As the basic concept of vector analysis, curl also comes from the study of quaternion by calculus. When Hamilton introduced quaternion operation, he put a quaternion

In is called "scalar part" and will be called "vector part". He introduced the partial differential operator of quaternion.

(i.e., the operator) to calculate the influence on the vector part of quaternion:

Maxwell in 1873 paper will be one of the "scalar part":

Called "convergence", and "vector part":

Called "curl" or "version". In a letter to Tate, he explained his idea and named it "Curvature". He originally wanted to call this part "twist", but it may also be understood as "screw" or "spiral"; The concept he wants to express is similar to "turn" or "version". He wanted to use the word "Twirl", but he thought it was too lively and energetic for mathematicians, so he finally used "curl". In the paper published in 1883: In some relations between static electricity and magnetism, Hyviside discussed the influence of operators on quaternions. He thinks it is necessary to separate the three parts and divide the vector part into divergent part and curl part.