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His position as a geometer is perhaps better understood from the assertion made respecting him by a modern mathematician, that he came as near to the discovery of the Differential Calculus as can be done without the aid of algebraic transformations.
It befell that after a High School Alumnus had gone to a Varsity and scaled the fearsome heights of Integral and Differential Calculus, he came home to get some more of Father's Shirts and Handkerchiefs and take a new Slant at Life's doubtful Vista, while getting his Board for nothing.
The week during which the committee sat on their report was a very anxious one; the divisions were known every day in the House of Commons; the alternations of success and discomfiture, and the balanced numbers that so often called for the interposition of the chairman, were calculated to sustain the excitement; and when, on the 29th of May, it was known that the report was at length agreed to, and that a committee of free traders had absolutely recommended a differential duty of 10s. in favour of our own produce, one might have fancied from the effect visibly produced, that a government was changed.
These give the laws governing the changes of aspects from one time to a slightly later time, with the same sort of differential approximation to exactness as we obtained for spatially neighbouring aspects through the laws of perspective. The particulars in one set are collected together by the laws of perspective; the successive sets are collected together by the laws of dynamics.
If a text-book in differential calculus, upon the turning of a page, had thrown problems to the winds and begun gibbering purple poems of passion, she could not have been more completely taken aback. However, there was no mistaking the utter and veracious impersonality of his tone. "Oh, do you think so? I'm very glad, because I'm afraid not many people do...." Mr. Queed remained silent.
In 1676 Newton had communicated to Leibnitz the fact that he had discovered a general method of drawing tangents, concealing the method in two sentences of transposed characters. Before Newton had published a single word upon fluxions the differential calculus had made rapid advances on the Continent.
He, too, sent his craft down, but just when a collision seemed about to take place, it was prevented by Mr. Vardon, who was a more skillful pilot. The propellers of the Abaris worked independently, on a sort of differential gear, like the rear wheels of an automobile.
The centre of pressure of the lower blade, being at a greater depth below the surface than the centre of pressure of the upper blade, acts upon a medium of greater resistance to displacement, and the differential of the pressures of the two blades produces inevitably a vibratory motion in the stern of the vessel.
Our equations really express only static relations between simultaneous phenomena; even the differential quotients they may contain in reality mark nothing but present tendencies; no change would take place in our calculations if the time were given in advance, instantaneously fulfilled, like a linear whole of points in numerical order, with no more genuine duration than that contained in the numerical succession.
"Now then what is this Integral Calculus of yours?" "It is a branch of Mathematics that has for its object the summation of a certain infinite series of indefinitely small terms: but for the solution of which, we must generally know the function of which a given function is the differential coefficient.
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