bernard makes the geometrical pace (which he also calls the land-surveyor's pace) to be five English feet. Greaves supposes that a pace of upwards of 69 inches was once in use in England. Ozanam makes the geometrical pace to be the same as the Roman pace. Eysenschmidt dues not mention, the measure at all. Paucton (who has a theory about the derivation of measures from parts of the human body) makes it only 4J Roman feet. Rome de L'Isle, who contends that Paucton has several times confounded the Greek Olympic foot with the Roman foot, makes it 4J Olympic feet, that is, 4J English feet very nearly. An older writer, Samson d'Abbeville, cited by Paucton, lays down the geometrical pace at 5 French feet, and nevertheless makes the Roman mile to contain a thousand such paces. The conclusion is, that the geometrical pace was an invention of the old writers, a needless addition to the confusion in which their accounts of antient measures were already enveloped. There is a pace mentioned in ecclesiastical writers called passus ecclesiasticus, or dexter (see Ducange, at the word Dextri), which Dr. Bernard, without stating any authority, makes of the same length as the English yard.
Note - this article incorporates content from The Penny Cyclopaedia of the Society for the Diffusion of Useful Knowledge (1840)