"My greatest difficulty arose with regard to the rigid line which Dr Todhunter had attempted to draw between mathematical and physical memoirs. Thus while including an account of Clausius' memoir of 1849, he had omitted Weber's of 1835, yet the consideration of the former demands the inclusion of the latter... elastic after-strain. What seemed... needful at... present... was to place before the mathematician the results of physical investigations that he might have some distinct guide to the direction in which research is required. ...I have endeavoured... to abrogate this divorce between mathematical elasticity on the one hand, and physical and technical elasticity on the other. With this aim... I have introduced the general conclusions of a considerable body of physical and technical memoirs in the hope that... I may bring the mathematician closer to the physicist and both to the practical engineer. I trust that in doing so I have rendered this History of value... and so increased the usefulness of Dr Todhunter's... years of patient historical research on the more purely mathematical side of elasticity. In this matter I have kept before me the labours of M. de Saint Venant as a true guide to the functions of the ideal elastician."

“Our conception of chance is one of law and order in large numbers; it is not that idea of chaotic incidence which vexed the mediaeval mind.”

“his work... is... intended to arouse and stimulate the reader's own thought, rather than to inculcate doctrine: this result is often best achieved by the assertion and contradiction which excite the reader to independent inquiry.”

“For the present the Grammar may yet be of service. After an eight years' life and... 4000 copies, it reappears in a revised and enlarged form.”

“Heredity. Given any organ in a parent and the same or any other organ in its offspring, the mathematical measure of heredity is the correlation of these organs for pairs of parent and offspring... The word organ here must be taken to include any characteristic which can be quantitatively measured.”

“Who can give us the assurance that the fields already occupied by science are alone those in which knowledge is possible? Who, in the words of Galilei, is willing to set limits to the human intellect?”

“I simply assert that the universe alters, is "becoming;" what it is becoming I will not venture to say. ...the individual too is altering, is not only a "being" but also a "becoming." These alterations... I shall—merely for convenience—term life.”