212 MATHEMATICAL MODES OF 



multiples of four, in extreme rapidity. Four cells would 

 always represent a flat figure, and recur in the form of a plate ; 

 all the angles might not in every case be alike, but it would 

 always be in laminse. The reproduction of the confervse was 

 also by the multiplication of cellules. Certain silicious poly- 

 gastric animals the Diatomacese, and some others existed in 

 two halves, reproducing each into two. These would always 

 form a line, or linear series, increasing in length, and not in 

 breadth. The line might form a curve, but this linear form 

 was a necessary consequence of the mode of reproduction. 



This was a sketch of what might be done ; and it ought 

 to be done by a mathematical investigation of the animal 

 body, its masses and organs, or what was of more importance, 

 its ultimate atoms. This was a difficult process, but we 

 should not despair of arriving at it. Suppose the science 

 were so far advanced that we could obtain the formal mathe- 

 matical expression of forms, the same as astronomers did 

 before the time of Newton, when they ascertained the motions 

 of the planets in their orbits, and the curves that bounded 

 these bodies. Newton, from the geometric forms, made out 



THE LAW OF THE FORCE. 



We have merely to ascertain the law of the force. This 

 can never be done till we have got the mathematical forms. 

 We are probably far from this. But meanwhile science makes 

 great progress on the principle explained at the beginning of 

 this lecture. There is room to get into another inquiry 

 naturalists have never dreamed of, probably from not having 

 had a mathematical education. Those of them who had such, 

 and a taste for biological studies, would do well to carry out 

 the mathematical study. What the chemical and other forces 

 had to do in the animal economy could only be made out after 

 the forms of matter were found out. It by no means trenched 

 on the other department the mental and spiritual although 

 the two went together. 



